State of matter

A state of matter is a broad category of material behavior. A solid resists a sustained change of shape, a liquid flows while remaining difficult to compress, and a gas expands to fill its container. These distinctions are useful first descriptions, but they do not enumerate all thermodynamic phases. Plasma adds collective behavior of charged particles, while liquid crystals show that flow and structural order need not disappear together.

Distinguish three questions: what broad state of matter does the material resemble, which thermodynamic phase is present, and what are its temperature, pressure and other state variables? Two samples at different temperatures can be in the same liquid thermodynamic phase. Conversely, crystal polymorphism gives different solid thermodynamic phases of the same substance, distinguished by their crystal structures. A phase transition between them need not change the broad state-of-matter category.

For an imagined substance with crystalline forms A and B, melting A produces a solid–liquid phase transition, while converting A to B produces a solid–solid phase transition. A sample containing A and B has two thermodynamic phases even though all its material is solid. Cutting one uniform crystal into two pieces does not create a second thermodynamic phase: count distinct equilibrium forms, rather than pieces or grains. This distinction matters when applying the phase rule.

A phase diagram locates stable thermodynamic phases using temperature and pressure. Its liquid–gas phase coexistence curve ends at a liquid-gas critical point, around which a path connects liquid and gas without a first-order phase transition. Broad categories can therefore remain useful without a sharp boundary.^[ref]

A crystal is a solid with spatially ordered constituents.

A magnetic unit cell repeats the ordered magnetic moments as well as the atomic positions. It can exceed the chemical primitive unit cell when translations interchange oppositely ordered magnetic sublattices. For a simple-cubic Néel pattern $(-1{)}^{n_x+n_y+n_z}$, translations preserving the sum's parity form an FCC lattice with conventional parameter twice the chemical spacing and a two-spin primitive basis.

A macroscopically planar crystal boundary characterized by a crystallographic orientation. Its Miller index specifies that orientation; visible facet area depends on surface thermodynamics and growth kinetics. A low surface energy and a slow growth rate are different properties.

A solid containing many differently oriented crystalline crystal grains. grain boundaries impose compatibility and act as transport paths or sinks for mobile defects.

A region with an approximately common crystal orientation, separated from other such regions by grain boundaries.

A measure of crystal grain elongation. It changes directional boundary spacings and can influence anisotropic defect transport independently of average grain size.

A measure of the spatial scale of crystal grains. Its definition must be stated for elongated crystal grains; size, aspect ratio and orientation distribution have distinct physical effects.

The spatial arrangement and intermolecular contacts of components in a crystal.

A crystalline phase containing two or more distinct molecular components in one lattice.

Close packing of triangular layers with ABAB stacking. Its nearest-layer geometry agrees with face-centered cubic stacking, but the further-layer registry differs.

A cubic crystal structure with lattice sites at cube corners and face centres. Its close-packed layers are (111) planes, stacked ABCABC.

The fixed-volume equilibrium crystal shape obtained by minimizing orientation-dependent surface free energy. Facet support-plane distances are proportional to their interfacial free energies under the construction assumptions.

An equilibrium construction for a supported particle that modifies the Wulff construction using particle-support and support-medium interfacial energies. The support truncates the corresponding free-particle shape.

In a homogeneous isotropic one-component fluid, $g(r)$ is the conditional number density at separation $r$ from a tagged particle divided by the bulk number density $n$. Thus the displayed shell contains the mean number of neighbours. For an uncorrelated ideal gas $g(r)=1$ away from the tagged particle; repulsive cores suppress small separations, while liquid coordination shells can produce damped oscillations approaching one at large distance. This is a pair correlation, not a normalized one-particle radial probability density. The static structure factor measures its Fourier-space counterpart.

For a differentiable central pair potential in a classical homogeneous three-dimensional fluid, the mechanical virial theorem gives the displayed pressure. The radial distribution function accounts for the probability of each pair separation. In the dilute limit, $g(r)=e^{-v(r)/(k_{B}T)}+O(n)$, and integration by parts yields $B_2(T)=-2\pi {\int }_0^{\infty }[e^{-v(r)/(k_{B}T)}-1]r^{2}dr$. Thus the second virial coefficient controls $p/(n{k}_{B}T)=1+B_{2}n+\cdots$. A few virial terms are a low-density approximation, not generally a converged description of a dense liquid. A discontinuous hard core needs its contact form or a limiting argument.

For a classical monatomic homogeneous fluid with pairwise central pair potential $v(r)$, the mean interaction energy is one half the sum over neighbours of a tagged particle. Using the radial distribution function gives the displayed formula; the factor one half prevents counting each pair twice. The kinetic term follows from the equipartition theorem. Its use requires the relevant integral to exist and a thermodynamic state specified by number density and temperature. Quantum kinetic contributions, many-body forces and internal molecular modes require modifications.

A historical physical name for a gas or vapour, emphasizing its mobility and appreciable compressibility. It does not imply an exactly ideal gas or prevent a vapour from undergoing condensation.

A relation among quantities such as pressure, volume, temperature and amount of substance for a gas.

Crystal polymorphism is the existence of different crystal structures for the same chemical substance. Each crystal polymorph can have its own mass density, melting behavior and range of stability on a phase diagram. A different external shape of the same crystal structure alone does not establish a different crystal polymorph.^[ref]

At fixed temperature and pressure, compare the chemical potentials of the possible crystal polymorphs. The lower value determines the stable bulk thermodynamic phase; equality permits phase coexistence when neither form is beaten by another thermodynamic phase. A higher-chemical potential form can persist through metastability, so finding it in a sample does not by itself locate an equilibrium boundary.

A solid thermodynamic phase with a particular crystal structure, among distinct crystalline forms of the same chemical substance. Crystal polymorphism names the existence of these alternatives; a crystal polymorph names one of the forms.