On the size dependence of the critical point of nanoscale interstitial solid solutions

It is shown that a size dependence of the critical temperature T_c of the miscibility gap in nanocrystalline and nanoscale particle interstitial solid solutions results from stress owing to elastic interaction of the bulk with layers of material at the grain boundaries or surfaces which have a small solute susceptibility (i.e. a weak dependence of the concentration on the chemical potential) at the phase transition. When the volume fraction occupied by the interfacial layers is not too large, then the changes in T_c and in the critical concentration x_c can be predicted on the basis of a series expansion of the solute chemical potential in the bulk about the critical point. The model can be extended to free-standing thin films and coherent multilayers. The dependence of the pressure on the hydrogen concentration in the crystal lattice of nanocrystalline palladium-hydrogen is measured on the basis of X-ray diffraction data. The result agrees with the predictions of the theory.