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References
Landau, L. D., “On the theory of phase transitions”, in Collected Papers of L. D. Landau (ed. D. Ter Haar), New York-London-Paris, Gordon and Breach and Pergamon Press 1965.
Batterman, B. W., & Barrett, C. S., Crystal structure of superconducting V3Si, Phys. Rev. Lett. 13, 390–392 (1964).
Anderson, P. W., & Blount, E. I., Symmetry considerations on martensitic transformations: “ferroelectric” metals?, Phys. Rev. Lett. 14, 217–219 (1965).
Michelson, A., “Weak Lifschitz condition” and the allowed types of ordering in second-order phase transitions, Phys. Rev. B18, 459–464 (1978).
Weger, M., Silbernagel, B. G., & Greiner, E. S., Effect of stress on the superconducting transition temperature of V3Si, Phys. Rev. Lett. 13, 521–523 (1964).
Gurtin, M. E., & Williams, W. O., Phases of elastic materials, ZAMP 18, 132–135 (1967).
Cauchy, A.-L., Sur les équations différentielles d'équilibre ou de mouvement pour un système de points materiels sollicités par des forces d'attraction ou de répulsion mutuelle. Ex. de Math. 4, (1829)≡Œuvres, 9 (2), 162–173 (1891).
Stakgold, I., The Cauchy relations in a molecular theory of elasticity, Quart. Appl. Math. 8, 169–186 (1949).
Ericksen, J. L., Nonlinear elasticity of diatomic crystals, Int. J. Solids Structures 6, 951–957 (1970).
Parry, G. P., On diatomic crystals, Int. J. Solids Structures 14, 283–287 (1978).
Ericksen, J. L., “Special Topics in Nonlinear Elastostatics”, in Advances in Applied Mechanics (ed. C.-S. Yih), vol. 17, New York, Academic Press, 1977.
Thompson, J. M. T., “Catastrophe Theory and its Role in Applied Mechanics”, in Theoretical and Applied Mechanics (ed. W. T. Koiter), Amsterdam-New YorkOxford, North Holland Publishing Co. 1976.
Gibbs, J. W., On the equilibrium of heterogeneous substances, Trans. Conn. Acad. 3, 108–248 (1875–6) and 343–524 (1877–8)≡Scientific Papers, London, Longmans & Green, 1906.
Thompson, J. M. T., & Hunt, G. W., “A General Theory of Elastic Stability”, London-New York-Sidney-Toronto, John Wiley & Sons, Ltd. 1973.
Testardi, L. E., & Bateman, T. B., Lattice instability of high-transition-temperature superconductors. II. Single-crystal V3Si results, Phys. Rev. 154, 402–410 (1967).
Ericksen, J. L., On the symmetry of deformable crystals, Arch. Rational Mech. Anal. 72, 1–13 (1979).
Keller, K. R., & Hanak, J. J., Ultrasonic measurements in Single-Crystal Nb3Sn, Phys. Rev. 154, 628–632 (1967).
Dafermos, C. M., The mixed initial-boundary value problem for the equations of nonlinear one-dimensional viscoelasticity, J. Differential Equal. 6, 71–86 (1969).
Parry, G. P., On the elasticity of monatomic crystals, Math. Proc. Camb. Phil. Soc. 30, 189–211 (1976).
Pitteri, M., Reconciliation of local and global symmetries of crystals, pending publication.
Ericksen, J. L., On the symmetry and stability of thermoelastic solids, J. Appl. Mech. 45, 740–744 (1978).
Love, A. E. H., “A Treatise on the Mathematical Theory of Elasticity”, 4th ed. Cambridge, Cambridge University Press 1927.
Rehwald, W., Lattice softening and stiffening of single crystal niobium stannide at low temperatures. Phys. Lett. 27A, 287–288 (1968).
Poincaré, H., Sur l'équilibre d'une masse fluide animée d'un mouvement de rotation, Acta Math. 7, 259–380 (1885).
Sengers, A. L., Hocken, R., & Sengers, J. V., Critical-point universality and fluids, Physics Today 30, 42–51 (1977).
Ericksen, J. L., Variations on a bifurication theorem by Poincaré, to appear in Meccanica.
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Communicated by D. D. Joseph
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Ericksen, J.L. Some phase transitions in crystals. Arch. Rational Mech. Anal. 73, 99–124 (1980). https://doi.org/10.1007/BF00258233
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DOI: https://doi.org/10.1007/BF00258233