A three-dimensional Landau theory for multivariant stress-induced martensitic phase transformations (PTs) was recently developed (V. I. Levitas and D. L. Preston, Phys. Rev. B 66, 134206 & 134207, 2002; V. I. Levitas, D. L. Preston, D. W. Lee, Phys. Rev. B, 134201, 2003). It allows inclusion of all temperature-dependent thermomechanical properties of austenite and martensite, describes transformations between austenite and martensitic variants and between martensitic variants for any symmetry, as well as typical stress-strain curves for shape memory alloys. Time independent and time dependent Ginzburg-Landau equations for this theory were considered. For one-dimensional spatial variation of the order parameter various types of static analytical solutions were found. More specifically, the structure and energetics of martensitic and austenitic critical nuclei and diffuse austenite-martensite and martensite- martensite interfaces were found. To study the stability of stationary solutions, both analytical and numerical methods were employed. For nanofilms, the solution represents some continuously varied phases with continuously varied properties, which were identified as functionally graded nanophases. The results suggest a way to produce such nanophases by dissolving material of nanofilm from both surfaces. An analytical solution for a diffuse propagating interface is found and its stability is studied numerically. Note that the Ginzburg-Landau equation is usually used to describe a wide class of first order PTs, which includes ferroelastic, martensitic, reconstructive, and ferroelectric and magnetoelastic PTs, PTs in liquid crystals, as well as twinning and dislocation generation. Most of obtained results are valid for these phenomena as well.
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