中文摘要：

借助于几何概率中的一些相关理论，从理论分析的角度，对表面为凸形曲线或曲面的二维和三维任意形状粒子建立了表观界面过渡区厚度统计平均值和实际界面过渡区厚度之间的定量关系。结果表明，对于二维凸形粒子，截面分析法所得的表观界面过渡区厚度的统计平均值与实际界面过渡区厚度之间的比值小于π／2。精确比值与粒子的形状有关。如果实际界面过渡区厚度与粒子的尺寸相比可以忽略的话，截面分析法所得的表观界面过渡区厚度的统计平均值与实际界面过渡区厚度之间的比值约等于π／2。对于三维凸形粒子，截面分析法所得的表观界面过渡区厚度的统计平均值与实际界面过渡区厚度之间的比值小于2，比值的精确解与粒子的形状有关。如果实际界面过渡区厚度与粒子的尺寸相比可以忽略的话，截面分析法所得的表观界面过渡区厚度的统计平均值与实际界面过渡区厚度之间的比值约等于2。

英文摘要：

This paper employs some related theorems as well as the results from the field of geometrical probability to explore the quantitative relationship between statistical mean values of the apparent interracial transition zone （ITZ） thickness and the actual ITZ thickness. In the 2 dimensional case as well as in the 3 dimensional case, the general solutions are derived for an arbitrary shape grain with closed convex curve （2D） or convex surface （3D）. The results show that： （1） For the 2D grains with the closed convex curve of an arbitrary shape, the ratio of the statistical mean apparent ITZ thickness to the actual ITZ thickness is less than π/2. The exact value depends on the shape of the grains. If the actual ITZ thickness is far less than the size of the grain, this ratio is approximately equal to π/2. （2） For the 3D grains with the closed convex surface of an arbitrary shape, the ratio of the statistical mean apparent ITZ thickness to the actual ITZ thickness is less than 2. The exact value also depends on the shape of the grains. If the actual ITZ thickness is far less than the size of the grain, the ratio of the statistical mean value of the apparent ITZ thickness to the actual ITZ thickness is approximately equal to 2.