anisotropes

An anisotrope, plural anisotropes, is a property, material, or system whose measured value varies with direction. In many fields, the term is used to describe phenomena that are not the same in all orientations. The broader concept is anisotropy, and the related adjective is anisotropic.

Anisotropes occur in a variety of contexts. In crystallography and mineralogy, most substances are anisotropic because their crystal lattices lack identical symmetry along all axes, leading to direction-dependent properties such as refractive index, stiffness, or thermal conductivity. In optics, anisotropic media like calcite show birefringence, where light speeds differ by polarization and direction. In geology and geophysics, rocks can display seismic anisotropy, affecting wave speeds. In materials science, composites and textured metals exhibit anisotropic mechanical strength and diffusion. In biology, diffusion processes in tissues can be anisotropic, as seen in brain white matter.

Mathematically, anisotropy is often described using tensors. Second-order tensors can capture direction-dependent properties such as conductivity, elasticity, or permeability, with principal axes revealing the directions of extreme and minimal response. Experimental approaches include polarized light experiments, diffraction, ultrasound, and diffusion imaging in medical contexts.

Understanding anisotropes is important for design and analysis across disciplines. It informs the engineering of directional materials, interpretation of geophysical data, and imaging techniques that rely on direction-sensitive signals. See also: isotropy, anisotropy, tensor, birefringence.