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借助MATLAB软件,分别调用插值函数(griddata)编写程序绘制Ag-Pb-Sn三维相图—插值法和回归函数(regress)编写程序绘制三维相图—拟合曲面方程法。结果表明:插值法得到的三维相图液相面很不光滑,局部波动很大,不能显示出相邻相区的析晶线和共晶点;拟合曲面方程法得到的液相面相对光滑,并能清晰的显示出相邻相区的析晶线和共晶点,拟合出的(Ag),Ag5Sn,Ag3Sn,(Pb),(Sn)等相区曲面方程的可决系数r2分别为1.0000,0.9819,0.9855,0.9872,0.9713,说明拟合出的曲面方程是可信的。为了进一步验证拟合出液相面的准确性,选择投影图上等温线数据,对比其原始温度值与拟合温度值,结果表明:原始值与拟合值的最大偏差为23.67℃,最小为0.26℃,偏差绝对值的平均值为6.57℃,相对误差绝对值的平均值为1.36%,原始值与拟合值相符,说明利用拟合曲面方程法获得Ag-Pb-Sn三维相图是准确、可行的。相对Ag-Pb-Sn的二维投影图,Ag-Pb-Sn三维相图不仅能获得液相面上任意一点的温度值,并且能直观显示出各个相区的温度变化趋势。
With MATLAB software, griddata programming program was used to draw Ag-Pb-Sn three-dimensional phase diagram - interpolation and regress programming to draw three-dimensional phase diagram-fitting surface equation method. The results show that the liquid phase of the three-dimensional phase diagram obtained by the interpolation method is very non-smooth and the local fluctuations are very large, and the crystallization phase and the eutectic point of the adjacent phase regions can not be displayed. The liquid surface obtained by the fitting surface equation method is relatively smooth , And can clearly show the adjacent phase zone of the crystallization line and the eutectic point, fitting (Ag), Ag5Sn, Ag3Sn, (Pb), (Sn) 1.0000,0.9819,0.9855,0.9872,0.9713, indicating that the fitted surface equation is credible. In order to further verify the accuracy of fitting the liquid surface, the isotherm data of the projection is selected and compared with the original temperature and the fitting temperature. The results show that the maximum deviation between the original value and the fitted value is 23.67 ℃, the minimum is 0.26 ℃, the absolute value of the deviation is 6.57 ℃, the absolute value of the relative error is 1.36%, the original value is consistent with the fitting value, which shows that the three-dimensional phase diagram of Ag-Pb-Sn obtained by the fitting surface equation is accurate ,feasible. Compared with the two-dimensional projection of Ag-Pb-Sn, the three-dimensional phase diagram of Ag-Pb-Sn can not only obtain the temperature at any point on the liquid surface, but also show the trend of temperature in each phase.