Abstract
A transformation equation can be used to describe the relationship between the one, two and three dimensional information regarding the composition of mineral particles of specified size. Linear or areal grade distribution f( g i ) can be transformed to an estimate of the volumetric grade distribution p( g) via a transformation function H( g i | g, Nn, …), a conditional probability function. The effect of the external particle strucuture (shape) and internal grain characteristics (grade, dispersion density, and grain size distribution) on the transformation matrix have been evaluated by computer simulation of randomly oriented, irregularly shaped, multiphase particles. Volumetric grade and dispersion density (number of grains per particle) are the most important variables which influence the transformation matrix. Least square minimization of fitted functions and the Phillips-Twomey inversion technique have been used to solve the transformation equation. Three examples, a computer simulated volumetric grade distribution and two experimental depth profiles of different monosize particle samples (iron ore and copper ore), provide evidence that such an approach can be useful for detailed liberation analysis.
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