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RETRACTED ARTICLE: Crystal’s anisotropic properties and tensor representation: a discussion

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This article was retracted on 27 March 2013

Abstract

For most applications, crystals need a careful selection to process an appropriate symmetry for a particular application. A crystal is innately symmetrical; hence it presents the same appearance from a number of different directions. Some of the physical properties of crystals which exhibit dependence on symmetry elements are presented. A method of using the inherent symmetry in order to simplify the formulation of the physical properties is needed. The use of tensors is one such tool. The authors review what tensors of different ranks are, and show how such tensors can be used to describe the directional variation of the physical properties within crystals. These arise when a tensor relates a vector to a second-rank tensor. Properties that involve third-rank tensors include the piezoelectric effect. However, to exhibit the reduction of the number of tensor components further, consider the fourth-rank tensors. Both stress and strain can be represented by second-rank tensors, the modulus can be represented by a fourth-rank tensor. Stress is the force acting in any direction divided by the area. The fourth-rank elasticity tensor of an anisotropic and linear elastic material of the material is considered.

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Author information

Authors and Affiliations

  1. Physics Department, Faculty of Science, Urmia University, Urmia, Iran

    E. Talebian & M. Talebian

Authors
  1. E. Talebian
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  2. M. Talebian
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Correspondence to E. Talebian.

Additional information

It has come to the attention of the European Physical Journal Plus that this article should not have been published because it repeats work already published in: (a) Chapter 7 of the textbook "Crystallography Applied To Solid State Physics" by A. R. Verma and O. N. Srivastava (New Age International, 1991); (b) Encyclopedia of Condensed Matter Physics, edited by G. Bassani, G. Liedl, P. Wyder (Elsevier, 2005) pp. 300-309; (c) E. Fjær, R.M. Holt, A. M. Raaen, P. Risnes and P. Horsrud, "Petroleum Related Rock Mechanics", Second Edition (Elsevier, 2008). Consequently, this paper has been retracted by the European Physical Journal Plus and should not be cited or referred to in the future.

A retraction note to this article can be found online at http://dx.doi.org/10.1140/epjp/i2013-13037-9.

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Talebian, E., Talebian, M. RETRACTED ARTICLE: Crystal’s anisotropic properties and tensor representation: a discussion. Eur. Phys. J. Plus 126, 128 (2011). https://doi.org/10.1140/epjp/i2011-11128-3

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  • DOI: https://doi.org/10.1140/epjp/i2011-11128-3

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