用MATLAB绘制Pb-Sn-Sb三维立体相图

Three-Dimensional Phase Diagrams of Pb-Sn-Sb Drawn by MATLAB

借助Getdata Graph Digitizer图像数字化软件,从三元相图液相面投影图提取原始数据;借助MATLAB编程软件,调用回归函数(regress)输出液相面曲面方程的回归系数;调用MATLAB三维绘图函数(plot3,mesh,surf),编写程序绘制Pb-Sn-Sb三维立体相图。结果表明:通过Getdata Graph Digitizer软件,可以准确提取三元相图液相面投影图的等温线数据,提高了人工手动读取数据的效率;通过拟合曲面方程法,可以得到各个液相面曲面方程的回归系数和曲面方程,拟合效果很好;MATLAB绘制的三维立体相图,通过分析原始温度和拟合温度,最大误差为5.8839℃,最小误差为0.0297℃,相对最大误差为2.23%,相对最小误差为0.01%,说明利用MATLAB绘制Pb-Sn-Sb三维立体相图的方法是准确可行的。利用已知三元相图液相面的曲面方程,可以获得等温线之间任意组分的液相面理论温度,进而为火法工艺提供一定的理论指导。

The original data were extracted from the ternary phase diagram liquid surface projection by Getdata Graph Digitizer image digitization software. The regression coefficients of liquid surface curved surface equations were got by regression function（regress） of MATLAB. The three-dimensional phase diagrams of Pb-Sn-Sb were plotted by writing programs with MATLAB in which the three dimensional plotting function（plot3,mesh,surf） was applied. The results showed that Getdata Graph Digitizer could extract theisotherm data of liquid surfacemore accurately and more effectively than manual read. By the fitting surface equation method,different surface equations and regression coefficients of liquid surface could be obtained and the fitting effect was good. By analyzing the original temperature and fitting temperature of three-dimensional phase diagrams,it was found that the maximum error was 5. 8839 ℃,the minimum error was 0. 0297 ℃,the relative maximum error was 2. 23%,the minimum relative error was 0. 01%. It was shown that drawing three-dimensional phase diagrams of Pb-Sn-Sb by MATLAB was accurate and feasible. Using the known liquid surface equation of ternary phase diagram on the surface,any theoretical temperature of liquid surface between the isotherms could be obtained,which provided certain theoretical guidance for pyrometallurgical process.