Abstract

In this paper, a new mathematical model has been presented to determine the equilibrium segregation (k₀) and effective segregation (k_eff) coefficients for neodymium (Nd) in YAG crystal grown by Czochralski (CZ) method. Determination of diffusion coefficient (D_L) of Nd impurity in molten YAG is also investigated. In this model, utilizing Lambert W-function is a new idea to solve the Scheil equation for calculation of effective segregation coefficient. The Nd concentration in the crystal has been measured by optical absorption method to calculate k_eff. The analyses show that the k_eff is related to the growth parameters such as crystal growth rate (u_g) and crystal rotation rate (ω), ( u_g/√{ω}) but it is independent of the Nd concentration in the initial melt (C₀). Based on obtained k_eff and experimental growth data, k₀ and D_L of Nd in molten YAG have been calculated. For all experiments, the average value of k₀=0.216 and D_L=1.4×10^-6 (cm²/s) are obtained. Our results are corroborated by the theoretical and experimental data from the literature.