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Temperature coefficients of elastic constants of trigonal and tetragonal crystals

Temperature coefficients of elastic constants of trigonal and tetragonal crystals,10.1109/FCS.2011.5977308,B. P. Sorokin,A. V. Telichko

Temperature coefficients of elastic constants of trigonal and tetragonal crystals  
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Temperature coefficients of elastic constants (TCij) for trigonal and tetragonal crystals have been obtained. The TCij of a number of trigonal and tetragonal crystals have been calculated and the comparison with known experimental data has been fulfilled. The nature of anomalous TC66 of quartz has been discussed. Normal temperature behavior of elastic constants for most of the crystals is proportionally decreased with temperature increasing and a small dependence (or lack thereof) at low temperatures. Knowledge of these dependences is important for the solid state physics and applications of crystals. One of most attractive properties of quartz is the temperature stability observed for some crystalline cuts and modes. Owing to combination of thermostability with piezoelectricity and small attenuation of acoustic waves quartz single crystal has great importance as a material for acoustoelectronic devices. There are only a few piezoelectric crystals possessing the same combination of properties. Nature of the temperature stability is closely connected with elastic anharmonicity of specified elastic modes in such crystals. In practice the search of cuts possessing thermostable orientation was commonly based on the data of temperature coefficients of elastic constants obtained from experiment. Unfortunately there is no exact theory which can be used for explanation of anharmonic behavior of crystals. Consequently a possibility to predict a trend of the search for the new thermostable materials and crystalline cuts is absent. On the basis of the theory explaining the small amplitude bulk acoustic waves (BAW) propagation in crystals under the influence of bias finite fields the temperature coefficients (TCIJ) of elastic constants (CIJ) of cubic crystals have been obtained earlier (1). Satisfactory agreement between calculation and experimental results for a number of cubic crystals has been achieved. The similar method of calculations of frequency dependences on temperature in quartz piezoelectric resonators has been used by authors (2). The main objective of this paper is to obtain the temperature coefficients for trigonal and tetragonal crystals.
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