Elastically Driven Phase Transitions Studied by A Continuous Monte Carlo Method

Abstract

An important element in phase transitions occurring between different solid phases is the accommodation problem. The formed structure may not fit with its parent phase in respect to either the lattice constants or the symmetry. This gives rise to elastic deformations and large scale epitaxial rotations and twin formation. These phenomena are difficult to treat accurately by means of standard lattice gas models and Monte Carlo simulations. Here we shall describe a continuous Monte Carlo method and illustrate its capabilities on the simple test case of particles adsorbed with different coverage on a graphite surface. This is in fact closely related to an alloy problem, namely, that in which one of the elements (B) is represented by vacancies, which only interact via’ elastic forces’ originating from the interaction between the other elements (A), i.e. the adsorbate particles and their interaction with the parent phase, i.e. the substrate. As a test case this system is ideal since the’ elastic forces’ thereby are emphasized, and further in the sense that detailed experiments exists for comparison with calculated phase diagrams and structures, and finally that the system by definition is two dimensional, which makes it possible to study rather large systems by means of Monte Carlo simulations. This is in particular important when dealing with the effectively long ranged’ elastic interactions’ and the resulting twin domains of mesoscale dimensions. In this short paper only the method and a few examples can be given. More detailed results are given elsewhere (Vives and Lindgard 1991, 1992).