The determination of the vibrational entropies of solute atoms in dilute copper solid solutions by the measurement of vapour pressures

Abstract

An effusion method has been used to investigate the equilibrium between dilute copper based solid solutions and their vapours over a large range of temperature. Neutron irradiated alloys were used and a gamma-ray spectrometer enabled measurements on very dilute alloys to be carried out. The change of vibrational entropy S + M − S 0 v occurring when a solvent atom is replaced by a solute atom and the corresponding enthalpy change H + u − H 0 v were derived from the experimental data. The results are given in the table together with the values of H + u , the energy of a solute atom in the solution with respect to a solute atom at rest in a vacuum. System H u + − H v 0 kcal mole H u + kcal mole S u + − S v 0 k Cu-0.1 At. %Ag 26.6 ± 0.69 −45.9 ± 0.69 4.71 ± 0.29 Cu-0.5 At. %Au 2.01 ± 0.29 −70.5 ± 0.29 7.07 ± 0.12 Cu-2.5 At. %Au 1.84 ± 0.26 −70.7 ± 0.26 6.85 ± 0.11 To explain the very large increases in vibrational entropy two models have been discussed. In the first, atomic force constants were used to estimate the change in vibrational frequency with solute diameter for a cluster of 13 atoms. In the second model elastic theory was used to calculate the change in entropy due to the shear and dilational strains around a solute atom. The experimental values of S + u - S 0 v lie between those derived from the two models. Experimental values of the vibrational entropies deduced by other workers from solvus curves and e.m.f. measurements are also compared with the calculated values.