Computer simulations of solid solutions
Published:January 01, 2001
Over the past few years, methods of computer simulations have carved out a particular niche amongst the many tools available for studies of mineral behaviour. In particular, simulations have a special role in addressing questions that may be inaccessible to experiment. This is particularly true for studies of cation ordering in minerals, where experimental problems may arise from the constraints of kinetics and metastability. Moreover, computer simulations may be able to provide insights that cannot be provided by experiment, because they have the ability to unpack the science issues into smaller constituent parts. Recently computer simulation methods have been developed for the study of cation-ordering phase transitions and solid solutions, and applied to issues such as the determination of ordering processes, the calculation of thermodynamic properties, and the interpretation of experimental data. The purpose of this chapter is to review recent work in this area, including both the methodology and examples.
The central component of the simulation analysis is that it is possible to represent the interactions between ordering cations in a way that is amenable to study using statistical methods. There are two aspects of this, namely that it is possible to calculate the energy of a configuration of cations within a crystal structure, and then to be able to represent this energy in terms of variables that describe the degree of order of the cations. With such a representation, the tools of statistical mechanics can be used to study the behaviour of an ensemble of ordering cations as a function of temperature. The approach discussed in this chapter is the Monte Carlo simulation method. This method enables the ensemble to evolve towards thermodynamic equilibrium, and using the equilibrium configurations it is possible to perform an analysis of the processes that give long-range or short-range order, and to determine the associated thermodynamic properties. The importance of this approach is that it is able to provide new insights into ordering processes and enable interpretation of experimental data. We will highlight several examples that illustrate the power this has.
This chapter has two main sections. In the first section we discuss the details of the methodology. Some of the more technical details are presented in the Appendix. The second section gives examples of applications of the methodology for the study of cation ordering over short-range and long-range length scales in a variety of systems, including several silicate solid solutions.
Figures & Tables
Solid Solutions in Silicate and Oxide Systems
The EMU book series or notes, as they are called, were introduced to provide university teachers with up-to-date reviews in important, rapidly evolving areas of mineralogy, petrology and geochemistry. They are also meant to introduce scientists into special and often interdisciplinary fields of research. In this regard, a volume on solid solutions is current and sorely needed. The solid Earth, as well as many meteorites and the other solid planets, consists for the most part of mineral solid solutions. Research on solid solutions is extremely broad encompassing work in physics and chemistry, metallurgy, materials science and, last but not least, mineralogy and petrology. Hence, because the theme is so strongly interdisciplinary in nature, the workshop was organised to include solid state physicists, physical chemists, crystallographers, mineralogists and petrologists. The various chapters reflect some of this diversity and show what mineralogy has become. Experimental investigations in mineralogy now routinely include different types of spectroscopies along with more traditional phase equilibrium, X-ray diffraction, calorimetry, and TEM methods. There have also been new and impressive developments in theory and computation. Many computational approaches relating to the study of solid solutions, for example, the Cluster Variation Method or Monte Carlo simulations, have been brought in from materials science, chemistry and physics. It can be concluded that the traditional or historical, and perhaps artificial, boundaries between the various disciplines are disappearing. Many current research efforts in mineralogy are similar to those in chemistry, materials science and physics.