Open AccessArticle

Particle Size-and Structure-Dependent Breakage Behaviors of EnAM-Containing Slags

Simon Bahnmüller

^1,*

Paul Hirschberger

Thu Trang Võ

Cindytami Rachmawati

³,

Arno Kwade

Urs Peuker

Harald Kruggel-Emden

² and

Carsten Schilde

Institut für Partikeltechnik, Technische Universität Braunschweig, Volkmaroder Straße 5, 38104 Braunschweig, Germany

Chair of Mechanical Process Engineering and Solids Processing, Technische Universität Berlin, Ernst-Reuter-Platz 1, 10587 Berlin, Germany

Institute of Mechanical Process Engineering and Mineral Processing, TU Bergakademie Freiberg, Agricolastraße 1, 09599 Freiberg, Germany

Author to whom correspondence should be addressed.

Minerals 2025, 15(2), 195; https://doi.org/10.3390/min15020195

Submission received: 23 December 2024 / Revised: 12 February 2025 / Accepted: 13 February 2025 / Published: 19 February 2025

(This article belongs to the Collection Engineered Artificial Minerals (EnAMs): A Geo-Metallurgical Tool to Recycle Critical Elements from Waste Streams: Synthesis, Characterization, Metallurgical and Mechanical Processing (SPP 2315))

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Figure 1
(a) A part of the homogeneous structure shown in element map overlay from micro X-ray fluorescence analysis and (b) the binary image of the observed clusters. "> Figure 2
Representative schematic representation of the structures: mineral grains and clusters in the slag sample are shown for three exemplary clusters, where a single hexagonal shape represents a single mineral grain and the accumulation of the connected single grains forms a cluster. "> Figure 3
Three-dimensional visualization of XCT data of three clusters consisting of smaller grains. Every grain is labelled with a unique color for easier differentiation. "> Figure 4
Size distributions of the determined grain size determined based on XCT image data (a) and the cluster size based on µXRF imaging (b) of the analyzed slag. "> Figure 5
SEM (a,b) and SEM/EDX (c,d) images of two samples (a–d) in the micro size range to investigate the structural composition on the surface. "> Figure 6
Side view of the load cell (Shimadzu AG-50kNX) during the piston tests (a) and a schematic representation of the load cell’s setup (b). "> Figure 7
Schematic representation of the two-roller breakage tester. "> Figure 8
Distribution of the breakage strength of particles in different size classes in the micro and macro size ranges. "> Figure 9
The specific breakage strength as a function of particle size, fitted based on the model by Tavares and King [<a href="#B33-minerals-15-00195" class="html-bibr">33</a>]. Grain and cluster sizes are highlighted as vertical lines. "> Figure 10
Normalized fragment size distribution in the micro and macro size ranges and normalized cluster and grain size distributions. "> Figure 11
Normalized fragment size distributions in the micro and macro ranges and fits for the breakage function by Zhu et al. [<a href="#B42-minerals-15-00195" class="html-bibr">42</a>]. ">

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Abstract

Slags containing critical minerals concentrated in artificial phases, so-called engineered artificial minerals (EnAMs), are a novel source of critical raw materials. To liberate the EnAMs, the slags need to be comminuted, reducing the size of the particles. This work investigated the dependence of the breakage behavior on particle size and mineral structure during the comminution of an EnAM-containing slag. Piston-die experiments were performed for particles in the 3 mm to 5 mm size range. Nanoindentation and two-roller breakage tester experiments were performed for those in the 50 µm to 200 µm size range. The investigations were accompanied by X-ray computed tomography (XCT) and scanning electron microscope/energy dispersive X-ray spectroscopy (SEM/EDX) measurements as well as a micro X-ray fluorescence analysis to examine the mineral microstructure. It was found that the commonly assumed exponential connection between particle size and strength differed in the two size ranges. This behavior can be linked to different grain and cluster sizes, which were found in the investigation of the mineral microstructure. In addition to particle size, it was found that mineral structure plays an important role when characterizing the breakage behavior.

Keywords:

slag; engineered artificial minerals (EnAMs); particle breakage; X-ray computed tomography (XCT); discrete element method (DEM)

1. Introduction

Critical raw materials such as indium (In) and lithium (Li) are gaining increasing importance due to their relevance for technical applications (e.g., indium for solar panels [1] and lithium for batteries) that aid the ongoing transition to climate neutrality. The high demand and the desire to reduce supply risks [2] lead to a need to increase the production and more efficient usage of these minerals. The recycling of secondary materials, e.g., slags from pyrometallurgical processes, presents an additional source of critical raw materials and the ability to better utilize the materials that are already in circulation [3]. However, current recycling strategies do not take structural material properties into account, resulting in inefficient and cost-intensive processes [4,5,6]. By modifying the cooling process of slags and using additives, critical raw materials can be enriched in artificial phases, so-called engineered artificial minerals (EnAMs) [3]. To access the EnAMs, the slags need to be comminuted to liberate the EnAMs from the gangue material [7]. As energy consumption in comminution processes is high [8,9], understanding the breakage behavior of these novel EnAM-containing slags is necessary to improve the efficiency of these processes. This study, therefore, provides an initial overview of the complex interactions governing breakage behavior across different size ranges and establishes a foundation for the development of new, more efficient strategies.

In addition, depending on feed particle size, the particle size must be reduced by a factor of around 100 to release the polycrystalline EnAM grains in the slag. Breakage events, as comminution on the particle level, can be characterized in terms of a breakage criterion and breakage function. The breakage criterion describes the critical stress a particle can sustain before breakage and the breakage function describes the size distribution of the fragments resulting from a given breakage event. Similarly, breakage is modeled using discrete element method (DEM) simulations or population balances [10,11,12,13].

Following Weibull statistics [14], it is generally assumed that an increase in particle size is accompanied by more defects and a corresponding reduction in particle strength [15,16,17,18]. This results in a single function for the size dependence of the particle’s strength or the breakage criterion. However, in this approach, the mineral structure specific to the material is not considered although it can be even more influential than the size effect [19]. The influence of the mineral structure on the breakage behavior of a particle varies depending on the size of the particle [18,20,21]. This is especially important in investigations spanning multiple size ranges in which the characteristics of the mineral structure change. In slags with a specifically synthesized artificial structure (e.g., EnAMs), insights into this influence can be used to define target mineral structures for optimal comminution and liberation behavior. So far, this has not been considered in breakage modeling, population balances and in DEM simulations in particular [21].

In this work, the breakage behavior of a lithium aluminate-containing slag was investigated in two different size ranges in terms of breakage strength and fragment size distributions. Piston-die experiments were performed for single particles in the 3 mm to 5 mm size range. A two-roller breakage tester was used to investigate the fragment size distribution in the 50 µm to 200 µm size range. Additionally, the breakage strength in this size range was investigated using nanoindentation. The results were compared and discussed with regard to the functional dependence of fragment size distribution and breakage strength on the parent particle size. Lastly, characterizations of the microstructure of the slag using X-ray computed tomography (XCT) were used in combination with micro X-ray fluorescence (µXRF) and SEM-EDX analyses to correlate the findings to the material properties. The insights gained in this study contribute to a better understanding of the limitations of existing models [22] and enable the targeted adaptation of future recycling strategies to the structural properties of the materials. This work shows that the validity ranges of breakage functions and strengths are influenced by the mineral structure. This is of particular importance in comminution processes and breakage modeling considering a large range of particle sizes in which breakage functions and strengths have to be considered to be particle size-dependent.

2. Materials and Methods

2.1. Materials

The slag utilized in this work was produced at IME Process Metallurgy and Metal Recycling (RWTH Aachen, Germany). A unique characteristic of this slag is its optimized cooling strategy, which facilitates the growth of lithium aluminate as the EnAM in its crystalline form. The slag was produced using varying proportions of salts such as Li₂O, MnO, Al₂O₃, SiO₂ and CaO. After heating the salts above their melting temperature, two holding times of approximately 5 h were introduced. The first holding time took place at 1400 °C as a homogenization melt, and the second took place at 1050 °C. The slag block was cooled at a controlled rate of 25 °C/h. Finally, the slag block was sawed into several sections to further simplify the sample preparation and processing. Afterwards, drill cores were removed. The final sample diameter was 6 mm and its length was 8 mm. The structure of the slag block was considered homogeneous throughout its entire volume. The structural characteristics are shown below and were obtained using the methods shown in Section 2.5.

To obtain the mineral composition of the slag, an X-ray diffraction (XRD) measurement was conducted using an Empyrean diffractometer (Malvern Panalytical, Almelo, The Netherlands). The measurement was performed in the 2θ range of 5–80° at 35 kV and 35 mA. The open-source software package Profex/BGMN version 5.1.0 [23] was used for the quantitative analysis. Based on the X-ray diffraction (XRD) analysis, the slag was composed of six distinct minerals, as shown in Table 1.

The element map obtained using micro X-ray fluorescence (µXRF) provided homogeneity information on the slag block. The µXRF measurement was performed using an M4 Tornado (Bruker Nano GmbH, Berlin, Germany). The measurement procedure was similar to that in the work of [24], using a rhodium (Rh) source (50 kV, 600 µA) and a measurement step size of 150 µm. Figure 1a shows the overlay map of the elements present, in which millimeter-sized objects can be observed. These objects represent the high accumulation of aluminum, along with other elements, forming clusters of multiphase minerals. These clusters primarily consisted of intergrown lithium aluminate, acting as an EnAM, and Mn-Al spinels. The cluster size was determined using Fiji (ImageJ 1.53b) software by applying the Color Threshold feature to segment the clusters and then using the Analyze Particles function, as shown in Figure 1b. The size distribution of the clusters is presented in Figure 4b.

The structural analysis provided a deeper insight into the structural composition of the analyzed slags, which consisted of minerals in crystalline phases, which varied depending on the production conditions during the melting process. As molten slags cools, mineral grains form. These mineral grains can locally aggregate into mineral clusters. These clusters represent local accumulations of multiple mineral grains. Both systems are schematically illustrated in Figure 2.

These clusters represent a local enrichment of one of the constituents of the slag and result in a locally increased concentration. The locally increased material concentrations can be determined using XCT, which allows cluster volumes to be defined (Figure 3). A detailed description of the XCT measurement settings and image processing used is given in Section 2.4.

The structural analysis also provided information on the average grain and cluster sizes. The grain size refers to a pure accumulation of crystals of a material and does not include any other material inclusions. These two characteristic structural sizes were therefore analyzed and are presented as a distribution in Figure 4. For the slag examined, an average grain size of 44 µm was found. The average cluster size was about 2260 µm.

To gain an understanding of the structural differences at the microscale, the slag blocks were milled using an impact mill (Bauermeister type UT-02) (Bauermeister Zerkleinerungstechnik GmbH, Norderstedt, Deutschland). They were then classified into five size classes between 25 µm and 250 µm using an air jet sieve (Hosokawa Alpine AG, Augsburg, Germany) for further specific characterization. This range will be referred to as the micro size range. Scanning electron microscopy (SEM)/energy dispersive X-ray spectroscopy (EDX) (Thermo Fisher Scientific GmbH, Dreieich, Deutschland) images of the particle classes were taken to analyze the surface composition. Figure 5 shows that particles in the 170 µm size class were composed of several materials on the surface, indicating multiple grains within the structure. This differed significantly compared to the particles with an average size of 54 µm, which were predominantly composed of a single material (sizes were measured by laser diffraction using a Mastersizer 3000 (Malvern Instruments, Kassel, Germany). This structural observation was consistent with the measured grain size.

2.2. Piston-Die Experiments

The lithium aluminate slag was processed in a jaw crusher (WEDAG, TE558501) to prepare particle sizes in the range of 3 mm to 5 mm. This is referred to as the macro size range. Individual size classes were obtained through sieving. Subsequently, particles in three size classes were prepared for the piston-die experiments: x_50,1 = 3.58 mm, x_50,2 = 4.25 mm and x_50,3 = 4.75 mm. In each size class, 40 particles were subjected to static loading in a stamping press (Shimadzu AG-50kNX) and the force displacement relationship was documented. After ensuring contact of the press with the particle by moving the stamp until a force of 2 N was measured, the stamp was moved at a velocity of 5 mm/min while measuring the applied force. The loading zone was shielded to ensure that no fragments were lost during breakage (Figure 6). Upon first breakage, determined by a drop to a force equal to 40% of the peak force measured for the particle, the experiment was terminated and the assembly of fragments was collected. The measured peak force was documented as the critical breakage force F_breakage. To calculate the cross-sectional area of the particle, a spherically shaped particle was assumed and calculated using the average diameter x₅₀. Using Equation (1), the corresponding breakage strength σ_crit was calculated. The collection of fragments was sieved and each size class was weighted to determine the fragment size distribution Q₃, assuming that the particles were of similar densities.

σ_{c r i t} = \frac{F_{b r e a k a g e}}{\frac{1}{4} π {x_{50}}^{2}}

(1)

2.3. Nanoindentation

In order to determine the breakage strength σ_crit of the multi-component particles in the micro size range, the particles were stressed to their individual breakage point using a nanoindentation device. This was performed using the TriboIndenter TI 900 from Hysitron, Inc. (Billerica, MA, USA) with a flat stamp with a diamond tip. To ensure the reliability of the results, up to 40 tests were performed for each of the five size classes [25,26].

An automated algorithm was employed to determine the breaking point for each size class by filtering the first point at which the force–displacement curve no longer registered any opposing force at a displacement of 500 nm. This approach prevents the registration of mere surface chipping. For each size class examined, the force F_breakage was recorded at the identified breakage point. This force was set in relation to the average cross-sectional area of the respective analyzed particle size class to calculate the particle strength of the size class (Equation (1)).

2.4. Two-Roller Breakage Tester

In order to determine the resulting particle size distribution at different specific applied energies, a two-roller breakage tester was used for particles in the size range of 50 µm to 200 µm, as the fragments obtained via nanoindentation could not be statistically evaluated in a meaningful way since they could not be taken out of the indenter after the breaking event. From the collected data, a breakage function could be determined by correlating the obtained fragments with the particle feed size. Furthermore, the material’s breakage strength could be determined, which was compared with the specific breakage energies obtained from nanoindentation. The two-roller breakage tester allows the gap between the rollers to be adjusted within a range of 5 µm to 180 µm, subjecting the particles to compressive stress. To ensure a precise gap width, the two roller bearings were preloaded against each other, enabling the gap to be set with an accuracy of 1 µm [17]. The gap was varied as a percentage of the particle feed size x_50,feed (30%, 40%, 50%, 60% and 70%). The rolls of the two-roller breakage tester always rotated at a speed corresponding to the fall velocity of the particles at the height of the gap. This average speed was determined in preliminary tests. A sample of 20 g was evenly distributed using a vibratory feeder (Retsch GmbH, Haan, Deutschland), ensuring that individual particles were introduced into the gap via a hopper system. To obtain efficient and meaningful measurements, a continuous and uniform particle flow consisting of individual particles across the length of the rollers must be maintained. In this manner, several thousands of particles per sample were individually analyzed and the sensors captured the final data on the applied force. Figure 7 shows the schematic design of the two-roller breakage tester [17].

In this study, specific critical breaking strengths σ_crit,tester were considered, which were determined for the two-roller breakage tester using Equation (2). The measured line load s, which was recorded along the roll with length l_roll, was integrated over the duration of the breakage event (t_breakage = t₁ − t₀). This force was distributed over the duration of the applied stress t_breakage and the cross-sectional area A_P of the particles, taking into account the number of simultaneously stressed particles N_P,RT [17].

σ_{c r i t, t e s t e r} = \frac{\int_{t_{0}}^{t_{1}} s d t l_{r o l l}}{t_{b r e a k a g e} A_{P} N_{P, R T}}

(2)

In addition, the crushed particles were collected by a vacuum system and the fragment size distribution was determined. The particle size distribution was measured using a wet measurement technique based on laser diffraction using a Mastersizer 3000 (Malvern Instruments).

In this study, samples that closely align with the nanoindentation results were analyzed to ensure comparability in the particle size distribution of particles broken in the two-roller breakage tester. The breakage ratio ξ_breakage was used as the selection criterion, defined as the relative change in the product particle size x_50,product compared to the original particle size x_50,feed [14] (see Equation (3)). Systematically conducted tests with varying gap width ratios relative to the initial particle size were performed. For each particle size class, the test with a gap size in which the breakage ratio first became greater than zero as the gap width ratio decreased was analyzed, marking the point where a change in the average particle size was detected and a first breakage event for the slag under investigation was recorded. The selected tests may exhibit slight deviations from the energy values obtained through nanoindentation due to the otherwise significant experimental effort required for precise determination of the breakage energy threshold. To keep the investigation timeframe practical, gap widths were systematically adjusted as a percentage of the feed particle size to develop a comprehensive view of the breakage behavior. Studies have demonstrated that the energy values at which initial breakage events are recorded by both methods (nanoindentation and two-roller breakage test) are consistent, confirming the validity of the selected experimental setups [17].

ξ_{b r e a k a g e} = \frac{x_{90, p r o d u c t}}{x_{90, f e e d}}

(3)

The resulting particle size distributions were analyzed for the investigations in the range of 50 µm to 200 µm and are discussed in detail in the respective sections.

2.5. X-Ray Computed Tomography Measurement and Reconstruction Settings

The measurement of a drill core was carried out using X-ray computed tomography (XCT) using a Zeiss Xradia VERSA 510 (Carl Zeiss, Oberkochen, Germany) equipped with a polychromatic X-ray source. Microscopy optics were used to further increase the magnification, resulting in a voxel size of 8.0635 µm, which provided sufficient detail to image the EnAMs. A total of 1601 projection images were reconstructed using XMReconstructor (version 11.1.8043), with minimal beam hardening correction. No beam hardening artifacts were observed in the reconstructed image stack. The measurement and reconstruction parameters are listed in Table 2.

Image Processing, Segmentation and Analysis

The XCT measurement was followed by image processing. It was important to ensure that the desired structures within the slag were accurately reflected with minimal loss of information when manipulating the image data. Therefore, relevant features should be preserved. The image processing steps needed to be applied to the entire image stack, and subsequent images should consider the coherence of structures. Image processing started with pre-processing, which was performed using commercially available Fiji software (ImageJ 1.53b). The pre-processing included denoising and contrast enhancement of the entire image stack. Then, the images were segmented using Ilastik software (version 1.4.0), which is based on machine learning techniques, particularly supervised learning algorithms. After segmentation, an image was generated that showed the matrix, air, target phase and mixing phase between the target and matrix phases. In this study, only the pure target phase was considered, which was extracted using thresholding of the segmented image data and analyzed based on its size and shape. Since a cluster consists of many connected crystal grains, the grains need to be separated from each other. Without separating them virtually, it is not possible to analyze them since most of the target phase volume is connected to each other. Therefore, the target phase was separated by using the distance transform watershed algorithm in Fiji. Each grain volume was then marked in one color and received a label. This enabled particle analysis in MorphoLibJ, another plugin in Fiji. All individual grains were visualized in VGSTUDIO MAX (version 3.3). A detailed list of the image processing steps, including the settings, can be found in Table 3.

3. Results and Discussions

The results on investigating the breakage behavior of the slag studied in two different size ranges are presented below. A size range between 3.58 mm and 4.75 mm was considered first; in this range, the breakage behavior was predominantly determined by the formed clusters. In addition, studies were conducted with feed particles in the size range between 50 µm and 200 µm to characterize the breakage behavior, which was predominantly determined by the grains.

3.1. Breakage Strength

This section addresses the breakage strength required to induce a breakage event for particles in the macro and micro size ranges. A total of up to 40 particles per size fraction were identified for this purpose. In the macro size range, compression tests (Section 2.2) were employed, while in the micro size range, the nanoindentation method (Section 2.3) was used. The breakage strength of each particle is plotted as a volumetric cumulative distribution in Figure 8, and the resulting mean strength for 50% of the distribution was determined from these data.

Upon reviewing Figure 8, which illustrates the breakage strength of each particle across the various size fractions, it was evident that the breakage strength increased as particle size decreased. In the macro size range, the breakage strengths were closely grouped, showing minimal differences in the average breaking strength. These observations are consistent with the results presented in the literature, indicating that size effects have little influence in the investigated range [32,33]. When considering the micro size range, a slight increase in the average breaking strength was observed. However, Figure 8 clearly demonstrates a significant increase in the average breakage strength with further reductions in particle size. This shows that, below a certain particle size, a substantially greater specific force and thus stress intensity is required to break smaller slag particles.

This phenomenon is well documented in scientific literature, attributed to the fact that smaller particles exhibit fewer material defects, such as pores or cracks [11,12,15,18,34,35,36]. These defects promote crack formation, which is the underlying cause of material breakage. This effect is particularly pronounced in multi-component systems, where material defects between components are more likely to occur.

In the macro size range, the clusters primarily defined the structural characteristics and the breakage behavior. The larger particles in this size range have much more material defects within their structure, so that a change in size does not significantly change the number of defects per particle volume and thus the breakage strength. The applied breakage force may lead to crack formation at defects between different materials, with the breakage strength generally remaining within a similar range.

In the micro size range, a marked increase in breakage strength was observed. In this size range, materials are structurally dominated by grains instead of clusters. Breakage between different components becomes less frequent, and breakage could primarily occur in an intragranular manner. The probability of material defects within particles, which encourage breakage events, gradually decreases. In addition to the decrease of the number of defects, the defect strength also varies. The defects differ in how much they promote breakage initiation. Initially, breakage occurs at the weakest defect sites. As the particle size decreases, the defect strength increases [32]. Consequently, at a given stress level, breakage events are favored at fewer locations, and higher forces are required at these defects, leading to an overall greater force needed to initiate breakage.

In order to investigate the breakage strengths σ₅₀ in the macro and micro size ranges, the determined breakage strengths σ_crit are plotted against the median feed size of the breaking particle x_50,feed in Figure 9. The mathematical relationship between the required breakage strength σ_crit and particle size x_50,feed in the data points as described using an exponential function based on the model by Tavares and King [33]. According to the model, the breakage energy increases as the particle size decreases but approaches an asymptotic limit for larger particles [33].

In this study, the model was adapted from the originally considered specific energy to focus on breakage strength. Breakage strength (force per area) and specific energy (energy per mass) are comparable measures, as both describe a material’s capacity to absorb or resist mechanical energy. Accordingly, the model was applied to breakage strength and fitted to the data using Equation (4).

σ_{c r i t, 50} = σ_{\infty} (1 + {(\frac{x_{0}}{x_{50, f e e d}})}^{ϕ})

(4)

In the model used in this work, σ_crit,₅₀ denotes the critical breakage strength necessary to break a particle, while σ_∞ represents the asymptotic breakage strength for infinitely large particles. The particle diameter x_50,feed defines the corresponding particle size, and x₀ serves as a reference diameter at which particle size has a significant effect on breakage strength. The exponent ϕ determines the sensitivity of the breakage strength to variations in particle size [33].

When examining the breakage strength data points in the macro size range, a slight increase with decreasing particle size was visible among the experimental data points. In contrast, within the micro size range, the breakage strength increased significantly with decreasing particle size x_50,feed. This trend corresponds to the results discussed in Figure 8, where the curves of smaller particle sizes shifted to higher breakage strengths.

Considering the model by Tavares and King (Equation (4)), the data points can be expressed mathematically. Consistent with literature reports, the breakage strength initially showed only a slight dependency on particle size [32,33] and approached an asymptotic limit of 22 N/mm², as defined by the parameter σ_∞. Below a critical particle size of 124 µm, however, the reference factor x₀ indicated a significant influence of particle size on the breakage strength, resulting in a more significant increase in breakage strength. This behavior is reflected in Figure 9.

In the macro size range, the increase in breakage strength with decreasing particle size can be explained statistically: larger particles have a higher probability of containing defects both between and within their grains [35]. These defects vary in their tendency to promote breakage, leading to a greater likelihood of critical defects in larger particles that weaken their structure [12]. In this size range, the dominant factor is probably the cluster structure—a network of grains composed of various materials, with numerous phases and phase boundaries that may harbor defects. As particle size decreases, the number of defects decreases, and breakage events have already occurred at most critical weak points. As a result, the force required to initiate breakage per unit particle surface area increases.

In the micro size range, the breakage strength increases drastically as the feed particle size decreases. Smaller particles contain fewer grains per particle, reducing the number and strength of grain boundaries. Furthermore, weaker defects were already broken and thus removed in previous breakage events. This reduction forces breakages events to propagate more frequently through a single material component, which typically requires greater breakage energy [37,38]. Additionally, material defects become increasingly rare and stronger at smaller volumes. This combination results in a steady increase in breakage strength.

When the feed particle size approaches the size of individual grains, another factor influences breakage behavior. A particle size nearing the grain size necessitates that breakages also form within individual grains. Each grain has a more stable internal structure that confers significant stability. At this point, the transition from brittle to ductile breakage behavior occurs [32,39]. Here, the force applied to the particle is initially absorbed by deformation, making crack formation more difficult [40]. The previously mentioned effects lead to reduced crack formation and a substantial increase in the required breakage force.

The observations emphasize the need for detailed analyses specific to each size range to develop a deeper understanding of size effects. Only through thorough investigations with additional data points can the complex relationship between structure and breakage strength across size ranges be further elucidated. Future studies should consider these aspects independently for each size range. The results indicate that the development of material-specific breakage functions based on the observed breakage behavior should be conducted only within specific size ranges. The resulting models, such as DEM simulations or population balance models that describe the breakage behavior of such multicomponent systems, should be specifically tailored to the area under investigation [41]. This ensures that the relevant structural influences are accurately represented within the model and that precise results can be achieved.

3.2. Fragment Size Distribution

When characterizing a breakage event, the size distribution of the fragments produced is an important aspect. It is, for example, needed to calibrate a breakage function in DEM simulations or population balances. Generally, the size distributions of the fragments are normalized to the size of the parent particle to formulate a description of the breakage behavior of the material that is independent of the size of the breaking particle.

In Figure 10, the sum distribution Q₃ of fragments is shown as a function of the nominal particle size x_product/x_50,feed in the micro and macro size ranges. It can be observed that within their respective size ranges, the normalized size distributions were similar, i.e., independent of the size of the parent particle. In the macro size range, the normalized size distributions were narrower and coarser fragments were produced. The larger fragments could be a direct result of the EnAM-containing clusters (see Section 2.1). Breakage events preferentially occur along the structural defects that form between clusters. As illustrated in Figure 4b, the clusters exhibited a uniform and narrow particle size distribution. Since breakage events primarily take place along cluster boundaries, the resulting fragments are of uniform size, as the clusters are more likely to break along these boundaries. This indicates a dependence of the fragmentation process on the cluster size distribution.

The normalized size distributions were similar, apart from minor deviations at larger fragment sizes. In the micro size range, a broader size distribution was observed, with fewer large fragments. Additionally, the normalized size distributions varied slightly more across the different feed sizes. As with the results for the material’s breakage strength, they can be attributed to the different phases within the particles. In smaller size classes, material properties span a wider range due to the liberated particles and particles with fewer and varying phases. However, the shape of the normalized size distributions remains consistent for the individual feed sizes, indicating similar underlying material characteristics.

The difference between the two regions in the resulting normalized particle size distributions can be attributed to variations in the grain and cluster size distributions. The normalized cluster size distribution generally exhibited a narrow distribution, which became considerably broader in the fine fraction. This suggests that the slag structure contained not only closely distributed clusters but also a significant number of very small clusters, representing local agglomerations of individual materials.

The normalized fragment size distributions in the macro size range did not exhibit a significant fine fraction or the broadness observed in the cluster size distribution. This suggests that fragmentation in this size range produced particles with a relatively uniform size. The curves for the normalized cluster size distribution in the fine fraction and the normalized fragment size distribution in the macro size range overlapped to some extent, while the fragment size distribution rose sharply. This indicates that the initially broadly distributed clusters in the slag system were fragmented into uniform sizes. This observation supports the earlier hypothesis that breakage predominantly occurs between the grains within the system. In contrast, the normalized grain size distribution was broader than the cluster size distribution. When examining the fragment size distribution, only a shift to a smaller size was observed, while the distribution width and shape remained nearly unchanged. This indicates that fragmentation occurred evenly across all size classes in the micro size range, with no material structure breaking preferentially during comminution.

Another factor is the varying number of defects in the considered particles. If defects are present within a particle, breakage is facilitated and breakages are preferentially initiated along these weaknesses in the particle structure. As discussed in Section 3.1, the observed differences between these size ranges can be attributed to the grain and cluster structures of the phases in the micro and macro size ranges. Consequently, when specific breakage sites are preferentially activated, breakage predominantly occurred at these locations, leading to a uniform breakage pattern, as observed in the macro size range. In contrast, when only isolated weak points remain and are less prone to inducing breakage events, the resulting fragments exhibited greater size variability, contributing to a broader size distribution (see micro size range).

In simulations of breakage events utilizing the DEM or population balances, a single breakage function is commonly used to define the number and size of fragments generated in each breakage event. However, it has been shown (see Figure 10) that the mineral structure of the material can significantly affect the size distributions of fragments produced in breakage events of different parent particle sizes. Consequently, the normalized size distribution of the fragments was no longer independent of the size of the parent particle. Since the shapes of the normalized size distributions were similar, it would be reasonable to define a separate breakage function in the micro and macro size ranges. In Figure 11, a fit for the breakage function by Zhu et al. [42] is shown for the micro and macro size ranges. It includes parameters such as m and b, where m defines the shape of the fragment size distribution and serves as a measure of the fineness of breakage, while b acts as a scaling factor for the overall distribution. A higher m value indicates a narrower distribution of fragments, whereas a lower value suggests a broader distribution. Similarly, a higher b value scales the distribution upward, whereas a lower value decreases it. The fit is able to represent the size distribution of fragments in both size ranges, albeit obtaining a better match (coefficient of determination

R^{2} = 0.999

) in the micro size range. The few large fragments generated in the macro size range were difficult to represent by the equation (coefficient of determination

R^{2} = 0.945

). Notably, both fits resulted in a similar

b v a l u e s (0.98)

. In the DEM simulations and population balances spanning both size ranges, a size dependence of the parameter

m

would be another possible adaptation. However, further investigations of the size ranges in the transition range are required.

4. Conclusions

The investigation into the breakage behavior of slag particles, studied across distinct size scales, highlights significant structural and mechanical differences between the macro and micro size ranges. In this study, two primary size ranges were analyzed: the macro size range (3.58 mm to 4.75 mm) and the micro size range (50 µm to 200 µm). Each range demonstrated notable distinctions in breakage strength and fragment size distribution.

The breakage strength was determined using compression tests for particles in the macro size range and micromanipulation with a nanoindenter for those in the micro size range. The results indicated that the breakage strength increased as the particle size decreased. In the macro size range, the breakage strength exhibited minimal variation. Conversely, in the micro size range, a power-law increase in breakage strength was observed with decreasing particle size. Complex structures, such as the clusters described in Section 2.1, also influenced the breakage behavior.

When plotting breakage strength against median feed size, the breakage behavior could be described and analyzed using the model by Tavares and King [28]. The macro size range, influenced by cluster structures, exhibited a moderate increase in breakage strength, while the micro size range showed a steeper increase.

The size distribution of the fragments after breakage was characterized: normalized fragment distributions were consistent within each size range but differed between the macro and micro size ranges. In the macro size range, the normalized distributions were narrower. In contrast, the micro size range exhibited broader distributions with fewer large fragments, influenced by the varied material properties of smaller particles and the liberation of fine materials. The normalized particle size distribution of the fragments matched the width and shape of the original grain size distribution.

The breakage function proposed by Zhu et al. [37] effectively modeled these distributions, achieving a better fit in the micro size range compared to the macro size range, where large fragments were underrepresented.

For numerical methods such as DEM and population balances, which model breakage and comminution behavior, the findings highlighted the need for size-specific breakage functions. The distinct behaviors observed suggest that a universal breakage function may be insufficient. Simulations would benefit from incorporating separate functions for micro and macro size ranges. The similarity in the normalized distributions suggests potential adaptability by modifying the parameters of the breakage functions used. However, further analysis is needed to refine models, particularly for the transition between size ranges.

Overall, this study highlights the importance of accounting for size-dependent breakage mechanisms in comminution modeling. Implementing tailored breakage functions that reflect structural variations and defect distributions can improve the predictive accuracy of simulations, ultimately optimizing energy efficiency in material processing and recycling.

Author Contributions

Conceptualization, S.B., P.H., T.T.V., H.K.-E. and C.S.; methodology, S.B., P.H., T.T.V. and C.R.; software, S.B., P.H., T.T.V. and C.R.; formal analysis, S.B. and P.H.; investigation, S.B., P.H. and T.T.V.; resources, C.R.; data curation, S.B., P.H., T.T.V. and C.R.; writing—original draft preparation, S.B., P.H. and T.T.V.; writing—review and editing, S.B., P.H., T.T.V., C.R., H.K.-E., C.S., A.K. and U.P.; visualization, S.B., P.H., T.T.V. and C.R.; supervision, C.S., H.K.-E., U.P. and A.K.; project administration, C.S., H.K.-E. and U.P.; funding acquisition, C.S., H.K.-E. and U.P. All authors have read and agreed to the published version of the manuscript.

Funding

We would like to acknowledge the financial support of the research work from the DFG (Deutsche Forschungsgemeinschaft), Germany, within the priority programme SPP 2315 “Engineered Artificial Minerals (EnAM)—a geo-metallurgical tool to recycle critical elements from waste streams” under grant numbers 470552553, 470536680, 470551727 and 470554192.

Data Availability Statement

The data presented in this study are available upon request from the corresponding author.

Acknowledgments

The authors would like to thank the DFG for the financial support that enabled this project within the priority programme 2315 EnAM and the support of Helmholtz Institute Freiberg in the XRD analysis and for providing the M4 Tornado µXRF equipment.

Conflicts of Interest

The authors declare no conflicts of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or in the decision to publish the results.

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Figure 1. (a) A part of the homogeneous structure shown in element map overlay from micro X-ray fluorescence analysis and (b) the binary image of the observed clusters.

Figure 2. Representative schematic representation of the structures: mineral grains and clusters in the slag sample are shown for three exemplary clusters, where a single hexagonal shape represents a single mineral grain and the accumulation of the connected single grains forms a cluster.

Figure 3. Three-dimensional visualization of XCT data of three clusters consisting of smaller grains. Every grain is labelled with a unique color for easier differentiation.

Figure 4. Size distributions of the determined grain size determined based on XCT image data (a) and the cluster size based on µXRF imaging (b) of the analyzed slag.

Figure 5. SEM (a,b) and SEM/EDX (c,d) images of two samples (a–d) in the micro size range to investigate the structural composition on the surface.

Figure 6. Side view of the load cell (Shimadzu AG-50kNX) during the piston tests (a) and a schematic representation of the load cell’s setup (b).

Figure 7. Schematic representation of the two-roller breakage tester.

Figure 8. Distribution of the breakage strength of particles in different size classes in the micro and macro size ranges.

Figure 9. The specific breakage strength as a function of particle size, fitted based on the model by Tavares and King [33]. Grain and cluster sizes are highlighted as vertical lines.

Figure 10. Normalized fragment size distribution in the micro and macro size ranges and normalized cluster and grain size distributions.

Figure 11. Normalized fragment size distributions in the micro and macro ranges and fits for the breakage function by Zhu et al. [42].

Table 1. XRD results of the investigated EnAM-containing slag sample.

Mineral	Weight Percentage
Lithium aluminate (LiAlO₂)	8.4
Eucryptite (LiAlSiO₄)	8.9
Gehlenite (Ca₂Al₂SiO₇)	30.9
Li₂MnSiO₄	14.9
Mn-Al spinel (MnAl₂O₄)	35.8
Quartz (SiO₂)	<1

Table 2. XCT measurement and reconstruction settings for a lithium aluminate slag drill core sample.

Measurement Setting
source distance in mm	16
detector distance in mm	120
optical magnification	0.4 ×
acceleration voltage in kV	80
electrical power in W	7
source filter (Zeiss standard)	LE4
voxel size in µm	8.0635
camera binning	2
number of projections	1601
exposure time (s)	1.5
angle range (°)	360
reconstruction settings	parameter
reconstruction algorithm	FBP
center shift	0.748
defect correction	none
ring removal	none
byte scaling	(0, 0.25)
beam hardening constant	0.2

Table 3. Image processing and analysis steps for the investigated lithium aluminate slag sample.

Image Processing	Step	Setting(s)	Ref.
pre-processing (Fiji) [27]	raw image (16-bit)	-
	non-local means denoising	s\|8, sf\|1	[28,29]
	unsharp mask	r\|1, mw\|0.6
	8-bit conversion	-
segmentation (Ilastik) [30]	pixel classification	four classes
	color/intensity	1.6
	edge	3.5
	texture	3.5
extraction of the target phase	thresholding (Fiji)
separation of the small grain units	Distance transform watershed (Fiji)	Borgefors 16 bits Dynamic 2.0 Connectivity 13	[31]
3D analysis	Analyze Particles, MorphoLibJ (Fiji)	-
visualization	VGSTUDIO MAX

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Bahnmüller, S.; Hirschberger, P.; Võ, T.T.; Rachmawati, C.; Kwade, A.; Peuker, U.; Kruggel-Emden, H.; Schilde, C. Particle Size-and Structure-Dependent Breakage Behaviors of EnAM-Containing Slags. Minerals 2025, 15, 195. https://doi.org/10.3390/min15020195

AMA Style

Bahnmüller S, Hirschberger P, Võ TT, Rachmawati C, Kwade A, Peuker U, Kruggel-Emden H, Schilde C. Particle Size-and Structure-Dependent Breakage Behaviors of EnAM-Containing Slags. Minerals. 2025; 15(2):195. https://doi.org/10.3390/min15020195

Chicago/Turabian Style

Bahnmüller, Simon, Paul Hirschberger, Thu Trang Võ, Cindytami Rachmawati, Arno Kwade, Urs Peuker, Harald Kruggel-Emden, and Carsten Schilde. 2025. "Particle Size-and Structure-Dependent Breakage Behaviors of EnAM-Containing Slags" Minerals 15, no. 2: 195. https://doi.org/10.3390/min15020195

APA Style

Bahnmüller, S., Hirschberger, P., Võ, T. T., Rachmawati, C., Kwade, A., Peuker, U., Kruggel-Emden, H., & Schilde, C. (2025). Particle Size-and Structure-Dependent Breakage Behaviors of EnAM-Containing Slags. Minerals, 15(2), 195. https://doi.org/10.3390/min15020195

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