迭代最小二乘回归方法估算蒙脱石标准生成Gibbs自由能ΔG_f^0的研究

EVALUATION OF STANDARD GIBBS FREE ENERGY FOR MONTMORILLONITE FORMATION BY ITERATIVE LEAST SQUARE REGRESSION METHOD

将迭代最小二乘法应用于硅酸盐矿物标准生成Gibbs自由能ΔG0f 的估算 ,以克服早期指数回归方法 (Chen ,1 975)的一些局限性。借助于树图理论实现了指数回归方程中指数幂xi 的优化选定 ,并采用迭代最小二乘法求解回归方程 ,得到一个估算硅酸盐矿物标准生成Gibbs自由能的改进回归方法。用此方法估算了几种化学计量已知的硅酸盐矿物以及非化学计量组成蒙脱石的标准生成Gibbs自由能 ,所得结果与文献值比较吻合得较好 ,相对误差一般小于0 .5% .

An iterative least square method was used for the evaluation of standard Gibbs free energy for the formation of silicate minerals in order to remove some of the limitations of the earlier exponential regression method. An optimum procedure for the assignment of exponential rankings of ΣΔ G 0 f i values is suggested based on the “tree diagram” theory and an iterative least_squares fitting technique is applied to solve the exponential regression equation. At last, an improved regression method for the evaluation of standard Gibbs free energy for the formation of silicate minerals is described in this paper. Using this improved method, the standard Gibbs free energies for the formation of several stoichiometric silicate minerals and some nonstoichiometric montmorillonites are estimated, and, in most cases, the estimated data are in accordance with the results fairly well as compared with those from the references, the error of estimation is usually less then 0.5%.