Newton compared the acceleration of the moon to the acceleration of objects on earth. Believing that gravitational forces were responsible for each, Newton was able to draw an important conclusion about the dependence of gravity upon distance. This comparison led him to conclude that the force of gravitational attraction between the Earth and other objects is inversely proportional to the distance separating the earth's center from the object's center. But distance is not the only variable affecting the magnitude of a gravitational force. Consider Newton's famous equation

F_net = m • a

Newton knew that the force that caused the apple's acceleration (gravity) must be dependent upon the mass of the apple. And since the force acting to cause the apple's downward acceleration also causes the earth's upward acceleration (Newton's third law), that force must also depend upon the mass of the earth. So for Newton, the force of gravity acting between the earth and any other object is directly proportional to the mass of the earth, directly proportional to the mass of the object, and inversely proportional to the square of the distance that separates the centers of the earth and the object.

But Newton's law of universal gravitation extends gravity beyond earth. Newton's law of universal gravitation is about the universality of gravity. Newton's place in the Gravity Hall of Fame is not due to his discovery of gravity, but rather due to his discovery that gravitation is universal. ALL objects attract each other with a force of gravitational attraction. Gravity is universal. This force of gravitational attraction is directly dependent upon the masses of both objects and inversely proportional to the square of the distance that separates their centers. Newton's conclusion about the magnitude of gravitational forces is summarized symbolically as

Since the gravitational force is directly proportional to the mass of both interacting objects, more massive objects will attract each other with a greater gravitational force. So as the mass of either object increases, the force of gravitational attraction between them also increases. If the mass of one of the objects is doubled, then the force of gravity between them is doubled. If the mass of one of the objects is tripled, then the force of gravity between them is tripled. If the mass of both of the objects is doubled, then the force of gravity between them is quadrupled; and so on.

Since gravitational force is inversely proportional to the square of the separation distance between the two interacting objects, more separation distance will result in weaker gravitational forces. So as two objects are separated from each other, the force of gravitational attraction between them also decreases. If the separation distance between two objects is doubled (increased by a factor of 2), then the force of gravitational attraction is decreased by a factor of 4 (2 raised to the second power). If the separation distance between any two objects is tripled (increased by a factor of 3), then the force of gravitational attraction is decreased by a factor of 9 (3 raised to the second power).

The proportionalities expressed by Newton's universal law of gravitation are represented graphically by the following illustration. Observe how the force of gravity is directly proportional to the product of the two masses and inversely proportional to the square of the distance of separation.

Another means of representing the proportionalities is to express the relationships in the form of an equation using a constant of proportionality. This equation is shown below.

The constant of proportionality (G) in the above equation is known as the universal gravitation constant. The precise value of G was determined experimentally by Henry Cavendish in the century after Newton's death. (This experiment will be discussed later in Lesson 3.) The value of G is found to be

G = 6.673 x 10^-11 N m²/kg²

The units on G may seem rather odd; nonetheless they are sensible. When the units on G are substituted into the equation above and multiplied by m₁• m₂ units and divided by d² units, the result will be Newtons - the unit of force.

Knowing the value of G allows us to calculate the force of gravitational attraction between any two objects of known mass and known separation distance. As a first example, consider the following problem.

The solution of the problem involves substituting known values of G (6.673 x 10^-11 N m²/kg²), m₁ (5.98 x 10²⁴ kg), m₂(70 kg) and d (6.38 x 10⁶ m) into the universal gravitation equation and solving for F_grav. The solution is as follows:

The solution of the problem involves substituting known values of G (6.673 x 10^-11 N m²/kg²), m₁ (5.98 x 10²⁴ kg), m₂(70 kg) and d (6.39 x 10⁶ m) into the universal gravitation equation and solving for F_grav. The solution is as follows:

Two general conceptual comments can be made about the results of the two sample calculations above. First, observe that the force of gravity acting upon the student (a.k.a. the student's weight) is less on an airplane at 40 000 feet than at sea level. This illustrates the inverse relationship between separation distance and the force of gravity (or in this case, the weight of the student). The student weighs less at the higher altitude. However, a mere change of 40 000 feet further from the center of the Earth is virtually negligible. This altitude change altered the student's weight changed by 2 N that is much less than 1% of the original weight. A distance of 40 000 feet (from the earth's surface to a high altitude airplane) is not very far when compared to a distance of 6.38 x 10⁶ m (equivalent to nearly 20 000 000 feet from the center of the earth to the surface of the earth). This alteration of distance is like a drop in a bucket when compared to the large radius of the Earth. As shown in the diagram below, distance of separation becomes much more influential when a significant variation is made.

The second conceptual comment to be made about the above sample calculations is that the use of Newton's universal gravitation equation to calculate the force of gravity (or weight) yields the same result as when calculating it using the equation presented in Unit 2:

Both equations accomplish the same result because (as we will study later in Lesson 3) the value of g is equivalent to the ratio of (G•M_earth)/(R_earth)².

The discovery of the relationship between magnetism and electricity was, like so many other scientific discoveries, stumbled upon almost by accident. The Danish physicist Hans Christian Oersted was lecturing one day in 1820 on the possibility of electricity and magnetism being related to one another, and in the process demonstrated it conclusively by experiment in front of his whole class! By passing an electric current through a metal wire suspended above a magnetic compass, Oersted was able to produce a definite motion of the compass needle in response to the current. What began as conjecture at the start of the class session was confirmed as fact at the end. Needless to say, Oersted had to revise his lecture notes for future classes! His serendipitous discovery paved the way for a whole new branch of science: electromagnetics.

Detailed experiments showed that the magnetic field produced by an electric current is always oriented perpendicular to the direction of flow. A simple method of showing this relationship is called the left-hand rule. Simply stated, the left-hand rule says that the magnetic flux lines produced by a current-carrying wire will be oriented the same direction as the curled fingers of a person's left hand (in the "hitchhiking" position), with the thumb pointing in the direction of electron flow:

The magnetic field encircles this straight piece of current-carrying wire, the magnetic flux lines having no definite "north" or "south' poles.

While the magnetic field surrounding a current-carrying wire is indeed interesting, it is quite weak for common amounts of current, able to deflect a compass needle and not much more. To create a stronger magnetic field force (and consequently, more field flux) with the same amount of electric current, we can wrap the wire into a coil shape, where the circling magnetic fields around the wire will join to create a larger field with a definite magnetic (north and south) polarity:

The amount of magnetic field force generated by a coiled wire is proportional to the current through the wire multiplied by the number of "turns" or "wraps" of wire in the coil. This field force is called magnetomotive force (mmf), and is very much analogous to electromotive force (E) in an electric circuit.

An electromagnet is a piece of wire intended to generate a magnetic field with the passage of electric current through it. Though all current-carrying conductors produce magnetic fields, an electromagnet is usually constructed in such a way as to maximize the strength of the magnetic field it produces for a special purpose. Electromagnets find frequent application in research, industry, medical, and consumer products.

As an electrically-controllable magnet, electromagnets find application in a wide variety of "electromechanical" devices: machines that effect mechanical force or motion through electrical power. Perhaps the most obvious example of such a machine is the electric motor.

Another example is the relay, an electrically-controlled switch. If a switch contact mechanism is built so that it can be actuated (opened and closed) by the application of a magnetic field, and an electromagnet coil is placed in the near vicinity to produce that requisite field, it will be possible to open and close the switch by the application of a current through the coil. In effect, this gives us a device that enables elelctricity to control electricity:

Relays can be constructed to actuate multiple switch contacts, or operate them in "reverse" (energizing the coil will open the switch contact, and unpowering the coil will allow it to spring closed again).

• REVIEW:
• When electrons flow through a conductor, a magnetic field will be produced around that conductor.
• The left-hand rule states that the magnetic flux lines produced by a current-carrying wire will be oriented the same direction as the curled fingers of a person's left hand (in the "hitchhiking" position), with the thumb pointing in the direction of electron flow.
• The magnetic field force produced by a current-carrying wire can be greatly increased by shaping the wire into a coil instead of a straight line. If wound in a coil shape, the magnetic field will be oriented along the axis of the coil's length.
• The magnetic field force produced by an electromagnet (called the magnetomotive force, or mmf), is proportional to the product (multiplication) of the current through the electromagnet and the number of complete coil "turns" formed by the wire.

The discovery of the relationship between magnetism and electricity was, like so many other scientific discoveries, stumbled upon almost by accident. The Danish physicist Hans Christian Oersted was lecturing one day in 1820 on the possibility of electricity and magnetism being related to one another, and in the process demonstrated it conclusively by experiment in front of his whole class! By passing an electric current through a metal wire suspended above a magnetic compass, Oersted was able to produce a definite motion of the compass needle in response to the current. What began as conjecture at the start of the class session was confirmed as fact at the end. Needless to say, Oersted had to revise his lecture notes for future classes! His serendipitous discovery paved the way for a whole new branch of science: electromagnetics.

Detailed experiments showed that the magnetic field produced by an electric current is always oriented perpendicular to the direction of flow. A simple method of showing this relationship is called the left-hand rule. Simply stated, the left-hand rule says that the magnetic flux lines produced by a current-carrying wire will be oriented the same direction as the curled fingers of a person's left hand (in the "hitchhiking" position), with the thumb pointing in the direction of electron flow:

The magnetic field encircles this straight piece of current-carrying wire, the magnetic flux lines having no definite "north" or "south' poles.

While the magnetic field surrounding a current-carrying wire is indeed interesting, it is quite weak for common amounts of current, able to deflect a compass needle and not much more. To create a stronger magnetic field force (and consequently, more field flux) with the same amount of electric current, we can wrap the wire into a coil shape, where the circling magnetic fields around the wire will join to create a larger field with a definite magnetic (north and south) polarity:

The amount of magnetic field force generated by a coiled wire is proportional to the current through the wire multiplied by the number of "turns" or "wraps" of wire in the coil. This field force is called magnetomotive force (mmf), and is very much analogous to electromotive force (E) in an electric circuit.

An electromagnet is a piece of wire intended to generate a magnetic field with the passage of electric current through it. Though all current-carrying conductors produce magnetic fields, an electromagnet is usually constructed in such a way as to maximize the strength of the magnetic field it produces for a special purpose. Electromagnets find frequent application in research, industry, medical, and consumer products.

As an electrically-controllable magnet, electromagnets find application in a wide variety of "electromechanical" devices: machines that effect mechanical force or motion through electrical power. Perhaps the most obvious example of such a machine is the electric motor.

Another example is the relay, an electrically-controlled switch. If a switch contact mechanism is built so that it can be actuated (opened and closed) by the application of a magnetic field, and an electromagnet coil is placed in the near vicinity to produce that requisite field, it will be possible to open and close the switch by the application of a current through the coil. In effect, this gives us a device that enables elelctricity to control electricity:

Relays can be constructed to actuate multiple switch contacts, or operate them in "reverse" (energizing the coil will open the switch contact, and unpowering the coil will allow it to spring closed again).

• REVIEW:
• When electrons flow through a conductor, a magnetic field will be produced around that conductor.
• The left-hand rule states that the magnetic flux lines produced by a current-carrying wire will be oriented the same direction as the curled fingers of a person's left hand (in the "hitchhiking" position), with the thumb pointing in the direction of electron flow.
• The magnetic field force produced by a current-carrying wire can be greatly increased by shaping the wire into a coil instead of a straight line. If wound in a coil shape, the magnetic field will be oriented along the axis of the coil's length.
• The magnetic field force produced by an electromagnet (called the magnetomotive force, or mmf), is proportional to the product (multiplication) of the current through the electromagnet and the number of complete coil "turns" formed by the wire.

A gravity pendulum is a weight on the end of a rigid or flexible line or rod, which, when given some initial lift from the vertical position, will swing back and forth under the influence of gravity over its central (lowest) point. Atorsion pendulum consists of a body suspended by a fine wire or elastic fiber in such a way that it executes rotational oscillations as the suspending wire or fiber twists and untwists.

Gravity pendulums

For small displacements, the movement of an ideal pendulum can be described mathematically as simple harmonic motion, as the change in potential energy at the bottom of a circular arc is nearly proportional to the square of the displacement. Real pendulums do not have infinitesimal displacements, so their behavior is actually non-linear. Real pendulums will also lose energy as they swing, and so their motion will be damped, with the size of the oscillation decreasing approximately exponentially with time.

In the case of a pendulum with a mass M swinging on an axis located at distance r above its center of mass, with a moment of inertia of I relative to that axis and an ambient gravity of g, the period of a complete oscillation is

<math>

This equation only applies when the amplitude of the swing is small; a complete description of a pendulum's behavior is not mathematically simple.

Two coupled pendulums form a double pendulum.

Torsion pendulums

If I is the moment of inertia of a body with respect to its axis of oscillation, and if K is the torsion coefficient[?] of the fivre (torque required to twist it through an angle of one radian), then the period of oscillation of a torsion pendulum is given by

<math>T = 2 \pi \sqrt{\frac{I}{K}}</math>

Both I and K may have to be determined by experiment. This can be done by measuring the period T and then adding to the suspended body another body of known moment of inertia I', giving a new period of oscillation T'

<math>T' = 2\pi \sqrt{\frac{I+I'}{K}}</math>

and then solving the two equations to get

<math>K = \frac{4\pi^2I'}{T'^2 - T^2}</math>

<math>I = \frac{T^2I'}{T'^2 - T^2}</math>

The oscillating balance wheel of a watch is in effect a torsion pendulum, with the suspending fiber replaced by hairspring and pivots. The watch is regulated, first roughly by adjusting I (the purpose of the screws set radially into the rim of the wheel) and then more accurately by changing the free length of the hairspring and hence the torsion coefficient K.

The thermodynamic free energy is the amount of work that a thermodynamic system can perform. The concept is useful in the thermodynamics of chemical or thermal processes in engineering and science. The free energy is the internal energy of a system less the amount of energy that cannot be used to perform work. This unusable energy is given by the entropy of a system multiplied by the temperature of the system.

Like the internal energy, the free energy is a thermodynamic state function.

Application

The experimental usefulness of these functions is restricted to conditions where certain variables (T, and V or external p) are held constant, although they also have theoretical importance in deriving Maxwell relations. Work other than pdV may be added, e.g., for electrochemical cells, or  work in elastic materials and in muscle contraction. Other forms of work which must sometimes be considered arestress-strain, magnetic, as in adiabatic demagnetization used in the approach to absolute zero, and work due to electric polarization. These are described by tensors.

In most cases of interest there are internal degrees of freedom and processes, such as chemical reactions and phase transitions, which create entropy. Even for homogeneous "bulk" materials, the free energy functions depend on the (often suppressed) composition, as do all proper thermodynamic potentials (extensive functions), including the internal energy.

N_i is the number of molecules (alternatively, moles) of type i in the system. If these quantities do not appear, it is impossible to describe compositional changes. The differentials for reversible processes are (assuming only pV work)

where μ_i is the chemical potential for the i-th component in the system. The second relation is especially useful at constant T and p, conditions which are easy to achieve experimentally, and which approximately characterize living creatures.

Any decrease in the Gibbs function of a system is the upper limit for any isothermal, isobaric work that can be captured in the surroundings, or it may simply be dissipated, appearing as T times a corresponding increase in the entropy of the system and/or its surrounding.

An example is surface free energy, the amount of increase of free energy when the area of surface increases by every unit area.

The path integral Monte Carlo method is a numerical approach for determining the values of free energies, based on quantum dynamical principles.

History

The quantity called "free energy" is a more advanced and accurate replacement for the outdated term affinity, which was used by chemists in previous years to describe the force that caused chemical reactions. The term affinity, as used in chemical relation, dates back to at least the time of Albertus Magnus in 1250.

From the 1998 textbook Modern Thermodynamics^[7] by Nobel Laureate and chemistry professor Ilya Prigogine we find: "As motion was explained by the Newtonian concept of force, chemists wanted a similar concept of ‘driving force’ for chemical change. Why do chemical reactions occur, and why do they stop at certain points? Chemists called the ‘force’ that caused chemical reactions affinity, but it lacked a clear definition."

During the entire 18th century, the dominant view with regard to heat and light was that put forth by Isaac Newton, called the Newtonian hypothesis, which states that light and heat are forms of matter attracted or repelled by other forms of matter, with forces analogous to gravitation or to chemical affinity.

In the 19th century, the French chemist Marcellin Berthelot and the Danish chemist Julius Thomsen had attempted to quantify affinity using heats of reaction. In 1875, after quantifying the heats of reaction for a large number of compounds, Berthelot proposed the principle of maximum work, in which all chemical changes occurring without intervention of outside energy tend toward the production of bodies or of a system of bodies which liberate heat.

In addition to this, in 1780 Antoine Lavoisier and Pierre-Simon Laplace laid the foundations of thermochemistry by showing that the heat given out in a reaction is equal to the heat absorbed in the reverse reaction. They also investigated the specific heat and latent heat of a number of substances, and amounts of heat given out in combustion. In a similar manner, in 1840 Swiss chemist Germain Hess formulated the principle that the evolution of heat in a reaction is the same whether the process is accomplished in one-step process or in a number of stages. This is known as Hess' law. With the advent of the mechanical theory of heatin the early 19th century, Hess’s law came to be viewed as a consequence of the law of conservation of energy.

Based on these and other ideas, Berthelot and Thomsen, as well as others, considered the heat given out in the formation of a compound as a measure of the affinity, or the work done by the chemical forces. This view, however, was not entirely correct. In 1847, the English physicist James Joule showed that he could raise the temperature of water by turning a paddle wheel in it, thus showing that heat and mechanical work were equivalent or proportional to each other, i.e., approximately, . This statement came to be known as the mechanical equivalent of heat and was a precursory form of the first law of thermodynamics.

By 1865, the German physicist Rudolf Clausius had shown that this equivalence principle needed amendment. That is, one can use the heat derived from a combustion reaction in a coal furnace to boil water, and use this heat to vaporize steam, and then use the enhanced high-pressure energy of the vaporized steam to push a piston. Thus, we might naively reason that one can entirely convert the initial combustion heat of the chemical reaction into the work of pushing the piston. Clausius showed, however, that we must take into account the work that the molecules of the working body, i.e., the water molecules in the cylinder, do on each other as they pass or transform from one step of or state of the engine cycle to the next, e.g., from (P₁,V₁) to (P₂,V₂). Clausius originally called this the “transformation content” of the body, and then later changed the name to entropy. Thus, the heat used to transform the working body of molecules from one state to the next cannot be used to do external work, e.g., to push the piston. Clausius defined thistransformation heat as dQ = TdS.

In 1873, Willard Gibbs published A Method of Geometrical Representation of the Thermodynamic Properties of Substances by Means of Surfaces, in which he introduced the preliminary outline of the principles of his new equation able to predict or estimate the tendencies of various natural processes to ensue when bodies or systems are brought into contact. By studying the interactions of homogeneous substances in contact, i.e., bodies, being in composition part solid, part liquid, and part vapor, and by using a three-dimensional volume-entropy-internal energy graph, Gibbs was able to determine three states of equilibrium, i.e., "necessarily stable", "neutral", and "unstable", and whether or not changes will ensue. In 1876, Gibbs built on this framework by introducing the concept of chemical potential so to take into account chemical reactions and states of bodies that are chemically different from each other. In his own words, to summarize his results in 1873, Gibbs states:

In this description, as used by Gibbs, ε refers to the internal energy of the body, η refers to the entropy of the body, and ν is the volume of the body.

Hence, in 1882, after the introduction of these arguments by Clausius and Gibbs, the German scientist Hermann von Helmholtz stated, in opposition to Berthelot and Thomas’ hypothesis that chemical affinity is a measure of the heat of reaction of chemical reaction as based on the principle of maximal work, that affinity is not the heat given out in the formation of a compound but rather it is the largest quantity of work which can be gained when the reaction is carried out in a reversible manner, e.g., electrical work in a reversible cell. The maximum work is thus regarded as the diminution of the free, or available, energy of the system (Gibbs free energy G at T = constant, P = constant or Helmholtz free energy F at T = constant, V = constant), whilst the heat given out is usually a measure of the diminution of the total energy of the system (Internal energy). Thus, G or F is the amount of energy “free” for work under the given conditions.

In nuclear physics, nuclear chemistry and astrophysics nuclear fusion is the process by which two or more atomic nuclei join together, or "fuse", to form a single heavier nucleus. This is usually accompanied by the release or absorption of large quantities of energy. Large-scale thermonuclear fusion processes, involving many nuclei fusing at once, must occur in matter at very high densities and temperatures.

The fusion of two nuclei with lower masses than iron (which, along with nickel, has the largest binding energy per nucleon) generally releases energy while the fusion of nuclei heavier than iron absorbs energy. The opposite is true for the reverse process, nuclear fission.

In the simplest case of hydrogen fusion, two protons have to be brought close enough for the weak nuclear force to convert either of the identical protons into a neutron forming the hydrogen isotope deuterium. In more complex cases of heavy ion fusion involving two or more nucleons, the reaction mechanism is different, but the same result occurs–one of combining smaller nuclei into larger nuclei.

Nuclear fusion occurs naturally in all active stars. Synthetic fusion as a result of human actions has also been achieved, although this has not yet been completely controlled as a source of nuclear power (see: fusion power). In the laboratory, successful nuclear physics experiments have been carried out that involve the fusion of many different varieties of nuclei, but the energy output has been negligible in these studies. In fact, the amount of energy put into the process has always exceeded the energy output.

Uncontrolled nuclear fusion has been carried out many times in nuclear weapons testing, which results in a deliberate explosion. These explosions have always used the heavy isotopes of hydrogen, deuterium (H-2) and tritium (H-3), and never the much more common isotope of hydrogen (H-1), sometimes called "protium".

Building upon the nuclear transmutation experiments by Ernest Rutherford, carried out several years earlier, the fusion of the light nuclei (hydrogen isotopes) was first accomplished by Mark Oliphantin 1932. Then, the steps of the main cycle of nuclear fusion in stars were first worked out by Hans Bethe throughout the remainder of that decade.

Research into fusion for military purposes began in the early 1940s as part of the Manhattan Project, but this was not accomplished until 1951 (see the Greenhouse Item nuclear test), and nuclear fusion on a large scale in an explosion was first carried out on November 1, 1952, in the Ivy Mike hydrogen bomb test. Research into developing controlled thermonuclear fusion for civil purposes also began in the 1950s, and it continues to this day.

Electromagnetic radiation (often abbreviated E-M radiation or EMR) is a form of energy exhibiting wave-like behavior as it travels through space. EMR has both electricand magnetic field components, which oscillate in phase perpendicular to each other and perpendicular to the direction of energy propagation.

Electromagnetic radiation is classified according to the frequency of its wave. In order of increasing frequency and decreasing wavelength, these are radio waves,microwaves, infrared radiation, visible light, ultraviolet radiation, X-rays and gamma rays (see Electromagnetic spectrum). The eyes of various organisms sense a small and somewhat variable window of frequencies called the visible spectrum. The photon is the quantum of the electromagnetic interaction and the basic "unit" of light and all other forms of electromagnetic radiation and is also the force carrier for the electromagnetic force.

EM radiation carries energy and momentum that may be imparted to matter with which it interacts

Physics

Theory

Shows the relative wavelengths of the electromagnetic waves of three different colors of light (blue, green and red) with a distance scale in micrometres along the x-axis.

James Clerk Maxwell first formally postulated electromagnetic waves. These were subsequently confirmed by Heinrich Hertz. Maxwell derived a wave form of the electric and magnetic equations, thus uncovering the wave-like nature of electric and magnetic fields, and their symmetry. Because the speed of EM waves predicted by the wave equation coincided with the measured speed of light, Maxwell concluded that light itself is an EM wave.

According to Maxwell's equations, a time-varying electric field generates a time-varying magnetic field and vice versa. Therefore, as an oscillating electric field generates an oscillating magnetic field, the magnetic field in turn generates an oscillating electric field, and so on. These oscillating fields together form a propagating electromagnetic wave.

A quantum theory of the interaction between electromagnetic radiation and matter such as electrons is described by the theory of quantum electrodynamics.

Properties

Electromagnetic waves can be imagined as a self-propagating transverse oscillating wave of electric and magnetic fields. This diagram shows a plane linearly polarized wave propagating from right to left. The electric field is in a vertical plane and the magnetic field in a horizontal plane.

The physics of electromagnetic radiation is electrodynamics. Electromagnetism is the physical phenomenon associated with the theory of electrodynamics. Electric and magnetic fields obey the properties of superposition. Thus, a field due to any particular particle or time-varying electric or magnetic field contributes to the fields present in the same space due to other causes. Further, as they are vectorfields, all magnetic and electric field vectors add together according to vector addition. For example, in optics two or more coherent lightwaves may interact and by constructive or destructive interference yield a resultant irradiance deviating from the sum of the component irradiances of the individual lightwaves.

Since light is an oscillation it is not affected by travelling through static electric or magnetic fields in a linear medium such as a vacuum. However in nonlinear media, such as some crystals, interactions can occur between light and static electric and magnetic fields — these interactions include the Faraday effect and the Kerr effect.

In refraction, a wave crossing from one medium to another of different density alters its speed and direction upon entering the new medium. The ratio of the refractive indices of the media determines the degree of refraction, and is summarized by Snell's law. Light disperses into a visible spectrum as light passes through a prism because of the wavelength dependent refractive index of the prism material (Dispersion).

EM radiation exhibits both wave properties and particle properties at the same time (see wave-particle duality). Both wave and particle characteristics have been confirmed in a large number of experiments. Wave characteristics are more apparent when EM radiation is measured over relatively large timescales and over large distances while particle characteristics are more evident when measuring small timescales and distances. For example, when electromagnetic radiation is absorbed by matter, particle-like properties will be more obvious when the average number of photons in the cube of the relevant wavelength is much smaller than 1. Upon absorption of light, it is not too difficult to experimentally observe non-uniform deposition of energy. Strictly speaking, however, this alone is not evidence of "particulate" behavior of light, rather it reflects the quantum nature of matter.^[1]

There are experiments in which the wave and particle natures of electromagnetic waves appear in the same experiment, such as the self-interference of a single photon. True single-photon experiments (in a quantum optical sense) can be done today in undergraduate-level labs.^[2] When a single photon is sent through an interferometer, it passes through both paths, interfering with itself, as waves do, yet is detected by a photomultiplier or other sensitive detector only once.

Wave model

Electromagnetic radiation is a transverse wave meaning that the oscillations of the waves are perpendicular to the direction of energy transfer and travel. An important aspect of the nature of light is frequency. The frequency of a wave is its rate of oscillation and is measured in hertz, the SI unit of frequency, where one hertz is equal to one oscillation per second. Light usually has a spectrum of frequencies which sum together to form the resultant wave. Different frequencies undergo different angles of refraction.

A wave consists of successive troughs and crests, and the distance between two adjacent crests or troughs is called the wavelength. Waves of the electromagnetic spectrum vary in size, from very long radio waves the size of buildings to very short gamma rays smaller than atom nuclei. Frequency is inversely proportional to wavelength, according to the equation:

where v is the speed of the wave (c in a vacuum, or less in other media), f is the frequency and λ is the wavelength. As waves cross boundaries between different media, their speeds change but their frequencies remain constant.

Interference is the superposition of two or more waves resulting in a new wave pattern. If the fields have components in the same direction, they constructively interfere, while opposite directions cause destructive interference.

The energy in electromagnetic waves is sometimes called radiant energy.

Particle model

Because energy of an EM interaction is quantized, EM waves are emitted and absorbed as discrete packets of energy, or quanta, called photons.^[3] Because photons are emitted and absorbed by charged particles, they act as transporters of energy, and are associated with waves with frequency proportional to the energy carried. The energy per photon can be related to the frequency via the Planck–Einstein equation:^[4]

where E is the energy, h is Planck's constant, and f is frequency. The energy is commonly expressed in the unit of electronvolt (eV). This photon-energy expression is a particular case of the energy levels of the more general electromagnetic oscillator, whose average energy, which is used to obtain Planck's radiation law, can be shown to differ sharply from that predicted by the equipartition principle at low temperature, thereby establishes a failure of equipartition due to quantum effects at low temperature.^[5]

As a photon is absorbed by an atom, it excites the atom, elevating an electron to a higher energy level. If the energy is great enough, so that the electron jumps to a high enough energy level, it may escape the positive pull of the nucleus and be liberated from the atom in a process called photoionisation. Conversely, an electron that descends to a lower energy level in an atom emits a photon of light equal to the energy difference. Since the energy levels of electrons in atoms are discrete, each element emits and absorbs its own characteristic frequencies.

Together, these effects explain the emission and absorption spectra of light. The dark bands in the absorption spectrum are due to the atoms in the intervening medium absorbing different frequencies of the light. The composition of the medium through which the light travels determines the nature of the absorption spectrum. For instance, dark bands in the light emitted by a distant star are due to the atoms in the star's atmosphere. These bands correspond to the allowed energy levels in the atoms. A similar phenomenon occurs for emission. As the electrons descend to lower energy levels, a spectrum is emitted that represents the jumps between the energy levels of the electrons. This is manifested in the emission spectrum of nebulae. Today, scientists use this phenomenon to observe what elements a certain star is composed of. It is also used in the determination of the distance of a star, using the red shift.

Speed of propagation

Any electric charge which accelerates, or any changing magnetic field, produces electromagnetic radiation. Electromagnetic information about the charge travels at the speed of light. Accurate treatment thus incorporates a concept known as retarded time (as opposed to advanced time, which is not physically possible in light of causality), which adds to the expressions for the electrodynamic electric field and magnetic field. These extra terms are responsible for electromagnetic radiation. When any wire (or other conducting object such as an antenna) conducts alternating current, electromagnetic radiation is propagated at the same frequency as the electric current. At the quantum level, electromagnetic radiation is produced when the wavepacket of a charged particle oscillates or otherwise accelerates. Charged particles in a stationary state do not move, but a superposition of such states may result in oscillation, which is responsible for the phenomenon of radiative transition between quantum states of a charged particle.

Depending on the circumstances, electromagnetic radiation may behave as a wave or as particles. As a wave, it is characterized by a velocity (the speed of light), wavelength, and frequency. When considered as particles, they are known as photons, and each has an energy related to the frequency of the wave given by Planck's relation E = hν, where E is the energy of the photon, h = 6.626 × 10⁻³⁴ J·s is Planck's constant, and ν is the frequency of the wave.

One rule is always obeyed regardless of the circumstances: EM radiation in a vacuum always travels at the speed of light, relative to the observer, regardless of the observer's velocity. (This observation led to Albert Einstein's development of the theory of special relativity.)

In a simple understanding space is something that we all know and that is measured in the three dimensions: length, width and height.

In physics a definition of space is difficult, because it cannot be explained by something else, because there is nothing more fundamental known at present. Therefore the only definition that one uses is done bymeasurement. (The same is done with time and mass).

The standard space interval, called a standard meter or simply meter, is defined as the distance traveled by light in a vacuum during a time interval of exactly 1/299,792,458 of a second. ^[1]

Before Einstein's work on relativistic physics, time and space were viewed as independent dimensions. Einstein's discoveries have shown that due to relativity of motion space and time can be mathematicallycombined into space-time.

Design

The shape behind the hourglass has hardly any written evidence of why its external form is the shape that it is. The glass bulbs used, however, have changed in style and design over time. While the main designs have always been ampoule in shape, the bulbs were not always connected. The first hourglasses were two separate bulbs with a cord wrapped at their union that was then coated in wax to hold the piece together and let sand flow in between. ^[2] It was not until 1760 that both bulbs were blown together to keep moisture out of the bulbs and regulate the pressure within the bulb that varied the flow of the granular substance. ^[6]

Material

While some hourglasses actually did use sand as the granular mixture to measure time, many did not use sand at all. The material used in most bulbs was a combination of “powdered marble, tin/lead oxides, and pulverized, burnt eggshell”. ^[4] Overtime, different textures of granule matter were tested to see which gave the most constant flow within the bulbs. It was later discovered that for the perfect flow to be achieved the ratio of granule bead to the width of the bulb neck needed to be 1/12 or more but not greater than 1/2 the neck of the bulb. ^[7]

Practical uses

3-minute egg timer

Hourglasses were an early dependable, reusable and accurate measure of time. The rate of flow of the sand is independent of the depth in the upper reservoir, and the instrument will not freeze in cold weather.^[4]

From the 15th century onwards, they were being used in a range of applications at sea, in the church, in industry and in cookery.

During the voyage of Ferdinand Magellan around the globe, his vessels kept 18 hourglasses per ship. It was the job of a ship's page to turn the hourglasses and thus provide the times for the ship's log. Noon was the reference time for navigation, which did not depend on the glass, as the sun would be at itszenith.^[8] More than one hourglass was sometimes fixed in a frame, each with a different running time, for example 1 hour, 45 minutes, 30 minutes, and 15 minutes.

Modern practical uses

While they are no longer widely used for keeping time, some institutions do maintain them. Both houses of the Australian Parliament use three hourglasses to time certain procedures, such as divisions.^[9]

The sandglass is still widely used as the kitchen egg timer; for cooking eggs, a three minute timer is typical,^[10] hence the name "egg timer" for three minute hourglasses. Egg timers are sold widely as souvenirs.^{[citation needed]}

The Timewheel in Budapest,Hungary.

Sand timers are also sometimes used in games such asPictionary and Boggle to implement a time constraint on rounds of play.

Symbolic uses

Pirate Christopher Moody's "Bloody Red" jack, c. 1714

Unlike most other methods of measuring time, the hourglass concretely represents the present as being between the pastand the future, and this has made it an enduring symbol of time itself.

The hourglass, sometimes with the addition of metaphorical wings, is often depicted as a symbol that human existence is fleeting, and that the "sands of time" will run out for every human life.^[11] It was used thus on pirate flags, to strike fear into the hearts of the pirates' victims. In England, hourglasses were sometimes placed in coffins,^[12] and they have graced gravestones for centuries. The hourglass was also used inalchemy as a symbol for hour.

Modern symbolic uses

Recognition of the hourglass as a symbol of time has survived its obsolescence as a timekeeper. For example, the American television soap opera Days of our Lives, since its first broadcast in 1965, has displayed an hourglass in its opening credits, with the narration, "Like sands through the hourglass, so are the days of our lives."

A clock is an instrument used to indicate, keep, and co-ordinate time. The word clock is derived ultimately (viaDutch, Northern French, and Medieval Latin) from the Celticwords clagan and clocca meaning "bell". A silent instrument missing such a mechanism has traditionally been known as a timepiece.^[1] In general usage today a "clock" refers to any device for measuring and displaying the time. Watches and other timepieces that can be carried on one's person are often distinguished from clocks.^[2]

Clock at the Royal Observatory, Greenwich

Replica of an ancient Chinese incense clock

The clock is one of the oldest human inventions, meeting the need to consistently measure intervals of time shorter than the natural units: the day; the lunar month; and theyear. Devices operating on several different physical processes have been used over the millennia, culminating in the clocks of today.

Early mechanical clocks

None of the first clocks survive from 13th century Europe, but various mentions in church records reveal some of the early history of the clock.

The word horologia (from the Greek ὡρα, hour, and λέγειν, to tell) was used to describe all these devices, but the use of this word (still used in several Romance languages) for all timekeepers conceals from us the true nature of the mechanisms. For example, there is a record that in 1176 Sens Cathedral installed a ‘horologe’^{[citation needed]} but the mechanism used is unknown. According to Jocelin of Brakelond, in 1198 during a fire at the abbey of St Edmundsbury (now Bury St Edmunds), the monks 'ran to the clock' to fetch water, indicating that their water clock had a reservoir large enough to help extinguish the occasional fire.^[9]

A new mechanism

The word clock (from the Latin word clocca, "bell"), which gradually supersedes "horologe", suggests that it was the sound of bells which also characterized the prototype mechanical clocks that appeared during the 13th century in Europe.

Outside of Europe, the escapement mechanism had been known and used in medieval China, as theSong Dynasty horologist and engineer Su Song (1020–1101) incorporated it into his astronomical clock-tower of Kaifeng in 1088.^[10] However, his astronomical clock and rotating armillary sphere still relied on the use of flowing water (i.e. hydraulics), while European clockworks of the following centuries shed this old habit for a more efficient driving power of weights, in addition to the escapement mechanism.

A mercury clock, described in the Libros del saber, a Spanish work from AD 1277 consisting of translations and paraphrases of Arabic works, is sometimes quoted as evidence for Muslim knowledge of a mechanical clock. The first mercury powered automata clock was invented by Ibn Khalafa al-Muradi^[11][12]

Between 1280 and 1320, there is an increase in the number of references to clocks and horologes in church records, and this probably indicates that a new type of clock mechanism had been devised. Existing clock mechanisms that used water power were being adapted to take their driving power from falling weights. This power was controlled by some form of oscillating mechanism, probably derived from existing bell-ringing or alarm devices. This controlled release of power - the escapement - marks the beginning of the true mechanical clock.

These mechanical clocks were intended for two main purposes: for signalling and notification (e.g. the timing of services and public events), and for modeling the solar system. The former purpose is administrative, the latter arises naturally given the scholarly interest in astronomy, science, astrology, and how these subjects integrated with the religious philosophy of the time. The astrolabe was used both by astronomers and astrologers, and it was natural to apply a clockwork drive to the rotating plate to produce a working model of the solar system.

Simple clocks intended mainly for notification were installed in towers, and did not always require faces or hands. They would have announced the canonical hours or intervals between set times of prayer. Canonical hours varied in length as the times of sunrise and sunset shifted. The more sophisticated astronomical clocks would have had moving dials or hands, and would have shown the time in various time systems, including Italian hours, canonical hours, and time as measured by astronomers at the time. Both styles of clock started acquiring extravagant features such asautomata.

In physics, the term "moment" can refer to many different concepts:

• Moment of force (often just moment) is the tendency of a force to twist or rotate an object; see the article torque for details. This is an important, basic concept in engineering and physics. (Note: In mechanical and civil engineering, "moment" and "torque" have different meanings, while in physics they are synonyms. See the discussion in the "torque" article, or the article couple (mechanics).)
  • Moment arm is a quantity used when calculating moments of force. See the article torque.
  • The Principle of moments is if an object is balanced then the sum of the clockwise moments about a pivot is equal to the sum of the anticlockwise moments about the same pivot.
  • A pure moment is a special type of moment of force. See the article couple (mechanics).
• Moment of a vector is a generalization of the moment of force. The moment M of a vector B about the point A is

where

 is the vector from point A to the position where quantity B is applied.

× represents the cross product of the vectors.

Thus M can be referred to as "the moment M with respect to the axis that goes through the point A", or simply "the moment M around A". If A is the origin, or, informally, if the axis involved is clear from context, one often omits A and says simply moment.

When B is the force, the moment of force is the torque as defined above.

• Moment of inertia () is analogous to mass in discussions of rotational motion.
• Moment of momentum or angular momentum () is the rotational analog of momentum.
• Magnetic moment () is a dipole moment measuring the strength and direction of a magnetic source.
• Electric dipole moment is a dipole moment measuring the charge difference and direction between two or more charges. For example, the electric dipole moment between a change of -q and q separated by a distance of d is ()

In physics, mass (from Ancient Greek: μᾶζα) commonly refers to any of three properties of matter, which have been shown experimentally to be equivalent:

• Inertial mass,
• active gravitational mass and
• passive gravitational mass.
  

CHUBBY TOES!!!! Ugly mass must be distinguished from matter in physics, because matter is a poorly-defined concept, and although all types of agreed-upon matter exhibit mass, it is also the case that many types of energy which are not matter— such as potential energy, kinetic energy, and trapped electromagnetic radiation (photons)— also exhibit mass. Thus, all matter has the property of mass, but not all mass is associated with identifiable matter.

In everyday usage, mass is often used interchangeably with weight, and the units of weight are often taken to be kilograms (for instance, a person may state that his weight is 75 kg). In proper scientific use, however, the two terms refer to different, yet related, properties of matter.

The inertial mass of an object determines its acceleration in the presence of an applied force. According to Newton's second law of motion, if a lungs of fixed mass m is subjected to a force F, its acceleration a is given by F/m.

A body's mass also determines the degree to which it generates or is affected by a gravitational field. If a first body of mass m₁ is placed at a distance r from a second body of mass m₂, each body experiences an attractive force F whose magnitude is

where G is the universal constant of gravitation, equal to 6.67×10−11
 kg⁻¹ m³ s⁻². This is sometimes referred to as gravitational mass (when a distinction is necessary, M is used to denote the active gravitational mass and m the passive gravitational mass). Repeated experiments since the 17th century have demonstrated that inertial and gravitational mass are equivalent; this is entailed in the equivalence principle of general relativity.

Special relativity shows that rest mass (or invariant mass) and rest energy are essentially equivalent, via the well-known relationship (E = mc²). This same equation also connects relativistic mass and "relativistic energy" (total system energy). These are concepts that are related to their "rest" counterparts, but they do not have the same value, in systems where there is a net momentum. In order to deduce any of these four quantities from any of the others, in any system which has a net momentum, an equation that takes momentum into account is needed.

Mass (so long as the type and definition of mass is agreed upon) is a conserved quantity over time. From the viewpoint of any single unaccelerated observer, mass can neither be created or destroyed, and special relativity does not change this understanding (though different observers may not agree on how much mass is present, all agree that the amount does not change over time). However, relativity adds the fact that all types of energy have an associated mass, and this mass is added to systems when energy is added, and the associated mass is subtracted from systems when the energy leaves. In such cases, the energy leaving or entering the system carries the added or missing mass with it, since this energy itself has mass. Thus, mass remains conserved when the location of all mass is taken into account.

On the surface of the Earth, the weight W of an object is related to its mass m by

where g is the Earth's gravitational field strength, equal to about 9.81 m s⁻². An object's weight depends on its environment, while its mass does not: an object with a mass of 50 kilograms weighs 491 newtons on the surface of the Earth; on the surface of the Moon, the same object still has a mass of 50 kilograms but weighs only 81.5 newtons.

Units of mass

In the International System of Units (SI), mass is measured in kilograms (kg). The gram (g) is ¹⁄₁₀₀₀ of a kilogram.

Other units are accepted for use in SI:

• The tonne (t) is equal to 1000 kg.
• The electronvolt (eV) is primarily a unit of energy, but because of the mass-energy equivalence it can also function as a unit of mass. In this context it is denoted eV/c², or simply as eV. The electronvolt is common in particle physics.
• The atomic mass unit (u) is defined so that a single carbon-12 atom has a mass of 12 u; 1 u is approximately 1.66×10−27
   kg.^{[note 1]} The atomic mass unit is convenient for expressing the masses of atoms and molecules.

Outside the SI system, a variety of different mass units are used, depending on context, such as the slug (sl), the pound (lb), the Planck mass (m_P), and the solar mass (M_⊙).

In normal situations, the weight of an object is proportional to its mass, which usually makes it unproblematic to use the same unit for both concepts. However, the distinction between mass and weight becomes important for measurements with a precision better than a few percent (because of slight differences in the strength of the Earth's gravitational field at different places), and for places far from the surface of the Earth, such as in space or on other planets.

A mass can sometimes be expressed in terms of length. The mass of a very small particle may be identified with its inverse Compton wavelength (1 cm⁻¹ ≈ 3.52×10−41
 kg). The mass of a very large star or black hole may be identified with its Schwarzschild radius (1 cm ≈ 6.73×1024
 kg). The mass is the electric dipole moment.

[edit]Summary of mass concepts and formalisms

In classical mechanics, mass has a central role in determining the behavior of bodies. Newton's second law relates the force F exerted in a body of mass m to the body's acceleration a:

Additionally, mass relates a body's momentum p to its velocity v:

and the body's kinetic energy E_k to its velocity:

In special relativity, relativistic mass is a formalism which accounts for relativistic effects by having the mass increase with velocity.

Since energy is dependent on reference frame (upon the observer) it is convenient to formulate the equations of physics in a way such that mass values are invariant (do not change) between observers, and so the equations are independent of the observer. For a single particle, this quantity is the rest mass; for a system of bound or unbound particles, this quantity is the invariant mass. The invariant mass m of a body is related to its energy E and the magnitude of its momentum p by

where c is the speed of light. 

Summary of mass related phenomena

The relation between properties of mass and their associated physical constants. Every massive object is believed to exhibit all five properties, however, due to extremely large or extremely small constants, it is generally impossible to verify more than two or three properties for any object.

• The Schwarzschild radius (r_s) represents the ability of mass to cause curvature in space and time.
• The standard gravitational parameter (μ) represents the ability of a massive body to exert Newtonian gravitational forces on other bodies.
• Inertial mass (m) represents the Newtonian response of mass to forces.
• Rest energy (E₀) represents the ability of mass to be converted into other forms of energy.
• The Compton wavelength (λ) represents the quantum response of mass to local geometry.

In physical science, one may distinguish conceptually between at least seven attributes of mass, or seven physical phenomena that can be explained using the concept of mass:^[1]

• The amount of matter in certain types of samples can be exactly determined through electrodeposition^{[disambiguation needed][clarification needed]} or other precise processes. The mass of an exact sample is determined in part by the number and type of atoms or molecules it contains, and in part by the energy involved in binding it together (which contributes a negative "missing mass," or mass deficit).

• Inertial mass is a measure of an object's resistance to changing its state of motion when a force is applied. It is determined by applying a force to an object and measuring the acceleration that results from that force. An object with small inertial mass will accelerate more than an object with large inertial mass when acted upon by the same force. One says the body of greater mass has greater inertia.

• Active gravitational mass is a measure of the strength of an object’s gravitational flux (gravitational flux is equal to the surface integral of gravitational field over an enclosing surface). Gravitational field can be measured by allowing a small ‘test object’ to freely fall and measuring its free-fall acceleration. For example, an object in free-fall near the Moon will experience less gravitational field, and hence accelerate slower than the same object would if it were in free-fall near the earth. The gravitational field near the Moon is weaker because the Moon has less active gravitational mass.

• Passive gravitational mass is a measure of the strength of an object's interaction with a gravitational field. Passive gravitational mass is determined by dividing an object’s weight by its free-fall acceleration. Two objects within the same gravitational field will experience the same acceleration; however, the object with a smaller passive gravitational mass will experience a smaller force (less weight) than the object with a larger passive gravitational mass.

• Energy also has mass according to the principle of mass–energy equivalence. This equivalence is exemplified in a large number of physical processes including pair production, nuclear fusion, and the gravitational bending of light. Pair production and nuclear fusion are processes through which measurable amounts of mass and energy are converted into each other. In the gravitational bending of light, photons of pure energy are shown to exhibit a behavior similar to passive gravitational mass.

• Curvature of spacetime is a relativistic manifestation of the existence of mass. Curvature is extremely weak and difficult to measure. For this reason, curvature wasn’t discovered until after it was predicted by Einstein’s theory of general relativity. Extremely precise atomic clocks on the surface of the earth, for example, are found to measure less time (run slower) than similar clocks in space. This difference in elapsed time is a form of curvature called gravitational time dilation. Other forms of curvature have been measured using the Gravity Probe B satellite.

• Quantum mass manifests itself as a difference between an object’s quantum frequency and its wave number. The quantum mass of an electron, theCompton wavelength, can be determined through various forms of spectroscopy and is closely related to the Rydberg constant, the Bohr radius, and the classical electron radius. The quantum mass of larger objects can be directly measured using a watt balance.

Elementary particles

Elementary particles are particles with no measurable internal structure; that is, they are not composed of other particles. They are the fundamental objects of quantum field theory. Many families and sub-families of elementary particles exist. Elementary particles are classified according to their spin. Fermions have half-integer spin while bosons have integer spin. All the particles of the Standard Model have been observed, with the exception of the Higgs boson.

Fermions

Fermions have half-integer spin; for all known elementary fermions this is ¹⁄₂. All known fermions are dirac fermions; that is, each known fermion has its own distinct antiparticle. Fermions are the basic building blocks of all matter. They are classified according to whether they interact via the color force or not. In the Standard Model, there are 12 types of elementary fermions: six quarks and six leptons.

Quarks

Composite particles

Hadrons

Hadrons are defined as strongly interacting composite particles. Hadrons are either:

• Composite fermions, in which case they are called baryons.
• Composite bosons, in which case they are called mesons.

Quark models, first proposed in 1964 independently by Murray Gell-Mann and George Zweig (who called quarks "aces"), describe the known hadrons as composed of valence quarks and/or antiquarks, tightly bound by the color force, which is mediated by gluons. A "sea" of virtual quark-antiquark pairs is also present in each hadron.

Baryons (fermions)

A combination of three u, d or s-quarks with a total spin of ³⁄₂ form the so-calledbaryon decuplet.

Proton quark structure: 2 up quarks and 1 down quark.

For a detailed list, see List of baryons.

Ordinary baryons (composite fermions) contain three valence quarks or three valence antiquarks each.

• Nucleons are the fermionic constituents of normal atomic nuclei:
  • Protons, composed of two up and one down quark (uud)
  • Neutrons, composed of two down and one up quark (ddu)
• Hyperons, such as the Λ, Σ, Ξ, and Ω particles, which contain one or more strange quarks, are short-lived and heavier than nucleons. Although not normally present in atomic nuclei, they can appear in short-lived hypernuclei.
• A number of charmed and bottom baryons have also been observed.

Some hints at the existence of exotic baryons have been found recently; however, negative results have also been reported. Their existence is uncertain.

• Pentaquarks consist of four valence quarks and one valence antiquark.

Mesons (bosons)

Mesons of spin 0 form a nonet

For a detailed list, see List of mesons.

Ordinary mesons are made up of a valence quark and a valence antiquark. Because mesons have spin of 0 or 1 and are not themselves elementary particles, they arecomposite bosons. Examples of mesons include the pion, kaon, the J/ψ. In quantum hadrodynamic models, mesons mediate the residual strong force between nucleons.

At one time or another, positive signatures have been reported for all of the following exotic mesons but their existence has yet to be confirmed.

• A tetraquark consists of two valence quarks and two valence antiquarks;
• A glueball is a bound state of gluons with no valence quarks;
• Hybrids mesons consist of one or more valence quark-antiquark pairs and one or more real gluons.

Atomic nuclei

A semi-accurate depiction of the helium atom. In the nucleus, the protons are in red and neutrons are in purple. In reality, the nucleus is also spherically symmetrical.

Atomic nuclei consist of protons and neutrons. Each type of nucleus contains a specific number of protons and a specific number of neutrons, and is called a nuclide orisotope. Nuclear reactions can change one nuclide into another. See table of nuclides for a complete list of isotopes.

Atoms

Atoms are the smallest neutral particles into which matter can be divided by chemical reactions. An atom consists of a small, heavy nucleus surrounded by a relatively large, light cloud of electrons. Each type of atom corresponds to a specific chemical element. To date, 118 elements have been discovered, while only the first 112 have received official names. Refer to the periodic table for an overview.

The atomic nucleus consists of protons and neutrons. Protons and neutrons are, in turn, made of quarks.

Molecules

Molecules are the smallest particles into which a non-elemental substance can be divided while maintaining the physical properties of the substance. Each type of molecule corresponds to a specific chemical compound. Molecules are a composite of two or more atoms. See list of compounds for a list of molecules.

Condensed matter

The field equations of condensed matter physics are remarkably similar to those of high energy particle physics. As a result, much of the theory of particle physics applies to condensed matter physics as well; in particular, there are a selection of field excitations, called quasi-particles, that can be created and explored. These include:

• Phonons are vibrational modes in a crystal lattice.
• Excitons are bound states of an electron and a hole.
• Plasmons are coherent excitations of a plasma.
• Polaritons are mixtures of photons with other quasi-particles.
• Polarons are moving, charged (quasi-) particles that are surrounded by ions in a material.
• Magnons are coherent excitations of electron spins in a material.

Other

• An anyon is a generalization of fermion and boson in two-dimensional systems like sheets of graphene which obeys braid statistics.
• A plekton is a theoretical kind of particle discussed as a generalization of the braid statistics of the anyon to dimension > 2.
• A WIMP (weakly interacting massive particle) is any one of a number of particles that might explain dark matter (such as the neutralino or the axion).
• The pomeron, used to explain the elastic scattering of Hadrons and the location of Regge poles in Regge theory.
• The skyrmion, a topological solution of the pion field, used to model the low-energy properties of the nucleon, such as the axial vector current coupling and the mass.
• A goldstone boson is a massless excitation of a field that has been spontaneously broken. The pions are quasi-Goldstone bosons (quasi- because they are not exactly massless) of the broken chiral isospin symmetry of quantum chromodynamics.
• A goldstino is a Goldstone fermion produced by the spontaneous breaking of supersymmetry.
• An instanton is a field configuration which is a local minimum of the Euclidean action. Instantons are used in nonperturbative calculations of tunneling rates.
• A dyon is a hypothetical particle with both electric and magnetic charges
• A geon is an electromagnetic or gravitational wave which is held together in a confined region by the gravitational attraction of its own field energy.
• An inflaton is the generic name for an unidentified scalar particle responsible for the cosmic inflation.
• A spurion is the name given to a "particle" inserted mathematically into an isospin-violating decay in order to analyze it as though it conserved isospin.

Classification by speed

• A tardyon or bradyon travels slower than light and has a non-zero rest mass.
• A luxon travels at the speed of light and has no rest mass.
• A tachyon (mentioned above) is a hypothetical particle that travels faster than the speed of light and has an imaginary rest mass.

Matter is a general term for the substance of which all physical objects consist.^[1][2] Typically, matter includes atoms and other particles which have mass. A common way of defining matter is as anything that has mass and occupies volume.^[3] In practice however there is no single correct scientific meaning of "matter," as different fields use the term in different and sometimes incompatible ways.

For much of the history of the natural sciences people have contemplated the exact nature of matter. The idea that matter was built of discrete building blocks, the so-called particulate theory of matter, was first put forward by the Greek philosophers Leucippus (~490 BC) and Democritus (~470–380 BC).^[4] Over time an increasingly fine structure for matter was discovered: objects are made from molecules, molecules consist of atoms, which in turn consist of interacting subatomic particles like protons and electrons.^[5][6]

Matter is commonly said to exist in four states (or phases): solid, liquid, gas and plasma. However, advances in experimental techniques have realized other phases, previously only theoretical constructs, such as Bose–Einstein condensates and fermionic condensates. A focus on an elementary-particle view of matter also leads to new phases of matter, such as the quark–gluon plasma.^[7]

In physics and chemistry, matter exhibits both wave-like and particle-like properties, the so-called wave–particle duality.^[8][9][10]

In the realm of cosmology, extensions of the term matter are invoked to include dark matter and dark energy, concepts introduced to explain some odd phenomena of the observable universe, such as the galactic rotation curve. These exotic forms of "matter" do not refer to matter as "building blocks", but rather to currently poorly understood forms of mass and energy.

Summary

The term "matter" is used throughout physics in a bewildering variety of contexts: for example, one refers to "condensed matter physics",^[35] "elementary matter",^[36] "partonic" matter, "dark" matter, "anti"-matter, "strange" matter, and "nuclear" matter. In discussions of matter and antimatter, normal matter has been referred to by Alfvén as koinomatter.^[37] It is fair to say that in physics, there is no broad consensus as to an exact definition of matter, and the term "matter" usually is used in conjunction with some modifier.

Definitions

Common definition

The DNA molecule is an example of matter under the "atoms and molecules" definition.

The common definition of matter is anything that has both mass and volume (occupies space).^[38][39] For example, a car would be said to be made of matter, as it occupies space, and has mass.

The observation that matter occupies space goes back to antiquity. However, an explanation for why matter occupies space is recent, and is argued to be a result of the Pauli exclusion principle.^[40][41] Two particular examples where the exclusion principle clearly relates matter to the occupation of space are white dwarf stars and neutron stars, discussed further below.

Relativity

In the context of relativity, mass is not an additive quantity.^[1] Thus, in relativity usually a more general view is taken that it is not mass, but the energy–momentum tensor that quantifies the amount of matter. Matter therefore is anything that contributes to the energy–momentum of a system, that is, anything that is not purely gravity.^[42][43] This view is commonly held in fields that deal withgeneral relativity such as cosmology.

Atoms and molecules definition

A definition of "matter" that is based upon its physical and chemical structure is: matter is made up of atoms andmolecules.^{[44][not in citation given]} As an example, deoxyribonucleic acid molecules (DNA) are matter under this definition because they are made of atoms. This definition can be extended to include charged atoms and molecules, so as to include plasmas (gases of ions) and electrolytes (ionic solutions), which are not obviously included in the atoms and molecules definition. Alternatively, one can adopt the protons, neutrons and electrons definition.

Protons, neutrons and electrons definition

A definition of "matter" more fine-scale than the atoms and molecules definition is: matter is made up of what atoms and moleculesare made of, meaning anything made of protons, neutrons, and electrons.^{[45][verification needed]} This definition goes beyond atoms and molecules, however, to include substances made from these building blocks that are not simply atoms or molecules, for examplewhite dwarf matter — typically, carbon and oxygen nuclei in a sea of degenerate electrons. At a microscopic level, the constituent "particles" of matter such as protons, neutrons and electrons obey the laws of quantum mechanics and exhibit wave–particle duality. At an even deeper level, protons and neutrons are made up of quarks and the force fields (gluons) that bind them together (see Quarks and leptons definition below).

Quarks and leptons definition

Under the "quarks and leptons" definition, the elementary and composite particles made of the quarks (in purple) and leptons (in green) would be "matter"; while the gauge bosons (in red) would not be "matter". However, interaction energy inherent to composite particles (for example, gluons involved in neutrons and protons) contribute to the mass of ordinary matter.

As may be seen from the above discussion, many early definitions of what can be called ordinary matter were based upon its structure or "building blocks". On the scale of elementary particles, a definition that follows this tradition can be stated as: ordinary matter is everything that is composed of elementary fermions, namely quarks and leptons.^{[46][not in citation given][47][not in citation given]} The connection between these formulations follows.

Leptons (the most famous being the electron), and quarks (of which baryons, such as protons and neutrons, are made) combine to formatoms, which in turn form molecules. Because atoms and molecules are said to be matter, it is natural to phrase the definition as: ordinary matter is anything that is made of the same things that atoms and molecules are made of. (However, notice that one also can make from these building blocks matter that is not atoms or molecules.) Then, because electrons are leptons, and protons and neutrons are made of quarks, this definition in turn leads to the definition of matter as being "quarks and leptons", which are the two types of elementary fermions. Carithers and Grannis state: Ordinary matter is composed entirely of first-generation particles, namely the [up] and [down] quarks, plus the electron and its neutrino.^[48] (Higher generations particles quickly decay into first-generation particles, and thus are not commonly encountered.^[49])

This definition of ordinary matter is more subtle than it first appears. All the particles that make up ordinary matter (leptons and quarks) are elementary fermions, while all the force carriers are elementary bosons.^[50] The W and Z bosons that mediate the weak force are not made of quarks or leptons, and so are not ordinary matter, even if they have mass.^[51] In other words, mass is not something that is exclusive to ordinary matter.

The quark–lepton definition of ordinary matter, however, identifies not only the elementary building blocks of matter, but also includes composites made from the constituents (atoms and molecules, for example). Such composites contain an interaction energy that holds the constituents together, and may constitute the bulk of the mass of the composite. As an example, to a great extent, the mass of an atom is simply the sum of the masses of its constituent protons, neutrons and electrons. However, digging deeper, the protons and neutrons are made up of quarks bound together by gluon fields (see dynamics of quantum chromodynamics) and these gluons fields contribute significantly to the mass of hadrons.^[52] In other words, most of what composes the "mass" of ordinary matter is due to thebinding energy of quarks within protons and neutrons.^[53] For example, the sum of the mass of the three quarks in a nucleon is approximately 12.5 MeV/c², which is low compared to the mass of a nucleon (approximately 938 MeV/c²).^[49][54] The bottom line is that most of the mass of everyday objects comes from the interaction energy of its elementary components.

Smaller building blocks?

The Standard Model groups matter particles into three generations, where each generation consists of two quarks and two leptons. The first generation is the up and down quarks, the electron and theelectron neutrino; the second includes the charm and strange quarks, the muon and the muon neutrino; the third generation consists of the top and bottom quarks and the tau and tau neutrino.^[55] The most natural explanation for this would be that quarks and leptons of higher generations are excited states of the first generations. If this turns out to be the case, it would imply that quarks and leptons are composite particles, rather than elementary particles.^[56]

Structure

In particle physics, fermions are particles which obey Fermi–Dirac statistics. Fermions can be elementary, like the electron, or composite, like the proton and the neutron. In the Standard Model there are two types of elementary fermions: quarks and leptons, which are discussed next.

Quarks

Quarks are a particles of spin-¹⁄₂, implying that they are fermions. They carry an electric charge of −¹⁄₃ e (down-type quarks) or +²⁄₃ e (up-type quarks). For comparison, an electron has a charge of −1 e. They also carry colour charge, which is the equivalent of the electric charge for the strong interaction. Quarks also undergo radioactive decay, meaning that they are subject to the weak interaction. Quarks are massive particles, and therefore are also subject to gravity.

Quark structure of a proton: 2 up quarks and 1 down quark.

Baryonic matter

Baryons are strongly interacting fermions, and so are subject to Fermi-Dirac statistics. Amongst the baryons are the protons and neutrons, which occur in atomic nuclei, but many other unstable baryons exist as well. The term baryon is usually used to refer to triquarks — particles made of three quarks. "Exotic" baryons made of four quarks and one antiquark are known as the pentaquarks, but their existence is not generally accepted.

Baryonic matter is the part of the universe that is made of baryons (including all atoms). This part of the universe does not include dark energy, dark matter, black holes or various forms of degenerate matter, such as compose white dwarf stars and neutron stars. Microwave light seen by Wilkinson Microwave Anisotropy Probe (WMAP), suggests that only about 4.6% of that part of the universe within range of the best telescopes (that is, matter that may be visible because light could reach us from it), is made of baryionic matter. About 23% is dark matter, and about 72% is dark energy.^[58]

A comparison between the white dwarf IK Pegasi B (center), its A-class companion IK Pegasi A (left) and the Sun (right). This white dwarf has a surface temperature of 35,500 K.

Degenerate matter

In physics, degenerate matter refers to the ground state of a gas of fermions at a temperature near absolute zero.^[59] The Pauli exclusion principlerequires that only two fermions can occupy a quantum state, one spin-up and the other spin-down. Hence, at zero temperature, the fermions fill up sufficient levels to accommodate all the available fermions, and for the case of many fermions the maximum kinetic energy called the Fermi energy and the pressure of the gas becomes very large and dependent upon the number of fermions rather than the temperature, unlike normal states of matter.

Degenerate matter is thought to occur during the evolution of heavy stars.^[60] The demonstration by Subrahmanyan Chandrasekhar that white dwarf stars have a maximum allowed mass because of the exclusion principle caused a revolution in the theory of star evolution.^[61]

Degenerate matter includes the part of the universe that is made up of neutron stars and white dwarfs.

Strange matter

Strange matter is a particular form of quark matter, usually thought of as a 'liquid' of up, down, and strange quarks. It is to be contrasted with nuclear matter, which is a liquid of neutrons and protons(which themselves are built out of up and down quarks), and with non-strange quark matter, which is a quark liquid containing only up and down quarks. At high enough density, strange matter is expected to be color superconducting. Strange matter is hypothesized to occur in the core of neutron stars, or, more speculatively, as isolated droplets that may vary in size from femtometers(strangelets) to kilometers (quark stars).

Two meanings of the term "strange matter"

In particle physics and astrophysics, the term is used in two ways, one broader and the other more specific.

1. The broader meaning is just quark matter that contains three flavors of quarks: up, down, and strange. In this definition, there is a critical pressure and an associated critical density, and when nuclear matter (made of protons and neutrons) is compressed beyond this density, the protons and neutrons dissociate into quarks, yielding quark matter (probably strange matter).
2. The narrower meaning is quark matter that is more stable than nuclear matter. The idea that this could happen is the "strange matter hypothesis" of Bodmer ^[62] and Witten.^[63] In this definition, the critical pressure is zero: the true ground state of matter is always quark matter. The nuclei that we see in the matter around us, which are droplets of nuclear matter, are actually metastable, and given enough time (or the right external stimulus) would decay into droplets of strange matter, i.e. strangelets.

Leptons

Leptons are a particles of spin-¹⁄₂, meaning that they are fermions. They carry an electric charge of −1 e (charged leptons) or 0 e (neutrinos). Unlike quarks, leptons do not carry colour charge, meaning that they do not experience the strong interaction. Leptons also undergo radioactive decay, meaning that they are subject to the weak interaction. Leptons are massive particles, therefore are subject to gravity.

Phases

In kinematics, the speed of an object is the magnitude of its velocity (the rate of change of its position); it is thus a scalar quantity. The average speed of an object in an interval of time is the distance traveled by the object divided by the duration of the interval; the instantaneous speed is the limit of the average speed as the duration of the time interval approaches zero .

Like velocity, speed has the dimensions of a length divided by a time; the SI unit of speed is the meter per second, but the most usual unit of speed in everyday usage is the kilometer per hour or, in the USA and the UK, miles per hour. For air and marine travel the knot is commonly used.

The fastest possible speed at which energy or information can travel, according to special relativity, is thespeed of light in vacuum c = 299,792,458 meters per second, approximately 1079 million kilometers per hour (671,000,000 mph). Matter cannot quite reach the speed of light, as this would require an infinite amount of energy.

Definition

The speed v is defined as the magnitude of the velocity v, that is the derivative of the position r with respect to time:

If s is the length of the path traveled until time t, the speed equals the time derivative of s:

In the special case where the velocity is constant (that is, constant speed in a straight line) this can be simplified to v=s/t. The average speed over a finite time interval is the total distance traveled divided by the time duration.

Expressed in graphical language, the slope of a tangent line of a distance-time graph is the instantaneous speed, and the slope of a chordline of distance-time graph is the average speed over the time interval between the ends of the chord.

[edit]Units

Units of speed include:

• Meters per second (symbol m s⁻¹ or m/s), the SI derived unit;
• Kilometers per hour (symbol km/h);
• Miles per hour (symbol mph);
• Knots (nautical miles per hour, symbol kn or kt);
• Feet per second (symbol fps or ft/s);
• Mach number, (dimensionless) speed divided by the speed of sound;
• The speed of light in vacuum (symbol c) is one of the natural units:

  c = 299,792,458 m/s.

(Values in bold face are exact.)

[edit]Examples of different speeds

Overview

Potential energy exists when a force acts upon an object that tends to restore it to a lower energy configuration. This force is often called a restoring force. For example, when a spring is stretched to the left, it exerts a force to the right so as to return to its original, unstretched position. Similarly, when a mass is lifted up, the force of gravity will act so as to bring it back down. The action of stretching the spring or lifting the mass requires energy to perform. The energy that went into lifting up the mass is stored in its position in the gravitational field, while similarly, the energy it took to stretch the spring is stored in the metal. According to the law of conservation of energy, energy cannot be created or destroyed; hence this energy cannot disappear. Instead, it is stored as potential energy. If the spring is released or the mass is dropped, this stored energy will be converted into kinetic energy by the restoring force, which is elasticity in the case of the spring, and gravity in the case of the mass. Think of a roller coaster. When the coaster climbs a hill it has potential energy. At the very top of the hill is its maximum potential energy. When the car speeds down the hill potential energy turns into kinetic. Kinetic energy is greatest at the bottom.

The more formal definition is that potential energy is the energy difference between the energy of an object in a given position and its energy at a reference position.

There are various types of potential energy, each associated with a particular type of force. More specifically, every conservative force gives rise to potential energy. For example, the work of an elasticforce is called elastic potential energy; work of the gravitational force is called gravitational potential energy; work of the Coulomb force is called electric potential energy; work of the strong nuclear force or weak nuclear force acting on the baryon charge is called nuclear potential energy; work of intermolecular forces is called intermolecular potential energy. Chemical potential energy, such as the energy stored in fossil fuels, is the work of the Coulomb force during rearrangement of mutual positions of electrons and nuclei in atoms and molecules. Thermal energy usually has two components: the kinetic energy of random motions of particles and the potential energy of their mutual positions.

As a general rule, the work done by a conservative force F will be

where ΔU is the change in the potential energy associated with that particular force. Common notations for potential energy are U, V, E_p, and PE.

Reference level

The potential energy is a function of the state a system is in, and is defined relative to that for a particular state. This reference state is not always a real state, it may also be a limit, such as with the distances between all bodies tending to infinity, provided that the energy involved in tending to that limit is finite, such as in the case of inverse-square law forces. Any arbitrary reference state could be used, therefore it can be chosen based on convenience.

Oxides

• iron(II) oxide, wüstite (FeO)
• iron(II,III) oxide, magnetite (Fe₃O₄)
• iron(III) oxide (Fe₂O₃)
  • alpha phase, hematite (α-Fe₂O₃)
  • beta phase, (β-Fe₂O₃)
  • gamma phase, maghemite (γ-Fe₂O₃)
  • epsilon phase, (ε-Fe₂O₃)

Hydroxides

• iron(II) hydroxide (Fe(OH)₂)
• iron(III) hydroxide (Fe(OH)₃), (bernalite)

Oxide/hydroxides

• goethite (α-FeOOH),
• akaganéite (β-FeOOH),
• lepidocrocite (γ-FeOOH),
• feroxyhyte (δ-FeOOH),
• ferrihydrite (Fe₅HO₈·4H₂O approx.), or 5Fe₂O₃•9H₂O, better recast as FeOOH•0.4H₂O

• high-pressure FeOOH
• schwertmannite (ideally Fe₈O₈(OH)₆(SO)·nH₂O or Fe³⁺₁₆O₁₆(OH,SO₄)_12-13·10-12H₂O

Iron ( /ˈaɪ.ərn/ or /ˈaɪərn/) is a chemical element with the symbol Fe (Latin: ferrum) and atomic number 26. It is a metal in the first transition series. It is the most common element in the whole planet Earth, forming much of Earth's outer and inner core, and it is the fourth most common element in the Earth's crust. It is produced in abundance as a result of fusion in high-mass stars, where the production of nickel-56 (which decays to iron) is the last nuclear fusion reaction that is exothermic, becoming the last element to be produced before collapse of a supernova leads to events that scatter the precursor radionuclides of iron into space.

Like other Group 8 elements, iron exists in a wide range of oxidation states, −2 to + 6, although +2 and +3 are the most common. Elemental iron occurs in meteoroidsand other low oxygen environments, but is reactive to oxygen and water. Fresh iron surfaces appear lustrous silvery-gray, but oxidize in normal air to give iron oxides, also known as rust. Unlike many other metals which form passivating oxide layers, iron oxides occupy more volume than iron metal, and thus iron oxides flake off and expose fresh surfaces for corrosion.

Iron metal has been used since ancient times, though lower-melting copper alloys were used first in history. Pure iron is soft (softer than aluminium), but is unobtainable by smelting. The material is significantly hardenened and strengthened by impurities from the smelting process, such as carbon. A certain proportion of carbon (between 0.2% and 2.1%) produces steel, which may be up to 1000 times harder than pure iron. Crude iron metal is produced in blast furnaces, where ore is reduced by coke to cast iron. Further refinement with oxygen reduces the carbon content to make steel. Steels and low carbon iron alloys with other metals (alloy steels) are by far the most common metals in industrial use, due to their great range of desirable properties.

Iron chemical compounds, which include ferrous and ferric compounds, have many uses. Iron oxide mixed with aluminium powder can be ignited to create a thermite reaction, used in welding and purifying ores. It forms binary compounds with the halogens and the chalcogens. Among its organometallic compounds, ferrocene was the first sandwich compound discovered.

Iron plays an important role in biology, forming complexes with molecular oxygen in hemoglobin and myoglobin; these two compounds are common oxygen transportproteins in vertebrates. Iron is also the metal used at the active site of many important redox enzymes dealing with cellular respiration and oxidation and reduction in plants and animals.

Characteristics

Mechanical properties

Mechanical properties of iron and its alloys are evaluated using a variety of tests, such as the Brinell test, Rockwell test, or tensile strength tests, among others; the results on iron are so consistent that iron is often used to calibrate measurements or to relate the results of one test to another.^[2][3] Those measurements reveal that mechanical properties of iron crucially depend on purity: Purest research-purpose single crystals of iron are softer than aluminium. Addition of only 10 parts per million of carbon doubles their strength.^[1] The hardness increases rapidly with carbon content up to 0.2% and saturates at ~0.6%.^[4] The purest industrially produced iron (about 99.99% purity) has a hardness of 20–30 Brinell.^[5]

Allotropes

Iron represents an example of allotropy in a metal. There are three allotropic forms of iron, known as α, γ and δ.

Phase diagram of pure iron

As molten iron cools down it crystallizes at 1538 °C into its δ allotrope, which has a body-centered cubic (bcc) crystal structure. As it cools further its crystal structure changes to face-centered cubic (fcc) at 1394 °C, when it is known as γ-iron, or austenite. At 912 °C the crystal structure again becomes bcc as α-iron, or ferrite, is formed, and at 770 °C (the Curie point, T_c) iron becomes magnetic. As the iron passes through the Curie temperature there is no change in crystalline structure, but there is a change in "domain structure", where each domain contains iron atoms with a particular electronic spin. In unmagnetized iron, all the electronic spins of the atoms within one domain are in the same direction; the neighboring domains point in various directions and thus cancel out. In magnetized iron, the electronic spins of all the domains are aligned, so that the magnetic effects of neighboring domains reinforce each other. Although each domain contains billions of atoms, they are very small, about 10 micrometres across.^[6]

Iron is of greatest importance when mixed with certain other metals and with carbon to form steels. There are many types of steels, all with different properties, and an understanding of the properties of the allotropes of iron is key to the manufacture of good quality steels.

Alpha iron, also known as ferrite, is the most stable form of iron at normal temperatures. It is a fairly soft metal that can dissolve only a small concentration of carbon (no more than 0.021% by mass at 910 °C).^[7]

Above 912 °C and up to 1400 °C α-iron undergoes a phase transition from bcc to the fcc configuration of γ-iron, also calledaustenite. This is similarly soft and metallic but can dissolve considerably more carbon (as much as 2.04% by mass at 1146 °C). This form of iron is used in the type of stainless steel used for making cutlery, and hospital and food-service equipment.^[6]

Isotopes

Much of the past work on measuring the isotopic composition of Fe has focused on determining ⁶⁰Fe variations due to processes accompanying nucleosynthesis (i.e.,meteorite studies) and ore formation. In the last decade however, advances in mass spectrometry technology have allowed the detection and quantification of minute, naturally occurring variations in the ratios of the stable isotopes of iron. Much of this work has been driven by the Earth and planetary science communities, although applications to biological and industrial systems are beginning to emerge.^[9]

The most abundant iron isotope ⁵⁶Fe is of particular interest to nuclear scientists as it represents the most stable nuclide possible. It is impossible to perform fission or fusion on ⁵⁶Fe and still liberate energy. Since ⁵⁶Ni is easily produced from lighter nuclei in the alpha process in nuclear reactions in supernovae (see silicon burning process), nickel-56 (14 alpha particles) is the endpoint of fusion chains inside extremely massive stars, since addition of another alpha particle would result in zinc-60, which requires a great deal more energy. This nickel-56, which has a half-life of about 6 days, is therefore made in quantity in these stars, but soon decays by two successive positron emissions within supernova decay products in the supernova remnant gas cloud, to first radioactive cobalt-56, and then stable iron-56. This last nuclide is therefore common in the universe, relative to other stable metals of approximately the same atomic weight.

In phases of the meteorites Semarkona and Chervony Kut a correlation between the concentration of ⁶⁰Ni, the daughter product of ⁶⁰Fe, and the abundance of the stable iron isotopes could be found which is evidence for the existence of ⁶⁰Fe at the time of formation of the solar system. Possibly the energy released by the decay of ⁶⁰Fe contributed, together with the energy released by decay of the radionuclide ²⁶Al, to the remelting and differentiation of asteroids after their formation 4.6 billion years ago^{[citation needed]}. The abundance of ⁶⁰Ni present in extraterrestrial material may also provide further insight into the origin of thesolar system and its early history. Of the stable isotopes, only ⁵⁷Fe has a nuclear spin (−1/2).

Nuclei of iron atoms have some of the highest binding energies per nucleon, surpassed only by the nickel isotope ⁶²Ni. This is formed by nuclear fusion in stars. Although a further tiny energy gain could be extracted by synthesizing ⁶²Ni, conditions in stars are unsuitable for this process to be favored. Elemental distribution on Earth greatly favors iron over nickel, and also presumably in supernova element production.^[10]

Iron-56 is the heaviest stable isotope produced by the alpha process in stellar nucleosynthesis; elements heavier than iron and nickel require a supernova for their formation. Iron is the most abundant element in the core of red giants, and is the most abundant metal in iron meteorites and in the dense metal cores of planets such as Earth.

Nucleosynthesis

Iron is created by extremely large, extremely hot (over 2.5 billion kelvin) stars, through a process called the silicon burning process. It is the heaviest stable element to be produced in this manner. The process starts with the second largest stable nucleus created by silicon burning: calcium. One stable nucleus of calcium fuses with one helium nucleus, creating unstable titanium. Before the titanium decays, it can fuse with another helium nucleus, creating unstable chromium. Before the chromium decays, it can fuse with another helium nucleus, creating unstable iron. Before the iron decays, it can fuse with another helium nucleus, creating unstable nickel-56. Any further fusion of nickel-56 consumes energy instead of producing energy, so after the production of nickel-56, the star does not produce the energy necessary to keep the core from collapsing. Eventually, the nickel-56 decays to unstable cobalt-56 which, in turn decays to stable iron-56 When the core of the star collapses, it creates a Supernova. Supernovas also create additional forms of stable iron via the r-process.

Occurrence

Planetary occurrence

Iron meteorites of similar composition of Earth's inner and outer core

Iron is the sixth most abundant element in the Universe, formed as the final step of nucleosynthesis, by silicon fusing in massive stars. Metallic iron is rarely found on the surface of the earth because it tends to oxidize, but its oxides are pervasive and represent the primary ores. While it makes up about 5% of the Earth's crust, both the Earth's inner and outer core are believed to consist largely of an iron-nickel alloy constituting 35% of the mass of the Earth as a whole. Iron is consequently the most abundant element on Earth, but only the fourth most abundant element in the Earth's crust.^[11][12] Most of the iron in the crust is found combined with oxygen as iron oxideminerals such as hematite and magnetite. Large deposits of iron are found in banded iron formations. These geological formations are a type of rock consisting of repeated thin layers of iron oxides, either magnetite (Fe₃O₄) or hematite (Fe₂O₃), alternating with bands of iron-poor shale and chert. The banded iron formations are common in the time between 3,700 million years ago and 1,800 million years ago^[13][14]

Description

Figure 1: The definition of surface integral relies on splitting the surface into small surface elements. Each element is associated with a vector dS of magnitude equal to the area of the element and with direction normal to the element and pointing outward.

Figure 2: A vector field of normals to a surface.

The magnetic flux through a given surface is proportional to the number of magnetic field lines that pass through the surface. This is the net number, i.e. the number passing through in one direction, minus the number passing through in the other direction. (See below for how the positive sign is chosen.) For a uniform magnetic field Bpassing through a perpendicular area the magnetic flux is given by the product of the magnetic field and the area element. The magnetic flux for a uniform B at any angle to a surface is defined by a dot product of the magnetic field and the area element vector.

where θ is the angle between B and a vector that is perpendicular (normal) to S.

In the general case, the magnetic flux through a surface S is defined as the integral of the magnetic field over the area of the surface (See Figures 1 and 2):

where  is the magnetic flux, B is the magnetic field,

S is the surface (area), denotes dot product, and dS is an infinitesimal vector, whose magnitude is the area of a differential element of S, and whose direction is thesurface normal. (See surface integral for more details.)

From the definition of the magnetic vector potential A and the fundamental theorem of the curl the magnetic flux may also be defined as:

where the closed line integral is over the boundary of the surface and dℓ is an infinitesimal vector element of that contour Σ.

The magnetic flux is usually measured with a fluxmeter. The fluxmeter contains measuring coils and electronics that evaluates the change of voltage in the measuring coils to calculate the magnetic flux.

Magnetic flux through a closed surface

Some examples of closed surfaces(left) and open surfaces (right). Left: Surface of a sphere, surface of a torus, surface of a cube. Right: Disk surface, square surface, surface of a hemisphere. (The surface is blue, the boundary is red.)

Gauss's law for magnetism, which is one of the four Maxwell's equations, states that the total magnetic flux through a closed surface is equal to zero. (A "closed surface" is a surface that completely encloses a volume(s) with no holes.) This law is a consequence of the empirical observation that magnetic monopoles have never been found.

In other words, Gauss's law for magnetism is the statement:

for any closed surface S.

Magnetic flux through an open surface

Figure 3: A vector field F ( r, t ) defined throughout space, and a surface Σ bounded by curve ∂Σ moving with velocity v over which the field is integrated.

While the magnetic flux through a closed surface is always zero, the magnetic flux through an open surface need not be zero and is an important quantity in electromagnetism. For example, a change in the magnetic flux passing through a loop of conductive wire will cause an electromotive force, and therefore an electric current, in the loop. The relationship is given by Faraday's law:

where (see Figure 3):

 is the EMF,

Φ_m is the flux through a surface with an opening bounded by a curve ∂Σ(t),

∂Σ(t) is a closed contour that can change with time; the EMF is found around this contour, and the contour is a boundary of the surface over which Φ_m is found,

dℓ is an infinitesimal vector element of the contour ∂Σ(t),

v is the velocity of the segment dℓ,

E is the electric field,

B is the magnetic field.

The EMF is determined in this equation in two ways: first, as the work per unit charge done against the Lorentz force in moving a test charge around the (possibly moving) closed curve ∂Σ(t), and second, as the magnetic flux thorough the open surface Σ(t).

This equation is the principle behind an electrical generator.

Comparison with electric flux

By way of contrast, Gauss's law for electric fields, another of Maxwell's equations, is

where

E is the electric field,

S is any closed surface,

Q is the total electric charge inside the surface S,

ε₀ is the electric constant (a universal constant, also called the "permittivity of free space").

Magnetization, M, is defined as the quantity ofmagnetic moment per unit volume, V:

Here, N is the number of magnetic moments in the sample. The quantity N/V is usually written as n, the number density of magnetic moments. The M-field is measured in amperes per meter (A/m) in SI units.^[1]

The origin of the magnetic moments responsible for magnetization can be either microscopic electric currents resulting from the motion of electrons inatoms, or the spin of the electrons or the nuclei. Net magnetization results from the response of a material to an external magnetic field, together with any unbalanced magnetic dipole moments that may be inherent in the material itself; for example, inferromagnets. Magnetization is not alwayshomogeneous within a body, but rather a function of position.

Magnetization in Maxwell's equations

The behavior of magnetic fields (B, H), electric fields (E, D), charge density (ρ), and current density (J) is described by Maxwell's equations. The role of the magnetization is described below.

Relations between B, H, and M

The magnetization defines the auxiliary magnetic field H as

 (SI units)

 (Gaussian units)

which is convenient for various calculations. The vacuum permeability μ₀ is, by definition,4π×10−7
 V·s/(A·m).

A relation between M and H exists in many materials. In diamagnets and paramagnets, the relation is usually linear:

where χ_m is called the volume magnetic susceptibility.

In ferromagnets there is no one-to-one correspondence between M and H because of hysteresis.

Magnetization current

The magnetization M makes a contribution to the current density J, known as themagnetization current or bound current:

so that the total current density that enters Maxwell's equations is given by

where J_f is the electric current density of free charges (also called the free current), the second term is the contribution from the magnetization, and the last term is related to the electric polarization P.

Magnetostatics

In the absence of free electric currents and time-dependent effects, Maxwell's equationsdescribing the magnetic quantities reduce to

These equations can be easily solved in analogy with electrostatic problems where

In this sense  plays the role of a "magnetic charge density" analogous to the electric charge density ρ (see also demagnetizing field).

Magnetization is volume density of magnetic moment. That is: if a certain volume has magnetization  then the volume element dV has a magnetic moment of 

Magnetization dynamics

Main article: Magnetization dynamics

Annealing, in metallurgy and materials science, is a heat treatment wherein a material is altered, causing changes in its properties such as strength and hardness. It is a process that produces conditions by heating to above the recrystallization temperature and maintaining a suitable temperature, and then cooling. Annealing is used to induce ductility, soften material, relieve internal stresses, refine the structure by making it homogeneous, and improve cold working properties.

In the cases of copper, steel, silver, and brass, this process is performed by substantially heating the material (generally until glowing) for a while and allowing it to cool. Unlike ferrous metals—which must be cooled slowly to anneal—copper, silver^[1] and brass can be cooled slowly in air or quickly by quenching in water. In this fashion the metal is softened and prepared for further work such as shaping, stamping, or forming.

Thermodynamics of annealing

Annealing occurs by the diffusion of atoms within a solid material, so that the material progresses towards its equilibrium state. Heat is needed to increase the rate of diffusion by providing the energy needed to break bonds. The movement of atoms has the effect of redistributing and destroying the dislocations in metals and (to a lesser extent) in ceramics. This alteration in dislocations allows metals to deform more easily, so increases their ductility.

The amount of process-initiating Gibbs free energy in a deformed metal is also reduced by the annealing process. In practice and industry, this reduction of Gibbs free energy is termed "stress relief".

The relief of internal stresses is a thermodynamically spontaneous process; however, at room temperatures, it is a very slow process. The high temperatures at which the annealing process occurs serve to accelerate this process.

The reaction facilitating the return of the cold-worked metal to its stress-free state has many reaction pathways, mostly involving the elimination of lattice vacancy gradients within the body of the metal. The creation of lattice vacancies is governed by the Arrhenius equation, and the migration/diffusion of lattice vacancies are governed by Fick’s laws of diffusion.^[2]

Mechanical properties, such as hardness and ductility, change as dislocations are eliminated and the metal's crystal lattice is altered. On heating at specific temperature and cooling it is possible to bring the atom at the right lattice site and new grain growth can improve the mechanical properties.

Stages of annealing

There are three stages in the annealing process, with the first being the recovery phase, which results in softening of the metal through removal of crystal defects (the primary type of which is the linear defect called a dislocation) and the internal stresses which they cause. Recovery phase covers all annealing phenomena that occur before the appearance of new strain-free grains.^[3] The second phase is recrystallization, where new strain-free grains nucleate and grow to replace those deformed by internal stresses.^[3] If annealing is allowed to continue once recrystallization has been completed, grain growth will occur, in which the microstructure starts to coarsen and may cause the metal to have less than satisfactory mechanical properties.

Annealing in a controlled atmosphere

The high temperature of annealing may result in oxidation of the metal’s surface, resulting in scale. If scale is to be avoided, annealing is carried out in a special atmosphere, such as with endothermic gas (a mixture of carbon monoxide, hydrogen gas, and nitrogen gas).

The magnetic properties of mu-metal (Espey cores) are introduced by annealing the alloy in a hydrogen atmosphere.

Setup and equipment

Typically, large ovens are used for the annealing process. The inside of the oven is large enough to place the workpiece in a position to receive maximum exposure to the circulating heated air. For high volume process annealing, gas fired conveyor furnaces are often used. For large workpieces or high quantity parts Car-bottom furnaces will be used in order to move the parts in and out with ease. Once the annealing process has been successfully completed, the workpieces are sometimes left in the oven in order for the parts to have a controlled cooling process. While some workpieces are left in the oven to cool in a controlled fashion, other materials and alloys are removed from the oven. After being removed from the oven, the workpieces are often quickly cooled off in a process known as quench hardening. Some typical methods of quench hardening materials involve the use of media such as air, water, oil, or salt.

Diffusion annealing of semiconductors

In the semiconductor industry, silicon wafers are annealed, so that dopant atoms, usually boron, phosphorus or arsenic, can diffuse into substitutional positions in the crystal lattice, resulting in drastic changes in the electrical properties of the semiconducting material.

Specialized annealing cycles

Normalization

Normalization is an annealing process in which a metal is cooled in air after heating in order to relieve stress.

It can also be referred to as: Heating a ferrous alloy to a suitable temperature above the transformation temperature range and cooling in air to a temperature substantially below the transformation range.

This process is typically confined to hardenable steel. It is used to refine grains which have been deformed through cold work, and can improve ductility and toughness of the steel. It involves heating the steel to just above its upper critical point. It is soaked for a short period then allowed to cool in air. Small grains are formed which give a much harder and tougher metal with normal tensile strength and not the maximum ductility achieved by annealing. It eliminates columnar grains and dendritic segregation that sometimes occurs during casting. Normalizing improves machinability of a component and provides dimensional stability if subjected to further heat treatment processes.

Process annealing

Process annealing, also called "intermediate annealing", "subcritical annealing", or "in-process annealing", is a heat treatment cycle that restores some of the ductility to a work piece allowing it be worked further without breaking. Ductility is important in shaping and creating a more refined piece of work through processes such as rolling, drawing, forging, spinning, extruding and heading. The piece is heated to a temperature typically below the austenizing temperature, and held there long enough to relieve stresses in the metal. The piece is finally cooled slowly to room temperature. It is then ready again for additional cold working. This can also be used to ensure there is reduced risk of distortion of the work piece during machining, welding, or further heat treatment cycles.

The temperature range for process annealing ranges from 500 °F to 1400 °F, depending on the alloy in question.

Full anneal

Full annealing temperature ranges

A full anneal typically results in the second most ductile state a metal can assume for metal alloy. It creates an entirely new homogeneous and uniform structure with good dynamic properties. To perform a full anneal, a metal is heated to its annealing point (about 50°C above the austenic temperature as graph shows) and held for sufficient time to allow the material to fully austenitize, to form austenite or austenite-cementite grain structure. The material is then allowed to cool slowly so that the equilibrium microstructure is obtained. In some cases this means the material is allowed to air cool. In other cases the material is allowed to furnace cool. The details of the process depend on the type of metal and the precise alloy involved. In any case the result is a more ductile material that has greater stretch ratio and reduction of area properties but a lower yield strength and a lower tensile strength. This process is also called LP annealing for lamellar pearlite in the steel industry as opposed to a process anneal which does not specify a microstructure and only has the goal of softening the material. Often material that is to be machined, will be annealed, then be followed by further heat treatment to obtain the final desired properties.

Short cycle anneal

Short cycle annealing is used for turning normal ferrite into malleable ferrite. It consists of heating, cooling, and then heating again from 4 to 8 hours.

Resistive heating

Resistive heating can be used to efficiently anneal copper wire; the heating system employs a controlled electrical short circuit. It can be advantageous because it does not require a temperature-regulated furnacelike other methods of annealing.

The process consists of two conductive pulleys (step pulleys) which the wire passes across after it is drawn. The two pulleys have an electrical potential across them, which causes the wire to form a short circuit. The Joule effect causes the temperature of the wire to rise to approximately 400 °C. This temperature is affected by the rotational speed of the pulleys, the ambient temperature, and the voltage applied. Where t is the temperature of the wire, K is a constant, V is the voltage applied, r is the number of rotations of the pulleys per minute, and t_a is the ambient temperature:

t = ((KV ²)/(r))+t_a

The constant K depends on the diameter of the pulleys and the resistivity of the copper.

Ferromagnetism is the basic mechanism by which certain materials (such as iron) form permanent magnets, or are attracted to magnets. In physics, several different types of magnetism are distinguished. Ferromagnetism is the strongest type; it is the only type that can produce forces strong enough to be felt, and is responsible for the common phenomena of magnetism encountered in everyday life. One example is refrigerator magnets. The attraction between a magnet and ferromagnetic material is "the quality of magnetism first apparent to the ancient world, and to us today," according to a classic text on ferromagnetism.^[1]

All permanent magnets (materials that can be magnetized by an external magnetic field and which remain magnetized after the external field is removed) are either ferromagnetic or ferrimagnetic, as are other materials that are noticeably attracted to them.

Historically, the term ferromagnet was used for any material that could exhibit spontaneous magnetization: a net magnetic moment in the absence of an external magnetic field. This general definition is still in common use. More recently, however, different classes of spontaneous magnetization have been identified^{[citation needed]}when there is more than one magnetic ion per primitive cell of the material, leading to a stricter definition of "ferromagnetism" that is often used to distinguish it from ferrimagnetism.^{[citation needed]} In particular, a material is "ferromagnetic" in this narrower sense only if all of its magnetic ions add a positive contribution to the net magnetization. If some of the magnetic ions subtract from the net magnetization (if they are partially anti-aligned), then the material is "ferrimagnetic".^{[citation needed]} If the moments of the aligned and anti-aligned ions balance completely so as to have zero net magnetization, despite the magnetic ordering, then it is an antiferromagnet. All of these alignment effects only occur at temperatures below a certain critical temperature, called the Curie temperature (for ferromagnets and ferrimagnets) or the Néel temperature (for antiferromagnets).

Among the first investigations of ferromagnetism are the pioneering works of Aleksandr Stoletov on measurement of the magnetic permeability of ferromagnetics, known as the Stoletov curve.

Ferromagnetic materials

There are a number of crystalline materials that exhibit ferromagnetism (or ferrimagnetism). The table on the right lists a representative selection of them, along with their Curie temperatures, the temperature above which they cease to exhibit spontaneous magnetization (see below).

Ferromagnetism is a property not just of the chemical makeup of a material, but of its crystalline structure and microscopic organization. There are ferromagnetic metal alloys whose constituents are not themselves ferromagnetic, called Heusler alloys, named after Fritz Heusler. Conversely there are nonmagnetic alloys, such as types of stainless steel, composed almost exclusively of ferromagnetic metals.

One can also make amorphous (non-crystalline) ferromagnetic metallic alloys by very rapid quenching (cooling) of a liquid alloy. These have the advantage that their properties are nearly isotropic (not aligned along a crystal axis); this results in low coercivity, low hysteresis loss, high permeability, and high electrical resistivity. A typical such material is a transition metal-metalloid alloy, made from about 80% transition metal (usually Fe, Co, or Ni) and a metalloid component (B, C, Si, P, or Al) that lowers the melting point.

A relatively new class of exceptionally strong ferromagnetic materials are the rare-earth magnets. They contain lanthanide elements that are known for their ability to carry large magnetic moments in well-localized f-orbitals.

Actinide ferromagnets

A number of actinide compounds are ferromagnets at room temperature or become ferromagnets below the Curie temperature (T_C). PuP is one actinide pnictide that is a paramagnet and has cubic symmetry at room temperature, but upon cooling undergoes a lattice distortion to tetragonal when cooled to below its T_c = 125 K. PuP has an easy axis of <100>,^[3] so that

• (c – a)/a = –(31 ± 1) × 10⁻⁴

at 5 K.^[4] The lattice distortion is presumably a consequence of strain induced by the magnetoelastic interactions as the magnetic moments aligned parallel within magnetic domains.

In NpFe₂ the easy axis is <111>.^[5] Above T_C ~500 K NpFe₂ is also paramagnetic and cubic. Cooling below the Curie temperature produces a rhombohedral distortion wherein the rhombohedral angle changes from 60° (cubic phase) to 60.53°. An alternate description of this distortion is to consider the length c along the unique trigonal axis (after the distortion has begun) and a as the distance in the plane perpendicular to c. In the cubic phase this reduces to c/a = 1.00. Below the Curie temperature

• (c – a)/a = –(120 ± 5) × 10⁻⁴

which is the largest strain in any actinide compound.^[4] NpNi₂ undergoes a similar lattice distortion below T_C = 32 K, with a strain of (43±5) × 10⁻⁴.^[4] NpCo₂ is a ferrimagnet below 15 K.

Lithium gas

In 2009, a team of MIT physicists demonstrated that a lithium gas cooled to less than one Kelvin can exhibit ferromagnetism.^[6] The team cooled fermionic lithium-6 to less than 150 billionths of one Kelvin above absolute zero using infrared laser cooling. This demonstration is the first time that ferromagnetism has been demonstrated in a gas.

Explanation

The Bohr–van Leeuwen theorem shows that magnetism cannot occur in purely classical solids. Without quantum mechanics, there would be no diamagnetism, paramagnetism or ferromagnetism. The property of ferromagnetism is due to the direct influence of two effects from quantum mechanics: spin and the Pauli exclusion principle.^[7]

Origin of magnetism

The spin of an electron, combined with its electric charge, results in a magnetic dipole moment and creates a small magnetic field. Although an electron can be visualized classically as a spinning ball of charge, spin is actually a quantum mechanical property with differences from the classical picture, such as the fact that it is quantized into discrete up/down states. The spin of the electrons in atoms is the main source of ferromagnetism, although there is also some contribution from the orbital angular momentum of the electron about the nucleus, whose classical analogue is a current loop. When these tiny magnetic dipoles are aligned in the same direction, their individual magnetic fields add together to create a measurable macroscopic field.

However in many materials (specifically, those with a filled electron shell), the total dipole moment of all the electrons is zero because the spins are in up/down pairs. Only atoms with partially filled shells (i.e., unpaired spins) can have a net magnetic moment, so ferromagnetism only occurs in materials with partially filled shells. Because of Hund's rules, the first few electrons in a shell tend to have the same spin, thereby increasing the total dipole moment.

These unpaired dipoles (often called simply "spins" even though they also generally include angular momentum) tend to align in parallel to an external magnetic field, an effect called paramagnetism. Ferromagnetism involves an additional phenomenon, however: the dipoles tend to align spontaneously, without any applied field.

Exchange interaction

According to classical electromagnetism, two nearby magnetic dipoles will tend to align in opposite directions, so their magnetic fields will oppose one another and cancel out. However in a few materials, the ferromagnetic ones, they tend to align in the same direction because of a quantum mechanical effect called the exchange interaction. The Pauli exclusion principle says that two electrons with the same spin cannot also have the same "position". Therefore, under certain conditions, when the orbitals of the unpaired outer valence electrons from adjacent atoms overlap, the distribution of their electric charge in space is further apart when the electrons have parallel spins than when they have opposite spins. This reduces the electrostatic energy of the electrons when their spins are parallel compared to their energy when the spins are anti-parallel, so the parallel-spin state is more stable. In simple terms, the electrons, which repel one another, can move "further apart" by aligning their spins, so the spins of these electrons tend to line up. This difference in energy is called the exchange energy.

The exchange interaction is also responsible for the other types of spontaneous ordering of atomic magnetic moments occurring in magnetic solids, antiferromagnetism and ferrimagnetism. In most ferromagnets the exchange interaction is much stronger than the competing dipole-dipole interaction. For instance, in iron (Fe) it is about 1000 times stronger than the dipole interaction. Therefore below the Curie temperature virtually all of the dipoles in a ferromagnetic material will be aligned.

Magnetic anisotropy

Although the exchange interaction keeps spins aligned, it does not align them in any particular direction. Without magnetic anisotropy, the spins in a magnet randomly change direction in response to thermal fluctuations and the magnet is superparamagnetic. There are several kinds of magnetic anisotropy, the most common of which is magnetocrystalline anisotropy. This is a dependence of the energy on the direction of magnetization relative to the crystallographic lattice. Another common source of anisotropy, inverse magnetostriction, is induced by internal strains. Single-domain magnets also can have a shape anisotropydue to the magnetostatic effects of the particle shape. As the temperature of a magnet increases, the anisotropy tends to decrease, and there is often a blocking temperature at which a transition to superparamagnetism occurs.^[8]

Magnetic domains

The above would seem to suggest that every piece of ferromagnetic material should have a strong magnetic field, since all the spins are aligned, yet iron and other ferromagnets are often found in an "unmagnetized" state.

Weiss domains microstructure

The reason for this is that a bulk piece of ferromagnetic material is divided into many tiny magnetic domains (also known as Weiss domains). Within each domain, the spins are aligned, but (if the bulk material is in its lowest energy configuration, i.e. "unmagnetized"), the spins of separate domains point in different directions and their magnetic fields cancel out, so the object has no net large scale magnetic field.

Ferromagnetic materials spontaneously divide into magnetic domains because this is a lower energy configuration. At long distances (after many thousands of ions), the exchange energy advantage is overtaken by the classical tendency of dipoles to anti-align. The boundary between two domains, where the magnetization flips, is called adomain wall (i.e., a Bloch/Néel wall, depending upon whether the magnetization rotates parallel/perpendicular to the domain interface) and is a gradual transition on the atomic scale (covering a distance of about 300 ions for iron).

Thus, an ordinary piece of iron generally has little or no net magnetic moment. However, if it is placed in a strong enough external magnetic field, the domains will re-orient in parallel with that field, and will remain re-oriented when the field is turned off, thus creating a "permanent" magnet. The domains don't go back to their original minimum energy configuration when the field is turned off because the domain walls tend to become 'pinned' or 'snagged' on defects in the crystal lattice, preserving their parallel orientation. This is shown by the Barkhausen effect: as the magnetizing field is changed, the magnetization changes in thousands of tiny discontinuous jumps as the domain walls suddenly "snap" past defects.

This magnetization as a function of the external field is described by a hysteresis curve. Although this state of aligned domains is not a minimal-energy configuration, it is extremely stable and has been observed to persist for millions of years in seafloor magnetite aligned by the Earth's magnetic field (whose poles can thereby be seen to flip at long intervals).

Alloys used for the strongest permanent magnets are "hard" alloys made with many defects in their crystal structure where the domain walls "catch" and stabilize. The net magnetization can be destroyed by heating and then cooling (annealing) the material without an external field, however. The thermal motion allows the domain boundaries to move, releasing them from any defects, to return to their low-energy unaligned state.

Curie temperature

As the temperature increases, thermal motion, or entropy, competes with the ferromagnetic tendency for dipoles to align. When the temperature rises beyond a certain point, called the Curie temperature, there is a second-order phase transition and the system can no longer maintain a spontaneous magnetization, although it still responds paramagnetically to an external field. Below that temperature, there is a spontaneous symmetry breaking and random domains form (in the absence of an external field). The Curie temperature itself is a critical point, where the magnetic susceptibility is theoretically infinite and, although there is no net magnetization, domain-like spin correlations fluctuate at all length scales.

Many techniques have been developed for the measurement of pressure and vacuum. Instruments used to measure pressure are called pressure gauges or vacuum gauges.

A manometer could also be referring to a pressure measuring instrument, usually limited to measuring pressures near to atmospheric. The term manometer is often used to refer specifically to liquid column hydrostatic instruments.

A vacuum gauge is used to measure the pressure in a vacuum—which is further divided into two subcategories: high and low vacuum (and sometimes ultra-high vacuum). The applicable pressure range of many of the techniques used to measure vacuums have an overlap. Hence, by combining several different types of gauge, it is possible to measure system pressure continuously from 10 mbardown to 10⁻¹¹ mbar.

Absolute, gauge and differential pressures - zero reference

Although no pressure is an absolute quantity, everyday pressure measurements, such as for tire pressure, are usually made relative to ambient air pressure. In other cases measurements are made relative to a vacuum or to some other ad hoc reference. When distinguishing between these zero references, the following terms are used:

• Absolute pressure is zero referenced against a perfect vacuum, so it is equal to gauge pressure plus atmospheric pressure.
• Gauge pressure is zero referenced against ambient air pressure, so it is equal to absolute pressure minus atmospheric pressure. Negative signs are usually omitted.
• Differential pressure is the difference in pressure between two points.

The zero reference in use is usually implied by context, and these words are only added when clarification is needed. Tire pressure and blood pressure are gauge pressures by convention, while atmospheric pressures, deep vacuum pressures, and altimeter pressures must be absolute. Differential pressures are commonly used in industrial process systems. Differential pressure gauges have two inlet ports, each connected to one of the volumes whose pressure is to be monitored. In effect, such a gauge performs the mathematical operation of subtraction through mechanical means, obviating the need for an operator or control system to watch two separate gauges and determine the difference in readings. Moderate vacuum pressures are often ambiguous, as they may represent absolute pressure or gauge pressure without a negative sign. Thus a vacuum of 26 inHg gauge is equivalent to an absolute pressure of 30 inHg (typical atmospheric pressure) − 26 inHg = 4 inHg.

Atmospheric pressure is typically about 100 kPa at sea level, but is variable with altitude and weather. If the absolute pressure of a fluid stays constant, the gauge pressure of the same fluid will vary as atmospheric pressure changes. For example, when a car drives up a mountain (atmospheric air pressure decreases), the (gauge) tire pressure goes up. Some standard values of atmospheric pressure such as 101.325 kPa or 100 kPa have been defined, and some instruments use one of these standard values as a constant zero reference instead of the actual variable ambient air pressure. This impairs the accuracy of these instruments, especially when used at high altitudes.

Use of the atmosphere as reference is usually signified by a (g) after the pressure unit e.g. 30 psi g, which means that the pressure measured is the total pressure minus atmospheric pressure. There are two types of gauge reference pressure: vented gauge (vg) and sealed gauge (sg).

A vented gauge pressure transmitter for example allows the outside air pressure to be exposed to the negative side of the pressure sensing diaphragm, via a vented cable or a hole on the side of the device, so that it always measures the pressure referred to ambient barometric pressure. Thus a vented gauge reference pressure sensor should always read zero pressure when the process pressure connection is held open to the air.

A sealed gauge reference is very similar except that atmospheric pressure is sealed on the negative side of the diaphragm. This is usually adopted on high pressure ranges such as hydraulics where atmospheric pressure changes will have a negligible effect on the accuracy of the reading, so venting is not necessary. This also allows some manufacturers to provide secondary pressure containment as an extra precaution for pressure equipment safety if the burst pressure of the primary pressure sensing diaphragm is exceeded.

There is another way of creating a sealed gauge reference and this is to seal a high vacuum on the reverse side of the sensing diaphragm. Then the output signal is offset so the pressure sensor reads close to zero when measuring atmospheric pressure.

A sealed gauge reference pressure transducer will never read exactly zero because atmospheric pressure is always changing and the reference in this case is fixed at 1 bar.

An absolute pressure measurement is one that is referred to absolute vacuum. The best example of an absolute referenced pressure is atmospheric or barometric pressure.

To produce an absolute pressure sensor the manufacturer will seal a high vacuum behind the sensing diaphragm. If the process pressure connection of an absolute pressure transmitter is open to the air, it will read the actual barometric pressure.

Units

Example reading: 1 Pa = 1 N/m²  = 10⁻⁵ bar  = 10.197×10⁻⁶ at  = 9.8692×10⁻⁶ atm  = 7.5006×10⁻³ torr  = 145.04×10⁻⁶ psi
etc.

The SI unit for pressure is the pascal (Pa), equal to one newton per square metre (N·m⁻² or kg·m⁻¹·s⁻²). This special name for the unit was added in 1971; before that, pressure in SI was expressed in units such as N/m². When indicated, the zero reference is stated in parenthesis following the unit, for example 101 kPa (abs). The pound per square inch (psi) is still in widespread use in the US and Canada, notably for cars. A letter is often appended to the psi unit to indicate the measurement's zero reference; psia for absolute, psig for gauge, psid for differential, although this practice is discouraged by the NIST.^[1]

Because pressure was once commonly measured by its ability to displace a column of liquid in a manometer, pressures are often expressed as a depth of a particular fluid (e.g. inches of water). The most common choices are mercury (Hg) and water; water is nontoxic and readily available, while mercury's density allows for a shorter column (and so a smaller manometer) to measure a given pressure.

Fluid density and local gravity can vary from one reading to another depending on local factors, so the height of a fluid column does not define pressure precisely. When 'millimetres of mercury' or 'inches of mercury' are quoted today, these units are not based on a physical column of mercury; rather, they have been given precise definitions that can be expressed in terms of SI units. The water-based units usually assume one of the older definitions of the kilogram as the weight of a litre of water.

Although no longer favoured by measurement experts, these manometric units are still encountered in many fields. Blood pressure is measured in millimetres of mercury in most of the world, and lung pressures in centimeters of water are still common. Natural gas pipeline pressures are measured in inches of water, expressed as '"WC' ('Water Column'). Scuba divers often use a manometric rule of thumb: the pressure exerted by ten metres depth of water is approximately equal to one atmosphere. In vacuum systems, the units torr, micrometre of mercury (micron), and inch of mercury (inHg) are most commonly used. Torr and micron usually indicates an absolute pressure, while inHg usually indicates a gauge pressure.

Atmospheric pressures are usually stated using kilopascal (kPa), or atmospheres (atm), except in American meteorology where the hectopascal (hPa) and millibar (mbar) are preferred. In American and Canadian engineering, stress is often measured in kip. Note that stress is not a true pressure since it is not scalar. In the cgs system the unit of pressure was the barye (ba), equal to 1 dyn·cm⁻². In the mtssystem, the unit of pressure was the pieze, equal to 1 sthene per square metre.

Many other hybrid units are used such as mmHg/cm² or grams-force/cm² (sometimes as kg/cm² and g/mol2 without properly identifying the force units). Using the names kilogram, gram, kilogram-force, or gram-force (or their symbols) as a unit of force is forbidden in SI; the unit of force in SI is the newton (N).

Static and dynamic pressure

Static pressure is uniform in all directions, so pressure measurements are independent of direction in an immovable (static) fluid. Flow, however, applies additional pressure on surfaces perpendicular to the flow direction, while having little impact on surfaces parallel to the flow direction. This directional component of pressure in a moving (dynamic) fluid is called dynamic pressure. An instrument facing the flow direction measures the sum of the static and dynamic pressures; this measurement is called the total pressure or stagnation pressure. Since dynamic pressure is referenced to static pressure, it is neither gauge nor absolute; it is a differential pressure.

While static gauge pressure is of primary importance to determining net loads on pipe walls, dynamic pressure is used to measure flow rates and airspeed. Dynamic pressure can be measured by taking the differential pressure between instruments parallel and perpendicular to the flow. Pitot-static tubes, for example perform this measurement on airplanes to determine airspeed. The presence of the measuring instrument inevitably acts to divert flow and create turbulence, so its shape is critical to accuracy and the calibration curves are often non-linear.

Applications

• Altimeter
• Barometer
• MAP sensor
• Pitot tube
• Sphygmomanometer

Definition

Pressure is an effect which occurs when a force is applied on a surface. Pressure is the amount of force acting on a unit area. The symbol of pressure is P.^[1][2]

Formula

Mathematically:

where:

P is the pressure,

F is the normal force,

A is the area.

Pressure is a scalar quantity. It relates the vector surface element (a vector normal to the surface) with the normal force acting on it. The pressure is the scalar proportionality constant that relates the two normal vectors:

The minus sign comes from the fact that the force is considered towards the surface element, while the normal vector points outwards.

It is incorrect (although rather usual) to say "the pressure is directed in such or such direction". The pressure, as a scalar, has no direction. It is the force given by the previous relation the quantity that has a direction. If we change the orientation of the surface element the direction of the normal force changes accordingly, but the pressure remains the same.

Pressure is transmitted to solid boundaries or across arbitrary sections of fluid normal to these boundaries or sections at every point. It is a fundamental parameter in thermodynamics and it is conjugate to volume.

Units

Mercury column

The SI unit for pressure is the pascal (Pa), equal to one newton per square meter (N/m² or kg·m⁻¹·s⁻²). This special name for the unit was added in 1971;^[3] before that, pressure in SI was expressed simply as N/m². pressure is a force that go any direction

Non-SI measures such as pounds per square inch and bar are used in some parts of the world, primarily in the United States of America. The cgs unit of pressure is thebarye (ba), equal to 1 dyn·cm⁻² or 0.1 Pa. Pressure is sometimes expressed in grams-force/cm², or as kg/cm² and the like without properly identifying the force units. But using the names kilogram, gram, kilogram-force, or gram-force (or their symbols) as units of force is expressly forbidden in SI. The technical atmosphere (symbol: at) is 1 kgf/cm² which, in US Customary units, is 14.223 psi.

Since a system under pressure has potential to perform work on its surroundings, pressure is a measure of potential energy stored per unit volume measured in J·m^-3, related to energy density.

Some meteorologists prefer the hectopascal (hPa) for atmospheric air pressure, which is equivalent to the older unit millibar (mbar). Similar pressures are given in kilo pascals (kPa) in most other fields, where the hecto- prefix is rarely used. The inch of mercury is still used in the United States. Oceanographers usually measure underwater pressure in decibars (dbar) because an increase in pressure of 1 dbar is approximately equal to an increase in depth of 1 meter. Scuba divers often use a manometric rule of thumb: the pressure exerted by ten meters depth of water is approximately equal to one atmosphere. Americans learn that 34 feet of fresh water or 33 feet of sea water equals one atm.

The standard atmosphere (atm) is an established constant. It is approximately equal to typical air pressure at earth mean sea level and is defined as follows:

standard atmosphere = 101325 Pa = 101.325 kPa = 1013.25 hPa.

Because pressure is commonly measured by its ability to displace a column of liquid in a manometer, pressures are often expressed as a depth of a particular fluid (e.g.,centimetres of water or inches of water). The most common choices are mercury (Hg) and water; water is nontoxic and readily available, while mercury's high density allows for a shorter column (and so a smaller manometer) to measure a given pressure. The pressure exerted by a column of liquid of height h and density ρ is given by the hydrostatic pressure equation p = ρgh. Fluid density and local gravity can vary from one reading to another depending on local factors, so the height of a fluid column does not define pressure precisely. When millimeters of mercury or inches of mercuryare quoted today, these units are not based on a physical column of mercury; rather, they have been given precise definitions that can be expressed in terms of SI units. One mmHg (millimeter of mercury) is equal to one torr. The water-based units still depend on the density of water, a measured, rather than defined, quantity. These manometric units are still encountered in many fields. Blood pressure is measured in millimeters of mercury in most of the world, and lung pressures in centimeters of water are still common.

Gauge pressure is often given in units with 'g' appended, e.g. 'kPag' or 'psig', and units for measurements of absolute pressure are sometimes given a suffix of 'a', to avoid confusion, for example 'kPaa', 'psia'. However, the US National Institute of Standards and Technology recommends that, to avoid confusion, any modifiers be instead applied to the quantity being measured rather than the unit of measure^[4] For example, "P_g = 100 psi" rather than "P = 100 psig".

Presently or formerly popular pressure units include the following:

• atmosphere (atm)
• manometric units:
  • centimeter, inch, and millimeter of mercury (torr)
  • millimeter, centimeter, meter, inch, and foot of water
• customary units:
  • kip, ton-force (short), ton-force (long), pound-force, ounce-force, and poundal per square inch
  • pound-force, ton-force (short), and ton-force (long)
• non-SI metric units:
  • bar, decibar, millibar
  • kilogram-force, or kilopond, per square centimetre (technical atmosphere)
  • gram-force and tonne-force (metric ton-force) per square centimetre
  • barye (dyne per square centimetre)
  • kilogram-force and tonne-force per square metre
  • sthene per square metre (pieze)

Example reading: 1 Pa = 1 N/m²  = 10⁻⁵ bar  = 10.197×10⁻⁶ at  = 9.8692×10⁻⁶ atm  = 7.5006×10⁻³ torr  = 145.04×10⁻⁶ psi
etc.

Examples

As an example of varying pressures, a finger can be pressed against a wall without making any lasting impression; however, the same finger pushing a thumbtack can easily damage the wall. Although the force applied to the surface is the same, the thumbtack applies more pressure because the point concentrates that force into a smaller area. Pressure is transmitted to solid boundaries or across arbitrary sections of fluid normal to these boundaries or sections at every point. Unlike stress, pressure is defined as a scalar quantity.

Another example is of a common knife. If we try and cut a fruit with the flat side it obviously won't cut. But if we take the thin side, it will cut smoothly. The reason is, the flat side has a greater surface area (less pressure) and so it does not cut the fruit. When we take the thin side, the surface area is reduced and so it cuts the fruit easily and quickly. This is one example of a practical application of pressure.

The gradient of pressure is called the force density. For gases, pressure is sometimes measured not as an absolute pressure, but relative to atmospheric pressure; such measurements are called gauge pressure (also sometimes spelled gage pressure).^[5] An example of this is the air pressure in an automobile tire, which might be said to be "220 kPa/32psi", but is actually 220 kPa/32 psi above atmospheric pressure. Since atmospheric pressure at sea level is about 100 kPa/14.7 psi, the absolute pressure in the tire is therefore about 320 kPa/46.7 psi. In technical work, this is written "a gauge pressure of 220 kPa/32 psi". Where space is limited, such as on pressure gauges, name plates, graph labels, and table headings, the use of a modifier in parentheses, such as "kPa (gauge)" or "kPa (absolute)", is permitted. In non-SItechnical work, a gauge pressure of 32 psi is sometimes written as "32 psig" and an absolute pressure as "32 psia", though the other methods explained above that avoid attaching characters to the unit of pressure are preferred.^[6]

Gauge pressure is the relevant measure of pressure wherever one is interested in the stress on storage vessels and the plumbing components of fluidics systems. However, whenever equation-of-state properties, such as densities or changes in densities, must be calculated, pressures must be expressed in terms of their absolute values. For instance, if the atmospheric pressure is 100 kPa, a gas (such as helium) at 200 kPa (gauge) (300 kPa [absolute]) is 50 % denser than the same gas at 100 kPa (gauge) (200 kPa [absolute]). Focusing on gauge values, one might erroneously conclude the first sample had twice the density of the second one.

Scalar nature

In a static gas, the gas as a whole does not appear to move. The individual molecules of the gas, however, are in constant random motion. Because we are dealing with an extremely large number of molecules and because the motion of the individual molecules is random in every direction, we do not detect any motion. If we enclose the gas within a container, we detect a pressure in the gas from the molecules colliding with the walls of our container. We can put the walls of our container anywhere inside the gas, and the force per unit area (the pressure) is the same. We can shrink the size of our "container" down to an infinitely small point, and the pressure has a single value at that point. Therefore, pressure is a scalar quantity, not a vector quantity. It has magnitude but no direction sense associated with it. Pressure acts in all directions at a point inside a gas. At the surface of a gas, the pressure force acts perpendicular (at right angle) to the surface.

A closely related quantity is the stress tensor σ, which relates the vector force F to the vector area A via

This tensor may be divided up into a scalar part (pressure) and a traceless tensor part shear. The shear tensor gives the force in directions parallel to the surface, usually due to viscous or frictional forces. The stress tensor is sometimes called the pressure tensor, but in the following, the term "pressure" will refer only to the scalar pressure.

According to the theory of general relativity pressure increases the strength of a gravitational field (see stress-energy tensor) and so adds to the mass-energy cause of gravity. This effect is unnoticable at every-day pressures but is significant in neutron stars, although it has not been experimentally tested.^[7]

Types

Explosion or deflagration pressures

Explosion or deflagration pressures are the result of the ignition of explosive gases, mists, dust/air suspensions, in unconfined and confined spaces.

Negative pressures

While pressures are generally positive, there are several situations in which negative pressures may be encountered:

• When dealing in relative (gauge) pressures. For instance, an absolute pressure of 80 kPa may be described as a gauge pressure of -21 kPa (i.e., 21 kPa below an atmospheric pressure of 101 kPa).
• When attractive forces (e.g., van der Waals forces) between the particles of a fluid exceed repulsive forces. Such scenarios are generally unstable since the particles will move closer together until repulsive forces balance attractive forces. Negative pressure exists in the transpiration pull of plants, and is used to suction water even higher than the ten metres that it rises in a pure vacuum.
• The Casimir effect can create a small attractive force due to interactions with vacuum energy; this force is sometimes termed 'vacuum pressure' (not to be confused with the negative gauge pressure of a vacuum).
• Depending on how the orientation of a surface is chosen, the same distribution of forces may be described either as a positive pressure along one surface normal, or as a negative pressure acting along the opposite surface normal.
• In the cosmological constant.

Stagnation pressure

Stagnation pressure is the pressure a fluid exerts when it is forced to stop moving. Consequently, although a fluid moving at higher speed will have a lower static pressure, it may have a higher stagnation pressure when forced to a standstill. Static pressure and stagnation pressure are related by the Mach number of the fluid. In addition, there can be differences in pressure due to differences in the elevation (height) of the fluid. See Bernoulli's equation (note: Bernoulli's equation only applies for incompressible, inviscid flow).

The pressure of a moving fluid can be measured using a Pitot tube, or one of its variations such as a Kiel probe or Cobra probe, connected to a manometer. Depending on where the inlet holes are located on the probe, it can measure static pressure or stagnation pressures.

Surface pressure

There is a two-dimensional analog of pressure – the lateral force per unit length applied on a line perpendicular to the force.

Surface pressure is denoted by π and shares many similar properties with three-dimensional pressure. Properties of surface chemicals can be investigated by measuring pressure/area isotherms, as the two-dimensional analog of Boyle's law, πA = k, at constant temperature.

Pressure of an ideal gas

In an ideal gas, molecules have no volume and do not interact. Pressure varies linearly with temperature, volume, and quantity according to the ideal gas law,

where:

P is the absolute pressure of the gas

n is the amount of substance

T is the absolute temperature

V is the volume

R is the ideal gas constant.

Real gases exhibit a more complex dependence on the variables of state.^[8]

Vapor pressure

Vapor pressure is the pressure of a vapor in thermodynamic equilibrium with its condensed phases in a closed system. All liquids and solids have a tendency to evaporate into a gaseous form, and all gases have a tendency to condense back to their liquid or solid form.

The atmospheric pressure boiling point of a liquid (also known as the normal boiling point) is the temperature at which the vapor pressure equals the ambient atmospheric pressure. With any incremental increase in that temperature, the vapor pressure becomes sufficient to overcome atmospheric pressure and lift the liquid to form vapor bubbles inside the bulk of the substance. Bubble formation deeper in the liquid requires a higher pressure, and therefore higher temperature, because the fluid pressure increases above the atmospheric pressure as the depth increases.

The vapor pressure that a single component in a mixture contributes to the total pressure in the system is called partial vapor pressure.

Liquid pressure or pressure at depth

Used with liquid columns of constant density or at a depth within a substance (ex. pressure at 20km depth in the earth).

P = gdh

Where:

P is Pressure

g is gravity

d is density of liquid or overlaying material

h is height of liquid of depth within material

Definition

The watt is the rate a source of energy uses or produces one joule during one second, so the same quantity may be referred to as a joule per second, with the symbol J/s. It can also be written as kg·m²·s⁻³.

It is equivalent to one volt ampere (1 V·A) or 1/746 of a horsepower. The power of a light bulb is measured in watts.

Energy is a word with more than one meaning.

• Energy broadly means the capacity of something, a person, an animal or a physical system to do work and produce change.
• It can refer to the ability for someone to act or speak in a lively and vigorous way.
• It is used in science to describe how much potential a physical system has to change.
• It may also be used in economics to describe the part of the market where energy itself is harnessed and sold to consumers.
• Energy in Science

• Energy is something that can do work.

  There are two basic forms of energy:

  • Kinetic energy
  • Potential energy

  
  Conservation of Energy

  When energy changes from one form to another, the amount of energy stays the same. Energy cannot be made or destroyed. This rule is called the "conservation law of energy".

  
  Example of Conservation Law of Energy

  Here is an example:

  1. the energy of a thing is measured to start with
  2. the energy changes from potential energy to kinetic energy and back again
  3. at the end the energy of the thing is measured again

  The measurements of energy at the start and end will always be the same.

  
  New Conservation of Energy Rule

  Scientists now know that matter can be made into energy through processes like nuclear fission and nuclear fusion. The law of conservation of energy has therefore been extended to become the Law of conservation of matter and energy.

  
  Types of Energy

  Scientist have identified many types of energy, and found that they can be changed from one kind into another. For example:

  • Electric energy
  • Light energy
  • Heat/Thermal energy
  • Internal energy
  • Sound energy
  • Chemical energy
  • Nuclear energy
  • Elastic energy
  • Gravitational potential energy
  • Water energy
  • Kinetic energy
  • Dark energy

  
  Measuring Energy

  Energy can be measured. That is, the amount of energy a thing has can be given a number.

  As in other kinds of measurements, there are measurement units. The units of measurement for measuring energy are used to make the numbers meaningful.

  
  Some units of Measurement for Energy

  The SI unit for both energy and work is the joule (J). It is named after James Prescott Joule. 1 joule is equal to 1 newton-metre. In terms of SI base units, 1 J is equal to 1 kg m² s⁻².

  The energy unit of measurement for electricity is the kilowatt-hour (kW·h). One kW·h is equivalent to 3,600,000 J (3600 kJ or 3.6 MJ)

In physics, power is the rate at which work is performed or energy is converted^[1][2]

If ΔW is the amount of work performed during a period of time of duration Δt, the average power P_avg over that period is given by the formula

It is the average amount of work done or energy converted per unit of time. The average power is often simply called "power" when the context makes it clear.

The instantaneous power is then the limiting value of the average power as the time interval Δt approaches zero.

In the case of constant power P, the amount of work performed during a period of duration T is given by:

In the context of energy conversion it is more customary to use the symbol E rather than W.

Units

The dimension of power is energy divided by time. The unit of power is the watt (W), which is equal to one joule per second. Other units of power include ergs per second (erg/s), horsepower (hp), metric horsepower (Pferdestärke (PS) or cheval vapeur, CV), and foot-pounds per minute. One horsepower is equivalent to 33,000 foot-pounds per minute, or the power required to lift 550 pounds by one foot in one second, and is equivalent to about 746 watts. Other units include dBm, a relative logarithmic measure with 1 milliwatt as reference; (food) calories per hour (often referred to as kilocalories per hour); Btu per hour (Btu/h); and tons of refrigeration (12,000 Btu/h).

Mechanical power

In mechanics, the work done on an object is related to the forces acting on it by

where

F is force

Δd is the displacement of the object.

This is often summarized by saying that work is equal to the force acting on an object times its displacement (how far the object moves while the force acts on it). Note that only motion that is along the same axis as the force "counts", however; a force in the same direction as motion produces positive work, and a force in an opposing direction of motion provides negative work, while motion perpendicular to the force yields zero work.

Differentiating by time gives that the instantaneous power is equal to the force times the object's velocity v(t):

.

The average power is then

.

This formula is important in characterizing engines—the power output of an engine is equal to the force it exerts multiplied by its velocity.

In rotational systems, power is related to the torque (τ) and angular velocity (ω):

.

Or

The average power is therefore

.

In systems with fluid flow, power is related to pressure, p and volumetric flow rate, Q:

where

p is pressure (in pascals, or N/m² in SI units)

Q is volumetric flow rate (in m³/s in SI units)

Electrical power

Instantaneous electrical power

The instantaneous electrical power P delivered to a component is given by

where

P(t) is the instantaneous power, measured in watts (joules per second)

V(t) is the potential difference (or voltage drop) across the component, measured in volts

I(t) is the current through it, measured in amperes

If the component is a resistor with time-invariant voltage to current ratio, then:

where

is the resistance, measured in ohms.

Peak power and duty cycle

In a train of identical pulses, the instantaneous power is a periodic function of time. The ratio of the pulse duration to the period is equal to the ratio of the average power to the peak power. It is also called the duty cycle (see text for definitions).

In the case of a periodic signal s(t) of period T, like a train of identical pulses, the instantaneous power p(t) = | s(t) | ² is also a periodic function of period T. The peak power is simply defined by:

P₀ = max(p(t)).

The peak power is not always readily measurable, however, and the measurement of the average power P_avg is more commonly performed by an instrument. If one defines the energy per pulse as:

then the average power is:

.

One may define the pulse length τ such that P₀τ = ε_pulse so that the ratios

are equal. These ratios are called the duty cycle of the pulse train.

Power in optics

In physics or chemistry, subatomic particles are the smaller particles composing nucleons andatoms. There are two types of subatomic particles: elementary particles, which are not made of other particles, and composite particles. Particle physics and nuclear physics study these particles and how they interact.^[1]

Elementary particles of the Standard Model include:^[2]

• Six "flavors" of quarks: up, down, bottom, top, strange, and charm;
• Six types of leptons: electron, electron neutrino, muon, muon neutrino, tau, tau neutrino;
• Twelve gauge bosons (force carriers): the photon of electromagnetism, the three W and Z bosons of the weak force, and the eight gluons of the strong force.

Composite subatomic particles (such as protons or atomic nuclei) are bound states of two or moreelementary particles. For example, a proton is made of two up quarks and one down quark, while the atomic nucleus of helium-4 is composed of two protons and two neutrons. Composite particles include all hadrons, a group composed of baryons (e.g., protons and neutrons) and mesons (e.g., pions andkaons).

There are hundreds of known subatomic particles. Most are either the result of cosmic rays interacting with matter, or have been produced by scattering processes in particle accelerators.

Introduction to particles

In particle physics, the conceptual idea of a particle is one of several concepts inherited fromclassical physics. This describes the world we experience, used ( for example ) to describe howmatter and energy behave at the molecular scales of quantum mechanics. For physicists, word "particle" means something rather different from the common sense of the term, reflecting the modern understanding of how particles behave at the quantum scale in ways that differ radically from what everyday experience would lead us to expect.

The idea of a particle underwent serious rethinking in light of experiments which showed that light could behave like a stream of particles (called photons) as well as exhibit wave-like properties. These results necessitated the new concept of wave-particle duality to reflect that quantum-scale "particles" are understood to behave in a way resembling both particles and waves. Another new concept, theuncertainty principle, concluded that analyzing particles at these scales would require a statisticalapproach. In more recent times, wave-particle duality has been shown to apply not only to photons, but to increasingly massive particles.^[3]

All of these factors ultimately combined to replace the notion of discrete "particles" with the concept of "wave-packets" of uncertain boundaries, whose properties are only known as probabilities, and whose interactions with other "particles" remain largely a mystery, even 80 years after the establishment of quantum mechanics.

Energy

In Einstein's hypotheses, Energy and matter are analogous. That is, matter can be simply expressed in terms of energy and vice-versa. Consequently, there are only two known mechanisms by which energy can be transferred. These are particles and waves. For example, light can be expressed as both particles and waves. This paradox is known as the Wave–particle Duality Paradox.^[4]

Through the work of Albert Einstein, Louis de Broglie, and many others, current scientific theory holds that all particles also have a wave nature.^[5] This phenomenon has been verified not only for elementary particles, but also for compound particles like atoms and even molecules. In fact, according to traditional formulations of non-relativistic quantum mechanics, wave–particle duality applies to all objects, even macroscopic ones; we can't detect wave properties of macroscopic objects due to their small wavelengths.^[6]

Interactions between particles have been scrutinized for many centuries, and a few simple laws underpin how particles behave in collisions and interactions. The most fundamental of these are the laws of conservation of energy and conservation of momentum, which facilitate us to elucidate calculations between particle interactions on scales of magnitude which diverge between planets andquarks.^[7] These are the prerequisite basics of Newtonian mechanics, a series of statements and equations in Philosophiae Naturalis Principia Mathematica originally published in 1687.

Dividing an atom

The negatively-charged electron has a mass equal to 1/1836 of that of a hydrogen atom. The remainder of the hydrogen atom's mass comes from the positively charged proton. The atomic numberof an element is the number of protons in its nucleus. Neutrons are neutral particles having a mass slightly greater than that of the proton. Different isotopes of the same element contain the same number of protons but differing numbers of neutrons. The mass number of an isotope is the total number of nucleons.

Chemistry concerns itself with how electron sharing binds atoms into molecules. Nuclear physicsdeals with how protons and neutrons arrange themselves in nuclei. The study of subatomic particles, atoms and molecules, and their structure and interactions, requires quantum mechanics. Analyzing processes that change the numbers and types of particles requires quantum field theory. The study of subatomic particles per se is called particle physics. Since most varieties of particle occur only as a result of cosmic rays, or in particle accelerators, particle physics is also called high energy physics.

History

In 1905, Albert Einstein demonstrated the physical reality of the photons, hypothesized by Max Planck in 1900, in order to solve the problem of black body radiation in thermodynamics.

In 1874, G. Johnstone Stoney postulated a minimum unit of electrical charge, for which he suggested the name electron in 1891.^[8] In 1897, J. J. Thomson confirmed Stoney's conjecture by discovering the first subatomic particle, the electron (now abbreviated e⁻). Subsequent speculation about the structure of atoms was severely constrained by Ernest Rutherford's 1907 gold foil experiment, showing that the atom is mainly empty space, with almost all its mass concentrated in a (relatively) tiny atomic nucleus. The development of the quantum theory led to the understanding of chemistry in terms of the arrangement of electrons in the mostly empty volume of atoms. In 1918, Rutherford confirmed that thehydrogen nucleus was a particle with a positive charge, which he named the proton, now abbreviatedp⁺. Rutherford also conjectured that all nuclei other than hydrogen contain chargeless particles, which he named the neutron. It is now abbreviated n. James Chadwick discovered the neutron in 1932. The word nucleon denotes neutrons and protons collectively.

Neutrinos were postulated in 1931 by Wolfgang Pauli (and named by Enrico Fermi) to be produced inbeta decays of neutrons, but were not discovered until 1956. Pions were postulated by Hideki Yukawaas mediators of the residual strong force which binds the nucleus together. The muon was discovered in 1936 by Carl D. Anderson, and initially mistaken for the pion. In the 1950s the first kaons were discovered in cosmic rays.

Background

In the nineteenth century, physicists such as Maxwell, Boltzmann, and Kelvin researched and experimented with creep and recovery of glasses, metals, and rubbers ^[2]. Viscoelasticity was further examined in the late twentieth century when synthetic polymers were engineered and used in a variety of applications ^[2]. Viscoelasticity calculations depend heavily on the viscosityvariable, η. The inverse of η is also known as fluidity, φ. The value of either can be derived as a function of temperature or as a given value (ie for a dashpot) ^[1].

Different types of responses (σ) to a change in strain rate (d/dt)

Depending on the change of strain rate versus stress inside a material the viscosity can be categorized as having a linear, non-linear, or plastic response. When a material exhibits a linear response it is categorized as a Newtonian material ^[1]. In this case the stress is linearly proportional to the strain rate. If the material exhibits a non-linear response to the strain rate, it is categorized as Non-Newtonian fluid. There is also an interesting case where the viscosity decreases as the shear/strain rate remains constant. A material which exhibits this type of behavior is known as thixotropic ^[1]. In addition, when the stress is independent of this strain rate, the material exhibits plastic deformation ^[1]. Many viscoelastic materials exhibit rubber like behavior explained by the thermodynamic theory of polymer elasticity. In reality all materials deviate from Hooke's law in various ways, for example by exhibiting viscous-like as well as elastic characteristics. Viscoelastic materials are those for which the relationship between stress and strain depends on time. Anelastic solids represent a subset of viscoelastic materials: they have a unique equilibrium configuration and ultimately recover fully after removal of a transient load.

Some phenomena in viscoelastic materials are: (i) if the stress is held constant, the strain increases with time (creep); (ii) if the strain is held constant, the stress decreases with time (relaxation); (iii) the effective stiffness depends on the rate of application of the load; (iv) if cyclic loading is applied, hysteresis (a phase lag) occurs, leading to a dissipation of mechanical energy; (v) acoustic waves experience attenuation; (vi) rebound of an object following an impact is less than 100%; (vii) during rolling, frictional resistance occurs.

a) Applied strain and b) induced stress as functions of time for a viscoelastic material.

All materials exhibit some viscoelastic response. In common metals such as steel or aluminum, as well as in quartz, at room temperature and at small strain, the behavior does not deviate much from linear elasticity. Synthetic polymers, wood, and human tissue as well as metals at high temperature display significant viscoelastic effects. In some applications, even a small viscoelastic response can be significant. To be complete, an analysis or design involving such materials must incorporate their viscoelastic behavior. Knowledge of the viscoelastic response of a material is based on measurement

Some examples of viscoelastic materials include amorphous polymers, semicrystalline polymers, biopolymers, metals at very high temperatures, and bitumen materials. Cracking occurs when the strain is applied quickly and outside of the elastic limit.

A viscoelastic material has the following properties:

• hysteresis is seen in the stress-strain curve.
• stress relaxation occurs: step constant strain causes decreasing stress
• creep occurs: step constant stress causes increasing strain

Elastic behavior versus viscoelastic behavior

Stress-Strain Curves for a purely elastic material (a) and a viscoelastic material (b). The red area is a hysteresis loop and shows the amount of energy lost (as heat) in a loading and unloading cycle. It is equal to , where σ is stress and  is strain. ^[1]

Unlike purely elastic substances, a viscoelastic substance has an elastic component and a viscous component. The viscosity of a viscoelastic substance gives the substance a strain rate dependent on time^[1]. Purely elastic materials do not dissipate energy (heat) when a load is applied, then removed^[1]. However, a viscoelastic substance loses energy when a load is applied, then removed. Hysteresis is observed in the stress-strain curve, with the area of the loop being equal to the energy lost during the loading cycle^[1]. Since viscosity is the resistance to thermally activated plastic deformation, a viscous material will lose energy through a loading cycle. Plastic deformation results in lost energy, which is uncharacteristic of a purely elastic material's reaction to a loading cycle^[1].

Specifically, viscoelasticity is a molecular rearrangement. When a stress is applied to a viscoelastic material such as a polymer, parts of the long polymer chain change position. This movement or rearrangement is called Creep. Polymers remain a solid material even when these parts of their chains are rearranging in order to accompany the stress, and as this occurs, it creates a back stress in the material. When the back stress is the same magnitude as the applied stress, the material no longer creeps. When the original stress is taken away, the accumulated back stresses will cause the polymer to return to its original form. The material creeps, which gives the prefix visco-, and the material fully recovers, which gives the suffix -elasticity^[2].

Types of viscoelasticity

Linear viscoelasticity is when the function is separable in both creep response and load. All linear viscoelastic models can be represented by a Volterra equation connecting stress and strain:

or

where

• t is time
• σ(t) is stress
• ε(t) is strain
• E_inst,creep and E_inst,relax are instantaneous elastic moduli for creep and relaxation
• K(t) is the creep function
• F(t) is the relaxation function

Linear viscoelasticity is usually applicable only for small deformations.

Nonlinear viscoelasticity is when the function is not separable. It is usually happens when the deformations are large or if the material changes its properties under deformations.

An anelastic material is a special case of a viscoelastic material: an anelastic material will fully recover to its original state on the removal of load.

Dynamic modulus

Viscoelasticity is studied using dynamic mechanical analysis. When we apply a small oscillatory strain and measure the resulting stress.

• Purely elastic materials have stress and strain in phase, so that the response of one caused by the other is immediate.
• In purely viscous materials, strain lags stress by a 90 degree phase lag.
• Viscoelastic materials exhibit behavior somewhere in the middle of these two types of material, exhibiting some lag in strain.

Complex Dynamic modulus G can be used to represent the relations between the oscillating stress and strain:

G = G' + iG''

where i² = − 1; G' is the storage modulus and G'' is the loss modulus:

where σ₀ and  are the amplitudes of stress and strain and δ is the phase shift between them.

Constitutive models of linear viscoelasticity

Viscoelastic materials, such as amorphous polymers, semicrystalline polymers, and biopolymers, can be modeled in order to determine their stress or strain interactions as well as their temporal dependencies. These models, which include the Maxwell model, the Kelvin-Voigt model, and the Standard Linear Solid Model, are used to predict a material's response under different loading conditions. Viscoelastic behavior has elastic and viscous components modeled as linear combinations of springs and dashpots, respectively. Each model differs in the arrangement of these elements, and all of these viscoelastic models can be equivalently modeled as electrical circuits. In an equivalent electrical circuit, stress is represented by voltage, and the derivative of strain (velocity) by current. The elastic modulus of a spring is analogous to a circuit's capacitance (it stores energy) and the viscosity of a dashpot to a circuit's resistance (it dissipates energy).

The elastic components, as previously mentioned, can be modeled as springs of elastic constant E, given the formula:

where σ is the stress, E is the elastic modulus of the material, and ε is the strain that occurs under the given stress, similar to Hooke's Law.

The viscous components can be modeled as dashpots such that the stress-strain rate relationship can be given as,

where σ is the stress, η is the viscosity of the material, and dε/dt is the time derivative of strain.

The relationship between stress and strain can be simplified for specific stress rates. For high stress states/short time periods, the time derivative components of the stress-strain relationship dominate. A dashpots resists changes in length, and in a high stress state it can be approximated as a rigid rod. Since a rigid rod cannot be stretched past its original length, no strain is added to the system^[3]

Conversely, for low stress states/longer time periods, the time derivative components are negligible and the dashpot can be effectively removed from the system - an "open" circuit. As a result, only the spring connected in parallel to the dashpot will contribute to the total strain in the system^[3]

Maxwell model

Maxwell model

The Maxwell model can be represented by a purely viscous damper and a purely elastic spring connected in series, as shown in the diagram. The model can be represented by the following equation:

.

Under this model, if the material is put under a constant strain, the stresses gradually relax, When a material is put under a constant stress, the strain has two components. First, an elastic component occurs instantaneously, corresponding to the spring, and relaxes immediately upon release of the stress. The second is a viscous component that grows with time as long as the stress is applied. The Maxwell model predicts that stress decays exponentially with time, which is accurate for most polymers. One limitation of this model is that it does not predict creep accurately. The Maxwell model for creep or constant-stress conditions postulates that strain will increase linearly with time. However, polymers for the most part show the strain rate to be decreasing with time^[2].

Application to soft solids:thermoplastic polymers in the vicinity of their melting temperature, fresh concrete ( neglecting its ageing), numerous metals at a temperature close to their melting point.

Kelvin–Voigt model

Schematic representation of Kelvin–Voigt model.

The Kelvin–Voigt model, also known as the Voigt model, consists of a Newtonian damper and Hookean elastic spring connected in parallel, as shown in the picture. It is used to explain the creep behaviour of polymers.

The constitutive relation is expressed as a linear first-order differential equation:

This model represents a solid undergoing reversible, viscoelastic strain. Upon application of a constant stress, the material deforms at a decreasing rate, asymptotically approaching the steady-state strain. When the stress is released, the material gradually relaxes to its undeformed state. At constant stress (creep), the Model is quite realistic as it predicts strain to tend to σ/E as time continues to infinity. Similar to the Maxwell model, the Kelvin–Voigt model also has limitations. The model is extremely good with modelling creep in materials, but with regards to relaxation the model is much less accurate.

Applications: organic polymers, rubber, wood when the load is not too high.

Standard linear solid model

Schematic representation of the Standard Linear Solid model.

The Standard Linear Solid Model effectively combines the Maxwell Model and a Hookean spring in parallel. A viscous material is modeled as a spring and a dashpot in series with each other, both of which are in parallel with a lone spring. For this model, the governing constitutive relation is:

Under a constant stress, the modeled material will instantaneously deform to some strain, which is the elastic portion of the strain, and after that it will continue to deform and asymptotically approach a steady-state strain. This last portion is the viscous part of the strain. Although the Standard Linear Solid Model is more accurate than the Maxwell and Kelvin-Voigt models in predicting material responses, mathematically it returns inaccurate results for strain under specific loading conditions and is rather difficult to calculate.

Generalized Maxwell Model

Schematic of Maxwell-Wiechert Model

The Generalized Maxwell also known as the Maxwell-Weichert model (after James Clerk Maxwell and Dieter Weichert) is the most general form of the models described above. It takes into account that relaxation does not occur at a single time, but at a distribution of times. Due to molecular segments of different lengths with shorter ones contributing less than longer ones, there is a varying time distribution. The Weichert model shows this by having as many spring-dashpot Maxwell elements as are necessary to accurately represent the distribution. The Figure on the right represents a possible Wiechert model ^[4]. Applications : metals and alloys at temperatures lower than one quarter of their absolute melting temperature (expressed in K).

Effect of temperature on viscoelastic behavior

The secondary bonds of a polymer constantly break and reform due to thermal motion. Application of a stress favors some conformations over others, so the molecules of the polymer will gradually "flow" into the favored conformations over time ^[5]. Because thermal motion is one factor contributing to the deformation of polymers, viscoelastic properties change with increasing or decreasing temperature. In most cases, the creep modulus, defined as the ratio of applied stress to the time-dependent strain, decreases with increasing temperature. Generally speaking, an increase in temperature correlates to a logarithmic decrease in the time required to impart equal strain under a constant stress. In other words, it takes less work to stretch a viscoelastic material an equal distance at a higher temperature than it does at a lower temperature.

Viscoelastic creep

a) Applied stress and b) induced strain (b) as functions of time over a short period for a viscoelastic material.

When subjected to a step constant stress, viscoelastic materials experience a time-dependent increase in strain. This phenomenon is known as viscoelastic creep.

At a time t₀, a viscoelastic material is loaded with a constant stress that is maintained for a sufficiently long time period. The material responds to the stress with a strain that increases until the material ultimately fails. When the stress is maintained for a shorter time period, the material undergoes an initial strain until a time t₁, after which the strain immediately decreases (discontinuity) then gradually decreases at times t > t₁ to a residual strain.

Viscoelastic creep data can be presented by plotting the creep modulus (constant applied stress divided by total strain at a particular time) as a function of time ^[6]. Below its critical stress, the viscoelastic creep modulus is independent of stress applied. A family of curves describing strain versus time response to various applied stress may be represented by a single viscoelastic creep modulus versus time curve if the applied stresses are below the material's critical stress value.

Viscoelastic creep is important when considering long-term structural design. Given loading and temperature conditions, designers can choose materials that best suit component lifetimes.

Measuring viscoelasticity

Solid is one of the major states of matter. It is characterized by structural rigidity and resistance to changes of shape or volume. Unlike a liquid, a solid object does not flow to take on the shape of its container, nor does it expand to fill the entire volume available to it like a gas does. The atoms in a solid are tightly bound to each other, either in a regular geometric lattice (crystalline solids, which include metals and ordinary water ice) or irregularly (an amorphous solid such as common window glass).

The branch of physics that deals with solids is called solid-state physics, and is the main branch of condensed matter physics (which also includes liquids).Materials science is primarily concerned with the physical and chemical properties of solids. Solid-state chemistry is especially concerned with thesynthesis of novel materials, as well as the science of identification and chemical composition.

Microscopic description

Model of closely packed atoms within a crystalline solid.

Schematic representation of a random-network glassy form (top) and ordered crystalline lattice (bottom) of identical chemical composition.

The atoms, molecules or ions which make up a solid may be arranged in an orderly repeating pattern, or irregularly. Materials whose constituents are arranged in a regular pattern are known as crystals. In some cases, the regular ordering can continue unbroken over a large scale, for example diamonds, where each diamond is a single crystal. Solid objects that are large enough to see and handle are rarely composed of a single crystal, but instead are made of a large number of single crystals, known ascrystallites, whose size can vary from a few nanometers to several meters. Such materials are called polycrystalline. Almost all common metals, and many ceramics, are polycrystalline.

In other materials, there is no long-range order in the position of the atoms. These solids are known as amorphous solids; examples include polystyrene and glass.

Whether a solid is crystalline or amorphous depends on the material involved, and the conditions in which it was formed. Solids which are formed by slow cooling will tend to be crystalline, while solids which are frozen rapidly are more likely to be amorphous. Likewise, the specific crystal structure adopted by a crystalline solid depends on the material involved and on how it was formed.

While many common objects, such as an ice cube or a coin, are chemically identical throughout, many other common materials comprise a number of different substances packed together. For example, a typical rock is an aggregate of several different minerals and mineraloids, with no specific chemical composition. Wood is a natural organic material consisting primarily of cellulose fibers embedded in a matrix of organic lignin. In materials science, composites of more than one constituent material can be designed to have desired properties.

Classes of solids

The forces between the atoms in a solid can take a variety of forms. For example, a crystal of sodium chloride (common salt) is made up of ionic sodium and chlorine, which are held together by ionic bonds. In diamond or silicon, the atoms share electrons and form covalent bonds. In metals, electrons are shared in metallic bonding. Some solids, particularly most organic compounds, are held together with van der Waals forces resulting from the polarization of the electronic charge cloud on each molecule. The dissimilarities between the types of solid result from the differences between their bonding.

Metals

The pinnacle of New York's Chrysler Building, the world's tallest steel-supported brick building, is clad with stainless steel.

Metals typically are strong, dense, and good conductors of both electricity and heat. The bulk of the elements in the periodic table, those to the left of a diagonal line drawn from boron to polonium, are metals. Mixtures of two or more elements in which the major component is a metal are known as alloys.

People have been using metals for a variety of purposes since prehistoric times. The strength and reliability of metals has led to their widespread use in construction of buildings and other structures, as well as in most vehicles, many appliances and tools, pipes, road signs and railroad tracks. Iron and aluminium are the two most commonly used structural metals, and they are also the most abundant metals in the Earth's crust. Iron is most commonly used in the form of an alloy, steel, which contains up to 2.1% carbon, making it much harder than pure iron.

Because metals are good conductors of electricity, they are valuable in electrical appliances and for carrying an electric current over long distances with little energy loss or dissipation. Thus, electrical power grids rely on metal cables to distribute electricity. Home electrical systems, for example, are wired with copper for its good conducting properties and easy machinability. The high thermal conductivity of most metals also makes them useful for stovetop cooking utensils.

The study of metallic elements and their alloys makes up a significant portion of the fields of solid-state chemistry, physics, materials science and engineering.

Metallic solids are held together by a high density of shared, delocalized electrons, known as "metallic bonding". In a metal, atoms readily lose their outermost ("valence")electrons, forming positive ions. The free electrons are spread over the entire solid, which is held together firmly by electrostatic interactions between the ions and the electron cloud.^[1] The large number of free electrons gives metals their high values of electrical and thermal conductivity. The free electrons also prevent transmission of visible light, making metals opaque, shiny and lustrous.

More advanced models of metal properties consider the effect of the positive ions cores on the delocalised electrons. As most metals have crystalline structure, those ions are usually arranged into a periodic lattice. Mathematically, the potential of the ion cores can be treated by various models, the simplest being the nearly free electron model.

Minerals

A collection of various minerals.

Minerals are naturally occurring solids formed through various geological processes under high pressures. To be classified as a true mineral, a substance must have acrystal structure with uniform physical properties throughout. Minerals range in composition from pure elements and simple salts to very complex silicates with thousands of known forms. In contrast, a rock sample is a random aggregate of minerals and/or mineraloids, and has no specific chemical composition. The vast majority of the rocks of the Earth's crust consist of quartz (crystalline SiO₂), feldspar, mica, chlorite, kaolin, calcite, epidote, olivine, augite, hornblende, magnetite, hematite, limonite and a few other minerals. Some minerals, like quartz, mica or feldspar are common, while others have been found in only a few locations worldwide. The largest group of minerals by far is the silicates (most rocks are ≥95% silicates), which are composed largely of silicon and oxygen, with the addition of ions of aluminium, magnesium, iron, calciumand other metals.

Ceramics

Si₃N₄ ceramic bearing parts

Ceramic solids are composed of inorganic compounds, usually oxides of chemical elements. They are chemically inert, and often are capable of withstanding chemical erosion that occurs in an acidic or caustic environment. Ceramics generally can withstand high temperatures ranging from 1000 to 1600 °C (1800 to 3000 °F). Exceptions include non-oxide inorganic materials, such as nitrides, borides and carbides.

Traditional ceramic raw materials include clay minerals such as kaolinite, more recent materials include aluminium oxide (alumina). The modern ceramic materials, which are classified as advanced ceramics, include silicon carbide and tungsten carbide. Both are valued for their abrasion resistance, and hence find use in such applications as the wear plates of crushing equipment in mining operations.

Most ceramic materials, such as alumina and its compounds, are formed from fine powders, yielding a fine grained polycrystalline microstructure which is filled with light scattering centers comparable to the wavelength of visible light. Thus, they are generally opaque materials, as opposed to transparent materials. Recent nanoscale (e.g.sol-gel) technology has, however, made possible the production of polycrystalline transparent ceramics such as transparent alumina and alumina compounds for such applications as high-power lasers. Advanced ceramics are also used in the medicine, electrical and electronics industries.

Ceramic engineering is the science and technology of creating solid-state ceramic materials, parts and devices. This is done either by the action of heat, or, at lower temperatures, using precipitation reactions from chemical solutions. The term includes the purification of raw materials, the study and production of the chemical compounds concerned, their formation into components, and the study of their structure, composition and properties.

Mechanically speaking, ceramic materials are brittle, hard, strong in compression and weak in shearing and tension. Brittle materials may exhibit significant tensile strength by supporting a static load. Toughness indicates how much energy a material can absorb before mechanical failure, while fracture toughness (denoted K_Ic ) describes the ability of a material with inherent microstructural flaws to resist fracture via crack growth and propagation. If a material has a large value of fracture toughness, the basic principles of fracture mechanics suggest that it will most likely undergo ductile fracture. Brittle fracture is very characteristic of most ceramic and glass-ceramic materials which typically exhibit low (and inconsistent) values of K_Ic.

For example of applications of ceramics, the extreme hardness of Zirconia is utilized in the manufacture of knife blades, as well as other industrial cutting tools. Ceramics such as alumina, boron carbide and silicon carbide have been used in bulletproof vests to repel large-caliber rifle fire. Silicon nitride parts are used in ceramic ball bearings, where their high hardness makes them wear resistant. In general, ceramics are also chemically resistant and can be used in wet environments where steel bearings would be susceptible to oxidation (or rust).

Radial rotor made from Si₃N₄ for a gas turbine engine

As another example of ceramic applications, in the early 1980s, Toyota researched production of an adiabatic ceramic engine with an operating temperature of over 6000 °F (3300 °C). Ceramic engines do not require a cooling system and hence allow a major weight reduction and therefore greater fuel efficiency. In a conventional metallic engine, much of the energy released from the fuel must be dissipated as waste heat in order to prevent a meltdown of the metallic parts. Work is also being done in developing ceramic parts for gas turbine engines. Turbine engines made with ceramics could operate more efficiently, giving aircraft greater range and payload for a set amount of fuel. However, such engines are not in production because the manufacturing of ceramic parts in the sufficient precision and durability is difficult and costly. Processing methods often result in a wide distribution of microscopic flaws which frequently play a detrimental role in the sintering process, resulting in the proliferation of cracks, and ultimate mechanical failure.

Glass ceramics

A high strength glass-ceramic cooktop with negligible thermal expansion.

Glass-ceramic materials share many properties with both non-crystalline glasses and crystalline ceramics. They are formed as a glass, and then partially crystallized by heat treatment, producing both amorphous and crystalline phases so that crystalline grains are embedded within a non-crystalline intergranular phase.

Glass-ceramics are used to make cookware (originally known by the brand name CorningWare) and stovetops which have both high resistance to thermal shock and extremely low permeability to liquids. The negative coefficient of thermal expansion of the crystalline ceramic phase can be balanced with the positive coefficient of the glassy phase. At a certain point (~70% crystalline) the glass-ceramic has a net coefficient of thermal expansion close to zero. This type of glass-ceramic exhibits excellent mechanical properties and can sustain repeated and quick temperature changes up to 1000 °C.

Glass ceramics may also occur naturally when lightning strikes the crystalline (e.g. quartz) grains found in most beach sand. In this case, the extreme and immediate heat of the lightning (~2500 °C) creates hollow, branching rootlike structures called fulgurite via fusion.

Organic solids

The individual wood pulp fibers in this sample are around 10 µm in diameter.

Organic chemistry studies the structure, properties, composition, reactions, and preparation by synthesis (or other means) of chemical compounds of carbon andhydrogen, which may contain any number of other elements such as nitrogen, oxygen and the halogens: fluorine, chlorine, bromine and iodine. Some organic compounds may also contain the elements phosphorus or sulfur. Examples of organic solids include wood, paraffin wax, naphthalene and a wide variety of polymersand plastics.

Wood

Wood is a natural organic material consisting primarily of cellulose fibers embedded in a matrix of lignin. Regarding mechanical properties, the fibers are strong in tension, and the lignin matrix resists compression. Thus wood has been an important construction material since humans began building shelters and using boats. Wood to be used for construction work is commonly known as lumber or timber. In construction, wood is not only a structural material, but is also used to form the mould for concrete.

Wood-based materials are also extensively used for packaging (e.g. cardboard) and paper which are both created from the refined pulp. The chemical pulping processes use a combination of high temperature and alkaline (kraft) or acidic (sulfite) chemicals to break the chemical bonds of the lignin before burning it out.

Polymers

STM image of self-assembledsupramolecular chains of the organic semiconductor quinacridone on graphite.

One important property of carbon in organic chemistry is that it can form certain compounds, the individual molecules of which are capable of attaching themselves to one another, thereby forming a chain or a network. The process is called polymerization and the chains or networks polymers, while the source compound is a monomer. Two main groups of polymers exist: those artificially manufactured are referred to as industrial polymers or synthetic polymers (plastics) and those naturally occurring as biopolymers.

Monomers can have various chemical substituents, or functional groups, which can affect the chemical properties of organic compounds, such as solubility and chemical reactivity, as well as the physical properties, such as hardness, density, mechanical or tensile strength, abrasion resistance, heat resistance, transparency, color, etc.. In proteins, these differences give the polymer the ability to adopt a biologically active conformation in preference to others (see self-assembly).

Household items made of various kinds of plastic.

People have been using natural organic polymers for centuries in the form of waxes and shellac which is classified as a thermoplastic polymer. A plant polymer namedcellulose provided the tensile strength for natural fibers and ropes, and by the early 19th century natural rubber was in widespread use. Polymers are the raw materials (the resins) used to make what we commonly call plastics. Plastics are the final product, created after one or more polymers or additives have been added to a resin during processing, which is then shaped into a final form. Polymers which have been around, and which are in current widespread use, include carbon-based polyethylene,polypropylene, polyvinyl chloride, polystyrene, nylons, polyesters, acrylics, polyurethane, and polycarbonates, and silicon-based silicones. Plastics are generally classified as "commodity", "specialty" and "engineering" plastics.

Composite materials

Simulation of the outside of the Space Shuttleas it heats up to over 1500 °C during re-entry

A cloth of woven carbon fiber filaments, a common element in composite materials

Composite materials contain two or more macroscopic phases, one of which is often ceramic. For example, a continuous matrix, and a dispersed phase of ceramic particles or fibers.

Applications of composite materials range from structural elements such as steel-reinforced concrete, to the thermally insulative tiles which play a key and integral role in NASA's Space Shuttle thermal protection system which is used to protect the surface of the shuttle from the heat of re-entry into the Earth's atmosphere. One example is Reinforced Carbon-Carbon (RCC), the light gray material which withstands reentry temperatures up to 1510 °C (2750 °F) and protects the nose cap and leading edges of Space Shuttle's wings. RCC is a laminated composite material made from graphite rayon cloth and impregnated with a phenolic resin. After curing at high temperature in an autoclave, the laminate is pyrolized to convert the resin to carbon, impregnated with furfural alcohol in a vacuum chamber, and cured/pyrolized to convert the furfural alcohol to carbon. In order to provide oxidation resistance for reuse capability, the outer layers of the RCC are converted to silicon carbide.

Domestic examples of composites can be seen in the "plastic" casings of television sets, cell-phones and so on. These plastic casings are usually a composite made up of a thermoplastic matrix such as acrylonitrile butadiene styrene (ABS) in which calcium carbonate chalk, talc, glass fibers or carbon fibers have been added for strength, bulk, or electro-static dispersion. These additions may be referred to as reinforcing fibers, or dispersants, depending on their purpose.

Thus, the matrix material surrounds and supports the reinforcement materials by maintaining their relative positions. The reinforcements impart their special mechanical and physical properties to enhance the matrix properties. A synergism produces material properties unavailable from the individual constituent materials, while the wide variety of matrix and strengthening materials provides the designer with the choice of an optimum combination.

Semiconductors

Semiconductor chip on crystalline silicon substrate.

Semiconductors are materials that have an electrical resistivity (and conductivity) between that of metallic conductors and non-metallic insulators. They can be found in the periodic table moving diagonally downward right from boron. They separate the electrical conductors (or metals, to the left) from the insulators (to the right).

Devices made from semiconductor materials are the foundation of modern electronics, including radio, computers, telephones, etc. Semiconductor devices include the transistor, solar cells, diodes and integrated circuits. Solar photovoltaic panels are large semiconductor devices that directly convert light into electrical energy.

In a metallic conductor, current is carried by the flow of electrons", but in semiconductors, current can be carried either by electrons or by the positively charged "holes" in the electronic band structure of the material. Common semiconductor materials include silicon, germanium and gallium arsenide.

Nanomaterials

Bulk silicon (left) and silicon nanopowder (right)

Many traditional solids exhibit different properties when they shrink to nanometer sizes. For example, nanoparticles of usually yellow gold and gray silicon are red in color; gold nanoparticles melt at much lower temperatures (~300 °C for 2.5 nm size) than the gold slabs (1064 °C);^[2] and metallic nanowires are much stronger than the corresponding bulk metals.^[3][4] The high surface area of nanoparticles makes them extremely attractive for certain applications in the field of energy. For example, platinum metals may be provide improvements as automotive fuel catalysts, as well as proton exchange membrane (PEM) fuel cells. Also, ceramic oxides (or cermets) of lanthanum, cerium, manganese and nickel are now being developed as solid oxide fuel cells (SOFC). Lithium, lithium titanate and tantalum nanoparticles are being applied in lithium ion batteries. Silicon nanoparticles have been shown to dramatically expand the storage capacity of lithium ion batteries during the expansion/contraction cycle. Silicon nanowires cycle without significant degradation and present the potential for use in batteries with greatly expanded storage times. Silicon nanoparticles are also being used in new forms of solar energy cells. Thin film deposition of silicon quantum dots on the polycrystalline silicon substrate of a photovoltaic (solar) cell increases voltage output as much as 60% by fluorescing the incoming light prior to capture. Here again, surface area of the nanoparticles (and thin films) plays a critical role in maximizing the amount of absorbed radiation.

Biomaterials

Collagen fibers of woven bone

The iridescent nacre inside a Nautilus shell.

Many natural (or biological) materials are complex composites with remarkable mechanical properties. These complex structures, which have risen from hundreds of million years of evolution, are inspiring materials scientists in the design of novel materials. Their defining characteristics include structural hierarchy, multifunctionality and self-healing capability. Self-organization is also a fundamental feature of many biological materials and the manner by which the structures are assembled from the molecular level up. Thus, self-assembly is emerging as a new strategy in the chemical synthesis of high performance biomaterials.

In physics, acceleration is the rate of change of velocity over time.^[1] In one dimension, acceleration is the rate at which something speeds up or slows down. However, since velocity is a vector, acceleration describes the rate of change of both the magnitude and the direction of velocity.^[2][3] Acceleration has the dimensions L T ⁻². In SI units, acceleration is measured in meters per second per second (m/s²).

In common speech, the term acceleration is used for an increase in speed (the magnitude of velocity); a decrease in speed is called deceleration. In physics, a change in the direction of velocity also is an acceleration: for rotary motion, the change in direction of velocity results in centripetal (toward the center) acceleration; where as the rate of change of speed is a tangential acceleration.

In classical mechanics, for a body with constant mass, the acceleration of the body is proportional to the net force acting on it (Newton's second law):

where F is the resultant force acting on the body, m is the mass of the body, and a is its acceleration.

Average and instantaneous acceleration

Average acceleration is the change in velocity (Δv) divided by the change in time (Δt). Instantaneous acceleration is the acceleration at a specific point in time which is for a very short interval of time as Δt approaches zero.

Tangential and centripetal acceleration

The velocity of a particle moving on a curved path as a function of time can be written as:

with v(t) equal to the speed of travel along the path, and

a unit vector tangent to the path pointing in the direction of motion at the chosen moment in time. Taking into account both the changing speed v(t) and the changing direction of u_t, the acceleration of a particle moving on a curved path on a planar surface can be written using the chain rule of differentiation as:

where u_n is the unit (inward) normal vector to the particle's trajectory, and R is its instantaneous radius of curvature based upon the osculating circle at time t. These components are called the tangential acceleration and the radial acceleration or centripetal acceleration (see also circular motion and centripetal force).

Extension of this approach to three-dimensional space curves that cannot be contained on a planar surface leads to the Frenet-Serret formulas.^[4][5]

Relation to relativity

In physics, a force is any influence that causes a free body to undergo an acceleration. Force can also be described by intuitive concepts such as a push or pull that can cause an object with mass to change its velocity (which includes to begin moving from a state of rest), i.e., to accelerate, or which can cause a flexible object to deform. A force has both magnitude and direction, making it a vector quantity. Newton's second law, F=ma, can be formulated to state that an object with a constant mass will accelerate in proportion to the net force acting upon and in inverse proportion to its mass, an approximation which breaks down near the speed of light. Newton's original formulation is exact, and does not break down: this version states that the net force acting upon an object is equal to the rate at which its momentum changes.^[1]

Related concepts to accelerating forces include thrust, increasing the velocity of the object, drag, decreasing the velocity of any object, and torque, causingchanges in rotational speed about an axis. Forces which do not act uniformly on all parts of a body will also cause mechanical stresses,^[2] a technical term for influences which cause deformation of matter. While mechanical stress can remain embedded in a solid object, gradually deforming it, mechanical stress in a fluid determines changes in its pressure and volume.^[3][4]

Philosophers in antiquity used the concept of force in the study of stationary and moving objects and simple machines, but thinkers such as Aristotle andArchimedes retained fundamental errors in understanding force. In part this was due to an incomplete understanding of the sometimes non-obvious force of friction, and a consequently inadequate view of the nature of natural motion^[5] A fundamental error was the belief that a force is requied to maintain motion, even at a constant velocity. Most of the previous misunderstandings about motion and force were eventually corrected by Sir Isaac Newton; with his mathematical insight, he formulated laws of motion that remained unchanged for nearly three hundred years.^[4] By the early 20th century, Einstein developed atheory of relativity that correctly predicted the action of forces on objects with increasing momenta near the speed of light, and also provided insight into the forces produced by gravitation and inertia.

With modern insights into quantum mechanics and technology that can accelerate particles close to the speed of light, particle physics has devised aStandard Model to describe forces between particles smaller than atoms. The Standard Model predicts that exchange particles called gauge bosons are the fundamental means by which forces are emitted and absorbed. Only four main interactions are known: in order of decreasing strength, they are: strong,electromagnetic, weak, and gravitational.^[3] High-energy particle physics observations made during the 1970s and 1980s confirmed that the weak and electromagnetic forces are expressions of a more fundamental electroweak interaction.

Response models

A material has a rest shape and its shape departs away from the rest shape due to stress. The amount of departure from rest shape is called deformation, the proportion of deformation to original size is called strain. If the applied stress is sufficiently low (or the imposed strain is small enough), almost all solid materials behave in such a way that the strain is directly proportional to the stress; the coefficient of the proportion is called the modulus of elasticity or Young's modulus. This region of deformation is known as the linearly elastic region.

It is most common for analysts in solid mechanics to use linear material models, due to ease of computation. However, real materials often exhibit non-linear behavior. As new materials are used and old ones are pushed to their limits, non-linear material models are becoming more common.

There are three models that describe how a solid responds to an applied stress:

1. Elastically – When an applied stress is removed, the material returns to its undeformed state. Linearly elastic materials, those that deform proportionally to the applied load, can be described by the linear elasticity equations such as Hooke's law.
2. Viscoelastically – These are materials that behave elastically, but also have damping: when the stress is applied and removed, work has to be done against the damping effects and is converted in heat within the material resulting in a hysteresis loop in the stress–strain curve. This implies that the material response has time-dependence.
3. Plastically – Materials that behave elastically generally do so when the applied stress is less than a yield value. When the stress is greater than the yield stress, the material behaves plastically and does not return to its previous state. That is, deformation that occurs after yield is permanent.