Electromagnetic emission caused by the fracturing of piezoelectric crystals with an arbitrarily oriented moving crack A.A. Gernets a , M.V. Makarets a , S.V. Koshevaya b, * , V.V. Grimalsky c , D.Ju arez Romero b , A.N. Kotsarenko d a Department of Physics, Kyiv National Shevchenko University, Volodymyrska, 64, Kyiv 01033, Ukraine b Research Center of Applied Sciences and Engineering, Autonomous University of State Morelos, CIICAp, FCQeI, Av. Universidad, Col. Chamilpa, 1001, ZP 62210 Cuernavaca, Mor., Mexico c National Institute for Astrophysics, Optics, and Electronics (INAOE), PO 51 & 216, ZP 72000 Puebla, Pue., Mexico d Centr e of Geo-Science, Juriquilla, UNAM, Apdo Postal 1-742, CP 76001, Queretaro, Mexico Received 3 June 2003; received in revised form 14 November 2003; accepted 5 December 2003 Available online 9 April 2004 Abstract Electromagneticemission(EME)causedbyfracturingofpiezoelectriceffectsinrockshasbeenstudied.Wehaveanalyzedafinite size piezocrystal undergoing such mechanical stresses which cause an uniform movement of a crack. Direction of the crack movementanditsfrontorientationhavebeenassumedarbitrarywithrespecttothecrystalaxes.Insuchacasepolarizationcurrents appear with potential and vortical components, corresponding to the electric polarization currents and magnetization currents. Amplitude–frequencycharacteristicsoftheEMEinlong-wavelengthregionhavebeenanalyzedtoo.ThiseffectofEMEisofgreat importance for natural hazards including volcano eruptions and earthquakes. Ó 2004 Elsevier Ltd. All rights reserved. Keywords: EME emission; Piezoeffect; Micro fracturing; Earthquake 1. Introduction Electromagnetic emission caused by fracturing of crystals in rocks has been studied theoretically and in the observations (Surkov et al., 2003; Makarets et al., 2002; Surkov, 2000). In particular, in Makarets et al. (2002) we have considered a piezocrystal of a finite size with a uniformly moving crack whose linear front is parallel to an optical axis of the crystal. The crack has instantly begun the uniform movement at a moment t ¼ 0 and analogously stopped at a moment t ¼ T > 0. It has been revealed that time-dependent mechanical stresses which exist in the vicinity of the crack’s apex, areasourceoftheelectromagneticwaves.TheEMEhas been investigated for the crystals of symmetry group 32 andotherssimilartotheminthefirstapproximationfor piezoelectric coefficients and in the zeroth approxima- tionforthedeviationsofanelastictensorofthecrystal from such an isotropic medium. It has been obtained thattheintensityoftheemissionhasalotsofmaximaas a function of frequency, whose wavelengths are deter- minedbythecrystalsizeandthecrack’svelocityandare located in a long-wavelength region of spectrum. It has also been found that a source of the emission is equiv- alent to a time-dependent magnetization dipole, and values of the magnetization vector and corresponding magnetization current have been estimated. 2. Model, equations, and method of solution Weconsiderapiezocrystalwithfinitesizeundersuch mechanical stresses, which cause a uniform movement of a crack through the crystal. As in Makarets et al. (2002) we assume the crack has instantly begun the uniformmovementatamoment t ¼ 0.Hence,thereare three different rectangular systems of coordinates, namely: (i) laboratory system; (ii) crystallographic sys- tem,an Oz-axisofwhichisdirectedalonganopticalaxis ofthecrystal;(iii)thecracksystem,the Oz-axisofwhich * Corresponding author. Tel.: +52-17-39-7084; fax: +52-17-329- 7084. E-mail address: svetlana@uaem.mx (S.V. Koshevaya). 1474-7065/$ - see front matter Ó 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.pce.2003.12.006 Physics and Chemistry of the Earth 29 (2004) 463–472 www.elsevier.com/locate/pce