Equilibrium Theory for X-ray Observations of Crystals

Abstract

In molecular theories of crystal elasticity, one needs some way of relating changes in atomic arrangements to macroscopic deformation. The oldest idea, introduced by CAUCHY, was that the gross motion agrees with atomic motion, at the mass points representing atoms. After appreciating reasons why this is not really sound, physically, BORN modi®ed this assumption in what seems to be a very reasonable way. His assumption, called the Born Rule, hereafter abbreviated to B.R., has become the standard assumption in this area. It is widely appreciated that it is not consistent with observations of phenomena involving slip, commonly associated with dislocation motion and what we call plasticity. While linear elasticity theory has been used extensively in studies of isolated dislocations, we all know that it is not a good theory to use for predicting what deformations will occur in a simple tension experiment, for example. Elasticity theory has been used successfully to deal with other kinds of deformations which can be large, associated with phase transitions involving changes of symmetry, including sophisticated descriptions of rather complicated arrangements of twins occurring with these. From this, it seems reasonable to include such deformations among those commonly regarded as elastic and, possibly, to use similar analyses for other kinds of twins which are rather di€erent, physically. Those alluded to above are transformation twins, occurring naturally in unstressed samples as the temperature changes, associated with phase transitions. Then there are the growth twins, occurring naturally as a crystal solidi®es from a melt or solution; some include twins occurring during annealing. Here again, elasticity theory has been useful in designing mechanical treatments to eliminate some of them. Early work of this kind, done during World War II, relating to Dauphine twins in quartz,