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).

形状记忆合金（SMA）是一类具有异常特性的材料，这归因于材料经历了马氏体相变（MPT）。经常出现在β相SMA奥氏体是一种B2立方结构，可转变为调制马氏体（MM）相。第一性原理计算结果表明，这些材料的最小能相不是MM，而是称为基态马氏体的短周期结构。迄今为止，还没有一种通用的方法来预测特定材料模型将观察到的MM结构的特性。在这项工作中，我们（I）通过使用分支跟随和分支（BFB）方法的显式原子模拟来证明MM的存在。在BFB研究中使用的自由能材料模型是由Guthikonda和Elliott（2011）开发的，并被证明可以捕获典型β的一般行为。相SMA。通过BFB研究，发现MM是自由能态的自然特征（表示为完美无穷晶体中晶格参数和单个原子位置的函数）。这项工作还提供了相对于基态马氏体的MM的自由能的洞察力，并研究了奥氏体运动相容性约束的影响，该约束与实验观察到的亚稳态MM的运动学相容性要求所稳定的低能相吻合。在MPT期间。（II）我们提出了一种将MM解释为两个短期基马氏体相的混合物的框架。仅从与两个基本马氏体相关的一小部分输入数据中，调制马氏体混合物模型（M ⁴）能够准确预测任意MM相的能量，晶格常数和结构细节。最后，（III）通过为零件（I）的原子模型发现和验证一个先前无法识别且高度兼容的MM结构，证明了M ⁴的预测能力。