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Vibrational Thermodynamics of Materials



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Vibrational Thermodynamics of Materials Brent Fultz California Institute of Technology W M Keck Laboratory Pasadena CA 91125 USA July 6 2009 Abstract The literature on vibrational thermodynamics of materials is reviewed The emphasis is on metals and alloys especially on the progress over the last decade in understanding differences in the vibrational entropy of different alloy phases and phase transformations Some results on carbides nitrides oxides hydrides and lithium storage materials are also covered Principles of harmonic phonons in alloys are organized into thermodynamic models for unmixing and ordering transformations on an Ising lattice and extended for non harmonic potentials Owing to the high accuracy required for the phonon frequencies quantitative predictions of vibrational entropy with analytical models prove elusive Accurate tools for such calculations or measurements were challenging for many years but are more accessible today Ab initio methods for calculating phonons in solids are summarized The experimental techniques of calorimetry inelastic neutron scattering and inelastic x ray scattering are explained with enough detail to show the issues of using these methods for investigations of vibrational thermodynamics The explanations extend to methods of data analysis that affect the accuracy of thermodynamic information It is sometimes possible to identify the structural and chemical origins of the differences in vibrational entropy of materials and the number of these assessments is growing There has been considerable progress in our understanding of the vibrational entropy of mixing in solid solutions compound formation from pure elements chemical unmixing of alloys order disorder transformations and martensitic transformations Systematic trends are available for some of these phase transformations although more examples are needed and many results are less reliable at high temperatures Nanostructures in materials can alter sufficiently the



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