Tweed in Martensites: A Potential New Spin Glass

We've been studying the ``tweed'' precursors above the martensitic transition in shape--memory alloys. These characteristic cross--hatched modulations occur for hundreds of degrees above the first--order shape--changing transition. Our two--dimensional model for this transition, in the limit of infinite elastic anisotropy, can be mapped onto a spin--glass Hamiltonian in a random field. We suggest that the tweed precursors are a direct analogy of the spin--glass phase. The tweed is intermediate between the high--temperature cubic phase and the low--temperature martensitic phase in the same way as the spin--glass phase can be intermediate between ferromagnet and antiferromagnet.Comment: 18 pages and four figures (included

Disorder-Driven Pretransitional Tweed in Martensitic Transformations

Defying the conventional wisdom regarding first--order transitions, {\it solid--solid displacive transformations} are often accompanied by pronounced pretransitional phenomena. Generally, these phenomena are indicative of some mesoscopic lattice deformation that ``anticipates'' the upcoming phase transition. Among these precursive effects is the observation of the so-called ``tweed'' pattern in transmission electron microscopy in a wide variety of materials. We have investigated the tweed deformation in a two dimensional model system, and found that it arises because the compositional disorder intrinsic to any alloy conspires with the natural geometric constraints of the lattice to produce a frustrated, glassy phase. The predicted phase diagram and glassy behavior have been verified by numerical simulations, and diffraction patterns of simulated systems are found to compare well with experimental data. Analytically comparing to alternative models of strain-disorder coupling, we show that the present model best accounts for experimental observations.Comment: 43 pages in TeX, plus figures. Most figures supplied separately in uuencoded format. Three other figures available via anonymous ftp

The Spin-glass nature of tweed precursors in martensitic transformations

Many displacive solid-solid transformations, despite being first order, show pronounced precursor effects, such as the mesoscopic, micron-scale, ‘‘tweed’’ pattern seen in shape-memory alloys. We model this tweed theoretically using a nonlinear, nonlocal elastic free energy, and argue that quenched concentration inhomogeneities drive the local tweed modulations. We report (1) the construction of a model for {11}/〈11¯〉 shear transformations in square systems, (2) a simulation including concentration inhomogeneities, and (3) a mapping of the disordered 2D martensite onto an infinite-range spin model, identifying tweed with the spin-glass phase