Isotropic solid

In condensed matter physics and continuum mechanics, an isotropic solid refers to a solid material for which physical properties are independent of the orientation of the system. While the finite sizes of atoms and bonding considerations ensure that true isotropy of atomic position will not exist in the solid state, it is possible for measurements of a given property to yield isotropic results, either due to the symmetries present within a crystal system, or due to the effects of orientational averaging over a sample (e.g. in an amorphous solid or a polycrystalline metal). Isotropic solids tend to be of interest when developing models for physical behavior of materials, as they tend to allow for dramatic simplifications of theory; for example, conductivity in metals of the cubic crystal system can be described with single scalar value, rather than a tensor. Additionally, cubic crystals are isotropic with respect to thermal expansion and will expand equally in all directions when heated. Isotropy should not be confused with homogeneity, which characterizes a system’s properties as being independent of position, rather than orientation. Additionally, all crystal structures, including the cubic crystal system, are anisotropic with respect to certain properties, and isotropic to others (such as density). The anisotropy of a crystal’s properties depends on the rank of the tensor used to describe the property, as well as the symmetries present within the crystal. The rotational symmetries within cubic crystals, for example, ensure that the dielectric constant (a 2nd rank tensor property) will be equal in all directions, whereas the symmetries in hexagonal systems dictate that the measurement will vary depending on whether the measurement is made within the basal plane. Due to the relationship between the dielectric constant and the optical index of refraction, it would be expected for cubic crystals to be optically isotropic, and hexagonal crystals to be optically anisotropic; Measurements of the optical properties of cubic and hexagonal CdSe confirm this understanding.