Dependence of thermodynamic properties on atomic masses and bonding in solids
Published:January 01, 2001
Thermophysical properties which depend on the atomic vibrations in solids define a research area which has evolved gradually for about 100 years. Many textbooks give them a very traditional presentation, which does not make contact with more recent developments. The purpose of this review is to present a modern theoretical approach, with emphasis on aspects important for geophysical and mineralogical applications.
The vibrations of atoms in solids depend on the masses of the atoms, and on the forces between them. While the masses of the constituent atoms are known, a theoretical account of the forces requires a detailed electronic structure calculation. This review discusses to what extent the role of masses and forces can be treated separately, in various thermodynamic quantities, including many cases where a precise knowledge of the forces is not crucial. Electronic structures are considered in the review by Heine (2001).
The key quantity in our approach is the density of states, F(ω), of the vibrational spectrum. The heat capacity, Cp, and thermodynamic quantities directly derived from Cp like the Gibbs free energy, G, have a major contribution from the atomic vibrations. The melting temperature, Tfus, is determined by the Gibbs free energy. Anharmonic effects in the vibrations give rise to thermal expansion. The long-wavelength (i.e., low-frequency) part of F(ω) is related to elastic properties, e.g., expressed by the elastic constants G (shear modulus), K (bulk modulus), E (Young’s modulus) and ν (Poisson’s ratio), the single-crystal elastic
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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.