Deviations from additivity of lattice spacings in transition metal alloy systems

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Abstract
Using published lattice spacing/composition curves, deviations Δa from additivity of lattice spacings have been calculated for solid solutions in the metals of groups IVA, VA and VIA of the periodic table of transition metals of group numbers 4 to 11 from the three long periods. The results are presented as typical diagrams. Where the components have the same group number, Δa is zero unless one component is from the first long period, when Δa is positive. In such cases the Δa/composition curves are similar in form. Pairs of systems involving a common component also frequently correspond with similar Δa/composition curves. For solvents of group VIA of the periodic table solutes of lower and higher group number give negative and positive Δa values, respectively. This regularity is less marked for group VA solvents, and lost for group IVA solvents, for solid solutions in which Δa is predominantly negative. The results are discussed, and it is suggested that they are consistent with the operation of two main factors. Firstly, solutes of higher group number than that of the solvent tend to give rise to positive Δa values, while solutes of lower group number correspond with negative Δa values. Secondly it is suggested that solution of elements of group number exceeding 4 in titanium, zirconium and hafnium stabilizes the body-centred cubic structure and thereby shortens the mean interatomic distances, giving rise to a lattice contraction which opposes the tendency for solutes of group number higher than that of the solvent to give rise to positive Δa values. The effects for solvents of group VIA differ, since this is the group in which the body-centred cubic structure attains its maximum stability.

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