Prediction for crystal growth rates in borides under supercooled temperature conditions

Two-types of phase-field (PF) calculations were developed to predict the crystallization of borides. The first calculation used an empirical PF mobility [Lexp = A(kBTΔT/6π2λ3η)B], which was determined from experimental crystal growth rates (vexp). The calculation results for various binary borides such as Li2O–2B2O3, Na2O–2B2O3, Na2O–4B2O3, K2O–4B2O3, BaO–2B2O3, and PbO–2B2O3, agreed well with the experimental vexp below their melting points. Furthermore, the A and B values of the Lexp for the borides depended on diffusivity and cation molar mass, including that it is important for cation transfers during crystallization. The second calculation solved the PF equation using versatile PF mobility (L′ ∼ rD/κ2), in which an interfacial process (r) was included. The calculation results agreed well with the first calculation results and the experimental vexp, except for Li2O–2B2O3. In Li2O–2B2O3, the interfacial process strongly affected the crystal growth rates because of the strong nonlinear phenomenon. For diffusive ceramics such as Li2O–2B2O3, we should use the empirical Lexp. However, the versatile PF equation, which includes the interfacial process (L′) can predict the vexp of many borides.