Controlled growth of large β-BaB₂O₄ crystals based on theoretical guidelines

The diagram of phase equilibria in the BaB₂O₄–NaF system has been used to deduce the relationship between the cooling speed (ΔT), the pulling speed (v), the crystal radius (R_s), the slope of liquidus (m), the solution component (x) and the total quantity of melt, namely ΔT = 0.00159R_s²vmx²/G. The theoretical curves of the crystal thickness dependence on cooling rate and pulling rate have also been drawn. Under the guidance of the deduced formulas, the controlled growth of β-BaB₂O₄ (BBO) crystals to a desired size has been achieved. A typical as-grown BBO crystal with dimensions of Ø76 × 33 mm (525.25 g) has been grown successfully by using the high-temperature top-seeded solution growth method. The measured optical homogeneity indicates that the as-grown BBO crystal has high optical quality (Δn ≃ 6.9 × 10⁻⁶). The experimental curves of the crystal thickness versus the cooling rate and pulling rate were in line with the theoretical curves. The phenomenon of diameter shrinkage in the crystal growth has also been explained according to theory and practice. The theoretical derivation and experimental results provide the rationale for further growth of large BBO crystals with high optical quality.