Propagation of Acoustic Waves in Calcium Tungstate Crystals
DOI:
https://doi.org/10.15407/ujpe68.2.92Keywords:
acoustic wave, Christoffel equation, acoustic wave shearAbstract
On the basis of the solution of Christoffel equation, the phase-velocity surfaces for a quasilongitudinal acoustic wave (AW) and the fast and slow quasi-transverse AWS in the CaWO4 crystals have been plotted, and the extreme velocity value for each AW type and the direction of its realization have been determined. It is shown that the maximum shear angle occurs for the AW propagating in the (001) plane; in the case, the shear angle can reach a value of about 45∘ for the quasi-transverse AW, and about 18∘ for the quasi-longitudinal one. The quadratic anisotropy coefficients W1 and W2 for various AW propagation directions are determined. It is shown that there exist such directions of the quasi-transverse AW propagation in the CaWO4 crystal for which the divergence (the quadratic anisotropy coefficient |W2|) significantly exceeds the divergence that would occur in the case of isotropic medium. A direction in which the crystal anisotropy induces an additional focusing of the acoustic beam of the slow quasitransverse AW or an additional divergence of the acoustic beam of the fast quasi-transverse AW is determined. The experimental values of the velocities and shear angles of the AWS are presented, which confirm the reliability of the obtained calculation results.
References
M.V. Sivers, M. Clark, P.C.F. Di Stefano, A. Erb, A. G¨utlein, J.-C. Lanfranchi, A. M¨unster, P. Nadeau, M. Piquemal, W. Potzel, S. Roth, K. Schreiner, R. Strauss, S. Wawoczny, M. Willers, A. Z¨oller. Low-temperature scintillation properties of CaWO4 crystals for rareevent searches. J. Appl. Phys. 118, 164505 (2015).
https://doi.org/10.1063/1.4934741
A. Phuruangrata, T. Thongtemb, S. Thongtema. Synthesis, characterisation and photoluminescence of nanocrystalline calcium tungstate. J. Exper. Nanosci. 5, 263 (2010).
https://doi.org/10.1080/17458080903513276
A. Shmilevich, D. Weiss, R. Chen, N. Kristianpoller. Phototransferred thermoluminescence of CaWO4 crystals. Radiation Protection Dosimetry 84, 131 (1999).
https://doi.org/10.1093/oxfordjournals.rpd.a032702
C. Michail, I. Valais, G. Fountos, A. Bakas, C. Fountzoula, N. Kalyvas, A. Karabotsos, I.A. Sianoudis, I. Kandarakis. Luminescence efficiency of calcium tungstate (CaWO4) under X-ray radiation: Comparison with Gd2O2S : Tb. Measurement 120, 213 (2018).
https://doi.org/10.1016/j.measurement.2018.02.027
F.B. Xiong, H.F. Lin, L.J. Wang, H.X. Shen, Y.P. Wang, W.Z Zhu. Luminescent properties of red-light-emitting phosphors CaWO4 : Eu3+, Li+ for near UV LED. Bull. Mater. Sci. 38, 1 (2015).
https://doi.org/10.1007/s12034-015-1039-0
H.P. Barbosa, .I.G.N. Silva, C.M.F.C. Felinto, E.E.S. Teotonio, O.L. Malta, H.F. Brito. Photoluminescence of singlephased white light emission materials based on simultaneous Tb3+, Eu3+ and Dy3+ doping in CaWO4 matrix. J. Alloy. Compd. 696, 820 (2017).
https://doi.org/10.1016/j.jallcom.2016.11.378
N. Faure, C. Borel, M. Couchaud, G. Basset, R. Templier, C. Wyon. Optical properties and laser performance of neodymium doped scheelites CaWO4 and NaGd(WO4)2. Appl. Phys. B 63, 593 (1996).
https://doi.org/10.1007/BF01830998
J. Chen, L. Dong, F. Liu, H. Xu, J. Liu. Investigation of Yb : CaWO4 as a potential new self-Raman laser crystal. Cryst. Eng. Comm. 23, 427 (2021).
https://doi.org/10.1039/D0CE01538E
A.S. Andrushchak, O.A. Buryy, N.M. Demyanyshyn, Z.Yu. Hotra, B.G. Mytsyk. Global maxima of the acoustooptic effect in CaWO4 crystals. Acta Phys. Pol. A 133, 928 (2018).
https://doi.org/10.12693/APhysPolA.133.928
B.G. Mytsyk, Ya.P. Kost, N.M. Demyanyshyn, A.S. Andrushchak, I.M. Solskii. Piezooptical coefficients of CaWO4 crystals. Crystallogr. Rep. 60, 130 (2015).
https://doi.org/10.1134/S1063774514050125
J.S. Kastelik, M.J. Gazalet, C. Bruneel, E. Bridox. Acoustic shear wave propagation in paratellurite with reduced spreading. J. Appl. Phys. 74, 2813 (1993).
https://doi.org/10.1063/1.354631
Yu. Sirotin, M. Shaskolskaja. Fundamentals of Crystal Physics (Mir Publishers, 1983).
J.M. Farley, G.A. Saunders. The elastic constants of CaWO4. Solid State Commum. 9, 965 (1971).
https://doi.org/10.1016/0038-1098(71)90441-8
A.G. Khatkevich. Diffraction and propagation of ultrasonic radiation beams in single crystals. Akust. Zh. 24, 108 (1978) (in Russian).
A.S. Andrushchak, T.I. Voronyak, O.V. Yurkevych, N.A. Andrushchak, A.V. Kityk. Interferometric technique for controlling wedge angle and surface flatness of optical slabs. Opt Laser Eng. 51, 342 (2013).
https://doi.org/10.1016/j.optlaseng.2012.12.006
E.P. Papadakis. Ultrasonic phase velocity by the pulse-echo overlap method incorporating diffraction phase correction. J. Acoust. Soc. Am. 42, 1045 (1967).
https://doi.org/10.1121/1.1910688
S. Kino. Acoustic Waves (Prentice Hall, 1987).
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