Critical line (thermodynamics)

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In thermodynamics, a critical line is the higher-dimensional equivalent of a critical point. [1] It is the locus of contiguous critical points in a phase diagram. These lines cannot occur for a single substance due to the phase rule, but they can be observed in systems with more variables, such as mixtures. Two critical lines may meet and terminate in a tricritical point.

Thermodynamics branch of physics concerned with heat, work, temperature, and thermal or internal energy

Thermodynamics is the branch of physics that has to do with heat and temperature and their relation to energy and work. The behavior of these quantities is governed by the four laws of thermodynamics, irrespective of the composition or specific properties of the material or system in question. The laws of thermodynamics are explained in terms of microscopic constituents by statistical mechanics. Thermodynamics applies to a wide variety of topics in science and engineering, especially physical chemistry, chemical engineering and mechanical engineering.

Critical point (thermodynamics) Temperature and pressure point where phase boundaries disappear

In thermodynamics, a critical point is the end point of a phase equilibrium curve. The most prominent example is the liquid-vapor critical point, the end point of the pressure-temperature curve that designates conditions under which a liquid and its vapor can coexist. At higher temperatures, the gas cannot be liquefied by pressure alone. At the critical point, defined by a critical temperatureTc and a critical pressurepc, phase boundaries vanish. Other examples include the liquid–liquid critical points in mixtures.

A phase diagram in physical chemistry, engineering, mineralogy, and materials science is a type of chart used to show conditions at which thermodynamically distinct phases occur and coexist at equilibrium.

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Phase (matter) region of space (a thermodynamic system), throughout which all physical properties of a material are essentially uniform; region of material that is chemically uniform, physically distinct, (often) mechanically separable

In the physical sciences, a phase is a region of space, throughout which all physical properties of a material are essentially uniform. Examples of physical properties include density, index of refraction, magnetization and chemical composition. A simple description is that a phase is a region of material that is chemically uniform, physically distinct, and (often) mechanically separable. In a system consisting of ice and water in a glass jar, the ice cubes are one phase, the water is a second phase, and the humid air is a third phase over the ice and water. The glass of the jar is another separate phase.

Superconductivity physical phenomenon

Superconductivity is a phenomenon of exactly zero electrical resistance and expulsion of magnetic flux fields occurring in certain materials, called superconductors, when cooled below a characteristic critical temperature. It was discovered by Dutch physicist Heike Kamerlingh Onnes on April 8, 1911, in Leiden. Like ferromagnetism and atomic spectral lines, superconductivity is a quantum mechanical phenomenon. It is characterized by the Meissner effect, the complete ejection of magnetic field lines from the interior of the superconductor during its transitions into the superconducting state. The occurrence of the Meissner effect indicates that superconductivity cannot be understood simply as the idealization of perfect conductivity in classical physics.

Phase transition transitions between solid, liquid and gaseous states of matter, and, in rare cases, plasma

The term phase transition is most commonly used to describe transitions between solid, liquid, and gaseous states of matter, as well as plasma in rare cases. A phase of a thermodynamic system and the states of matter have uniform physical properties. During a phase transition of a given medium, certain properties of the medium change, often discontinuously, as a result of the change of external conditions, such as temperature, pressure, or others. For example, a liquid may become gas upon heating to the boiling point, resulting in an abrupt change in volume. The measurement of the external conditions at which the transformation occurs is termed the phase transition. Phase transitions commonly occur in nature and are used today in many technologies.

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The phase rule is a general principle governing systems in thermodynamic equilibrium. If F is the number of degrees of freedom, C is the number of components and P is the number of phases, then

In physics, critical phenomena is the collective name associated with the physics of critical points. Most of them stem from the divergence of the correlation length, but also the dynamics slows down. Critical phenomena include scaling relations among different quantities, power-law divergences of some quantities described by critical exponents, universality, fractal behaviour, and ergodicity breaking. Critical phenomena take place in second order phase transitions, although not exclusively.

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Critical exponents describe the behavior of physical quantities near continuous phase transitions. It is believed, though not proven, that they are universal, i.e. they do not depend on the details of the physical system, but only on some of its general features. For instance, for ferromagnetic systems, the critical exponents depend only on:

A quantum critical point is a point in the phase diagram of a material where a continuous phase transition takes place at absolute zero. A quantum critical point is typically achieved by a continuous suppression of a nonzero temperature phase transition to zero temperature by the application of a pressure, field, or through doping. Conventional phase transitions occur at nonzero temperature when the growth of random thermal fluctuations leads to a change in the physical state of a system. Condensed matter physics research over the past few decades has revealed a new class of phase transitions called quantum phase transitions which take place at absolute zero. In the absence of the thermal fluctuations which trigger conventional phase transitions, quantum phase transitions are driven by the zero point quantum fluctuations associated with Heisenberg's uncertainty principle.

In condensed matter physics, dealing with the macroscopic physical properties of matter, a tricritical point is a point in the phase diagram of a system at which three-phase coexistence terminates. This definition is clearly parallel to the definition of an ordinary critical point as the point at which two-phase coexistence terminates.

Multicritical points are special points in the parameter space of thermodynamic or other systems with a continuous phase transition. At least two thermodynamic or other parameters must be adjusted to reach a multicritical point. At a multicritical point the system belongs to a universality class different from the "normal" universality class.

Spinodal

In thermodynamics, the limit of local stability with respect to small fluctuations is clearly defined by the condition that the second derivative of Gibbs free energy is zero. The locus of these points is known as the spinodal curve. For compositions within this curve, infinitesimally small fluctuations in composition and density will lead to phase separation via spinodal decomposition. Outside of the curve, the solution will be at least metastable with respect to fluctuations. In other words, outside the spinodal curve some careful process may obtain a single phase system. Inside it, only processes far from thermodynamic equilibrium, such as physical vapor deposition, will enable one to prepare single phase compositions. The local points of coexisting compositions, defined by the common tangent construction, are known as binodal (coexistence) curve, which denotes the minimum-energy equilibrium state of the system. Increasing temperature results in a decreasing difference between mixing entropy and mixing enthalpy, thus, the coexisting compositions come closer. The binodal curve forms the bases for the miscibility gap in a phase diagram. Since the free energy of mixture changes with temperature and concentration, the binodal and spinodal meet at the critical or consulate temperature and composition.

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Phase line (mathematics)

In mathematics, a phase line is a diagram that shows the qualitative behaviour of an autonomous ordinary differential equation in a single variable, . The phase line is the 1-dimensional form of the general -dimensional phase space, and is very simple to analyze.

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References

  1. B. Widom, Theory of Phase Equilibrium, J. Phys. Chem 1996, 13190-13199