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Crystal optics is the branch of optics that describes the behaviour of light in anisotropic media, that is, media (such as crystals) in which light behaves differently depending on which direction the light is propagating. The index of refraction depends on both composition and crystal structure and can be calculated using the Gladstone–Dale ...
The Tensorial Anisotropy Index A T [5] extends the Zener ratio for fully anisotropic materials and overcomes the limitation of the AU that is designed for materials exhibiting internal symmetries of elastic crystals, which is not always observed in multi-component composites. It takes into consideration all the 21 coefficients of the fully ...
The net force on each ion is generally calculated explicitly at each numerical step. From this, the stress tensor of the system can be calculated and usually is calculated by the numerical package. By varying the convergence criteria, one can either seek a lowest energy structure or a structure that produces a desired stress tensor.
Tensor descriptions of material properties can be used to determine the directional dependence of that property. For a monocrystalline material, anisotropy is associated with the crystal symmetry in the sense that more symmetric crystal types have fewer independent coefficients in the tensor description of a given property.
In physics, tensor is an orientational order parameter that describes uniaxial and biaxial nematic liquid crystals and vanishes in the isotropic liquid phase. [1] The Q {\displaystyle \mathbf {Q} } tensor is a second-order, traceless, symmetric tensor and is defined by [ 2 ] [ 3 ] [ 4 ]
Ellipsometry can probe the complex refractive index or dielectric function tensor, which gives access to fundamental physical parameters like those listed above. It is commonly used to characterize film thickness for single layers or complex multilayer stacks ranging from a few angstroms or tenths of a nanometer to several micrometers with an ...
Each layer has approximately the same properties in-plane but different properties through-the-thickness. The plane of each layer is the plane of isotropy and the vertical axis is the axis of symmetry. A transversely isotropic material is one with physical properties that are symmetric about an axis that is normal to a plane of isotropy. This ...
Nearly all single crystal systems are anisotropic with respect to mechanical properties, with Tungsten being a very notable exception, as it is a cubic metal with stiffness tensor coefficients that exist in the proper ratio to allow for mechanical isotropy. In general, however, cubic crystals are not mechanically isotropic.