Prediction for crystal growth rates in borides under supercooled temperature conditions

Abstract

Two-types of phase-field (PF) calculations were developed to predict the crystallization of borides. The first calculation used an empirical PF mobility [L_exp = A(k_BTΔT/6π²λ³η)^B], which was determined from experimental crystal growth rates (v_exp). 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 v_exp below their melting points. Furthermore, the A and B values of the L_exp 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 v_exp, 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 L_exp. However, the versatile PF equation, which includes the interfacial process (L′) can predict the v_exp of many borides.