Open AccessAN ANALYTICAL METHOD OF SOLUTION OF THE DISTRIBUTION FUNCTION OF CRYSTAL SIZES IN A VOLUME
Author(s) -
Kun Cheng
Publication year - 1957
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.13.58
Subject(s) - laplace transform , variance (accounting) , function (biology) , computation , distribution (mathematics) , mathematics , computer science , distribution function , algebraic number , volume (thermodynamics) , algebraic equation , mathematical analysis , algorithm , nonlinear system , physics , thermodynamics , accounting , quantum mechanics , evolutionary biology , business , biology
The distribution function of crystal sizes on a cross-sectional surface can be obtained by direct observation. By using the well-known Scheil-салIтъIков method one can deduce the volume distribution function. Their method consists chiefly in solving a system of simultaneous linear algebraic equations, in which certain approximations are adopted without explicit criterions. The present paper proposes an analytical method of solution, in which operational calculus and Laplace transform are applied. The density function thus obtained is somewhat in variance with those of Scheil and others; namely, values obtained by the previous authors appear a little lowered as compared with ours. As the present method is rigourous and the numerical computations so far performed are within criterious in accuracy, the difference may well be attributed to the errors introduced by the approximations in the old methods. This fact is fully demonstrated by a concrete example in the text.