Description |
A 2D model of three-valued discrete-strain pseudospins S (r)=0, +1,-1 is studied in Monte Carlo simulations, under systematic temperature quenches, without extrinsic disorder [1]. The reduced model is from Landau minima of a continuum-strain free energy of the square-rectangle martensitic transition. The pseudospins interact via a power-law anisotropic potential obtained from the St Venant Compatibility constraint. The same procedure yields pseudospin models for other 2D and 3D transitions [2]. After a temperature quench, dilute martensitic seeds in an austenite background, induce sequential domain-wall phases of a 'vapour' of a martensite droplet in austenite; a 'liquid' of disordered martensite domain walls; and a ‘crystal’ of oriented-wall twins. The evolution is tracked through Temperature-Time –Transformation (TTT) curves, with time scales for conversion to martensite t_m (T); and Compatibility-driven domain-wall orientation, t_C (T). Depending on elastic constants, t_m (T) can either be thermally activated and slow, as in 'isothermal' martensites; or non-activated and explosive, as in 'athermal' martensites below a martensite start temperature ~ T_1. For quenching to above such a temperature, we find (generically) a delay tail, that rises towards a temperature T=T_4 > T_1. This is identified with the puzzling delay tail in t_m (T) found by Kakeshita [3]. The mean time shows glass-like Vogel-Fulcher behaviour, t_m ~ exp [ 1/( T_4 - T)], and distributions are log-normal [1]. The times are insensitive to the Hamiltonian energy scale E_0, and are attributed to entropy barriers that vanish/ diverge at T_1 and T_4. The conversion delays are from searches in Fourier space on constant-energy surfaces, for rare energy-lowering pathways. The 'vapour' phase structure-factor peak has to find pathways to distort and roll into a small anisotropic 'golf hole'; to be then guided by a 'funnel' into a 'liquid' phase; and finally symmetry-broken, to a 'crystal' phase. A time- dependent effective temperature re-equilibrates to the bath temperature. The entropic golf-hole, and energetic funnel, are concepts from protein folding [4]. [1] N. Shankaraiah, K.P.N. Murthy, T. Lookman and S.R .Shenoy, Europhys. Lett. 92, 36002 (2010); Phys. Rev. B 84, 064119 (2011) ; and unpublished. [2] S.R. Shenoy, T. Lookman and A. Saxena, Phys. Rev. B 82, (2010). [3] T. Kakeshita, T. Fukuda and T. Saburi, Scr. Mater. 34, 1 (1996); L. Mueller, U. Klemradt and T.R. Finlayson, Mater. Sci. Eng. A, 438, 122 (2006). [4] P.G. Wolynes, et al. Science 267, 1619 (1995); D.J. Bicout and A. Szabo, Protein Science 9, 452 (2000); N. Nakagawa, Phys. Rev. Lett.98, 128104 (2007). |
Joint ICTP/SISSA Informal seminar on Statistical Physics : "Entropy barriers and glass-like behaviour in
martensitic models without extrinsic disorder"
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