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Elastic Constants and Internal Friction of Advanced Materials

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Book cover Electromagnetic Acoustic Transducers

Part of the book series: Springer Series in Measurement Science and Technology ((SSMST))

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Abstract

Elastic constants are important material parameters not only for designing structures but also for studying thermodynamics of materials. They are determined inversely by measuring free-vibration resonance frequencies of the material, and the EMAR method has been applied for this purpose. By controlling the magnetic force symmetry on the material, a specific vibrational group can be excited and detected, contributing to mode identification. The noncontacting nature of EMAR allows accurate internal friction measurement as well. This chapter shows the mode-selective principle of the EMAR and its application for measuring elastic anelastic coefficients of various materials including metals, composites, ceramics, porous materials, thin films, and piezoelectric materials.

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References

  • Aktas, O., Fan, Z. F., Mohammad, S. N., Botchkarev, A. E., & Morkoç, H. (1996). High temperature characteristics of AlGaN/GaN modulation doped field-effect transistors. Applied Physics Letters, 69, 3872–3874.

    Article  ADS  Google Scholar 

  • Armyanov, S., Vitkova, S., & Blajiev, O. (1997). Internal stress and magnetic properties of electrodeposited amorphous Fe-P alloys. Journal of Applied Electrochemistry, 27, 185–191.

    Article  Google Scholar 

  • Auld, A. B. (1973). Acoustic Fields and Waves in Solids. New York: Wiley.

    Google Scholar 

  • Barmatz, M., & Chen, H. S. (1974). Young’s modulus and internal-friction in metallic glass alloys from 1.5 to 300 K. Physical Review B, 9, 4073–4083.

    Article  ADS  Google Scholar 

  • Bungo, A., Jian, C., Yamaguchi, K., Sawada, Y., Uda, S., & Pisarevsky, Y. (1999). Analysis of surface acoustic wave properties of the rotated Y-cut langasite substrate. Japanese Journal of Applied Physics, 38, 3239–3243.

    Article  ADS  Google Scholar 

  • Davis, B. M., Seidman, D. N., Moreau, A., Ketterson, J. B., Mattson, J., & Grimsditch, M. (1991). Supermodulus effect in Cu/Pd and Cu/Ni superlattices. Physical Review B, 43, 9304–9307.

    Article  ADS  Google Scholar 

  • Debye, P. (1929). Polar Molecules (p. 93). New York: Dover Publications Inc.

    MATH  Google Scholar 

  • Demarest, J. H, Jr. (1971). Cube resonance method to determine the elastic constants of solids. The Journal of the Acoustical Society of America, 49, 768–775.

    Article  ADS  Google Scholar 

  • Dunn, M. L., & Ledbetter, H. (1995a). Elastic moduli of composites reinforced by multiphase particles. Journal of Applied Mechanics, 62, 1023–1028.

    Article  ADS  MATH  Google Scholar 

  • Dunn, M. L., & Ledbetter, H. (1995b). Poisson’s ratio of porous and microcracked solids: Theory and application to oxide superconductors. Journal of Materials Research, 10, 2715–2722.

    Article  ADS  Google Scholar 

  • Dunn, M. L., & Ledbetter, H. (1997). Elastic-plastic behavior of textured short-fiber composites. Acta Materialia, 45, 3327–3340.

    Article  Google Scholar 

  • Eer Nisse, E. P. (1967). Variational method for electroelastic vibration analysis. IEEE Transactions on Sonics and Ultrasonics, SU-14, 153–160.

    Google Scholar 

  • Eshelby, J. D. (1957). The determination of the elastic field of an ellipsoidal inclusion and related problems. Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 241, 376–396.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Fisher, E. S., & Renken, C. J. (1964). Single-crystal elastic moduli and the hcp → bcc transformation in Ti, Zr, and Hf. Physical Review, 135, A482–A494.

    Article  ADS  Google Scholar 

  • Hearmon, R. F. S. (1966). Elastische, piezoelektrische, piezooptische und elektro-optische Konstanten von Kristallen, in Landolt-Börnstein Zahlenwerte und Funktionen aus Naturwissenschaften und Technik, Neue Serie; Gruppe 3, Kristall- und Festkorperphysik (Vol. 1). Berlin: Springer.

    Google Scholar 

  • Heitz, R., Maxim, P., Eckey, L., Thurian, P., Hoffmann, A., Broser, I., Pressel, K., & Meyer, K. (1997). Excited states of Fe3+ in GaN. Physical Review B, 55, 4382–4387.

    Article  ADS  Google Scholar 

  • Heyliger, P. (2000). Traction-free vibration of layered elastic and piezoelectric rectangular parallelepipeds. The Journal of the Acoustical Society of America, 107, 1235–1245.

    Article  ADS  Google Scholar 

  • Holland, R. (1968). Resonant properties of piezoelectric ceramic rectangular parallelepipeds. The Journal of the Acoustical Society of America, 43, 988–997.

    Article  ADS  Google Scholar 

  • Huang, H., & Spaepen, F. (2000). Tensile testing of free-standing Cu, Ag and Al thin films and Ag/Cu Multilayers. Acta Materialia, 48, 3261–3269.

    Article  Google Scholar 

  • Hutson, A. R., & White, D. L. (1962). Elastic wave propagation in piezoelectric semiconductors. Journal of Applied Physics, 33, 40–47.

    Article  ADS  Google Scholar 

  • Hyun, S. K., Murakami, K., & Nakajima, H. (2001). Anisotropic mechanical properties of porous copper fabricated by unidirectional solidification. Materials Science and Engineering A, 299, 241–248.

    Article  Google Scholar 

  • Hyun, S. K., & Nakajima, H. (2001). Fabrication of lotus-structured porous iron by unidirectional solidification under nitrogen gas, In Cellular Metals and Metal Forming Technology (pp. 181–186). Bremen: MIT-Verlag.

    Google Scholar 

  • Ichitsubo, T., Tane, M., Ogi, H., Hirao, M., Ikeda, T., & Nakajima, H. (2002a). Anisotropic elastic constants of lotus-type porous copper: Measurements and micromechanics modeling. Acta Materialia, 50, 4105–4115.

    Article  Google Scholar 

  • Ichitsubo, T., Ogi, H., Hirao, M., Tanaka, K., Osawa, M., Yokokawa, T., et al. (2002b). Elastic constant measurement of ni-base superalloy with the RUS and mode selective EMAR methods. Ultrasonics, 40, 211–215.

    Article  Google Scholar 

  • IEEE. (1984). IEEE Standard on Piezoelectricity, Part II, IEEE Transactions on Sonics and Ultrasonics, SU31.

    Google Scholar 

  • Ilyaev, A., Umarov, B., Shabanova, L., & Dubovik, M. (1986). Temperature dependence of electromechanical properties of LGS crystals. Physica Status Solidi (a), 98, K109–K114.

    Article  ADS  Google Scholar 

  • Inoue, K., & Sato, K. (1998). Propagation characteristics of surface acoustic waves on langasite. Japanese Journal of Applied Physics, 37, 2909–2913.

    Article  ADS  Google Scholar 

  • Isaak, D., Carnes, J., Anderson, O., & Oda, H. (1998). Elasticity of fused silica spheres under pressure using resonant ultrasound spectroscopy. The Journal of the Acoustical Society of America, 104, 2200–2206.

    Article  ADS  Google Scholar 

  • Jansson, S., Dève, H. E., & Evans, A. G. (1991). The anisotropic mechanical properties of a Ti matrix composite reinforced with SiC fibers. Metallurgical Transactions A, 22, 2975–2984.

    Article  ADS  Google Scholar 

  • Johnson, W., Kim, S., & Lauria, D. (2000). Anelastic loss in langatate, In Proceedings of the 2000 IEEE/EIA International Frequency Control Symposium and Exhibition (pp. 186–190).

    Google Scholar 

  • Kaminskii, A., Silvestrova, I., Sarkisov, S., & Denisenko, G. (1983). Investigation of trigonal (La1−xNdx)3Ga5SiO14 crystals. Physica Status Solidi (a), 80, 607–620.

    Article  ADS  Google Scholar 

  • Kim, J. O., Achenbach, J. D., Shinn, M., & Barnett, S. A. (1992). Effective elastic constants and acoustic properties of single-crystal TiN/NbN superlattices. Journal of Materials Research, 7, 2248–2256.

    Article  ADS  Google Scholar 

  • Kinoshita, N., & Mura, T. (1971). Elastic fields of inclusions in anisotropic media. Physica Status Solidi (a), 5, 759–768.

    Article  ADS  Google Scholar 

  • Kröner, E. (1978). Self-consistent scheme and graded disorder in polycrystal elasticity. Journal of Physics F: Metal Physics, 8, 2261–2267.

    Article  ADS  Google Scholar 

  • Kuokkala, V.-T., & Schwarz, R. B. (1992). The use of magnetostriction film transducers in the measurement of elastic moduli and ultrasonic attenuation of solids. Review of Scientific Instruments, 63, 3136–3142.

    Article  ADS  Google Scholar 

  • Ledbetter, H., Dunn, M., & Couper, M. (1995c). Calculated elastic constants of alumina-mullite ceramic particles. Journal of Materials Science, 30, 639–642.

    Article  ADS  Google Scholar 

  • Ledbetter, H., Fortunko, C. M., & Heyliger, P. (1995a). Orthotropic elastic constants of a boron-aluminum fiber-reinforced composite: An acoustic-resonance-spectroscopy study. Journal of Applied Physics, 78, 1542–1546.

    Article  ADS  Google Scholar 

  • Ledbetter, H., Fortunko, C. M., & Heyliger, P. (1995b). Elastic constants and internal friction of polycrystalline copper. Journal of Materials Research, 10, 1352–1353.

    Article  ADS  Google Scholar 

  • Ledbetter, H. (2003). Acoustic Studies of Composite-Materials Interfaces, in Nondestructive Characterization of Materials, Vol. 11, 689–696.

    Google Scholar 

  • Lei, M., Ledbetter, H., & Xie, Y. (1994). Elastic constants of a material with orthorhombic symmetry: An alternative measurement approach. Journal of Applied Physics, 76, 2738–2741.

    Article  ADS  Google Scholar 

  • Leisure, R. G., & Willis, F. A. (1997). Resonant ultrasound spectroscopy. Journal of Physics: Condensed Matter, 9, 6001–6029.

    ADS  Google Scholar 

  • Logan, J., & Ashby, M. F. (1974). Mechanical properties of 2 metallic glasses. Acta Metallurgica, 22, 1047–1054.

    Article  Google Scholar 

  • Look, D. C., Reynolds, D. C., Kim, W., Aktas, Ö., Botchkarev, A., Salvador, A., & Morkoç, H. (1996). Deep-center hopping conduction in GaN. Journal of Applied Physics, 80, 2960–2963.

    Article  ADS  Google Scholar 

  • Maeda, N., Tsubaki, K., Saitoh, T., & Kobayashi, N. (2001). High-temperature electron transport properties in AlGaN/GaN heterostructures. Applied Physics Letters, 79, 1634–1636.

    Article  ADS  Google Scholar 

  • Maier, K., Kunzer, M., Kaufmann, U., Schneider, J., Monemar, B., Akasaki, I., & Amano, H. (1994). Iron acceptors in gallium nitride (GaN). Materials Science Forum, 143–147, 93–98.

    Article  Google Scholar 

  • Malguth, E., Hoffmann, A., Gehlhoff, W., Gelhausen, O., Phillips, M. R., & Xu, X. (2006). Structural and electronic properties of Fe3+ and Fe2+ centers in GaN from optical and EPR esxperiments. Physical Review B, 74, 165202.

    Article  ADS  Google Scholar 

  • Malocha, D., Cunha, M., Adler, E., Smythe, R., Frederick, S., Chou, M., Helmbold, R., & Zhou, Y. (2000). Recent measurements of material constants versus temperature for langatate, langanite and langasite, In Frequency Control Symposium and Exhibition, 2000. Proceedings of the 2000 IEEE/EIA International (pp. 200–205).

    Google Scholar 

  • Mason, W. P. (1965). Effect of impurities and phonon process on the ultrasonic attenuation of germanium, crystal quartz, and silicon, In Physical Acoustics (Vol. 3B, pp. 235–286). New York: Academic Press.

    Google Scholar 

  • Maynard, J. (1992). The use of piezoelectric film and ultrasound resonance to determine the complete elastic tensor in one measurement. The Journal of the Acoustical Society of America, 91, 1754–1762.

    Article  ADS  Google Scholar 

  • Maynard, J. (1996). Resonant Ultrasound Spectroscopy. Physics Today, 49, 26–31.

    Article  ADS  Google Scholar 

  • Migliori, A., & Sarrao, J. (1997). Resonant Ultrasound Spectroscopy. New York: Wiley-Interscience.

    Google Scholar 

  • Migliori, A., Sarrao, J., Visscher, M. W., Bell, T., Lei, M., Fisk, Z., & Leisure, R. (1993). Resonant ultrasound spectroscopy techniques for measurement of the elastic moduli of solids. Physica B: Condensed Matter, 183, 1–24.

    Article  ADS  Google Scholar 

  • Mital, S. K. (1994). Micro-fracture in high-temperature metal-matrix laminates. Composite Science and Technology, 50, 59–70.

    Article  ADS  Google Scholar 

  • Miyazaki, T., Nakamura, K., & Mori, H. (1979). Experimental and theoretical investigations on morphological changes of γ′ precipitates in Ni-Al single-crystals during uniaxial stress-annealing. Journal of Materials Science, 14, 1827–1837.

    Article  ADS  Google Scholar 

  • Mochizuki, E. (1987). Application of group theory to free oscillations of an anisotropic rectangular parallelepiped. Journal of Physics of the Earth, 35, 159–170.

    Article  Google Scholar 

  • Monemar, B., & Lagerstedt, O. (1979). Properties of VPE-grown GaN doped with Al and some iron-group metals. Journal of Applied Physics, 50, 6480–6491.

    Article  ADS  Google Scholar 

  • Moreau, A., Ketterson, J. B., & Huang, J. (1990). Three methods for measuring the ultrasonic velocity in thin films. Materials Science and Engineering A, 126, 149–154.

    Article  Google Scholar 

  • Mori, T., & Tanaka, K. (1973). Average stress in matrix and average elastic energy of materials with misfitting inclusions. Acta Metallurgica, 21, 571–574.

    Article  Google Scholar 

  • Mott, N. F. & Twose, W. D. (1961). The theory of impurity conduction. Advances in Physics, 10(7), 107–163.

    Google Scholar 

  • Mura, T. (1987). Micromechanics of Defects in Solids (2nd ed.). The Hague: Martinus Nijhoff.

    Google Scholar 

  • Nakamura, N., Sakamoto, M., Ogi, H., & Hirao, M. (2012). Elastic constants of langasite and α quartz at high temperatures measured by antenna transmission acoustic resonance. Review of Scientific Instruments, 83, 073901.

    Article  ADS  Google Scholar 

  • Ogi, H., Ledbetter, H., Kim, S., & Hirao, M. (1999a). Contactless mode-selective resonance ultrasound spectroscopy: Electromagnetic acoustic resonance. The Journal of the Acoustical Society of America, 106, 660–665.

    Article  ADS  Google Scholar 

  • Ogi, H., Takashima, K., Ledbetter, H., Dunn, M. L., Shimoike, G., Hirao, M., & Bowen, P. (1999b). Elastic constants and internal friction of an SiC-fiber-reinforced Ti-alloy-matrix crossply composite: Measurement and theory. Acta Materialia, 47, 2787–2796.

    Article  Google Scholar 

  • Ogi, H., Dunn, M., Takashima, K., & Ledbetter, H. (2000). Elastic properties of a SiCf/Ti unidirectional composite: Acoustic resonance measurements and micromechanics predictions. Journal of Applied Physics, 87, 2769–2774.

    Article  ADS  Google Scholar 

  • Ogi, H., Ledbetter, H., Takashima, K., Shimoike, G., & Hirao, M. (2001). Elastic properties of a crossply SiCf/Ti composite at elevated temperatures. Metallurgical and Materials Transactions A: Physical Metallurgy and Materials Science, 32, 425–429.

    Article  Google Scholar 

  • Ogi, H., Shimoike, G., Hirao, M., Takashima, K., & Higo, Y. (2002a). Anisotropic elastic-stiffness coefficients of an amorphous Ni-P film. Journal of Applied Physics, 91, 4857–4862.

    Article  ADS  Google Scholar 

  • Ogi, H., Shimoike, G., Takashima, K., & Hirao, M. (2002b). Measurement of elastic-stiffness tensor of an anisotropic thin film by electromagnetic acoustic resonance. Ultrasonics, 40, 333–336.

    Article  Google Scholar 

  • Ogi, H., Kai, S., Ichitsubo, T., Hirao, M., & Takashima, K. (2003a). Elastic-stiffness coefficients of a silicon-carbide fiber at elevated temperatures: Acoustic spectroscopy and micromechanics modeling. Philosophical Magazine, 83, 503–512.

    Article  ADS  Google Scholar 

  • Ogi, H., Nakamura, N., Sato, K., Hirao, M., & Uda, S. (2003b). Elastic, anelastic, and piezoelectric coefficients of langasite (La3Ga5SiO14): Resonance ultrasound spectroscopy with laser-doppler interferometry. IEEE Transactions on Ultrasonics Ferroelectrics, and Frequency Control, UFFC-50, 553–560.

    Article  Google Scholar 

  • Ogi, H., Kai, S., Ledbetter, H., Tarumi, R., Hirao, M., & Takashima, K. (2004). Titanium’s high-temperature elastic constants through the hcp-bcc phase transformation. Acta Materialia, 52, 2075–2080.

    Article  Google Scholar 

  • Ogi, H., Tsutsui, Y., Nakamura, N., Nagakubo, A., Hirao, M., Imade, M., et al. (2015). Hopping conduction and piezoelectricity in Fe-doped GaN studied by non-contacting resonant ultrasound spectroscopy. Applied Physics Letters, 106, 091901.

    Article  ADS  Google Scholar 

  • Ohno, I. (1976). Free vibration of a rectangular parallelepiped crystal and its application to determination of elastic constants of orthorhombic crystals. Journal of Physics of the Earth, 24, 355–379.

    Article  MathSciNet  Google Scholar 

  • Ohno, I. (1990). Rectangular parallelepiped resonance method for piezoelectric crystals and elastic constants of alpha-quartz. Physics and Chemistry of Minerals, 17, 371–378.

    Article  ADS  Google Scholar 

  • Papachristos, V. D., Panagopoulos, C. N., Christoffersen, L. W., & Markaki, A. (2001). Young’s modulus, hardness and scratch adhesion of Ni-P-W multilayered alloy coatings produced by pulse plating. Thin Solid Films, 396, 173–182.

    Article  Google Scholar 

  • Peraud, S., Pautrot, S., Villechaise, P., Mendez, J., & Mazot, P. (1997). Determination of Young’s modulus by a resonant technique applied to two dynamically ion mixed thin films. Thin Solid Films, 292, 55–60.

    Article  ADS  Google Scholar 

  • Pineau, A. (1976). Influence of uniaxial stress on morphology coherent precipitates during coarsening-elastic energy considerations. Acta Metallurgica, 24, 559–564.

    Article  Google Scholar 

  • Reddy, J. N. (1987). A generalization of two-dimensional theories of laminated composite plates. Communications in Applied Numerical Methods, 3, 173–181.

    Article  MATH  Google Scholar 

  • Sakai, S., Tanimoto, H., & Mizubayashi, H. (1999). Mechanical behavior of high-density nanocrystalline gold prepared by gas deposition method. Acta Materialia, 47, 211–217.

    Article  Google Scholar 

  • Sakharov, S., Senushencov, P., Medvedev, A., & Pisarevsk, Y. (1995), New data on temperature stability and acoustical losses of langasite crystals, in 49th Proceedings of the 1995 IEEE International Frequency Control Symposium (pp. 647–652).

    Google Scholar 

  • Sil’vestrova, I., Pisarevskii, Y., Senyushchenkov, P., & Krupnyi, A. (1986). Temperature dependence of the properties of La3Ga5SiO14 single crystal. Soviet Physics Solid State, 28, 1613–1614.

    Google Scholar 

  • Simone, A. E., & Gibson, L. J. (1996). The tensile strength of porous copper made by the GASAR process. Acta Metallurgica, 44, 1437–1447.

    Google Scholar 

  • Smith, R., & Welsh, F. (1971). Temperature dependence of the elastic, piezoelectric, and dielectric constants of lithium tantalate and lithium niobate. Journal of Applied Physics, 42, 2219–2230.

    Article  ADS  Google Scholar 

  • Sullivan, C. P., Webster, G. A., & Piearcey, B. J. (1968). Effect of stress cycling on creep behaviour of a wrought nickel-base alloy at 955 °C. Journal of the Institute Metals, 96, 274–281.

    Google Scholar 

  • Sumino, Y., Ohno, I., Goto, T., & Kumazawa, M. (1976). Measurement of elastic constants and internal friction in single-crystal MgO by rectangular parallelepiped resonance. Journal of Physics of the Earth, 24, 263–273.

    Article  Google Scholar 

  • Takashima, K., Ogura, A., Ichikawa, Y., Shimojo, M., & Higo, Y. (2000). Anisotropic fracture behavior of electroless deposited Ni-P amorphous alloy thin films, In MRS 2000 Fall Meeting Abstract (pp. 574–579).

    Google Scholar 

  • Takashima, K., Shimojo, M., Higo, Y., & Swain, M. V. (2001). Fracture behavior of micro-sized specimens with fatigue pre-crack prepared from a Ni-P amorphous alloy thin film, in ASTM STP1413. (pp. 72–81).

    Google Scholar 

  • Tanaka, K., & Koiwa, M. (1996). Single-crystal elastic constants of intermetallic compounds. Intermetallics, 4, S29–S39.

    Article  Google Scholar 

  • Tanaka, K., Okamoto, K., Inui, H., Minonishi, Y., Yamaguchi, M., & Koiwa, M. (1996a). Elastic constants and their temperature dependence for the intermetallic compound Ti3Al. Philosophical Magazine A, 73, 1475–1488.

    Article  ADS  Google Scholar 

  • Tanaka, K., Ichitsubo, T., Inui, H., Yamaguchi, M., & Koiwa, M. (1996b). Single-crystal elastic constants of γ-TiAl. Philosophical Magazine Letters, 73, 71–78.

    Article  ADS  Google Scholar 

  • Tien, J. K., & Copley, S. M. (1971). Effect of uniaxial stress on periodic morphology of coherent gamma prime precipitations in Nickel-base superalloy crystals. Metallurgical Transactions, 2, 215–219.

    Article  ADS  Google Scholar 

  • Wadsworth, J., & Froes, F. H. (1989). Developments in metallic materials for aerospace applications. JOM, 41, 12–19.

    Article  ADS  Google Scholar 

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  1. Osaka University, Toyonaka, Japan

    Masahiko Hirao & Hirotsugu Ogi

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  1. Masahiko Hirao
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Hirao, M., Ogi, H. (2017). Elastic Constants and Internal Friction of Advanced Materials. In: Electromagnetic Acoustic Transducers. Springer Series in Measurement Science and Technology. Springer, Tokyo. https://doi.org/10.1007/978-4-431-56036-4_8

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