Shape Memory Alloys (SMAs) are a class of materials with unusual properties that have been attributed to the material undergoing a martensitic phase transformation (MPT). Often in β-phase SMAs the austenite is a B2 cubic configuration that transforms into a modulated martensite (MM) phase. First-principles computational results have shown that the minimum energy phase for these materials is not a MM, but a short-period structure called the ground state martensite. To date, a general approach for predicting the properties of the MM structure that will be observed for a particular material model has not been available. In this work, we (I) demonstrate the existence of MMs through explicit atomistic simulations using the branch-following and bifurcation (BFB) method. The free-energy material model used in the BFB study was developed by Guthikonda and Elliott (2011) and was shown to capture the general behavior of typical β-phase SMAs. Through the BFB study, MMs are found to be natural features of the free energy landscape (expressed as a function of the lattice parameters and individual atomic positions within a perfect infinite crystal). This work also yields insight into the free energies of MMs relative to the ground state martensite and examines the effect of an austenite kinematic compatibility constraint which agrees with the justification of the experimental observation of metastable MMs as low-energy phases stabilized by the kinematic compatibility requirement during a MPT. (II) We present a framework for the interpretation of MMs as a mixture of two short-period base martensite phases. From only a small set of input data associated with the two base martensites the modulated martensite mixture model (M4) is capable of accurately predicting the energy, lattice constants, and structural details of an arbitrary MM phase. Finally, (III) the predictive capability of the M4 is demonstrated through the discovery and verification of a previously unidentified and highly compatible MM structure for the atomistic model of part (I).
Bibliographical noteFunding Information:
The authors would like to thank Richard D. James and Ellad B. Tadmor for the helpful discussion related to this manuscript. This work has been supported by the National Science Foundation CAREER Grant CMMI-0746628, Grant CMMI-1462826, and by The University of Minnesota Supercomputing Institute.
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- Kinematic compatibility
- Martensitic transformations
- Material stability
- Modulated martensites
- Shape memory alloys