The use of Monte Carlo simulations in the study of a real lattice gas and its application to the alpha ' Pd-D system

Abstract

In alpha ' Pd-D at low temperatures the deuterons become ordered on the octahedral sites of the Pd lattice due to D-D interactions. As this process does not measurably disrupt the palladium lattice the system provides an excellent approximation to a lattice gas. The Monte Carlo method of predicting the behaviour of the lattice gas model for particular values of the D-D interactions is described and it is shown that for repulsive first nearest-neighbour (V₁) and second nearest-neighbour (V₂) interactions with V₂=0.25 V₁, the Monte Carlo method gives similar results to those obtained by a cluster variation method calculation. However, the latter method only predicts the transition temperature accurately near stoichiometric compositions. The above choice of interactions also gives a good description of the real system for D concentrations between 64 and 68% and it is suggested how agreement at higher concentrations could be achieved by introducing longer range interactions. A method of estimating the values of V_n from diffuse neutron scattering above the transition temperature is also proposed.