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Ultrasonic spectroscopy is a technique widely used in solid-state physics, materials science, and geology that utilizes acoustic waves to determine fundamental physical properties of materials, such as their elasticity and mechanical energy dissipation. This book provides complete coverage of the main issues relevant to the design, analysis, and interpretation of ultrasonic experiments. Topics including elasticity, acoustic waves in solids, ultrasonic loss, and the relation of elastic constants to thermodynamic potentials are covered in depth. Modern techniques and experimental methods including resonant ultrasound spectroscopy, digital pulse-echo, and picosecond ultrasound are also introduced and reviewed. This self-contained book includes extensive background theory and is accessible to students new to the field of ultrasonic spectroscopy, as well as to graduate students and researchers in physics, engineering, materials science, and geophysics.


'The perfect textbook for students and teachers who want to understand the use of non-destructive acoustic techniques in the evaluation of material properties in general, and phase transitions in particular. Each subject covered in the book is given a rigorous mathematical treatment, accompanied by relevant references. This book will be especially valuable for advanced undergraduate-graduate level students, and for practicing scientists.'

Ricardo B. Schwarz - Los Alamos National Laboratory, US National Academy of Engineering

'We expected a top-quality treatment from Professor Leisure, and we received one. The author shows a keen eye for breadth - depth balance and a critical eye for including all essentials and excluding bothersome details. The book blends basic principles with fresh research topics successfully and Professor Leisure achieves a harmonious, well-integrated, balanced mix of measurement and theory and range of topics. Students will enjoy this easy-reading book and old-hands will want this book on their shelf.'

Hassel Ledbetter - Engineering and Applied Sciences College, University of Colorado

‘The book covers expected subjects such as continuum mechanics of elastic solids, the acoustic approximation and the elastic constants, experimental methods, and ultrasound attenuation … [this review recommends] this book for anyone entering the field of ultrasonics in solids, the book should be acquired as a ready reference by scientists and engineers who have already been working the field.’

J. D. Maynard Source: The Journal of the Acoustical Society of America

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[1] R., Truell, C., Elbaum, and B.B., Chick. Ultrasonic methods in solid state physics. Academic Press, 1969.
[2] R.T., Beyer and S.V., Letcher. Physical ultrasonics. Academic Press, 1969.
[3] B., Lüthi. Physical acoustics in the solid state. Springer, 2005.
[4] J.F., Nye. Physical properties of crystals. Oxford, 1979.
[5] L.D., Landau and E.M., Lifshitz. Theory of elasticity. 3rd ed. Butterworth Heinemann, 1986.
[6] F.I., Fedorov. Theory of elastic waves in crystals. Oxford, 1986.
[7] D.C., Wallace. Thermodynamics of crystals. Wiley, 1972.
[8] R.L., Melcher. “Physical acoustics.” In: ed. by W.P., Mason and R.N., Thurston Vol. XII. Academic Press, 1976. Chap. 1.
[9] G., Arfken. Mathematical methods for physicists. 3rd ed. Academic Press, 1985.
[10] K.D., Swartz and A.V., Granato. “Experimental test of the Laval Raman Viswanathan theory of elasticity.” In: J. Acoust. Soc. Amer 38 (1965), p. 824.
[11] B.A., Auld. Acoustic fields and waves in solids. Second. Vol. 1. Krieger, 1990.
[12] W.A., Wooster. A textbook on crystal physics. Cambridge University Press, 1938.
[13] W., Voigt. Lehrbuch der kristallphysik. Johnson Reprint Corporaton, 1966.
[14] M., Levy. “Handbook of Elastic Properties of Solids, Liquids, and Gases.” In: ed. by M., Levy, H.E., Bass, and R.R., Stern. Vol. II. Academic Press, 2001. Part 1, Chapter 1.
[15] D.B., Litvin. “The icosahedral point groups.” In: Acta Cryst. 47 (1991), p. 70.
[16] P.S., Spoor. “Elastic properties of novel materials using PVDF film and resonance ultrasound spectroscopy.” PhD thesis. Pennsylvania State University, 1997.
[17] M.A., Chernikov, H.R., Ott, A., Bianchi, A., Migliori, and T.W., Darling. “Elastic moduli of a single quasicrystal of decagonal Al-Ni-Co: Evidence for transverse elastic isotropy.” In: Phys. Rev. Lett 80 (1998), p. 321.
[18] D., Levine, T.C., Lubensky, S., Ostlund, S., Ramaswamy, P.J., Steinhardt, and J., Toner. “Elasticity and dislocations in pentagonal and icosahedral quasicrystals.” In: Phys. Rev. Lett. 54 (1985), p. 1520.
[19] Y., Ishii. “Phason softening and structural transitions in icosahedral quasicrystals.” In: Phys. Rev. B 45 (1992), p. 5228.
[20] M., Oxborrow and C.L., Henley. “Random square-triangle tilings.” In: J. Non-Cryst. Solids 153 (1993), p. 210.
[21] M., Oxborrow and C.L., Henley. “Random square-triangle tilings: A model for twelvefold-symmetric quasicrystals.” In: Phys. Rev. B 48 (1993), p. 6966.
[22] K., Foster, S.L., Fairburn, R.G., Leisure, S., Kim, D., Balzar, G., Alers, and H., Ledbetter. “Acoustic study of texture in polycrystalline brass.” In: Acoust. Soc. Amer 105 (1999), pp. 2663–2668.
[23] R., Lakes. “Foam structures with a negative poissons ratio.” In: Science 235 (1987), p. 1038.
[24] R.F.S., Hearmon. An introduction to applied anisotropic elasticity. Oxford University Press, 1961.
[25] S.P., Timoshenko and J.N., Goodier. Theory of elasticity. McGraw-Hill, 1970.
[26] S.G., Lekhnitskii. Theory of elasticity of an anisotropic elastic body. Holden-Day, 1963.
[27] G., Simmons and H., Wang. Single crystal elastic constants and calculated aggregate properties: a handbook. MIT Press, 1971.
[28] H., Ledbetter. “Handbook of elastic properties of solids, liquids, and gases.” In: ed. by M., Levy and L., Furr. Vol. III. Academic Press. Chap. 11, p. 313.
[29] W.C., Cady. Piezoelectricity. Vol. One. Dover, 1964.
[30] J.R., Neighbours and G.E., Schacher. “Determination of elastic constants from soundvelocity measurements in crystals of general symmetry.” In: J. Appl. Phys. 38 (1967), p. 5366.
[31] H., Ledbetter, R.G., Leisure, A., Migliori, J., Betts, and H., Ogi. “Low-temperature elastic and piezoelectric constants of paratellurite (α-TeO2).” In: J. Appl. Phys 96 (2004), p. 6201.
[32] E.B., Christoffel. “Uber die Fortpflanzung von Stossen durch elastische feste Korper.” In: Ann. Mat. Pura Appl. 8 (1877), p. 193.
[33] D., Royer and E., Dieulesaint. Elastic waves in solids I. Springer, 1996.
[34] E.S., Fisher and C.J., Renken. “Single-crystal elastic moduli and the hcp bcc transformation in Ti, Zr, and Hf.” In: Phys. Rev. 135 (1964), A482.
[35] M.H., Manghnani. “Elastic constants of single-crystal rutile under pressures to 7.5 kilobars.” In: J. Geophy. Res. 74 (1969), p. 4317.
[36] W.J., Alton and A.J., Barlow. “Acoustic-wave propagation in tetragonal crystals and measurement of elastic constants of calcium molybate.” In: J. Appl. Physics. 38 (1967), p. 3817.
[37] H.J., McSkimin. “Temperature dependence of the adiabatic elastic moduli of singlecrystal alpha uranium.” In: J. Appl. Phys. 31 (1960), p. 1627.
[38] J.D., Jackson. Classical electrodynamics. Wiley, 1999.
[39] C., Kittel. Introduction to solid state physics. 8th edn. Wiley, 2005.
[40] N.W., Ashcroft and N.D., Mermin. Solid state physics. Saunders, 1976.
[41] M.P., Marder. Condensed matter physics. Wiley, 2010.
[42] G., Burns. Solid state physics. Academic Press, 1985.
[43] M., Born and K., Huang. Dynamical theory of crystal lattices. Clarendon Press, 1954.
[44] H., Böttger. Principles of the theory of lattice dynamics. Physik-Verlag, 1983.
[45] M.T., Dove. Introduction to lattice dynamics. Cambridge University Press, 1993.
[46] B.T.M., Willis and A.W., Pryor. Thermal vibratons in crystallography. Cambridge University Press, 1975.
[47] W., Cochran. “Lattice vibrations.” In: Rep. Prog. Phys. 26 (1963), p. 1.
[48] F., Herman. “Lattice vibrational spectrum of germanium.” In: J. Phys. Chem. Solids. 8 (1959), p. 405.
[49] G.P., Srivastava. The physics of phonons. Taylor Francis Group, 1990.
[50] Y.-L, Chen and D.-P., Yang. Mössbauer effect in lattice dynamics. Wiley-VCH, 2007.
[51] M., Ortiz and R., Phillips. “Advances in applied mechanics.” In: ed. by E. van der, Giessen and T.Y., Wu. Vol. 36. Academic Press, 1999. Chap. Nanomechanics of defects in solids.
[52] S.K., Sinha. “Lattice dynamics of copper.” In: Phys. Rev. 143 (1966), p. 422.
[53] J.L., Warren, J.L., Yarnell, G., Dolling, and R.A., Cowley. “Lattice dynamics of diamond.” In: Phys. Rev. 158 (1967), p. 805.
[54] M.E., Straumanis and L.S., Yu. “Lattice parameters, densities, expansion coefficients and perfection of structure of Cu and Cu-In alpha phase.” In: Acta Cryst. A25 (1969), p. 676.
[55] W.C., Overton Jr. and J., Gaffney. “Temperature variation of the elastic constants of cubic elements. I. Copper.” In: Phys. Rev. 98 (1955), p. 969.
[56] C., Kittel and H., Kroemer. Thermal physics. 2nd ed. Freeman, 1980.
[57] F., Reif. Fundamentals of statistical and thermal physics. McGraw Hill, 1965.
[58] J.P., Sethna. Entropy, order parameters, and complexity. Oxford University Press, 2006.
[59] A., Einstein. “The Planck theory of radiation and the theory of specific heat.” In: Ann. d. Physik 22 (1906), p. 180.
[60] P., Debye. “The theory of specific warmth.” In: Ann. d. Physik 39 (1912), p. 789.
[61] D.K., Hsu and R.G., Leisure. “Elastic constants of palladium and beta-phase palladium hydride between 4 and 300-K.” In: Phys. Rev. B 20 (1979), p. 1339.
[62] M., Moss, P.M., Richards, E.L., Venturini, J.H., Grieske, and E.J., Graeber. “Hydrogen contribution to the heat capacity of single phase, face centered cubic scandium deuteride.” In: J. Chem. Phys. 84 (1986), p. 956.
[63] L.A., Nygren and R.G., Leisure. “Elastic constants of β-phase PdHx over the temperature range 4–300 K.” In: Phys. Rev. B 37 (1988), p. 6482.
[64] M.A., Omar. Elementary solid state physics. Addison Wesley, 1975.
[65] O.L., Anderson. “A simplified method for calculating Debye temperatures from elastic constants.” In: J. Phys. Chem. Solids 24 (1963), p. 909.
[66] R.A., Robie and J.L., Edwards. “Some Debye temperatures from single-crystal elastic constant data.” In: J. Appl. Phys. 37 (1966), p. 2659.
[67] J.J., Adams. “Elastic constants of monocrystal iron form 3 to 500K.” MA thesis. Physics Dept., Colorado State Univ., Fort Collins, CO USA, 2006.
[68] J.D., Maynard. “The use of piezoelectric film and ultrasound resonance to determine the complete elastic tensor in one measurement.” In: J. Acoust. Soc. Am. 91 (1992), p. 1754.
[69] D.I., Bolef and J.C., Miller. “Physical acoustics.” In: ed. by W.P., Mason and R.N., Thurston. Vol. VIII. Academic Press, 1971. Chap. 3.
[70] N.F., Foster. “Cadium sulphide evaporated-layer transducers.” In: Proc. IEEE 53 (1965), p. 1400.
[71] J. de, Klerk. “Physical acoustics”. In: ed. by W.P., Mason. Vol. IVA. Academic Press, 1966. Chap. 5.
[72] R.G., Leisure and D.I., Bolef. “CW microwave spectrometer for ultrasonic paramagnetic resonance.” In: Rev. Sci. Instrum. 39 (1968), p. 199.
[73] H.A., Spetzler, G., Chen, S., Whitehead, and I.C., Getting. “A new ultrasonic interferometer for the determination of equation of state parameters of sub-millimeter single crystals.” In: PAGEOPH 141 (1993), p. 341.
[74] Q., Zhou, S., Lau, D., Wu, and K., Shung. “Piezoelectric films for high frequency ultrasonic transducers in biomedical applications.” In: Prog. Mater. Sci. 56 (2011), p. 139.
[75] E.P., Pakadakis and T.P., Lerch. “Handbook of elastic properties of solids, liquids and gases.” In: ed. by M., Levy, H.E., Bass, and R., Stern. Vol. I. Academic Press, 2001. Chap. 2, p. 39.
[76] S., Eros and J.R., Reitz. “Elastic constants by the ultrasonic pulse echo method.” In: J. Appl. Phys. 29 (1958), p. 683.
[77] H.J., McSkimin. “Pulse superposition method for measuring ultrasonic wave velocities in solid.” In: J. Acoust. Soc. Am. 33 (1961), p. 12.
[78] H.J., McSkimin and P., Andreatch. “Analysis of the pulse superposition method for measuring ultrasonic wave velocities as a function of temperature and pressure.” In: J. Acoust. Soc. Am. 34 (1962), p. 609.
[79] E.P., Papadakis. “Ultrasonic phase velocity by pulse-echo-overlap method incorporating diffraction phase corrections.” In: J. Acoust. Soc. Amer. 42 (1967), p. 1045.
[80] C., Pantea, D.G., Rickel, A., Migliori, R.G., Leisure, J.Z., Zhang, Y.S., Zhao, S., El-Khatib, and B.S., Li. “Digital ultrasonic pulse-echo overlap system and algorithm for unambiguous determination of pulse transit time.” In: Rev. Sci Instrum. 76 (2005), p. 114902.
[81] A.E., Petrova and S.M., Stishov. “A digital technique for measuring the velocity and attenuation of sound.” In: Instrum. Exp. Tech. 52 (2009), p. 609.
[82] H., Niesler and I., Jackson. “Pressure derivatives of elastic wave velocities from ultrasonic interferometric measurements on jacketed polycrystals.” In: J. Acoust. Soc. Am. 86 (1989), p. 1573.
[83] D.I., Bolef and M., Menes. “Measurement of elastic constants of RbBr, RbI, CsBr, and CsI by an ultrasonic cw resonance technique.” In: J. Appl. Phys. 31 (1960), p. 1010.
[84] D.I., Bolef. “Elastic constants of single crystals of the bcc transition elements V, Nb, and Ta.” In: J. Appl. Phys. 32 (1961), p. 100.
[85] D.I., Bolef and J.D., Klerk. “Anomalies in the elastic constants and thermal expansion of chromium single crystals.” In: Phys. Rev. 129 (1963), p. 1063.
[86] D.I., Bolef and M., Menes. “Nuclear magnetic resonance acoustic absorption in KI and KBr.” In: Phys. Rev. 114 (1959), p. 1441.
[87] D.I., Bolef. “Physical acoustics.” In: ed. by W.P., Mason. Vol. IVA. Academic Press, 1966. Chap. 3.
[88] R.G., Leisure and D.I., Bolef. “Temperarure dependence of ultrasonic paramagnetic resonance in MgO.Fe2+.” In: Phys. Rev. Lett. 19 (1967), p. 957.
[89] W.C., Cady. Piezoelectricity. Vol. Two. Dover, 1964.
[90] A.S., Nowick and B.S., Berry. Anelastic relaxation in crystalline solids. Academic Press, 1972.
[91] W., Hermann and H.-G., Sockel. “Handbook of elastic properties of solids, liquids and gases.” In: ed. by M., Levy, H.E., Bass, and R.R., Stern. Vol. I. Academic Press, 2001. Chap. 13.
[92] I., Ohno.Free vibration of a rectangular parallelepiped crystal and its application to determination of elastic constants of orthorhombic crystals.” In: J. Phys. Earth 24 (1976), p. 355.
[93] A., Migliori, J.L., Sarrao, W.M., Visscher, T.M., Bell, M., Lei, Z., Fisk, and R.G., Leisure. “Resonant ultrasound spectroscopic techniques for measurement of the elastic moduli of solids.” In: Physica B: Conden. Matt. 183 (1993), p. 1.
[94] A., Migliori and J.L., Sarrao. Resonant ultrasound spectroscopy. Wiley, 1997.
[95] A., Migliori and J.D., Maynard. “Implementation of a modern resonant ultrasound spectroscopy system for the measurement of the elastic moduli of small solid specimens.” In: Rev. Sci. Instrum. 76 (2005), p. 121301.
[96] R.G., Leisure and F.A., Willis. “Resonant ultrasound spectroscopy.” In: J. Condens. Matter 9 (1997), p. 6001.
[97] H., Ekstein and T., Schiffman.Free Vibrations of Isotropic Cubes and Nearly Cubic Parallelepipeds.” In: J. Appl. Phys. 27 (1956), p. 405.
[98] R., Holland and E.P. Eer, Nisse. “Variational evaluation of admittances of multielectroded 3-dimensional piezoelectric structures.” In: IEEE Trans. Sonics Ultrasonics SU-15 (1968), p. 119.
[99] H.H., Demarest, Jr. “Cube resonance method to determine the elastic constants of solids.” In: J. Acoust. Soc. Am. 49 (1971), p. 768.
[100] P., Heyliger, A., Jilani, H., Ledbetter, R.G., Leisure, and C.-L., Wang. “Elastic constants of isotropic cylinders using resonant ultrasound.” In: J. Acoust. Soc. Am. 94 (1993), p. 1482.
[101] W.M., Visscher, A., Migliori, T.M., Bell, and R.A., Reinert. “On the normal modes of free vibrations of inhomogeneous and anisotropic elastic objects.” In: J. Acoust. Soc. Am. 90 (1991), p. 2154.
[102] H., Goldstein. Classical mechanics. Addison-Wesley, 1959.
[103] E.P., Eer Nisse.Resonances of 1-dimensional composite piezoelectric and elastic structures.” In: IEEE Trans. Sonics Ultrasonics SU-14 (1967), p. 59.
[104] W.H., Press, B.P., Flannery, S.A., Teukolsky, and W.T., Vetterling. Numerical recipes. Cambridge University Press, 1986.
[106] J.R., Taylor. Classical mechanics. University Science Books, 2005.
[107] J.B., Mehl. “Analysis of resonance standing-wave measurements.” In: J. Acoust. Soc. Am. 64 (1978), p. 1523.
[108] R.G., Leisure, K., Foster, J.E., Hightowoer, and D.S., Agosta. “Internal friction studies by resonant ultrasound spectroscopy.” In: Mater. Sci. Eng. A 370 (2004), p. 34.
[109] C., Thomsen, J., Strait, Z., Vardeny, H.J., Maris, J., Tauc, and J.J., Hauser. “Coherent phonon generation and detection by picosecond light pulses.” In: Phys. Rev. Lett. 53 (1984), p. 989.
[110] C., Thomsen, H.T., Grahn, H.J., Maris, and J., Tauc. “Surface generation and detection of phonons by picosecond light pulses.” In: Phys. Rev. B 34 (1986), p. 4129.
[111] H.T., Grahn, H.J., Maris, and J., Tauc. “Picosecond ultrasonics.” In: IEEE J. Quantum Electron. 25 (1989), p. 2562.
[112] G.L., Eesley, B.M., Clemens, and C.A., Paddock. “Generation and detection of picosecond acoustic pulses in thin metal films.” In: Appl. Phys. Lett. 50 (1987), p. 717.
[113] O.B., Wright and K., Kawashima. “Coherent phonon detection from ultrafast surface vibrations.” In: Phys. Rev. Lett. 1668 (1992), p. 2029.
[114] T.C., Zhu, H.J., Maris, and J., Tauc. “Attenuation of longitudinal-acoustic phonons in amorphous SiO2 at frequencies up to 440 GHz.” In: Phys. Rev. B 44 (1991), p. 4281.
[115] C., Thomsen, H.T., Grahn, H.J., Maris, and J., Tauc. “Picosecond interferometric technique for study of phonons in the Brillouin frequency range.” In: Optics Commun. 60 (1986), p. 55.
[116] A., Devos and R., Côte. “Strong oscillations detected by picosecond ultrasonics in silicon: Evidence for an electronic-structure effect.” In: Phys. Rev. B 70 (2004), p. 125208.
[117] P., Emery and A., Devos. “Strong oscillations detected by picosecond ultrasonics in silicon: Evidence for an electronic-structure effect.” In: Appl. Phys. Lett. 89 (2006), p. 191904.
[118] A., Devos, M., Foret, S., Ayrinhac, P., Emery, and B., Rufflé. “Hypersound damping in vitreous silica measured by picosecond acoustics.” In: Phys. Rev. B 77 (2008), 100201.
[119] R., Côte and A., Devos. “Refractive index, sound velocity and thickness of thin transparent films from multiple angles picosecond ultrasonics.” In: Rev. Sci. Instrum. 76 (2005), p. 053906.
[120] H., Ogi, T., Shagawa, N., Nakamura, M., Hirao, H., Okada, and N., Kihara. “Elastic constant and Brillouin oscillations in sputtered vitreous SiO2 thin films.” In: Phys. Rev. B 78 (2008), p. 134204.
[121] A., Nagakubo, H., Ogi, H., Ishida, M., Hirao, T., Yokoyama, and T., Nisihara. “Temperature behavior of sound velocity of fluorine-doped vitreous silica thin films studied by picosecond ultrasonics.” In: J. Appl. Phys. 118 (2015), p. 014307.
[122] T., Dehoux and B., Audoin. “Non-invasive optoacoustic probing of the density and stiffness of single biological cells.” In: J. Appl. Phys. 112 (2012), p. 124702.
[123] F., Pérez-Coda, R.J., Smith, E., Moradi, L., Marques, K.F., Webb, and M., Clark. “Thin-film optoacoustic transducers for subcellular Brillouin oscillation imaging of individual biological cells.” In: Appl. Opt. 54 (2015), p. 8388.
[124] K., Shinokita, K., Reimann, M., Woerner, T., Elsaesser, R., Hey, and C., Flytzanis. “Strong amplification of coherent acoustic phonons by intraminiband currents in a semiconductor superlattice.” In: Phys. Rev. Lett. 116 (2016), p. 075504.
[125] H., Ledbetter. “Materials at low temperatures.” In: ed. by R.P., Reed and A.F., Clark. American Society for Metals, 1983. Chap. Elastic properties, pp. 1–45.
[126] A.B., Bhatia. Ultrasonic absorption. Clarendon Press, 1967.
[127] C.Y., Ho and R.E., Taylor. Thermal expansion of solids. ASM International, 1998.
[128] VASP, The Vienna ab initio simulation package, is available at
[129] Quantum Espresso is available at
[130] R., Arroyave, D., Shin, and Z.-K., Liu. “Ab initio thermodynamic properties of stoichiometric phases in the NiAl system.” In: Acta Mater. 53 (2005), p. 1809.
[131] J.A., Garber and A.V., Granato. “Theory of the temperature dependence of secondorder elastic constants in cubic materials.” In: Phys. Rev. B 11 (1975), p. 3990.
[132] G., Steinle-Neumann, L., Stixrude, and R.E., Cohen. “First-principles elastic constants for the hcp transition metals Fe, Co, and Re at high pressure.” In: Phys. Rev. B 60 (1999), p. 791.
[133] R., Golesorkhtabar, P., Pavone, J., Spitaler, P., Puschnig, and C., Drax. “ElaStic: a tool for calculating second-order elastic constants from first principles.” In: Comput. Phys. Commun. 184 (2013), p. 1861.
[134] H., Ledbetter. “Sound velocities, elastic constants: temperature dependence.” In: Mater. Sci. Eng., A 442 (2006), p. 31.
[135] E.I., Isaev, S.I., Simak, A.S., Mikhaylushkin, Yu. Kh., Vekilov, E. Yu., Zarechnaya, L., Dubrovinsky, N., Dubrovinskaia, M., Merlini, M., Hanfland, and I.A., Abrikosov.Impact of lattice vibrations on equation of state of the hardest boron phase.” In: Phys. Rev. B 83 (2011), p. 132106.
[136] G., Liebfried and W., Ludwig. “Solid state physics.” In: ed. by F., Sietz and D., Turnbull. Vol. 12. Academic Press, 1961, p. 276.
[137] S., Shang, Y., Wang, and Z.K., Liu. “First-principles calculations of phonon and thermodynamic properties in the boron-alkaline earth metal binary systems: B-Ca, B-Sr, and B-Ba.” In: Phys. Rev. B 75 (2007), p. 024302.
[138] Y., Wang, J.J., Wang, H. Zhang, V.R., Manga, S.L., Shang, L.-Q., Chen, and Z.-K., Liu. “A first-principles approach to finite temperature elastic constants.” In: J. Phys. Condens. Matter 22 (2010), p. 225404.
[139] K., Kadas, L., Vitos, R., Ahuja, B., Johansson, and J., Kollar. “Temperature dependent elastic properties of alpha beryllium from first principles.” In:Phys. Rev. B 76 (2007), p. 235109.
[140] W.J., Golumbfskie, R., Arroyave, D., Shin, and Z.-K., Liu. “Finite-temperature thermodynamic and vibrational properties of Al-Ni-Y compounds via first-principles calculations.” In: Acta Mater. 54 (2006), p. 2291.
[141] L.D., Landau and E.M., Lifshitz. Statistical physics. Pergamon Press, 1980.
[142] M., Sob, M., Friak, D., Legut, J., Fiala, and V., Vitek. “The role of ab initio electronic structure calculations in studies of the strength of materials.” In: Mater. Sci. Eng. A387 (2004), p. 148.
[143] A., Wang, S.-L., Shang, M., He, Y., Du, L., Chen, R., Zhang, D., Chen, B., Fan, F., Meng, and Z.-K., Liu. “Temperature-dependent elastic stiffness constants of fcc-based metal nitrides from first-principles calculations.” In: J. Mater. Sci. 49 (2014), p. 424.
[144] D.C., Wallace. “Thermoelasticity of stressed materials and comparison of various elastic constants.” In: Phys. Rev. 162 (1967), p. 776.
[145] A.F., Jankowski and T., Tsakalakos. “The effect of strain on the elastic constants of noble metals.” In: J.Phys, F: Met. Phys 15 (1985), p. 1279.
[146] F., Birch. “Finite elastic strain of cubic crystals.” In: Phys. Rev. 71 (1947), p. 809.
[147] Y., Hiki, J.F., Thomas Jr., and A.V., Granato. “Anharmonicity in noble metals: some thermal properties.” In: Phys. Rev. 153 (1967), p. 764.
[148] K., Brugger. “Generalized Gruneisen parameters in the anisotroyic Debye model.” In: Phys. Rev. 137 (1965), A1826.
[149] Z., Wu and R.M., Wentzcovitch. “Quasiharmonic thermal elasticity of crystals: an analytical approach.” In: Phys. Rev. B. 83 (2011), p. 184115.
[150] D.J., Safarik and R.B., Schwarz. “Evidence for highly anharmonic low-frequency vibrational modes in bulk amorphous Pd40Cu40P20.” In: Phys. Rev. B 80 (2009), p. 094109.
[151] A, Migliori, H., Ledbetter, R.G., Leisure, C., Pantea, and J.B., Betts. “Diamonds elastic stiffnesses from 322 K to 10 K.” In: J. Appl. Phys. 104 (2008), p. 053512.
[152] H.S., Robertson. Statistical thermophysics. Prentice Hall, 1993.
[153] B.T., Bernstein. “Electron contribution to the temperature dependence of the elastic constants of cubic metals. I. Normal metals.” In: Phys. Rev. 132 (1963), p. 50.
[154] G.A., Alers. “Physical acoustics.” In: ed. by W.P., Mason. Vol. IV Part A. Academic Press, 1966. Chap. 7.
[155] Y.P., Varshni. “Temperature dependence of the elastic constants.” In: Phys. Rev. B 2 (1970), p. 3952.
[156] H., Ledbetter. “Relationship between bulk-modulus temperature-dependence and thermal expansivity.” In: Phys. Stat. Solidi B 181 (1994), p. 81.
[157] P., Toledano and V., Dmitriev. Reconstructive phase transitions. World Scientific, 1996.
[158] J.-C., Toledano and P., Toledano. Landau theory of phase transitions. World Scientific, 1987.
[159] W., Rehwald. “Study of structural phase-transitions by means of ultrasonic experimets.” In: Advances in Physics 22 (1973), p. 721,
[160] M.A., Carpenter and E.K.H., Salje. “Elastic anomalies in minerals due to structural phase transitions.” In: Eur. J. Mineral. 10 (1998), p. 693.
[161] F., Cordero, F., Trequattrini, V.B., Barbeta, R.F., Jardim, and M.S., Torikachvili.Anelastic spectroscopy study of the metal-insulator transition of Nd1-xEuxNiO3.” In: Phys. Rev. B 84 (2011), p. 125127.
[162] A.V., Granato, K.L., Hultman, and K.-F., Huang. “Ultrasonic response to two and four level quantum systems.” In: J. Physique Colloque C10 (1985), pp. C10–C23.
[163] C., Zener. “Stress induced preferential orientation of pairs of solute atoms in metallic solid solution.” In: Phys. Rev. 71 (1947), p. 34.
[164] F.M., Mazzolai, P.G., Bordoni, and F.A., Lewis. “Elastic energy-dissipation effects in alpha+beta and beta-phase composition ranges of the palladium-hydrogen system.” In: J. Phys. F: Met. Phys. 11 (1981), p. 337.
[165] R.G., Leisure, T., Kanashiro, P.C., Riedi, and D.K., Hsu. “Hydrogen motion in singlecrystal palladium hydride as studied ultrasonically.” In: Phys. Rev. B 27 (1983), p. 4872.
[166] J.L., Snoek. “Mechanical after effect and chemical constitution.” In: Physica 6 (1939), p. 591.
[167] R.G., Leisure, S., Kern, F.R., Drymiotis, H., Ledbetter, A., Migliori, and J.A., Mydosh. “Complete elastic tensor through the first-order transformation in U2Rh3Si5.” In: Phys. Rev. Lett. 95 (2005), p. 075506.
[168] B., Lüthi, M.E., Mullen, and E., Bucher. “Elastic constants in singlet ground-state Systems: PrSb and Pr.” In: Phys. Rev. Lett. 31 (1973), p. 95.
[169] R.S., Lakes. Viscoelastic solids. CRC Press, 1998.
[170] M., O'Donnell, E.T., Jaynes, and J.G., Miller. “Kramers-Kronig relationship between ultrasonic-attenuation and phase-velocity.” In: J. Acoust. Soc. Am. 69 (1981), p. 696.
[171] V., Mangulis. “Kramers-Kronig or dispersion relations in acoustics.” In: J. Acoust. Soc. Am. 36 (1964), p. 211.
[172] V.L., Ginzberg. “Concerning the general relationship between absorption and dispersion of sound waves.” In: Akust.Zh. 1 (1955). English translation in Soviet Phys. Acoust. 1, 32 (1957), p. 32.
[173] J.P., Wittmer, H., Xu, O., Benzerara, and J., Baschnagel. “Fluctuation-dissipation relation between shear stress relaxation modulus and shear stress autocorrelation function revisited.” In: Molecular Physics 113 (2015), p. 2881.
[174] D., Chandler. Introduction to modern statistical mechanics. Oxford University Press, 1987.
[175] A.A., Gusev, M.M., Zeldner, and U.W., Suder. “Fluctuation formula for elastic constants.” In: Phys. Rev. B, Brief Reports 54 (1996), p. 1.
[176] C., Zener. Elasicity and anelasicity of metals. University of Chicago Press, 1948.
[177] M., Callens-Raadschelders, R. De, Batist, and R., Gevers. “Debye relaxation equations for a standard linear solid with high relaxation strength.” In: J. Materials Sci. 12 (1977), p. 251.
[178] K., Lücke. “Ultrasonic attenuation caused by thermoelastic heat flow.” In: J. Appl. Phys. 27 (1956), p. 1433.
[179] B.C., Daly, K., Kang, Y., Yang, and D.G., Cahill. “Picosecond ultrasonic measurements of attenuation of longitudinal acoustic phonons in silicon.” In: Phys. Rev. B 80 (2009), p. 174112.
[180] H.E., Bömmel and K., Dransfield. “Excitation and attenuation of hypersonic waves in quartz”. In: Phys. Rev. 117 (1960), p. 1245.
[181] J. de, Klerk. “Behavior of coherent microwave phonons at low temperatures in Al2O3 using vapor-deposited thin-film piezoelectric transducers”. In: Phys. Rev. 139 (1965), A 1635.
[182] S., Stoffels, E., Autizi, R. Van, Hoof, S., Severi, R., Puers, A., Witvrouw, and H.A.C., Tilmans. “Physical loss mechanisms for resonant acoustical waves in boron doped poly-SiGe deposited with hydrogen dilution.” In: J. Appl. Phys. 108 (2010), p. 084517.
[183] L., Landau and G., Rumer. “Uber schallabsorption in festen korpern.” In: Phys. Z. Sowjetunion 11 (1937), p. 18.
[184] P.G., Klemens. “Physical acoustics.” In: ed. by W.P., Mason. Vol. III Part B. Academic Press, 1965. Chap. 5.
[185] H.J., Maris. “Physical acoustics.” In: ed. by W.P., Mason and R.N., Thurston. Vol. VIII. Academic Press, 1971. Chap. 6.
[186] A., Akhieser. “On the absorption of sound in solids.” In: J. Phys. (Moscow) 1 (1939), p. 277.
[187] T.O, Woodruff and H., Ehrenreich. “Absorption of sound in insulators.” In: Phys. Rev. 123 (1961), p. 1553.
[188] H.E., Bömmel.Ultrasonic attenuation in superconducting lead.” In: Phys. Rev. 96 (1954), p. 220.
[189] W.P., Mason.Ultrasonic attenuation due to lattice-electron interaction in normal conducting metals.” In: Phys. Rev. 97 (1955), p. 557.
[190] R.W., Morse.Ultrasonic attenuation in metals by electron relaxation.” In: Phys. Rev. 97 (1955), p. 1716.
[191] A.B., Pippard.Ultrasonic attenuation in metals.” In: Phil. Mag. 46 (1955), p. 1104.
[192] A.B., Pippard.Theory of ultrasonic attenuation in metals and magnetoacoustic oscillations.” In: Proc. Roy. Soc. A 257 (1960), p. 165.
[193] J., Bardeen, L.N., Cooper, and J.R., Schrieffer.Theory of superconductivity.” In: Phys. Rev. 108 (1957), p. 1175.
[194] M., Gottlieb, M., Garbuny, and C.K., Jones.Physical acoustics.” In: ed. by W.P., Mason and R.N., Thurston. Vol. VII. Academic Press, 1970. Chap. 1.
[195] J.A., Rayne and C.K., Jones.Physical, acoustics.” In: ed. by W.P., Mason and R.N., Thurston. Vol. VII. Academic Press, 1970. Chap. 3.
[196] M., Levy. “Physical acoustics.” In: ed. by W.P., Mason and R.N., Thurston. Vol. XX. Academic Press, 1992. Chap. 1.
[197] B.W., Roberts.Physical acoustics.” In: ed. by W.P., Mason. Vol. IV Pt. B. Academic Press, 1968. Chap. 10.
[198] L.R., Testardi and J.H., Condon.Physical acoustics.” In: ed. by W.P., Mason and R.N., Thurston. Vol. VIII. Academic Press, 1971. Chap. 2.
[199] Y., Eckstein. “Ultrasonic attenuation in antimony. 1. Geometric resonance.” In: Phys. Rev. 129 (1963), p. 12.
[200] M.P., Greene, A.R., Hoffman, A. Houghton, and J.J., Quinn.Ultrasonic attenuation in oblique magnetic fields.” In: Phys. Rev. 156 (1967), p. 798.
[201] M.H., Cohen, M.J., Harrison, and W.A., Harrison.Magnetic-field dependence of the ultrasonic attentuation in metals.” In: Phys. Rev. 117 (1960), p. 937.
[202] J.R., Hook and H.E., Hall. Solid state physics. Wiley, 1991.
[203] H.P., Myers. Introductory solid state physics. Taylor and Francis, 1991.
[204] M., Mongy. “Quantum oscillations of ultrasonic attenuation in gold.” In: J. Phys. Chem. Solids 33 (1972), p. 1355.
[205] W.D., Wallace and H.V., Bohm.Quantum oscillations in attenuation of transverse ultrasonic waves in field-cooled chromium.” In: J. Phys. Chem. Solids 29 (1968), p. 721.
[206] A., Granato and K., Lücke. “Theory of mechanical damping due to dislocations.” In: J. Appl. Phys. 27 (1956), p. 583.
[207] T.A., Read.Internal friction of single crystals of copper and zinc.” In: Trans. Am. Inst. Mining Met. Engrs. 143 (1941), p. 30.
[208] J.S., Koehler. Imperfections in nearly perfect crystals. Wiley, 1952.
[209] A.S., Nowick.Internal friction and dynamic modulus of cold-worked metals.” In: J. Appl. Phys. 25 (1954), p. 1129.
[210] A.V., Granato and K., Lücke. “Physical acoustics.” In: ed. by W.P., Mason. Vol. IV Part A. Academic Press, 1966. Chap. 6.
[211] R.M., Stern and A.V., Granato.Overdamped resonance of dislocations in copper.” In: Acta Met. 10 (1962), p. 358.
[212] C., Wert and C., Zener. “Interstitial atomic difusion coefficients.” In: Phys. Rev. 76 (1949), p. 1169.
[213] C.R., Ko, K., Salama, and J.M., Roberts.Effect of hydrogen on the temperaturedependence of the elastic constants of vanadium single crystals.” In: J. Appl. Phys. 51 (1980), p. 1014.
[214] J., Buchholz, J., Völkl, and G., Alefeld. “Anomalously small elastic Curie constant of hydrogen in tantulam.” In: Phys. Rev. Lett. 30 (1973), p. 318.
[215] K., Foster, J.E., Hightower, R.G., Leisure, and A.V., Skripov.Ultrasonic attenuation and dispersion due to hydrogen motion in the C15 Laves-phase compound TaV2Hx.” In: J. Phys.:Condensed Matter 13 (2001), p. 7327.
[216] R.G., Leisure, T. Kanashiro, P.C., Riedi, and D.K., Hsu.An ultrasonic study of stressinduced ordering of hydrogen in single-crystal palladium hydride.” In: J. Phys. F: Met. Phys. 13 (1983), p. 2025.
[217] R.G., Leisure, L.A., Nygren, and D.K., Hsu.Ultrasonic relaxation rates in palladium hydride and palladium deuteride.” In: Phys. Rev. B 33 (1986), p. 8325.
[218] J.O., Fossum and K., Fossum. “Measurements of ultrasonic attenuation and velocity in Verneuil-grown and flux grown SrTiO3.” in: J. Phys. C: Solid State Phys. 18 (1985), p. 5549.
[219] L.D., Landau and I.M., Khalatnikov. In: Sov. Phys. Dokl. 96 (1954), p. 469.
[220] J.O., Fossum.A phenomenological analysis of ultrasound near phase transitions.” In: J. Phys. C: Solid State Phys. 18 (1985), p. 5531.
[221] A., Abragam. The principles of nuclear magnetism. Oxford University Press, 1961.
[222] C.P., Slichter. The principles of magnetic resonancee. Harper and Row, 1963.
[223] R.A., Alpher and R.J., Rubin.Magnetic dispersion and attenuation of sound in conducting fluids and solids.” In: J. Acoust. Soc. Am. 26 (1954), p. 452.
[224] J., Buttet, E.H., Gregory, and P.K., Bailey.Nuclear acoustic resonance in aluminum via coupling to magnetic dipole moment.” In: Phys. Rev. Lett. 23 (1969), p. 1030.
[225] R.G., Leisure, D.K., Hsu, and B.A., Seiber.Nuclear-acoustic-resonance absorption and dispersion in aluminum.” In: Phys. Rev. Lett. 30 (1973), p. 1326.
[226] R., Guermeur, J., Joffrin, A., Levelut, and J., Penne. “Mesure de la variation de la vitesse de phase dune onde ultrasonore se propageant dans un cristal paramagnetique.” In: Phys. Lett. 13 (1964), p. 107.
[227] E.B., Tucker.Physical acoustics.” In: ed. by W.P., Mason. Vol. IV Pt. A. Academic Press, 1966. Chap. 2.
[228] R.C., Zeller and R.O., Pohl.Thermal conductivity and specific heat of noncrystalline solids.” In: Phys. Rev. B 4 (1971), p. 2029.
[229] P.W., Anderson, B.I., Halperin, and C.M., Varma.Anomalous low-temperature thermal properties of glasses and spin glasses.” In: Phil. Mag. 25 (1972), p. 1.
[230] W.A., Phillips.Tunneling states in amorphous solids.” In: J. Low Temp. Phys. 7 (1972), p. 351.
[231] J., Jäckle. “Ultrasonic attenuation in glasses at low temperatures.” In: Z. Physik 257 (1972), p. 212.
[232] P., Doussineau, C., Frénois, R.G., Leisure, A., Levelut, and J.-Y., Prieur. “Amorphouslike acoustical properties of Na doped beta Al2O3.” In: J. Phys (Paris) 41 (1980), p. 1193.
[233] S.N., Coppersmith and B., Golding. “Low-temperature acoustic properties of metallic glasses.” In: Phys. Rev. B 47 (1993), p. 4922.
[234] A.J., Leggett and D.C., Vural.Tunneling two-level systems model of lowtemperature properties of glasses: Are smoking-gun tests possible?” In: J. Phys. Chem. B 117 (2013), p. 12966.
[235] D.R., Queen, X., Liu, J., Karel, T.H., Metcalf, and F., Hellman. “Excess specific heat in evaporated amorphous silicon.” In: Phys. Rev. Lett. 110 (2013), p. 135901.
[236] G.S., Kino. Acoustic waves: devices, imaging and analog signal processing. Prentice- Hall, 1987.
[237] T.F., Hueter and R.H., Bolt. Sonics. Wiley, 1955.
[238] C.G., Montgomery, R.H., Dicke, and E.M., Purcell. Principles of microwave circuits. The Institute of Engineering and Technolog, 1987, p. 67.
[239] E.P., Papadakis.Ultrasonic diffraction loss and phase change in anisoptric materials.” In: J. Acoust. Soc. Am. 40 (1966), p. 863.
[240] E.P., Papadakis.Physical acoustics.” In: ed. by W.P., Mason and R.N., Thurston. Vol. XI. Academic Press, 1975. Chap. 3.
[241] P.R., Saulson.Thermal noise in mechanical experiments.” In: Phys. Rev. D 42 (1990), p. 2437.
[242] J.R., Neighbours and G.A., Alers.Elastic constants of silver and gold.” In: Phys. Rev. 111 (1958), p. 707.
[243] Y.S., Touloukian, R.K., Kirby, R.E., Taylor, and P.D., Desa. Thermophysical properies of matter. Vol. 12. Plenum, 1975.
[244] Y., Hiki and A.V., Granato.Anharmonicity in noble metals; higher order elastic constants.” In: Phys. Rev. 144 (1966), p. 411.
[245] J.M., Lang, Jr. and Y.M., Gupta.Experimental determination of third-order elastic constants of diamond.” In: Phys. Rev. Lett. 106 (2011), p. 125502.
[246] C., Giles, C., Adriano, A.F., Lubambo C., Cusatis I., Mazzaro and M.G., Honnicke.Diamond thermal expansion measurement using transmitted X-ray backdiffraction.” In: J. Synchrotron Radiation 12 (2005), p. 349.
[247] J., Philip and M.A., Breazeale.Third order elastic constants and Grüneisen parameters of silicon and germanium between 3 and 300K.” In: J. Appl. Phys. 54 (1983), p. 752.
[248] K., Salama and G.A., Alers.Third-order elastic constants of copper at low temperature.” In: Phys. Rev. 161 (1967), p. 673.


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