Fig. 1.

(a) Evolution of crystal temperature during flash-cooling from 293 to 77 K for a spherical crystal with radius a = 0.1 mm and thermal diffusivity κ = 1.2 × 10^–7 m² s^–1. The three curves refer to the spatially averaged temperature in the inner, middle, and outer thirds of the crystal volume. (b) Temperature dependence of the equilibrium population, , of the low-enthalpy state A in a two-state equilibrium with ΔH = 25 kJ mol^–1 and ΔS = 100 J K^–1 mol^–1. (c) Temperature dependence of the exchange time, 1/k_ex, as predicted by Eqs. 7 and 8 with τ₀ = 10 ns, ΔH^# = 40 kJ mol^–1, D(T) from the Vogel–Tamman–Fulcher fit for water, and as in b. (d) Evolution of A state population x_A(t) during flash-cooling, computed numerically with the aid of Eq. 6, and based on the temperature profiles in a, the equilibrium population in b, and the exchange time in c. The dashed curves correspond to the equilibrium Boltzmann population, , at the time-dependent temperature.