First order phase transformations: scaling relations for grain self-correlation functions

Abstract

At high pressure many alkali halides transform from the NaCl (B1) structure to the CsCl (B2) structure. We have recently studied this transformation in polycrystalline RbI, which transforms at a critical pressure, P/sub c/ = 3.5 kbar. By observing the time development of the neutron diffraction pattern after sudden increase of hydrostatic pressure from P<P/sub c/ to P>P/sub c/ we directly deduced X(t), the fraction of the sample converted from metastable to stable phase, as a function of time. We showed that X(t) taken at different P could be approximately scaled onto a universal growth curve by introducing an adjustable characteristic time tau(P) for each curve. The success of the Kolmogorov in fitting X(t) suggests that comparisons of model predictions with other experimental observables be made on the system. For example, by a trivial (in principle) extension of the neutron diffraction techniques described above, one might determine the broadening of the powder diffraction peaks due to finite grain size as a function of time throughout growth. This particle size broadening is related by Fourier transformation to the grain autocorrelation function, G/sub s/(r,t), which measures the ensemble average of the overlap of grains with themselves upon translation of the grain pattern by an amount r. We present some results of a study of the scaling properties of G/sub s/(r,t) for the Kolmogorov model for d=1 and d=2. Although the model is highly idealized, it is perhaps the simplest conceivable one which obeys correlation function scaling in early stages of growth and undergoes nontrivial saturation due to volume fraction effects in the late stages. 4 refs., 6 figs