It is generally accepted that the simplest kinds of crystals exhibit 14 kinds of symmetry, the Bravais lattices described in texts treating crystals. Briefly, Bravais's idea was to regard two configurations as having the same symmetry provided they can be connected by a special kind of path, in the space of lattice vectors. However, with his assumptions, he overlooked the possibility that some of the 14 can be joined by such paths, which reduces the 14 to 11. To be explored is the question of whether paths found to connect the different Bravais lattices are thermodynamically possible, when pressure and temperature are suitably controlled.
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References
1.
. BravaisA.Mémoire sur Ies systèmes formés par des points distribuès régulierment sur un plan ou dans l'espace?J. École Polytechnique, 19, 1–128 (1850).
2.
. PitteriM.ZanzottoG.: On the definition and classification of Bravais lattices. Manuscript submitted for publication.
3.
. EricksenJ. L.On the symmetry of deformable crystals?Arch. Rat. Mech. Analysis, 72, 1–13 (1979).
. EricksenJ. L.: Thermal expansion involving phase transitions in certain thermoelastic crystals. Meccanica, (in press).
6.
. PitteriM.Reconciliation of local and global symmetries of crystals?J. Elasticity, 14, 175–190 (1984).
7.
. BallJ. M.JamesR. D.: Proposed experimental tests of a theory of fine microstructure and the two well problem. Phil. Trans. R. Soc. Lond., A338, 389–450 (1992).
8.
. GibbsJ. W.: On the equilibrium of heterogeneous substances. Trans. Conn. Acad., III, 108–248 (1875–1876) and 343–524 (1877–1878).
9.
. BhattacharyaK.FiroozyeN.B.JamesR. D.KohnR. V.: Restrictions on microstructure. Proc. Roy. Soc. Edinburgh, 124A, 843–878 (1994).
10.
. ManC.-S.Material stability, the Gibbs conjecture and the first phase rule for substances?Arch. Rat. Mech. Analysis, 91, 1–53 (1985).
11.
. TruesdellC.: A First Course in Rational Continuum Mechanics, vol. 1, Academic, New York, 1977.
12.
. LoveA.E.H.: A Treatise on the Mathematical Theory of Elasticity, 4th ed., Cambridge University Press, Cambridge, UK, 1927.
13.
. PippardA. B.: The Elements of Classical Thermodynamics, Cambridge University Press, Cambridge, UK, 1957.
