Tweed in martensites: a potential new spin glass

Abstract

ABSTRACT:We've been studying the "tweed" precursors above the martensitic transition in shapememory 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.

Continuous elastic phase transitions in pure and disordered crystals

“…However, a simplifying elastic Ginzburg-Landau free energy has been proposed (Falk 1980(Falk , 1983, which is of the form (2.1), but with a negative fourth-order term and including a sixth-order term in order to describe a first-order transition. Recently, an explanation for the experimentally observed "tweed" pattern in microscopic images of martensitic materials for temperatures far above the transition temperature has been suggested on a similar basis (Kartha et al 1991, Sethna et al 1992, Kartha et al 1995. Namely, such pseudo-periodic lattice deformations were found to emerge in an elastic model including defects that locally modify the transition temperature in a random manner.…”

Enhanced Critical Current in Tl-Ba-Ca-Cu-O Superconductors Prepared by Diffusion Process with Fluorine Addition

“…Taking the mean J i j to be non-zero [24] permits competition (and transition) between two types of frozen phase, spin glass and ferromagnet (or anti-ferromagnet). An exactly soluble version is the infinite-range extension of Sherrington and Kirkpatrick 6 [5,25]. A tempting analogue in the present case is a variant of the Ghatak-Sherrington model [28] (see also [29,30]), with…”

“…The suggestion that tweed is an analogue of a spin glass and a description of these systems in terms of a spin glass model is not new [4][5][6], but the modelling here is somewhat different and, hopefully, instructive. It also suggests interesting new models (or variations) for study by spin glass physicists.…”

“…There should be a corresponding difference in uniaxial compliances (or, inversely, compressibilities) in tweed measured along principal axes 5 . This effect is a consequence of the multiplicity of metastable states of spin glasses, their non-trivial evolution under changes of control parameters (such as temperature or applied field) and consequential slow dynamics in exploring all of phase space [31,32].…”

“…I thank James Sethna for drawing my attention to [5,17] and also for helpful comments on a draft of this paper. Financial support was provided by EPSRC through grant GR/R83712/01 and by the US Department of Energy through CNLS, Los Alamos National Laboratory.…”