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To test a Partial Equilibration Scenario (PES) of Ritort and colleagues, we do Monte Carlo simulations of discretized-strain spin models, for four 3D martensitic structural transitions under quenches to a bath temperature $T

We do Monte Carlo simulations of four 3D structural transitions, with vector-spin models of their martensitic strain domains under quenches to $T$, to test a generic post-quench Partial Equilibration Scenario (PES) of Ritort. We indeed confirm that energy-lowering passages between fixed-energy shells induce a signature PES distribution of an exponential tail in heat releases, scaled in an effective search temperature. A linear vanishing of this $T_{eff}(T)\sim T_d -T$ at a temperature $T_d$ where PES passage-searches freeze, explains the Vogel-Fulcher like divergence of equilibration times $ e^{1/ T_{eff} (T)}\sim e^{1/(T_d -T)}$, extracted from incubation-time delays of simulations and martensitic alloys., Comment: 6 pages, 7 figures, and 4 videos

Snapshots of colloidal particles moving on disordered two-dimensional substrates can be used to extract equal-time many-body correlations in their positions. To understand the systematics of these correlations, we perform Monte Carlo simulations of a two-dimensional model fluid placed in a quenched disordered background. We use configurations generated from these simulations to compute translational and orientational two-point correlations at equal time, concentrating on correlations in local orientational order as a function of density and disorder strength. We calculate both the disorder averaged version of conventional two-point correlation functions for orientational order, as well as the disorder averaged version of a novel correlation function of time-averaged disorder-induced inhomogeneities in local orientation analogous to the Edwards-Anderson correlation function in spin systems. We demonstrate that these correlations can exhibit interesting non-monotonic behavior in proximity to the underlying fluid-solid transition and suggest that this prediction should be experimentally accessible., Comment: 9 pages, 5 figures

We use protein folding energy landscape concepts such as golf-course and funnel to study re-equilibration in athermal martensite parameter regime of triangle-to-centered rectangle, square-to-oblique, and triangle-to-oblique transitions under systematic temperature-quench Monte Carlo simulations. On quenching below a transition temperature, the seeded high-symmetry parent-phase austenite that converts to the low-symmetry product-phase martensite, through autocatalytic twinning or elastic photocopying, has both rapid conversions and incubation-delays in the temperature-time-transformation phase diagram. We find the rapid (incubation-delays) conversions at low (high) temperatures arises from the presence of large (small) size of golf-course edge that has funnel inside for negative energy states. In the incubating state, the strain structure factor enters into the Brillouin zone golf-course through searches for finite transitional pathways which closes off at the transition temperature with Vogel-Fulcher divergences that are insensitive to Hamiltonian energy scales and log-normal distributions, as signatures of dominant entropy barriers. The crossing of the entropy barrier is identified through energy occupancy distributions, Monte Carlo acceptance fractions, heat emission and internal work. The above ideas had previously been presented for the scalar order parameter case. Here we show similar results are also obtained for vector order parameters.

In the conceptual framework of phase ordering after temperature quenches below transition, we consider the underdamped Bales-Gooding-type 'momentum conserving' dynamics of a 2D martensitic structural transition from a square-to-rectangle unit cell. The one-component or $N_{\rm OP} =1$ order parameter is one of the physical strains, and the Landau free energy has a triple well, describing a first-order transition. We numerically study the evolution of the strain-strain correlation, and find that it exhibits dynamical scaling, with a coarsening length $L(t) \sim t^{\alpha}$. We find at intermediate and long times that the coarsening exponent sequentially takes on respective values close to $\alpha=2/3$ and $\alpha=1/2$. For deep quenches, the coarsening can be arrested at long times, with $\alpha \simeq 0$. These exponents are also found in 3D. To understand such behaviour, we insert a dynamical-scaling ansatz into the correlation function dynamics to give, at a dominant scaled separation, a nonlinear kinetics of the curvature $g (t) \equiv 1/ L(t)$. The curvature solutions have time windows of power-law decays $g \sim 1/t^\alpha$, with exponent values $\alpha$ matching simulations, and manifestly independent of spatial dimension. Applying this curvature-kinetics method to mass-conserving Cahn-Hilliard dynamics for a double-well Landau potential in a scalar $N_{\rm OP}=1$ order parameter yields exponents $\alpha = 1/4$ and $1/3$ for intermediate and long times. For vector order parameters with $N_{\rm OP} \geq 2$, the exponents are $\alpha = 1/4$ only, consistent with previous work. The curvature kinetics method could be useful in extracting coarsening exponents for other phase-ordering dynamics., Comment: 18 pages, 16 figures

We present systematic temperature-quench Monte Carlo simulations on discrete-strain pseudospin model Hamiltonians to study microstructural evolutions in 2D ferroelastic transitions with two-component vector order parameters ($N_{OP}=2$). The zero value pseudospin is the single high-temperature phase while the low-temperature phase has $N_v$ variants. Thus the number of nonzero values of pseudospin are triangle-to-centered rectangle ($N_v=3$), square-to-oblique ($N_v=4$) and triangle-to-oblique ($N_v=6$). The model Hamiltonians contain a transition-specific Landau energy term, a domain wall cost or Ginzburg term, and power-law anisotropic interaction potential, induced from a strain compatibility condition. On quenching below a transition temperature, we find behaviour similar to the previously studied square-to-rectangle transition ($N_{OP} =1, N_v = 2$), showing that the rich behaviour found, is generic. Thus we find for two-component order parameters, that the same Hamiltonian can describe both athermal and isothermal martensite regimes for different material parameters. The athermal/isothermal/austenite parameter regimes and temperature-time-transformation diagrams are understood, as previously, through parametrization of effective-droplet energies. In the athermal regime, we find rapid conversions below a spinodal like temperature and austenite-martensite conversion delays above it, as in the experiment. The delays show early incubation behaviour, and at the transition to austenite the delay times have Vogel-Fulcher divergences and are insensitive to Hamiltonian energy scales, suggesting that entropy barriers are dominant., Comment: 11 pages, 16 Figures

Entropy barriers and ageing states appear in martensitic structural-transition models, slowly re-equilibrating after temperature quenches, under Monte Carlo dynamics. Concepts from protein folding and ageing harmonic oscillators turn out to be useful in understanding these nonequilibrium evolutions. We show how the athermal, non-activated delay time for seeded parent-phase austenite to convert to product-phase martensite, arises from an identified entropy barrier in Fourier space. In an ageing state of low Monte Carlo acceptances, the strain structure factor makes constant-energy searches for rare pathways, to enter a Brillouin zone `golf hole' enclosing negative energy states, and to suddenly release entropically trapped stresses. In this context, a stress-dependent effective temperature can be defined, that re-equilibrates to the quenched bath temperature., Comment: 11 pages, 12 figures. Under process with Phys. Rev. B (2015)