Partial Equilibration Scenario in 3D athermal martensites quenched below first-order transition temperatures

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 $T <T_0$ below a first-order transition. The ageing system faces entropy barriers, in {\it searches} for energy-lowering passages between quasi-microcanonical energy shells. We confirm the PES signature of an exponential-tail distribution of intermittent heat releases to the bath, scaled in an effective temperature, that in our case, depends on the quench. When its inverse $\beta_{eff} (T) \equiv 1/T_{eff} (T)$ vanishes below a `martensite start' temperature $T_1$ of avalanche conversions, then entropy barriers vanish. When this search temperature $T_{eff} (T)$ vanishes, PES cooling is arrested, as entropy barriers diverge. We find a {\it linear} vanishing of $T_{eff}(T)\sim T_d -T$, below a delay-divergence temperature $T_d$ in between, $T_1 < T_d < T_0$. Martensitic conversion delays $e^{1/T_{eff}} \sim e^{1/(T_d -T)}$ thus have Vogel-Fulcher-Tammann like divergences. Post-quench delay data extracted from simulations and athermal martensitic alloys, are both consistent with predictions.