Crystal growth kinetics of boron oxide under pressure

Abstract

We have measured the crystal growth rate u of B2O3-I in the amorphous phase, as it varied over five orders of magnitude with changes in temperature and pressure. We eliminated the crystal nucleation barrier by seeding the surface of boron oxide glass with crystals. u became measurable only when the pressure exceeded a threshold level near 10 kbar. Using the published thermodynamic information on the B2O3 system and a crude free-energy model for the crystal and glass phases, we account qualitatively for our results with the theory of crystal growth limited by the rate of two-dimensional nucleation of monolayers. The constants for the prefactor, activation energy, activation volume, and ledge tension are determined by fitting. By adjusting the thermodynamic parameters to a set of values that are well within the ranges delineated by their experimental uncertainties, we account quantitatively for the measured growth rates from 300 to 500 °C and from 0 to 30 kbar with the following relation: u(T,P)=(785 m/s)[‖ΔGm‖/(RT)]1/6 ×exp[π×3 Å(420 erg/cm2)2(28 cm3/mole)/(3 kTΔGm)]exp[−10 366 cal/mole/(RT)] ×exp[−P×16 cm3/mole/(RT)]×{1−exp[ΔGm/(RT)]}2/3, with the driving free energy given by ΔGm(T,P)=(13 cm3/mole) [PM(T)−P] and the melting curve given by PM(T)=(T−450 °C)/(42.6 K/kbar). The ‘‘B2O3 crystallization anomaly’’, that crystals have never been observed to grow at atmospheric pressure, is explained, since according to our model, the frequency of two-dimensional nucleation is negligible at all temperatures at pressures less than 10 kbar.