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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 tensor and pseudovector forms of the Berry curvature are related to each other through the Levi-Civita antisymmetric tensor as , =,. In contrast to the Berry connection, which is physical only after integrating around a closed path, the Berry curvature is a gauge-invariant local manifestation of the geometric properties of the wavefunctions ...
Note that for biaxial crystals the index ellipsoid will not be an ellipsoid of revolution ("spheroid") but is described by three unequal principle refractive indices n α, n β and n γ. Thus there is no axis around which a rotation leaves the optical properties invariant (as there is with uniaxial crystals whose index ellipsoid is a spheroid).
Optical properties of common minerals Name Crystal system Indicatrix Optical sign Birefringence Color in plain polars Anorthite: Triclinic: Biaxial (-) 0.013
An example of the tetragonal crystals, wulfenite Two different views (top down and from the side) of the unit cell of tP30-CrFe (σ-phase Frank–Kasper structure) that show its different side lengths, making this structure a member of the tetragonal crystal system. In crystallography, the tetragonal crystal system is one of the 7 crystal systems.
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 ]
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.
Lithium tantalate (Li Ta O 3) is a crystal exhibiting both piezoelectric and pyroelectric properties, which has been used to create small-scale nuclear fusion ("pyroelectric fusion"). [20] Recently, pyroelectric and piezoelectric properties have been discovered in doped hafnium oxide ( Hf O 2 ), which is a standard material in CMOS manufacturing.