Segregation during crystal growth from melt and absorption cross section determination by optical absorption method

Segregation during crystal growth from melt under two conditions is studied by using crystal mass, which can be measured easily, as an independent variable, and a method to determine the effective segregation coefficient and absorption cross section of optical dopant is given. When the segregated solute disperses into the whole or just a part of melt homogenously, the concentration C _s in solid interface will change by different formulas. If the crystal growth interface is conical and segregated solute disperses into melt in total or part, the solute concentration at r = 2/3R, where r is the distance from the growth cross section center and R the crystal radius, is independent on the shape of the crystal growth interface, and its variation at r = 2/3R can be regarded as the result from crystal growth in flat interface. With C _s variation formula in solid and absorption cross section σ for optical dopant, the absorption coefficients along the crystal growth direction can be calculated, and the corresponding experimental value can be obtained through the crystal optical absorption spectra. By minimizing the half sum, whose independent variables are k, ΔW or σ, of the difference square between the calculated and experimental absorption coefficients from one or more absorption peaks along the crystal growth direction, k and σ, or k and ΔW, can be determined at the same time through the Levenberg-Marquardt iteration method. Finally, the effective segregation coefficient k, ΔW and absorption cross sections of Nd:GGG were determined, the results fitted by two formula gave more closed effective segregation coefficient, and the value ΔW also indicates that the segregated dopant had nearly dispersed into the whole melt. Experimental results show that the method to determine effective segregation coefficient k, ΔW and absorption cross sections σ is convenient and reliable, and the two segregation formulas can describe the segregation during the crystal growth from melt relatively commendably. Supported by the National Natural Science Foundation of China (Grant No. 50772112)