A Revisit to the Notation of Martensitic Crystallography

Yipeng Gao

doi:10.3390/cryst8090349

Abstract

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.

Highlights

In the literature, martensitic crystallography is one of the earliest theories of phase transformations [1,2,3,4]
The starting point of martensitic crystallography is the concept of lattice correspondence, which originated from Bain’s discovery of the transformation path between face-centered cubic (FCC) and body-centered cubic (BCC) crystals in 1924 [12]
In order to show the utilization of the new notation in martensitic crystallography, we arranged

Summary

Introduction

Martensitic crystallography is one of the earliest theories of phase transformations [1,2,3,4]. The fundamental concepts and mathematical treatments in martensitic crystallography are widely adopted by other crystallographic theories, such as O-lattice theory, edge-to-edge theory, structural ledge theory, invariant line theory, topological theory, etc. Theory and Bowles-Mackenzie (BM) theory [13,14,15,16], in which the so-called invariant plane strain condition is introduced as a fundamental geometric constraint. Following this line, a few classic books are finished, which generalize the geometric constraint to compatibility condition and establish a mathematical framework in a continuum form [1,2,3,17]. The focus of the second branch is the change of crystal structure and symmetry during martensitic transformations [18,19,20,21]

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Conclusion