Stereological bias for spherical particles with various particle compositions

Abstract

Two-dimensional (2D) measurements of the cross-sections of polished mineral samples suffer from an overestimation of the degree of liberation known as stereological bias. Stereological bias is believed to be affected by the particle texture, i.e., the stereological bias of a simple locking particle is high, while the bias of a particle with a complex texture is negligible. However, scant work has been performed on the development of a quantitative and versatile modeling of stereological bias. We performed a series of numerical simulations: modeling particle assembly using the discrete element method; modeling the binary texture of particles by imposing phase patterns to the particles; systematical generation of 8608 types of phase patterns; liberation assessments in 2D and in three-dimension (3D) based on the error-free geometrical calculation; and stereological bias assessment by a comparison between liberations in 2D and 3D. Through these simulations, the correlation between the stereological biases of the phases and particle texture was investigated. Finally, the particle texture complexity was assessed using the fractal dimension of image intensity, and stereological bias for the matrix phase was successfully correlated with the fractal dimension and area fraction of the core phase. Fractal dimension and area fraction values are easily obtained by 2D measurements and subsequent image analysis. These results may lead to the establishment of a versatile stereological correction model that depends only on measurable 2D parameters.