Anisotropy

Anisotropy is the dependence of a material’s properties on the direction in which they are measured. It contrasts with isotropy, where properties are direction-independent.

Crystal symmetry: The set of symmetry operations that leave a crystal lattice unchanged. Crystal symmetry constrains which material properties can vary with direction.
X-ray diffraction: A technique that uses X-ray scattering to determine structures and properties of materials. Diffraction patterns reveal crystal orientation and directional structure.
Isotropy: The condition in which a material’s properties are the same in every direction. It is the direct opposite of directional dependence.
Crystal lattice: A repeating three-dimensional arrangement of points representing the periodic structure of a crystal. Lattice arrangement provides the structural basis for many crystalline anisotropies.
Tensor: A mathematical object that represents relationships between quantities independently of coordinate choice. Tensors encode many direction-dependent properties, including stress, conductivity, and optical response.
Polarized light microscopy: A microscopy method that uses polarizers to reveal optical properties of samples. It detects birefringence arising from anisotropic structure.
Orthotropy: A form of anisotropy with three mutually perpendicular symmetry axes. It describes a common, structured subset of directional material behavior.
Symmetry (physics): A transformation that leaves the relevant laws or physical system unchanged. Material symmetry determines which directions can be physically distinct.
Elasticity tensor: A fourth-rank tensor relating stress to strain in an elastic material. Its components describe how stiffness changes with loading direction.
Ultrasound imaging: An imaging method that forms images from reflected high-frequency sound waves. Anisotropic tissue can alter sound speed and echoes with probe orientation.

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