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根据成核理论,当仅考虑均匀核化时,在过冷熔体中结晶成核率可用下式表示: I=N_v~°kT/(3πα_°~3η)exp(-16πα~3β/3T_rΔT_r~2) (1)其中α=(N_v~°)~(1/3)σ/ΔH_m,β=1ΔH_m/RT_m=T/T_m, ΔT_r=T_m-T/T_m.各参量分别表示:I,成核率(cm~(-3)·s~(-1);N_v~°单位体积中的分子数(cm~(-3);η,粘滞系数(P);σ,比表面能(cal·cm~(-2));ΔH_m,熔化时的焓变(cal·mol~(-1));N,阿佛加德罗常数;v,克分子体积;T,熔体温度(K);T_m,熔点(K);k,玻尔兹曼常数;R,气体常数;α_0,分子直径。
According to the nucleation theory, when only uniform nucleation is considered, the nucleation rate of nucleation in a subcooled melt can be expressed as follows: I = N_v ~ ° kT / (3πα_ ° ~ 3η) exp (-16πα ~ 3β / 3T_rΔT_r ~ (1) where α = (N_v ~) ~ (1/3) σ / ΔH_m, β = 1ΔH_m / RT_m = T / T_m and ΔT_r = T_m-T / T_m. (Cm ~ (-3) · s -1; N_v ~ ° Number of molecules per unit volume (cm -3; η, viscosity coefficient (P); σ, specific surface energy ΔH_m, enthalpy change at melting (cal · mol -1), N, Avogadro’s number, v, molecular volume, T, melt temperature (K) T_m, melting point (K); k, Boltzmann constant; R, gas constant; α_0, molecular diameter.