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This paper introduces a novel method for characterizing fracture mechanisms in composite materials using 3D image data gained by computed tomography (CT) measurements. In mineral liberation, the understanding of these mechanisms is crucial, particularly whether fractures occur along the boundaries of mineral phases (intergranular fracture) and/or within mineral phases (transgranular fracture). Conventional techniques for analyzing fracture mechanisms are focused on globally comparing the surface exposure of mineral phases extracted from image measurements before and after fracture. Instead, we present a virtual reassembling algorithm based on image registration techniques, which is applied to 3D data of composite materials before and after fracture in order to determine and characterize the individual fracture surfaces. This enables us to conduct a local quantitative analysis of fracture mechanisms by voxelwise comparing adjacent regions at fracture surfaces. A quantitative analysis of fracture mechanisms is especially important in the context of geometallurgical recycling processes. As primary deposits are decreasing worldwide, the focus is shifting to secondary raw materials containing low concentrations of valuable elements such as lithium. To extract these elements, they can be enriched as engineered artificial minerals in the slag phase of appropriately designed cooling processes. The subsequent liberation through comminution processes, such as crushing, is essential for the extraction of valuable minerals. A better understanding of crushing processes, especially fracture mechanisms in slags, is crucial for the success of recycling. The reassembling algorithm presented in this paper is evaluated through a simulation study, followed by an application to a naturally occurring ore and a slag resulting from a recycling process.

The demand for lithium, as well as other critical resources, needed for electrochemical energy storage is expected to grow significantly in the future. Slags obtained from pyrometallurgical recycling represent a promising resource of valuable materials, among them lithium and rare earth elements found in artificial minerals particulate phases. This study investigates the flotation separation of engineered artificial minerals (EnAMs) in slags, such as lithium aluminate and gehlenite as valuable and gangue phases, respectively. Flotation experiments are carried out in a Partridge-Smith cell using oleic acid (OA) as a benchmark surfactant. Particle characterization is performed using SEM-based Mineral Liberation Analysis (MLA), which provides particle discrete information. From this information, bivariate Tromp functions based on non-parametric kernel density estimation are computed to characterize the separation behavior with respect to particle descriptors. This approach enables investigating the influence of particle size and shape on separation behavior of EnAMs. Furthermore, these results allow for the optimization of flotation experiments for enriching Li-bearing EnAMs.

Particle separation is typically investigated regarding one particulate property only. Virtually all separation processes, however, act on various particle properties in different ways. Modern particle analytical modalities enable a statistically meaningful multidimensional particle characterization. Within this study, individual particle fractions of magnesite, calcite and fluorite (-71 $\mu m$) are processed via the turbulent cross-flow separator cascade Cyclosizer (M16, MARC Technologies Pty Ltd), consisting of 5 hydrocyclones, thus producing 5 different product streams. Particle characterization is achieved via dynamic image analysis from which information on the particle shape and size is obtained. Using this data, bivariate Tromp functions are computed, which show the combined effect of the particle descriptors of roundness and area-equivalent diameter on the separation behavior. While the first cyclones recover predominantly coarse particles with high roundness values, fine particles with varying roundness are recovered in the latter cyclones.

Froth flotation predominantly separates particles according to their differences in wettability. However, other particle properties such as size, shape or density significantly influence the separation outcome as well. Froth flotation is most efficient for particles within a size range of about $20-200\mu m$, but challenges arise for very fine or coarse particles that are accompanied by low recoveries and poor selectivity. While the impact of particle size on the separation behavior in flotation is well-known by now, the effect of particle shape is less studied and varies based on the investigated zone (suspension or froth) and the separation apparatus used. A multidimensional perspective on the separation process, considering multiple particle properties, enhances the understanding of their collective influence. In this paper the two-dimensional case is studied, i.e., a parametric modeling approach is applied to determine bivariate Tromp functions from scanning electron microscopy-based image data of the feed and the separated fractions. With these functions it is possible to characterize the separation behavior of particle systems. Using a model system of ultrafine ($<10\mu m$) particles, consisting of differently shaped glass particles with different wettability states as the floatable and magnetite as the non-floatable fraction, allows for investigating the influence of particle size, shape and wettability, on the separation. In this way, the present paper contributes to a better understanding of the complex interplay between certain property vectors for the case of ultrafine particles. Furthermore, it demonstrates the benefits of using multivariate Tromp functions for evaluating separation processes, and points out the limitations of SEM based image measurements by means of mineral liberation analysis (MLA) for the studied particle size fraction.