It was recalled that the link between molecular descriptions of crystalline configurations, and continuum theories of crystal mechanics, was provided by the Born rule. An extensive investigation was made of the validity of this rule, as well as of the possible application of non-linear elasticity to mechanical twinning and its implications for the invariance group of the energy density of the crystal. The analysis led to the conclusion that, in the generic case, the Born rule did not hold true and non-linear elasticity theory could not provide a reliable model for crystal mechanics because an unphysical energy invariance was implied. However, the Born rule and associated elasticity theory could be applied to crystals whose twinning shears satisfied some rather restrictive non-generic conditions. This class of non-generic materials included shape-memory alloys, and substances whose crystal structure was a simple Bravais lattice.

G.Zanzotto: Acta Crystallographica A, 1996, 52[6], 839-49