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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.
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 expression for the Grüneisen constant of a 1D chain with Mie potential exactly coincides with the results of MacDonald and Roy. [4] Using the relation between the Grüneisen parameter and interatomic potential one can derive the simple necessary and sufficient condition for Negative Thermal Expansion in perfect crystals with pair interactions ‴ > ″ ().
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.
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.
Nye has introduced a set of tensor (so-called Nye's tensor) to calculate the geometrically necessary dislocation density. [4] For a three dimension dislocations in a crystal, considering a region where the effects of dislocations is averaged (i.e. the crystal is large enough). The dislocations can be determined by Burgers vectors.
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 ...
Crystal powder is obtained by grinding crystals, resulting in powder particles, made up of one or more crystallites. Both polycrystals and crystal powder consist of many crystallites with varying orientation. Crystal phases are defined as regions with the same crystal structure, irrespective of orientation or twinning. Single and twinned ...