规化形状因子新概念及测算方法研究

A new concept and calculating method for quantitative form description: regular form factor

本文提出基于椭圆形状的描述平面粒子形状不规则（或规则）程度的规化形状因子新概念及计算方法。定义在平面上粒子形状与同其长、短轴相同椭圆的接近程度为规化形状因子（ＲＦＦ），导出以下计算式：ＲＦＦ＝Ａ［３（ｄ１＋ｄ２）－２√（ｄ１·ｄ２）］／（ｄ１·ｄ２·Ｃ），或ＲＦＦ＝Ａ［１５（ａ＋ｂ）－√（ａ·ｂ］／（ａ·ｂ·Ｃ）。式中Ａ、Ｃ、ｄ１、ｄ２分别为平面上粒子的面积、周长、长轴和短轴，ａ＝ｄ１／２，ｂ＝ｄ２／２。粒子形状为椭圆或圆时，ＲＦＦ＝１；粒子形状不规则时，ＲＦＦ＜１；粒子形状越接近椭圆或圆，则ＲＦＦ越接近１；粒子形状越不规则；则ＲＦＦ越小。对测算误差进行了分析，并导出有关校正式，举例说明了有关测算方法。

A new concept and calculating method for form description, regular form factor (RFF) was put forward. RFF was defined as the extent that a structure differs from (or be simular to) an ellipse or circle of which the major and minor diameters are respectively equal to the described structure. The formulae have been deduced as following:  RFF =A[3(d 1+d 2)-2√(d 1·d 2)]/(d 1·d 2·C); or:  RFF =A[1 5(a+b)-√(a·b]/(a·b·C). In the formulae, A, C, d 1, d 2 mean respectively the area, circumference, major and minor diameter of the structure, a=d 1/2, b=d 2/2. RFF=1 for ellipase or circle; RFF<1 for irregular structures. The more are the structures irregular, the smaller are the values of RFF; the more are the structures regular, the closer to 1 are the values of RFF. RFF was compared with Form AR and the result showed that RFF is more sensible to describe a structure irregularity than Form AR. An example was given to show how to calculate RFF. The error was analysed and the correcting formulae for RFF have been deduced.