High Temperature Resonant Ultrasound Spectroscopy: A Review

High Temperature Resonant Ultrasound Spectroscopy: A Review
Department of Physics and Astronomy, National Center for Physical Acoustics, The University of Mississippi, MS 38677, USA Received 6 August 2010; Accepted 24 November 2010 Academic Editor: Jaan Laane Copyright © 2010 G. Li and J. R. Gladden. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract The measurement of elastic constants plays an important role in condensed matter physics and materials characterization. This paper presents the resonant ultrasound spectroscopy (RUS) method for the determination of elastic constants in a single crystal or amorphous solid. In RUS, the measured resonance spectrum of a properly prepared sample and other information such as geometry, density, and initial estimated elastic constants are used to determine the elastic constants of the material. We briefly present the theoretical background and applications to specific materials; however, the focus of this review is on the technical applications of RUS, especially those for high-temperature measurements. 1. Introduction: Elastic Constants and Measurement Methods The elastic response of a solid is determined by the full set of independent elastic constants, which are a measure of the material’s interatomic forces and, specifically, the curvature of the potentials around the equilibrium spacing. Elastic constants are a sensitive probe into the atomic environment of a crystal lattice, and changes in elastic constants are a useful tool for investigating critical phenomenon. Elastic constants are involved in many fundamental phenomena in solid-state physics: they are important parameters in equations of state, lattice dynamics, and phonon spectra; they are also linked to other quantities in thermodynamics such as coefficient of thermal expansion, Debye temperature, Grüneisen parameter, and so on. The measurement of elastic constants is of interest not only to engineers and materials scientists, but also to researchers in many areas of fundamental and applied physics. Numerous theoretical and experimental methods are available for evaluating elastic constants. If the equation for the interatomic potential is known, the elastic constant can be calculated from first principles. The results from ab initio calculations for some crystalline solids with known atomic structures and potentials are usually in reasonable agreement with the experimental data. For simple, accurate and efficient determination of elastic properties of materials, various ultrasonic and nonultrasonic experimental techniques are often preferred. Many experimental techniques [1–3] have been developed and employed for measuring the elastic constants of different types of materials. The selection of technique depends on factors such as the composition, structural characteristic and size of the sample, desired accuracy of measurement, and, of course, the availability of equipment and expertise. Various common techniques can be roughly categorized according to the major parameters that are evaluated or the primary equipment that are used (Table 1). The accuracy of a given experimental method depends on many factors other than the fundamental nature of the method itself. However, frequencies are one of the easiest quantities to measure, and resonance methods typically depend on many more frequency measurements than variables being determined. For these reasons, RUS has emerged as one of the most accurate methods for elastic constant measurements.

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