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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.
identifying important raw materials and minerals as well as their names and chemical formulae. describing the crystal structure of important materials and determining their atomic details; learning the systematics of crystal and glass chemistry. understanding how physical and chemical properties are related to crystal structure and microstructure.
The symmetry properties of crystal are described by the concept of space groups. [1] All possible symmetric arrangements of particles in three-dimensional space may be described by 230 space groups. The crystal structure and symmetry play a critical role in determining many physical properties, such as cleavage , electronic band structure , and ...
The directional dependence of a crystal's physical property is described by a 3D tensor and depends on the orientation of the crystal. Tensor shapes are more palpable by adding lighting effects (reflection and shadow). 2D sections of interest are selected for display by rotating the tensor interactively around one or more axes.
Crystal systems that have space groups assigned to a common lattice system are combined into a crystal family. The seven crystal systems are triclinic, monoclinic, orthorhombic, tetragonal, trigonal, hexagonal, and cubic. Informally, two crystals are in the same crystal system if they have similar symmetries (though there are many exceptions).
Controlled heating of the crystal can be used to fine-tune phase matching in the medium due to a slight variation of the dispersion with temperature. Periodic poling uses the largest value of lithium niobate's nonlinear tensor, d 33 = 27 pm/V. Quasi-phase-matching gives maximum efficiencies that are 2/π (64%) of the full d 33, about 17 pm/V. [24]
Vegard's law assumes that both components A and B in their pure form (i.e., before mixing) have the same crystal structure. Here, a A (1-x) B x is the lattice parameter of the solid solution, a A and a B are the lattice parameters of the pure constituents, and x is the molar fraction of B in the solid solution.