Linde's law in alloys of normal metals
Abstract
It has been established from experimental data on the effect of various impurities on residual resistivity ρ0 of 14 metallic hosts (Li, Cu, Ag, Au, Mg, Zn, Cd, Hg, Al, Ga, In, Ti, Sn, Pb) that, for elements belonging to one period, the law Δρ/c = αΔZ2+bΔZ + d = α(ΔZ—α)2+β is obeyed, where Δρ/c is the experimentally determined change in resistivity of the host metal upon solution of 1 at. % of an impurity, and ΔZ is the difference between the valences of host and impurity. Analysis of 40 parabolas showed that the above relationship is satisfied for impurities from all periods, except that of the host metal itself. In the latter case one finds the relationship Δρ/c = α AZ2 Thus, in no case is the well known Linde law (Δρ/c= αΔZ2 + d) observed, except in the case of period VI impurities in lead. It was found that the most frequent values of the coefficient α are 0.4±0.1 and 0.8±0.l, while for several host metals there is a tendency to increase in α with increase in the host valence. It is proposed that the most significant cause of the observed shift in the parabolas α, aside from distortion of the host lattice by the impurity upon solution, is structural differenes between the host and impurity ions. The nature of the dependence of Δρ/c on ΔZ is also considered for transition metals alloyed with normal metal impurities and the contrary case. Using empirical parabolic dependences of Δρ/c on ΔZ, values of Δρ/c are predicted for 55 impurity-host pairs for which experimental data are lacking.