12/26/2023 0 Comments Lattice parameter![]() ![]() Correlation of some physical properties and chemical composition of solid solution. "Phase strength effects on chemical mixing in extensively deformed alloys". "Quantitative size-factors for metallic solid solutions". "Die Konstitution der Mischkristalle und die Raumfüllung der Atome". When considering the empirical correlation of some physical properties and the chemical composition of solid compounds, other relationships, rules, or laws, also closely resembles the Vegard's law, and in fact the more general rule of mixtures: If the concept of the volume fraction is introduced, density, coefficient of thermal expansion, compressibility and refractive index can be correlated linearly with the volume fraction in an ideal system.“ See also The linear correlation of refractive index and chemical composition of an isotropic solid solution can be derived from the Gladstone–Dale equation, but it is required that the system must be ideal and the molar volumes of the components are equal or nearly equal. But when the solid solution is ideal, the linear correlation of molar heat capacities and chemical composition is possible. …Ĭoefficients of thermal expansion and compressibilities of the ideal solid solution can be discussed in the same manner. In particular, a family of lattice planes of a given (direct) Bravais lattice is determined by three integers h, k, and, the Miller indices. Miller indices form a notation system in crystallography for lattice planes in crystal (Bravais) lattices. In mineralogy, the tacit assumption for the linear correlation of the density and the chemical composition of a solid solution is twofold: one is an ideal solid solution and the other identical or nearly identical molar volumes of the components. Planes with different Miller indices in cubic crystals. The following excerpt from Takashi Fujii (1960) summarises well the limits of the Vegard’s law in the context of mineralogy and also makes the link with the Gladstone–Dale equation: In 1921, Lars Vegard discovered that the lattice parameter of a solid solution of two constituents is approximately a weighted mean of the two constituents' lattice parameters at the same temperature: a A ( 1 − x ) B x = ( 1 − x ) a A + x a B Mineralogy In crystallography, materials science and metallurgy, Vegard's law is an empirical finding ( heuristic approach) resembling the rule of mixtures. ![]()
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