Stereological Correction for Mineral Liberation Based on Texture Analysis of Ore Particle Sections

"Accurate assessment of the liberation state of crushed ore particles is important for efficient mineral processing. In general, the liberation state is assessed by two-dimensional (2D) measurement of polished ore sample sections. However, this 2D measurement inevitably suffers from overestimation of the degree of liberation, known as stereological bias. This arises from the fact that biphase particle sections of which only one phase happens to have been cut are indistinguishable from liberated particles. To date, several stereological correction methods have been proposed, but their applicability for various types of particles has not yet been sufficiently examined, and this tends to undermine their practicality. We have addressed this problem using a numerical-analytical approach in which various types of biphase particles are modeled, and the 2D sectional information is compared with actual three-dimensional (3D) information. Through simulations, we revealed a general relationship between the internal mineral structure of particles and the stereological bias. Finally, we have developed a unique stereological correction method in which the texture (a 2D pattern characteristic) of particle sections is used to estimate the internal structure of particles, and thereby the stereological bias. KEYWORDS Mineral liberation, stereological bias, texture analysis INTRODUCTION Mineral liberation assessment of 2D particle sections inevitably suffers from stereological bias; that is, overestimation of the degree of liberation. Stereological bias is caused by the fact that a composite particle can be misidentified as a liberated particle when only one phase happens to have been cut in sectional measurement. Stereological bias has attracted attention since Gaudin pointed out its importance in 1939 (Gaudin, 1939). Several attempts have been made to measure the 3D liberation state directly, avoiding the bias, using X-ray computed tomography (Gay and Morrison, 2006; Lin and Miller, 1996; Miller et al., 2003; Miller et al., 2009; Reyes et al., 2017; Videla et al., 2007). These have provided useful information through laboratory testing, but further technical refinement is necessary for practical usage, to overcome the technique’s limitations in terms of resolution, assessment of minerals of similar density, and speed. Therefore, for practical purposes, detailed information regarding mineral phase geometry is obtained by sectional analysis, using automated scanning electron microscopy/energy-dispersive X-ray spectroscopy (SEM/EDX)-based analysis (e.g., with a mineral liberation analyzer (MLA) (Fandrich et al., 2007; Sandmann, 2015)); and the development of an effective method of stereological correction, which predicts the relevant bias and transforms the measurable 2D degree of liberation into its 3D counterpart, is an important research aim."