Abstract
Certain properties of a crystalline substance may appear only below, for instance, a certain critical temperature and are frequently accompanied by equilibrium states exhibiting a marked decrease in symmetry. One such example of this is the appearance of twinned crystals in what sometimes may be regarded as an austenite/martensite transition. In the higher temperature austenite the crystal is cubic, while in the lower temperature martensite it is tetragonal. Another example is the appearance of spontaneous polarization in a ferroelectric, like Rochelle salt. Also in this instance, the crystal structure is more symmetric in the absence of spontaneous polarization.
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References
Agmon, S., Douglis, A., and Nirenberg, L., Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions, II., CPAM 22 (1964), 35–92.
Ball, J.M., Constitutive inequalities and existence theorems in nonlinear elastostatics, Heriot-Watt Symp. vol. I, (R. Knops, ed.) Pitman (1976).
Ball, J.M. and James, R., Fine phase mixtures as minimizers of energy
Chi pot, M. and Kinderlehrer, Equilibrium configurations of crystals, to appear.
Chipot, M., Kinderlehrer, D., and Vergara-Caffarelli, G., The smoothness of linear laminates, IMA Preprint 199, Arch. Rat. Mech. and Anal.
Devonshire, A.F., Theory of Ferroelectrics, Adv. in Physics, 3 (1954), 85–130.
Ericksen, J.L., Special topics in elastostatics, Adv. in Appl. Mech. (C.-S. Yih, ed.), Academic Press (7 (1977), 189–243).
Ericksen, J.L., Some simpler cases of the Gibbs phenomenon for thermo-elastic solids, J. of thermal stresses, 4 (1981), 13–30.
Ericksen, J.L., Twinning of crystals (1), these proceedings, 1986.
Ericksen, J.L., Special topics in elastostatics, Adv. in appl. mechanics, (C.-S. Yih, ed.) Academic Press 7, (1977), 189–243.
Ericksen, J.L., Some phase transitions in crystals, Arch. Rat. Mech. Anal. 73 (1980), 99–124.
Fonseca, I. Thesis, University of Minnesota, Arch, for Rat. Mech. and Anal.
Fonseca, I. Thesis, The lower quasiconvex envelope of the stored energy function for an elastic crystal.
Grindlay, J. An introduction to the phenomenologiçal theory of ferroelectrics, Pergamon (1970).
Gurtin, M.E., and Spector, S. On stability and uniqueness in finite elasticity, Arch. Rat. Mech, and Anal. 70 (1979), 153–165.
James, R., Finite deformation by mechanical twinning, Arch. Rat. Mech. Anal. 22 (1981), 143–176.
James, R., Diplacive phase transitions in solids, J. of Mech. and Physics of Solids (1986).
Kanzig, W., Ferroelectrics and antiferroelectrics, Academic Press (1957).
Lines, M.E. and Glass, A.M., Principles and applications of ferroelectrics and related materials, Oxford (1977).
Love, A.E.H., A treatise on the mathematical theory of elasticity, Dover (1948).
Mitsui, M., Tatsuzaki, I., and Nakamura, E., An introduciton to the physics of ferroelectrics, Gordon and Breach (1976).
Pitteri, M., Reconciliation of local and global symmetries of crystals, J. Elasticity 14 (1984), 175–190.
Podio-Guidugli, P. and Vergara-Caffarelli, G., On a class of traction problems in elasticity (preprint).
Podio-Guidguli, P., Vergara-Caffarelli, G., and Virga, E., The role of ellipticity and normality assumptions in formulating live boundary conditions in elasticity, (preprint).
Simpson, H. and Spector, S., On Hadamard stability in finite elasticity, IMA preprint 171, Arch. Rat. Mech. and Anal.
Spector, S., On uniqueness in finite elasticity with general loading, J. Elasticity 10 (1980), 145–161.
Tisza, L. On the general theory of phase transformations in solids, (Smoluchowski, R. Mayer, J.E., and Weyl, W.A. eds.) Wiley (1951), 1–35.
Toupin, R. The elastic dielectric, J. Rat. Mech. Anal. 5, (1956), 849–915.
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Kinderlehrer, D. (1987). Twinning of Crystals (II). In: Antman, S.S., Ericksen, J.L., Kinderlehrer, D., Müller, I. (eds) Metastability and Incompletely Posed Problems. The IMA Volumes in Mathematics and Its Applications, vol 3. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-8704-6_12
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DOI: https://doi.org/10.1007/978-1-4613-8704-6_12
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