Abstract: Most of the available methods for the calculation of the three dimensional(3D)grain size dis- tribution functions(SDF)are based on the S model and lead a grave systematical error.The origin is the basic supposition of spherical grains in the S model,which does not correspond with the feature of real grains.A new model called A model is developed based on the hypothe- sis of polvhedral grains.The probability functions of the A model and the method to calculate the 3D SDFs using the A model are given in the present paper.The theoretical analyses and experimental tests have demonstrated that the A model reduces the systematical error radical- ly.It is nearly as simple as the so far used S model,but gives much better results in repro- ducing of 3D SDFs from the measured ID or 2D SDFs.

Key words: grain size, grain size distribution, stereology, geometric model