Joint ICTP/SISSA Informal seminar on Statistical Physics : "Entropy barriers and glass-like behaviour in
martensitic models without extrinsic disorder"
Starts 4 Feb 2013 15:00
Ends 4 Feb 2013 20:00
Central European Time
SISSA, Santorio Building, Room 5 (ground floor)
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 . 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 . 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 . The mean time shows glass-like Vogel-Fulcher behaviour, t_m ~ exp [ 1/( T_4 - T)], and distributions are log-normal . 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 .
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