Dissemination of IT for the Promotion of Materials Science (DoITPoMS)

DoITPoMS Teaching & Learning Packages Introduction To Anisotropy Summary
Introduction To Anisotropy AimsBefore you startIntroductionMechanical analogy of anisotropic responseAnisotropic thermal conductivityDerivation of the anisotropy ellipsoidAnisotropic electrical conductivityAnisotropic diffusionAnisotropic dielectric permittivityOptical anisotropy and the optical indicatrixLiquid crystalsSummaryQuestionsGoing further
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Summary

In some materials a property will be the same, irrespective of the direction in which it is measured, but this is not always the case. On completion of this TLP, you should now understand the concept of anisotropy, and be able to appreciate that a response can be non-parallel to the applied stimulus. Anisotropy in a range of properties has been discussed, including electrical and thermal conductivity, diffusion, dielectric permittivity, and optical properties. You should also now be familiar with the use of representation surfaces for a range of anisotropic properties, including the basis behind their mathematical description.

Anisotropic properties are exploited in many applications. In polarised-light microscopy, a quartz wedge can be used to determine birefringence and optical sign. Liquid crystals have electronic uses such as displays, and the liquid crystalline state has advantages in the processing of polymers (such as Kevlar). The anisotropic thermal conductivity in polymer thin films has use in microelectronic devices, for example, solid-state transducers.

Anisotropic properties described by higher than second rank tensors (not discussed here) can also have useful applications. Examples include:

  • Piezoelectricity (relating an applied stress to the induced polarisation)
  • The electro-optic effect (when a field causes a change in the dielectric impermeability)
  • Elastic compliance and elastic stiffness (relating stress and strain)
  • Piezo-optical effect (when a stress induces a change in refractive index)
  • Electrostriction (strain arising from an electric field)

Non-tensor properties can also demonstrate anisotropy; for example, yield stress can vary with direction of applied stress.

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