# Anisotropy

Anisotropy (from ancient Greek ἀν- Toggle "un-" [ Alpha privativum ] ἴσος isos "equal to" and τρόπος tropos "rotation direction"), the direction depending on a property or a process. Anisotropy is the opposite of isotropy . In this sense, the term is applied in physics (e.g. radiation , magnetism , speed of propagation of earthquake waves ), materials science , crystallography and mathematics to different properties of the systems under consideration .

## Examples

• The radiation of the sun is isotropic, that of a laser anisotropic.
• Directional arrangement of the crystallites in metal ( texture ): This results in anisotropy of elastic and plastic deformability .
• The birefringence ( optics ) is based on an anisotropy of the refractive index .
• Liquid crystals are anisotropic liquids .
• An element of a square module ( M , q ) is called anisotropic if . Elements with are called isotropic .${\ displaystyle x}$${\ displaystyle q (x) \ neq 0}$${\ displaystyle x \ neq 0}$${\ displaystyle q (x) = 0}$
• The electrical anisotropy is found in thin layers such as nanowire layers or CNT layers on structures.
• The elasticity of materials is often anisotropic. This is described with the laws of elasticity . The best known anisotropic elasticity laws are the triclinic anisotropic , the orthotropic and the transversely isotropic elasticity law.
Examples:
plastics reinforced with glass or carbon fibers ( GRP and CFRP ) and stretched plastics have a direction-dependent law of elasticity, but not unreinforced plastics or metals.
• Wood is anisotropic material in many ways. The main anisotropic directions are axial (also called longitudinal or in the grain direction), radial (in relation to the cylindrical tree trunk) and tangential. Cleavage, elasticity, hardness and changes in length (drying, heat) are examples of anisotropic wood properties.
• Additive manufacturing processes such as 3D printing sometimes produce anisotropic workpieces because they build up the workpiece in layers and the material properties in the layer plane differ from those orthogonal to it.
• Anisotropic etching of semiconductors enables a more precise control of the material removal. For this purpose, etchants are used which work preferentially in certain directions of the crystal lattice.
• All crystals (and thus also minerals ) are anisotropic with some properties.
• Fluorescence can be anisotropic to a certain extent, that is, the emerging fluorescence radiation is not evenly distributed with respect to its plane of oscillation in these cases (see fluorescence anisotropy ).
• In cell biology, the uniform enlargement of a cell after cell division is called isotropic; if it is more pronounced in one direction (i.e. elongation of the cell), it is called anisotropic.

## Individual evidence

1. Will Kleber , Hans-Joachim Bautsch , Joachim Bohm (1990): Introduction to Crystallography. Publishing house technology. ISBN 3-341-00479-3 , pages 14 f.