Vegard's law

Vegard'sche the rule describes the linear dependence of the lattice constant of a substitution mixed crystal or of an alloy of the percentages of the various components.

For a mixed crystal consisting of the two components A and B, it can be mathematically formulated as follows:

Here, the lattice constant of the resulting mixed crystal and the lattice constants of the pure components, and the percentage content of component B.

Requirement is that both components have the same structure type. The difference in the atomic or ionic radii is usually less than 15%.

This rule is used especially in alloys. The lattice constant of the alloy decreases at a smaller atomic volume of the alloying element in a larger atomic volume are increasing. For example, the addition of tantalum, titanium or zirconium leads to an increase in the lattice constant, while increasing the levels of vanadium or molybdenum lowering.

Although the Vegard'sche rule is not exactly fulfilled in many cases, it still serves as a guide for the study of mixed crystals. There are therefore often deviations from the rule Vegard'schen investigated.

To lie in alloys, the lattice constants slightly above the Vegardgerade when the binding forces between different types of atoms are smaller than between the same types of atoms (eg, alloys Cu - Au and Cu - Pd) are, in the opposite case, the lattice constants of this straight line (z. example, the alloys Ag - Au and Ag - Pd).