Electronic specific heats of silver-gold alloys

A contribution to the electronic specific heats of alloys due to the simultaneous presence of the electron-phonon and electron-impurity interactions is theoretically investigated by means of the perturbation method. The electron-phonon interaction modifies the energy spectrum of an electron and the electron-impurity interaction gives rise to the finite lifetime on this quasi-particle. Because of the level broadening due to the uncertainty relation, all densities of states in the neighbourhood of the Fermi level, which are formed from the real part of the self-energy of the system, contribute to the specific heat. It follows that the enhancement of specific heats due to the electron-phonon interaction tends to decrease as the concentration of impurity atoms is increased, and becomes only 10% of that for a pure metal when the broadenings of levels lying near the Fermi level reach about four times k B Θ D , where k B and Θ D are Boltzmann's constant and the Debye temperature, respectively. On the basis of this theory, the recent data of the silver-gold alloy, which show an interesting behaviour with a minimum value for about 15 at.% Au in Ag, are analysed. It is found that the enhancement of specific heats for pure silver due to the electron-phonon interaction is about 7% of the ordinary contribution from the density of states formed by the band structure. For the spin paramagnetism in alloys it is shown that there is no contribution from the electron-phonon interaction and the electron-impurity interaction has an effect resulting from the level broadening.