QUANTIFYING THE STEREOLOGICAL BIAS PRESENT IN MINERAL LIBERATION DATA
MEASURED IN PARTICLE CROSS-SECTIONS
C. L. Evans* and E. M. Wightman
The University of Queensland, Sustainable Minerals Institute, Julius Kruttschnitt Mineral Research
Centre, 40 Isles Road, Indooroopilly, QLD 4068, Australia.
Telephone +61 7 3365 5888.
Emails: c.evans@uq.edu.au (corresponding author)
e.wightman@uq.edu.au
ABSTRACT
The majority of routine mineralogical measurements of mineral liberation are made on polished sections of
particulate material. The measured areal mineral liberation distribution (sometimes termed the apparent
liberation) is an estimate of the true volumetric distribution due to the effects of stereology. The difference
between the observed areal (2D) liberation and the actual volumetric (3D) liberation is termed stereological
bias or stereological error. This bias results in the proportion of liberated mineral being over-estimated
when measured in two dimensions in polished section but the degree of this bias is difficult to estimate,
particularly since the magnitude of the bias varies with the texture of the particle.
This paper describes how the application of X-ray micro-tomography allows users to measure the mineral
liberation distribution of particles in three dimensions and provides an opportunity to quantify the
magnitude of stereological bias that occurs when the same samples are measured in two-dimensional
polished sections. Comparisons of 2D and 3D measurements made on base metal sulphide ores are used
provide insights into the magnitude of the bias that is present in measurements of liberation in typical
sulphide ores.
Quantifying the magnitude of the stereological bias and its relationship to the mineral characteristics of the
ore being analysed will improve the knowledge of end-users of the accuracy of their mineral liberation data.
The relative contributions to the overall measurement error from the stereological bias and the size of
sample (number of particles) measured will be discussed.
KEYWORDS
Process mineralogy, X-ray tomography, liberation, stereology