Anisotropy

Anisotropy refers to the directional dependence of a material or physical property. A substance is anisotropic when a given property varies with direction, in contrast to isotropy, where the property is the same in all directions.

In materials science and crystallography, anisotropy arises from internal structure such as crystal lattices, texture, or layered microstructures. Mechanical properties like stiffness, strength, and ductility may differ along different crystallographic axes. Thermal and electrical conductivities, refractive indices, and magnetic or electrical susceptibilities can also be direction dependent. Crystals exhibit strong anisotropy except for certain highly symmetric lattices; materials such as graphite, wood, composites, and rolled metals show pronounced anisotropy.

In optics, anisotropy leads to birefringence, where light with different polarizations travels at different speeds. Liquid crystals and other anisotropic media manipulate polarization for displays and photonics.

In geophysics and geology, seismic waves propagate at different speeds in different directions because of rock fabric, layering, or mineral alignment, producing seismic anisotropy used to infer subsurface structure.

Mathematically, anisotropy is described using tensors; many properties are second-order tensors whose components depend on direction. A common simple measure is the ratio of a property along two principal directions; larger ratios indicate higher anisotropy.