Effect of Particle Shape on the Stereological Bias of the Degree of Liberation of Biphase Particle Systems

Abstract

It is well known that in sectional measurements of polished ore samples, the degree of liberation is overestimated by stereological bias. The stereological bias is affected by particle shape, but the effect of particle shape on the stereological bias has not been studied systematically. In this study, particles of various shapes were modeled using a geodesic grid, and the internal structures of the particles were randomly designed. The stereological bias of liberation was assessed quantitatively by comparing the computed sectional information and the original three-dimensional information. The following results were obtained: 1) the effect of aspect ratio on the stereological bias is less than 12% when comparing cases with α ranging from 1.0 to 2.0; 2) the effect of particle surface roughness on the stereological bias is smaller than 7.6% when comparing cases with surface roughness (the quotient of the surface area of the volume equivalent ellipsoid and the surface area of a particle) ranging from 0.833 to 0.996. It was also con rmed that the previously proposed stereological correction method is applicable to irregularly shaped particles because the estimation error of the degree of liberation dramatically dropped from 56.4%-64.4% without any correction to 1.16%-3.41% using the proposed method.

Determination of Liberation Degree of Mechanically Processed Waste Printed Circuit Boards by Using the Digital Microscope and SEM-EDS Analysis

“…Such phenomena could mislead the determination of the liberation degree, since plastics/other metals might be aggregated within such ball-shaped particles, hence, it could overestimate the liberation degree of the metallic particles, especially with the digital microscope image analysis. In addition, in general, the stereological bias in 2D sectional analysis [6] might affect the results obtained via both digital microscope and SEM-EDS image analyses.…”

“…The degree of liberation, indicating how much the target component is liberated from the non-valuable components, is a key factor when establishing the liberation performance of the comminution to determine the success of subsequent process for valuable material recovery [4]. The study of the degree of liberation was initially introduced in the mineral processing field, where the main objective was to achieve selective liberation of the valuable minerals of interest aiming for the coarsest particle size possible, saving energy on the grinding process and reducing the amount of non-desirable fine fractions produced [5,6].…”

Comparison of Seven Texture Analysis Indices for Their Applicability to Stereological Correction of Mineral Liberation Assessment in Binary Particle Systems

“…Each irregularly shaped particle was modeled using a geodesic grid [32]. Briefly, an ellipsoid was fitted with a triangular mesh, each node of which was randomly relocated in the radical direction to form surface roughness.…”

“…The core phase could be spherical [20][21][22][28][29][30], regularly-shaped [16,30,31], or irregularly-shaped [32]. This differed from the Boolean model (below) because the core phases did not overlap with each other.…”