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The Zener ratio is a dimensionless number that is used to quantify the anisotropy for cubic crystals. It is sometimes referred as anisotropy ratio and is named after Clarence Zener. [1] Conceptually, it quantifies how far a material is from being isotropic (where the value of 1 means an isotropic material). Its mathematical definition is [1] [2]
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.
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 ‴ > ″ ().
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.
In crystallography, crystal structure is a description of ordered arrangement of atoms, ions, or molecules in a crystalline material. [1] Ordered structures occur from intrinsic nature of constituent particles to form symmetric patterns that repeat along the principal directions of three-dimensional space in matter.
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.
A crystal structure is defined as the spatial distribution of the atoms within a crystal, usually modeled by the idea of an infinite crystal pattern.An infinite crystal pattern refers to the infinite 3D periodic array which corresponds to a crystal, in which the lengths of the periodicities of the array may not be made arbitrarily small.
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 ...