A Revisit to the Notation of Martensitic Crystallography

As one of the most successful crystallographic theories for phase transformations, martensitic crystallography has been widely applied in understanding and predicting the microstructural features associated with structural phase transformations. In a narrow sense, it was initially developed based on the concepts of lattice correspondence and invariant plane strain condition, which is formulated in a continuum form through linear algebra. However, the scope of martensitic crystallography has since been extended; for example, group theory and graph theory have been introduced to capture the crystallographic phenomena originating from lattice discreteness. In order to establish a general and rigorous theoretical framework, we suggest a new notation system for martensitic crystallography. The new notation system combines the original formulation of martensitic crystallography and Dirac notation, which provides a concise and flexible way to understand the crystallographic nature of martensitic transformations with a potential extensionality. A number of key results in martensitic crystallography are reexamined and generalized through the new notation.

Selection of Lattice Invariant Shear in Dilute Zr-Nb Alloy for bcc-hcp Martensitic Transformation

The morphology and substructure of martensite is considered to arise from the lattice invariant shear (LIS) associated with the transformation and this may be slip, twinning or both. Out of the several possible slip shears and twin modes only a few satisfy invariant plane strain criteria of the phenomenological theory of martensite (PTMC). On the basis of crystallographic and energetic criteria, a simple model has been proposed for determining the factors which influence the selection of the preferred LIS mode. In the present work, it is found that for b ® a' martensitic transformation in Zr-2.5 wt%Nb alloy, the preferred slip system is {1101}a'<2113>a' and the preferred twin system is {1101}a'<415 3>a'.

Stress-Induced Phase Transformations in SiC

Tetrahedrally co-ordinated materials can undergo stress-induced structural transformations often under invariant plane strain conditions; examples of such transformations are twinning and polytypism. The structure of a tetrahedrally co-ordinated material, XY, may be considered in terms of an assembly of “normal”, Ti’and “twinned” tetrahedra, T'I’all connected to each other at their corners. In some of these materials, e.g. SiC, GaN or CdS, these corner-sharing tetrahedra may be connected to each other in different ways, giving rise to different polytypes. In this paper, a dislocation model for polytypic transformations is discussed and a few examples of stress-induced transformations are illustrated.In general, dislocations in XY polytypes he on basal (0001) planes and are generally dissociated into “leading’ and “trailing” partial dislocations with Burgers vectors b1 and bt’ respectively. There is also good evidence that dissociated dislocations in tetrahedrally-coordinated materials belong to the glide set and move on the slip plane in a dissociated manner.

Transformation strains in lattices

A generalized theory of transformation strains in lattices is developed which incorporates earlier analyses of both deformation twinning and martensite crystallography in addition to other new transformation mechanisms. In the formal analysis two different lattices are related by an invariant plane strain, a rotation and a further strain which characterizes the particular transformation being considered. A general solution is then obtained for the invariant plane strain in terms of this characteristic strain. The special cases of twinning shears, invariant plane transformation strains and martensite crystallography theories are examined in detail for mechanisms involving either single or double strains. In these cases the characteristic strain consists of appropriate combinations of shears, pure strains, invariant plane strains and lattice invariant deformations. Applications of the particular mechanisms examined to transformations of technological interest in crystalline materials are discussed and further special cases and extensions of the analysis considered.