Double twinning

Abstract

Descriptions of the ‘{3034}’ bands observed in magnesium in terms of conventional twinning mechanisms have proved inadequate and it has been reported that the bands are in fact composed of doubly twinned material. A general theory of double twinning based on an invariant plane strain hypothesis is thus developed and various degeneracies are discussed in detail. It is shown that each double twinning mechanism may be described by a simple equivalent twinning mode which in general has four irrational elements. This type of mode has not been reported previously. The two twinning modes which are reported to be responsible for both the ‘{3034}’ and the similar ‘{1013}’ bands in Mg are used as initial data for the theory. This proves to be a particularly illustrative application as it allows the effect of the various degeneracies of the theory to be clearly demonstrated. The results indicate that the mechanism suggested for the ‘{1013}’ bands, {1013} twinning followed by {1012} re-twinning, accounts satisfactorily for the observed crystallographic features. The ‘{3034}’ habit is not predicted however by the corresponding mechanism of twinning on ‘{1011}’ and ‘{1012}’ planes. The discrepancy cannot be accounted for by allowing accommodating deformation of either the parent or the product structures. Relations between the present theory and current theories of martensite crystallography, which are also based on an invariant plane strain hypothesis, are discussed.