A brief review on com­puter simulations of chal­co­py­rite surfaces: structure and reactivity

Nascimento, G.R.; Bazan, S.F.; de Lima, G.F.

doi:10.1107/S2053229624006867

crystallography in latin america

STRUCTURAL
CHEMISTRY

ISSN: 2053-2296

Volume 80| Part 9| September 2024| Pages 458-471

https://doi.org/10.1107/S2053229624006867

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A brief review on computer simulations of chalcopyrite surfaces: structure and reactivity

Guilherme Randow Nascimento,^a Selma Fabiana Bazan ^b and Guilherme Ferreira de Lima ^a ^*

^aGrupo de pesquisa em Química Inorgânica Teórica – GPQIT, Departamento de Química, Universidade Federal de Minas Gerais, Brazil, and ^bLaboratório de Química Computacional – LaQC, Instituto de Física e Química, Universidade Federal de Itajubá, Brazil
^*Correspondence e-mail: gflima@ufmg.br

Edited by R. Diniz, Universidade Federal de Minas Gerais, Brazil (Received 22 May 2024; accepted 12 July 2024; online 8 August 2024)

This article is part of the collection Crystallography in Latin America: a vibrant community.

Chalcopyrite, the world's primary copper ore mineral, is abundant in Latin America. Copper extraction offers significant economic and social benefits due to its strategic importance across various industries. However, the hydrometallurgical route, considered more environmentally friendly for processing low-grade chalcopyrite ores, remains challenging, as does its concentration by froth flotation. This limited understanding stems from the poorly understood structure and reactivity of chalcopyrite surfaces. This study reviews recent contributions using density functional theory (DFT) calculations with periodic boundary conditions and slab models to elucidate chalcopyrite surface properties. Our analysis reveals that reconstructed surfaces preferentially expose S atoms at the topmost layer. Furthermore, some studies report the formation of disulfide groups (S₂²⁻) on pristine sulfur-terminated surfaces, accompanied by the reduction of Fe³⁺ to Fe²⁺, likely due to surface oxidation. Additionally, Fe sites are consistently identified as favourable adsorption locations for both oxygen (O₂) and water (H₂O) molecules. Finally, the potential of computer modelling for investigating collector–chalcopyrite surface interactions in the context of selective froth flotation is discussed, highlighting the need for further research in this area.

Keywords: chalcopyrite; DFT; surfaces; oxidation; collectors; copper ore mineral.

1. Introduction

Copper is a strategic metal for civil construction, electronic devices, technology and many other fields. Properties such as high ductility, malleability, thermal and electrical conductivity, and stability in the face of corrosion make it essential for industrialization and urbanization (Kosanovic et al., 2007 ). For this reason, high consumption is expected in the 21st century, especially in countries like China and India (Liu et al., 2013 ). Approximately 53% of copper reserves are in Chile, Peru and Australia. These regions are poised to attract investments totalling around 38 billion USD in the next few years, particularly in Latin America, for exploration of these valuable resources (Liu et al., 2013). One particular challenge lies in the extraction of copper from low-grade ores, necessitating ongoing scientific and technological advancements.

Copper is predominantly found in nature as chalcopyrite (CuFeS₂), constituting approximately 80% of all copper ores, with chalcocite (Cu₂S), covellite (CuS), bornite (Cu₅FeS₄) and malachite [Cu₂(CO₃)(OH)₂] present in smaller quantities (Kimball, 2013 ). Nowadays, copper extraction methods include both pyrometallurgical and hydrometallurgical routes, alongside the increasingly prevalent practice of recycling devices that contain the metal (Davenport, 2002 ; Wang, 2005 ; Baba et al., 2012 ; Schlesinger et al., 2022 ).

The primary method for copper extraction is pyrometallurgical. This process involves the sequential isolation of Cu–Fe–S or Cu–S mineral particles through froth flotation, followed by smelting it to molten high-Cu matte. Afterward, this matte is converted to impure molten copper subsequently purified by electrorefining to obtain ultrapure copper. However, this approach necessitates a significant enrichment step in the beginning, where the ore is concentrated to around 20–30% copper content (Davenport, 2002). This requirement can be a significant impediment for the economic application of the process to low-grade copper ores.

As the availability of high-grade copper ores dwindles (Liu et al., 2013), methods for extracting copper from low-grade resources become increasingly necessary. In this context, hydrometallurgy presents a competitive alternative, currently accounting for approximately 20% of global copper production. This process involves leaching the ore with sulfuric acid, followed by solvent extraction to concentrate the copper-bearing electrolyte. Finally, pure copper cathodes are electrodeposited from enriched electrolyte (Davenport, 2002). Its advantages lie in the possibility of treating low-grade ores and better waste control.

The pyrometallurgical and hydrometallurgical routes both involve a preceding concentration stage using froth flotation (Davenport, 2002), which consists of modifying the chalcopyrite surface by adsorbing molecules known as collectors to change how its particles interact with air bubbles. The gangue minerals separate the chalcopyrite particles due to their density differences, but selective collectors for low-grade ores remain a challenge (Liu et al., 2017 ).

Chalcopyrite, the Earth's crust's most abundant copper-containing mineral (Davenport, 2002), crystallizes in the tetragonal space group I $[\overline{4}]$ 2d, with four formula units of CuFeS₂ per unit cell (Fig. 1). Its lattice parameters are a = 5.289 Å and c = 10.423 Å, as determined by Burdick & Ellis (1917 ) using X-ray diffraction. Each metal atom is tetrahedrally coordinated to four S atoms. On the other hand, each S atom bonds to two Cu and Fe atoms in a tetrahedral arrangement. The S—Cu and S—Fe bond lengths are reported as 2.30 and 2.26 Å, respectively (Burdick & Ellis, 1917). Chalcopyrite is typically described with oxidation states of Cu⁺, Fe³⁺ and S²⁻ (Llanos et al., 1995 ; Von Oertzen et al., 2006 ; Raj et al., 1968 ). However, some studies propose alternative oxidation states of Cu²⁺, Fe²⁺ and S²⁻ (Mikhlin et al., 2005 ). Notably, chalcopyrite is an antiferromagnetic material, characterized by alternate layers of iron ions with opposing spins along the crystallographic c axis (Von Oertzen et al., 2006; Oguchi et al., 1980 ; Fujisawa et al., 1994 ).

Figure 1
Crystal structure of chalcopyrite.

Extracting copper through hydrometallurgy hinges on efficiently leaching chalcopyrite. Fe³⁺, being a cost-effective option, reigns supreme as the leaching agent. Dutrizac (1981 ) highlights that temperature, surface area, pH and agitation all significantly influence this reaction, as illustrated by Equations (1) and (2).

$[{\rm CuFeS_2 + 4Fe^{3+} } \rightarrow {\rm Cu^{2+} + 5Fe^{2+} + 2S^0} \eqno(1)]$

$[ \eqalign{{\rm CuFeS_2 \ + \ } & {\rm 16Fe^{3+} + 8H_2O} \rightarrow \cr & {\rm Cu^{2+} + 17Fe^{2+} + 2SO_4^{2-} + 16H^+}} \eqno(2)]$

However, the process remains incompletely understood. While initial leaching stages exhibit relatively high copper extraction efficiencies, the reaction subsequently slows down significantly after some hours, leaving a substantial portion of copper unrecovered from the ore (Córdoba et al., 2008 ; Li et al., 2013 ; Klauber, 2008 ; Bogdanović et al., 2020 ). Unfortunately, this decrease in reaction rate throws a wrench in the overall efficiency. While the exact reasons behind this slowdown remain elusive, potential explanations point towards alterations in the mineral's surface chemistry (Kaksonen et al., 2020 ; Panda et al., 2015 ; Zhang et al., 2020 ; Crundwell, 2021 ; Harmer et al., 2006 ; Hackl et al., 1995 ; O'Connor & Eksteen, 2020 ; Klauber, 2003 , 2008; Von Oertzen et al., 2006). Numerous experimental investigations have been carried out to elucidate the surface evolution of chalcopyrite during leaching under various conditions. However, a consensus regarding the factors hindering its dissolution remains elusive. The formation of polysulfides (Gomes et al., 2022 ; Parker et al., 2008a ,b ; Harmer et al., 2006), elemental sulfur (Ma et al., 2021 ; Mo et al., 2014 ; Sokić et al., 2010 ), metal-deficient sulfides (Lu et al., 2000 ; Arce & González, 2002 ; Antonijević & Bogdanović, 2004 ) and jarosite (Klauber, 2008; Ma et al., 2021; Samadzadeh Yazdi et al., 2020 ; Stott et al., 2000 ) have all been implicated in diminishing leaching kinetics.

Understanding the interplay between chalcopyrite's chemical structure and reactivity is critical for developing efficient hydrometallurgical routes for copper extraction. However, several experimental hurdles complicate this task. Firstly, synthesizing pure chalcopyrite is challenging, necessitating the use of natural samples for most experiments. These natural samples inherently contain contaminants, and their influence on leaching behaviour remains unclear. Secondly, current surface analysis techniques present limitations. Powerful methods like X-ray photoelectron spectroscopy (XPS) and X-ray absorption spectroscopy (XAS) are valuable for solid-state analysis, but their beams typically probe beyond the first 15 atomic layers, making it difficult to isolate information specifically from the crucial surface region. A comprehensive understanding of chalcopyrite's electronic structure holds the key to unlocking new avenues for efficient leaching processes (Crundwell, 1988 , 2021; Crundwell et al., 2015 ; Osseo-Asare, 1992 ).

This brief review summarizes how these computational approaches have shed light on the structure, stability and reactivity of various surfaces. We will specifically focus on the simulation of oxidation process and the interactions with collectors, both of which are crucial aspects for hydrometallurgical copper extraction.

2. Slab models

Modelling the system under study is a crucial step in any computer simulation. While small molecules are simple because they can be readily represented by their molecular structures, computational limitations can pose challenges for large molecules. Nevertheless, in both cases, a discrete model can be employed to represent the system of interest.

Crystalline solids are slightly more complicated. Although theoretically infinite, they can be effectively modelled using a finite simulation cell with periodic boundary conditions (Kaxiras, 2003 ). This approach leverages Bloch's theorem to accurately represent the electronic structure of the solid (Kittel, 2005 ; Ashcroft, 2021 ). The choice of cell size depends on the phenomenon under investigation. The unit cell itself may suffice for certain studies, while others investigating defects (e.g. atomic vacancies) might require a supercell containing multiple unit cells to achieve a defect concentration comparable to experimental conditions.

Surfaces can be modelled using the periodic boundary conditions framework, which is available in several computational codes. Modelling a surface in a periodic framework of calculations necessitates breaking periodicity along one direction, resulting in a discontinuity (Kittel, 2005; Ashcroft, 2021). Slab models (Fig. 2) offer a valuable approach for such simulations, but careful consideration of several parameters is crucial to minimize artifacts (Jug & Bredow, 2004 ).

Figure 2
Scheme of a slab model used to simulate surfaces. The blue and red planes correspond to two surfaces formed by the introduction of a vacuum along the c direction. These planes may or may not be the same.

A slab is constructed by the introduction of a vacuum region in the direction normal to the surface plane. This strategy results in two surfaces, shown by a blue and a red plane in Fig. 2. They may or may not be equal, depending on the solid's structure and cleavage plane. To prevent spurious interactions due to periodic boundary conditions, an adequate vacuum size is essential. A vacuum size of about 12 Å is typically used. Calculations using plane waves incur considerable computing cost since the vacuum region is likewise filled by plane waves. Methodologies that use a localized bases set can help to mitigate this impact, but they introduce additional convergence concerns.

Another critical parameter is the number of atomic layers within the slab. Ideally, the electronic structure and geometry of the central layers should resemble the bulk crystal structure. Alternatively, keeping a number of layers proportional to the unit cell can reduce polarization effects. It is typical to freeze some of the atoms in the deep layers frozen at their bulk position to reduce the computational cost.

The slab size perpendicular to the surface is particularly important for studying adsorption and reconstruction phenomena. Small slabs can limit the extent of possible surface reconstructions. For adsorption studies, tiny slabs might allow interaction between the adsorbate molecule and its periodic image, resulting in nonphysical artifacts. The size of the slab can also restrict the possibilities of reconstruction. As will be discussed in the following section, de Oliveira & Duarte (2010 ) and de Oliveira et al. (2012 ) achieved distinct reconstruction by simply modifying the size of the slab.

A properly constructed slab, together with a good level of theory, can help in the understanding of how the chalcopyrite's surfaces behave under various conditions.

3. Modelling the chalcopyrite surface structure

Understanding the structure and the reactivity is crucial for developing successful hydrometallurgical routes to extract copper from low-grade chalcopyrite ore. A significant challenge in theoretical investigation lies in the absence of a preferential cleavage plane, a characteristic often observed in brittle materials, resulting in a conchoidal surface (Li et al., 2013). It is suggested that this outcome is a combination of different surface orientations (Von Oertzen et al., 2006; Harmer et al., 2004 ).

Von Oertzen et al. (2006) used a combination of conventional and synchrotron XPS techniques to explore the sulfur environment on chalcopyrite surfaces. Synchrotron radiation provides the advantage of increased surface sensibility. Their analysis, which was consistent with prior findings by Harmer et al. (2004), revealed the presence of two distinct sulfur species. One species exhibited a 2P_3/2 peak at 160.84 eV, which was attributed as monomeric sulfur, while the other, at 161.88 eV, is indicative of polymeric sulfur.

Building on the identification of two distinct sulfur species on the chalcopyrite surface using XPS, the authors employed DFT simulations to bolster their hypothesis. Slab models representing the (012) and (11 $[\overline{2}]$ ) surfaces were created and optimized using the PBE/Ultrasoft/plane waves method within the CASTEP code (Segall et al., 2002 ). Mülliken charge analysis was then utilized to identify S atoms in different oxidation states.

The (012) surface exposes an equal number of S and metal (M) atoms in the top layer. After optimization, the slab model adopted a more irregular structure, which included both under-coordinated and fully coordinated S atoms. Mülliken charge analysis revealed different charge distributions for these species, with the lower coordinated S atoms being more reduced.

The (11 $[\overline{2}]$ ) surface has differing compositions on opposite sides of the slab model, with one side terminated by S atoms and the other by metal atoms. Optimization resulted in major structural changes, exposing S atoms on both sides, and promoting polymer formation on the sulfur-rich layer. The estimated charges revealed that the charge of the S atoms included in these polymers is lower than that of bulk S atoms. These findings support the experimental observations of Harmer et al. (2004), who attributed the observed shift in S 2p peak binding energy to a higher oxidation state.

de Oliveira & Duarte (2010) studied the reconstruction of the (001) chalcopyrite surface, which has two distinct terminations: (001)-S terminated by S atoms and (001)-M terminated by metal atoms. Slab models were constructed based on the optimized bulk structure and optimized with PBE functional and plane waves. Notably, de Oliveira et al. (2012) found constraints in employing a tiny (1 × 1) slab model for appropriate reconstruction analysis.

In the (001)-S surface reconstruction, S atoms in the top layer formed S—S bonds measuring 2.158 Å. The Electron Localization Function (ELF) analysis confirms the establishment of this new chemical bond. Density of States (DOS) and Local Density of States (LDOS) calculations indicate bond formation through S-atom oxidation to S₂²⁻ groups (de Oliveira & Duarte, 2010). The released electrons were proposed to reduce Fe³⁺ to Fe²⁺. These findings are consistent with Klauber's detection of disulfide groups on the chalcopyrite surface using XPS under ultra-high vacuum conditions (Klauber, 2003) and the identification of Fe²⁺ on the surface using XPS by Harmer et al. (2004).

The (001)-M surface underwent a more drastic reconstruction. Metal atoms in the top layer migrated downwards, forming a combined metal–sulfur layer. Cu—S and Fe—S bond lengths ranged from 2.123 to 2.315 Å, while Fe—Fe and Cu—Cu distances were calculated to be 2.481 and 2.578 Å, respectively (de Oliveira et al., 2012). Notably, Von Oertzen et al. (2006) also observed S-atom migration to the surface in their (11 $[\overline{2}]$ ) surface study. DOS analysis of the reconstructed (001)-M surface by de Oliveira & Duarte (2010) revealed significant modifications compared to the non-reconstructed surface, indicating adjustments in chemical bonding due to the new geometric arrangement.

In computational surface reconstruction investigations, it is critical to understand the limitations of slab model size. de Oliveira & Duarte (2010) employed a (1 × 1) slab model (the size equivalent of 1 lattice parameter a and 1 lattice parameter b) to investigate the (001) surface of chalcopyrite. While this approach provided valuable insights, the small model size inherently limited the types of reconstructions that could be observed. For instance, in the (001)-S surface, the presence of only two S atoms in the top layer restricts the possibility of observing polymer formation. This highlights the importance of carefully selecting an appropriate slab model size that can accommodate the desired surface processes.

Building upon the work of de Oliveira and Duarte (2010), de Oliveira et al. (2012) investigated the reconstruction of nine chalcopyrite surfaces: (001), (100), (101), (110), (111) and (112). Notably, surfaces (001), (100) and (111) exhibit distinct metal and sulfur terminations (Fig. 3), and both were considered in their analyses.

Figure 3
Schematic representations of the different reconstruction mechanisms for the chalcopyrite surface observed by de Oliveira et al. (2012

DFT calculations were performed using periodic boundary conditions, the PW91 functional (Perdew & Wang, 1992 ), plane waves and ultrasoft pseudopotentials. Slab models were appropriately constructed to allow for more substantial reconstructions. For example, the (001) and (100) surfaces were modeled using (2 × 2) slabs. The k-point mesh was optimized for each slab model. This extended study revealed three general reconstruction mechanisms, as illustrated in Fig. 3 (de Oliveira et al., 2012).

Sulfur-terminated surfaces, including (001)-S, (100)-S, (111)-S and (112), reconstruct to form disulfide (S₂²⁻) groups within the topmost atomic layer, as represented in Fig. 4. ELF analyses confirm the presence of a chemical bond between these S atoms. DOS results suggest an oxidative process leading to the reduction of Fe³⁺ to Fe²⁺, consistent with previous observations by de Oliveira & Duarte (2010), Klauber (2003) and Harmer et al. (2004), as referenced previously.

Figure 4
(001) The surface of chalcopyrite (a) without relaxation, (b) reconstructed (001)-S and (c) reconstructed (001)-M.

The utilization of large slab models enabled the investigation of various reconstruction possibilities on the same surface. For instance, both (1 × 1) and (2 × 2) reconstructions were explored for the (001)-S surface, revealing a minimal energy difference of only 0.1 eV. Notably, the formation of polymeric sulfur structures on these surfaces was not observed in this study. The reconstruction can be attributed to the tetrahedral coordination of S atoms to metal atoms in the bulk crystal (Fig. 1). Cleavage of the surface disrupts this coordination, resulting in dangling bonds that readily overlap to form new S—S bonds.

Metal-terminated surfaces, such as (001)-M and (100)-M, undergo more substantial reconstructions compared to their sulfur-terminated counterparts. These reconstructions involve inwards migration of metal atoms, while S atoms are promoted to the topmost atomic layer, as shown in Fig. 4(c). This process results in the formation of an alloy-like structure containing numerous metal–metal bonds with bond lengths around 2.6 Å. ELF and DOS analyses substantiate the formation of these new bonds.

The formation of metal–metal bonds can be explained by the dangling bonds arising from the surface cleavage. In the bulk structure, the d_xy, d_xz and d_yz of the metal atoms form bonds with the sp³ orbitals of S atoms. Cleavage disrupts these bonds, leaving the metal d orbitals unbonded to any other orbitals. When metal atoms move inwards during reconstruction, these orbitals can overlap face-to-face, facilitating the formation of δ bonds. The reconstruction of the (111)-M surface deviates slightly, forming metallic aggregates on the first atomic layer instead of an alloy-like structure observed on other metal-terminated surfaces. However, the underlying reconstruction mechanism remains similar.

de Oliveira et al. (2012) further observed that step surfaces like (110) and (101) exhibit minimal reconstruction. These surfaces undergo a slight relaxation, with atomic movements that optimize bonding angle to accommodate the new chemical environment at the cleavage plane.

Thinius et al. (2018 ) explored the reconstruction of several chalcopyrite surfaces not previously studied by de Oliveira et al. (2012), including (010), (011), (012), (120), (121), (122) and (221). They employed DFT calculations using the revPBE functional, and incorporated advanced techniques like ab initio molecular dynamics (AIMD) in conjunction with simulated annealing via a minima-hopping algorithm (Goedecker, 2004 ). This approach facilitated the exploration of various surface configurations. The reconstructed surfaces exhibited a decrease in surface energy of approximately 0.05 J m⁻². Consistent with prior studies, their findings revealed the formation of S₂²⁻ on sulfur-terminated surfaces and a metallic alloy layer on metal-terminated surfaces (Thinius et al., 2018), similar to those observed by de Oliveira et al. (2012).

de Lima et al. (2018 ) employed periodic DFT calculations with the PBE+U method, plane waves and the PAW scheme (Blöchl, 1994 ) to investigate the electronic structure of the (001)-S chalcopyrite surface. A 2 × 2 × 2 k-point mesh was generated using the Monkhorst–Pack method (Monkhorst & Pack, 1976 ) within the first Brillouin zone. To elucidate the chemical modifications within the topmost atomic layers, the authors simulated X-ray absorption near edge structure (XANES) spectra (de Lima et al., 2018) and compared them with experimental data (Mikhlin et al., 2017 ). Analysis of the simulated S K-edge and Fe K-edge absorption spectra revealed that surface S atoms are more prone to modifications compared to Fe atoms. The formation of disulfides and the oxidation with the inclusion of the O atoms modify the spectra.

Building upon the work of de Oliveira et al. (2012) and de Lima et al. (2018), several key observations can be generalized regarding chalcopyrite surface reconstructions. Firstly, S atoms preferentially migrate toward the surface, even when cleavage reveals a metal-rich plane. This behaviour suggests a lower surface energy for sulfur-terminated surfaces compared to metal-terminated ones. Secondly, when S atoms become close on the reconstructed surface, S₂²⁻ groups form through an oxidative process, accompanied by the reduction of Fe³⁺ to Fe²⁺. This finding aligns well with experimental observations of disulfide presence on chalcopyrite surfaces (Klauber, 2003). Notably, de Lima et al. (2018) demonstrated consistency between their simulated XANES spectra and experimental data, further supporting the proposed oxidation mechanism.

More recently, Wei et al. (2019 ) employed a combined approach of X-ray diffraction (XRD) and DFT simulations to investigate the chalcopyrite surface. They observed that the most intense peaks in the XRD pattern corresponded to (112), (204) and (312) surfaces, with lower intensity peaks assigned to other orientations. They suggested that surfaces with the strongest XRD reflections likely exhibit the lowest surface energy. The authors further calculated the density of broken bonds at the surface and proposed a reactivity order based on these calculations: (112)-S < (112)-M < (102) < (312) < (001)-S < (001)-M. They examined the reconstruction of surfaces such as (112) and (001), and their findings are consistent with those reported in prior investigations.

While previous simulations (Wei et al., 2019; de Lima et al., 2011 , 2018; de Oliveira et al., 2012) did not predict polymer formation, it is crucial to consider that these simulations represent idealized cleavage scenarios. The absence of external factors that might promote polymer growth could explain this discrepancy. Finally, the reconstructions of metal-terminated surfaces suggest the formation of either alloy-like structures or metallic aggregates. These findings could potentially explain the observed decrease in leaching kinetics. However, experimental verification of these specific structures predicted by de Oliveira et al. (2012) is still required.

Nasluzov et al. (2019 ) investigated the influence of defects on chalcopyrite surface chemistry by introducing Fe-atom vacancies on the (012) and (110) surfaces. Utilizing DFT calculations with the PW91+U functional and a 5 × 4 × 1 Monkhorst–Pack k-point grid, they employed cryo-XPS simulations to predict the surface structure. Their findings revealed the formation of sulfur polymers, primarily S₅²⁻ and S₃²⁻ species, upon defect introduction, with a portion of the surface remaining as sulfur monomers (Nasluzov et al., 2019). These results align with experimental observations of sulfur polymer formation on chalcopyrite surfaces using synchrotron S 2p XPS techniques, as reported by Harmer et al. (2004).

The contrasting observations of sulfur polymer formation in the studies by de Oliveira et al. (2012) and Nasluzov et al. (2019) highlight the crucial role of surface defects. The absence of polymers in the de Oliveira et al. (2012) study, which simulated perfectly cleaved surfaces, suggests that defect-free surfaces may impede sulfur polymerization. Conversely, the introduction of defects by Nasluzov et al. (2019) promotes polymer formation. This finding suggests that defect-induced structural rearrangements and enhanced surface reactivity might facilitate the formation of sulfur polymers on chalcopyrite surfaces.

4. Modelling chalcopyrite oxidation

The surface of chalcopyrite undergoes transformation during leaching, a process where redox reactions are crucial for efficient copper extraction (Li et al., 2013; Wei et al., 2019; Antonijević & Bogdanović, 2004; Xiong et al., 2018 ; Wang et al., 2016 ; Zhao et al., 2019a ; de Oliveira et al., 2012).

Flotation, another key step in copper extraction, consists in the adherence of a collector to a mineral surface changing its polarity to promote its interaction with air bubbles (Liu et al., 2017), permitting separation from gangue minerals (Mkhonto et al., 2021 , 2022 ; Jiang et al., 2023 ; Duan et al., 2021 ; Wu et al., 2020 ; Liu et al., 2020 ; Kumar et al., 2022 ; Sun et al., 2022 ; Luo et al., 2023 ; Jia et al., 2019 ). During flotation, water and O₂ interact with chalcopyrite, causing its oxidation due to its semiconducting properties (Hadjab et al., 2018 ; Ranjan et al., 2021 ; Salehi & Gordanian, 2016 ; Das et al., 2022 ).

In both cases, knowing the oxidation mechanism is critical for designing efficient copper-extraction technologies, especially from low-grade ores.

Chalcopyrite is only sparingly soluble in water. However, it readily dissolves in the presence of strong oxidizing agents, generating various products. The proposed mechanism for chalcopyrite oxidation involves several steps: (i) adsorption of O₂: oxygen molecules adsorb onto the surface of CuFeS₂. (ii) Water dissociation and speciation: water molecules adsorb on S sites and dissociate into H⁺ and OH⁻ ions. These ions then adsorb at neighbouring sites. (iii) Iron(II) to iron(III) oxidation: O atoms from adsorbed water react with Fe²⁺ ions on the CuFeS₂ surface, oxidizing them to Fe³⁺. These Fe³⁺ ions can then participate in other reactions. (iv) Sulfide (S²⁻) oxidation: S²⁻ ions are oxidized to either elemental sulfur (S⁰) or sulfate (SO₄²⁻). The oxidation reaction can be expressed using Equations (3)–(8) (Li et al., 2013; Parker et al., 2003 ; Nicol et al., 2010 ; Huang et al., 2020 ).

$[{\rm CuFeS_2\left( s \right) + 4O_2 \rightarrow Fe^{2+} + Cu^{2+} + 2SO_4^{2-}} \eqno(3)]$

$[{\rm CuFeS_2\left( s \right) + 4O_2 + 4H^+\rightarrow Fe^{2+} + Cu^{2+} + 2S^0 + H_2O} \eqno(4)]$

$[\eqalign {{\rm CuFeS_2\left( s \right) + 16Fe^{3+} +} & {\rm 8H_2O} \rightarrow \cr & {\rm 17Fe^{2+} + Cu^{2+} + 2SO_4^{2-} + 16H^+}} \eqno(5)]$

$[{\rm S^0\left( s \right) + 2H_2O + 3O_2 \rightarrow 2SO_4^{2-} + 4H^+} \eqno(6)]$

$[{\rm CuFeS_2 \left( s \right) \rightarrow Fe^{2+} + Cu^+ + 2S^0 \left( s \right) + 3e^-} \eqno(7)]$

$[\eqalign{{\rm CuFeS_2 \left( s \right) \ + \ } & {\rm 8H_2O_2} \rightarrow \cr & {\rm Fe^{3+} + Cu^{2+} + 2SO_4^{2-} + 8H_2O + 2H^+}} \eqno(8)]$

Chalcopyrite oxidation by oxygen produces a variety of secondary products. Iron cations are more susceptible to hydrolysis than copper cations, particularly in acidic environments. These iron cations react with water to form iron hydroxides and products of their oxidation states (Fe²⁺ and Fe³⁺). The subsequent interaction of these oxidation products with other ions and molecules on the chalcopyrite surface can lead to the formation of: (i) iron sulfates: FeSO₄ (ferrous sulfate) and Fe₂(SO₄)₃ (ferric sulfate); (ii) iron hydroxides: Fe(OH)₂ (ferrous hydroxide) and Fe(OH)₃ (ferric hydroxide); (iii) iron oxides: FeO (wüstite) amd Fe₂O₃ (hematite); (iv) elemental sulfur (S⁰).

Several computational models has been developed to better understand the nuances of this oxidation mechanism. The most recent studies are reviewed here.

The galvanic effect, observed in conductive or semiconductor minerals such as pyrite (Hiskey & Wadsworth, 1975 ; Liu et al., 2008 , 2024 ; Wu et al., 2020; Ruiz et al., 2015 ; Ke & Chen, 2022 ), occurs when different minerals are in contact during leaching. In this process, the medium facilitates charge transfer, enabling oxidation–reduction reactions to take place.

Analysis of electrochemical reactions on mineral surfaces reveals distinct anodic and cathodic zones dependent on resting potentials. Anodic areas, characterized by lower resting potentials, facilitate oxidation reactions that consume electrons from the mineral. Conversely, reduction reactions, which donate electrons to the mineral, occur at cathodic areas with higher resting potentials. Equation (9) depicts anodic oxidation, releasing metal ions (M), and Equation (10) shows the cathodic reduction process.

$[{\rm MS } \rightarrow {\rm S }^{2+} + {\rm S + 2e^-} \eqno(9)]$

$[{{1}\over{2}} {\rm O_2 + H_2O + 2e^- \rightarrow 2OH^-} \eqno(10)]$

The oxidation of chalcopyrite has been studied extensively through various experiments and theoretical analyses (Liu et al., 2024; Luo et al., 2022 ; Ke & Chen, 2022; Ranjan et al., 2021; Zhang et al., 2020; Wu et al., 2020; O'Connor & Eksteen, 2020; Khoshkhoo et al., 2017 ; Ruiz et al., 2015; Todd et al., 2003 ; Yin et al., 2000 ). The interaction between water and oxygen molecules with chalcopyrite surfaces promotes its oxidation, resulting in the generation of soluble sulfur oxides (Li et al., 2013; Yin et al., 2000). Since leaching and flotation processes involve water and oxygen, understanding the behaviour of oxidation reactions occurring on chalcopyrite surfaces is crucial for designing efficient copper extraction projects.

Studies have shown that Fe atoms are the preferred sites for oxidation reactions, forming iron oxides and oxy-hydroxides. To understand this preferential oxidation and the overall mechanism, the oxygen and water adsorption on the surface will be analysed from three aspects: (i) oxygen adsorption (whether it dissociates or not), (ii) water adsorption and (iii) co-adsorption of oxygen and water on the surface.

XPS studies and DFT calculations reveal that Fe atoms on the chalcopyrite surface are preferentially oxidized to FeO(OH), while Cu and S atoms remain relatively unreactive (Xiong et al., 2018; Khoshkhoo et al., 2017; Yin et al., 2000; Harmer et al., 2006). This passivation process forms a protective layer that hinders further oxidation reactions (Li et al., 2013; O'Connor & Eksteen, 2020; Sokić et al., 2010; Zhao et al., 2019b ). The formation of FeO(OH) is considered a key step in surface passivation. Additionally, surface reconstruction plays a crucial role during oxidation (Wei et al., 2019; Xiong et al., 2018; de Lima et al., 2012 ; Bazan et al., 2022 ; de Oliveira et al., 2012).

4.1. Oxygen adsorption

4.1.1. Non-dissociative adsorption

Non-dissociative adsorption involves oxygen molecules binding the surface without breaking their chemical bond. Experiments and theoretical calculations suggest that Fe atoms are preferentially oxidized compared to copper (Wei et al., 2016 ; Xiong et al., 2018). This leads to the formation of iron oxides or oxy-hydroxides on the surface (Todd et al., 2003; Li et al., 2014 ) and theoretical studies support this evidence through adsorption energies (Xiong et al., 2018; Wei et al., 2019; Liu et al., 2023 ). Table 1 summarizes the O₂ adsorption energy evaluated considering different surfaces and sites. Wei et al. (2019) carried out calculations at the PW91/plane waves level using slab models of the (001) and (112) surfaces terminating in metal (M) or sulfur (S) and demonstrated that adsorption in a non-dissociative configuration on Fe sites is more common than those on S sites. Furthermore, for these systems, there are two possible adsorption geometries of O₂: vertical and parallel (Fig. 5). The parallel configuration is more favourable than the vertical one. These configurations have adsorption energies of −132.9 and −148.9 kcal mol⁻¹ for the (001)-M and (112)-M surfaces at Fe sites, respectively. S sites have energies of −45.2 and −49.5 kcal mol⁻¹ for (001)-S and (112)-S, respectively. The authors did not investigate the possibility of adsorption on metal atoms in the sulfur-terminated surfaces. These results indicate that O₂ adsorption is more favourable on metal-terminated surfaces, particularly the (112)-M surface. Analysis of the bonding effects between Fe and O atoms through density of states (DOS)/projected density of states (PDOS) shows that the Fe atom can be easily oxidized, which corroborates previous works.

Table 1
Oxygen adsorption energy (kcal mol⁻¹) in different chalcopyrite surfaces

Surface	Theory level	Adsorption site	Adsorption energy	Reference
(112)-M	PW91/plane waves/	Fe—S	−49.5^a	Liu et al. (2023)
	dispersion correction	Fe—Fe	−56.9^a
		Cu—Cu	−18.4^a
		Cu	−10.5
		Fe	−42.1
(112)-S	PW91/plane waves	Fe	−148.9	Wei et al. (2019)
			−159.5^b
		S	−49.5
			−95.4^b
(001)-M	PW91/plane waves	Fe	−132.9
			−137.0^b
	PBE/plane waves	Fe	−39.7	Xiong et al. (2018)
		Cu	−16.1
(001)-S	PW91/plane waves	S	−45.2	Wei et al. (2019)
Notes: (a) parallel adsorption; (b) dissociated.

Figure 5
(a) Vertical and (b) parallel adsorption modes of O₂ in chalcopyrite, and (c) mechanisms of dissociation of O₂ in the (001) chalcopyrite surface. Colour key: Fe brown, Cu blue, S yellow and O red.

Xiong et al. (2018) investigated the non-dissociation adsorption of O₂ on (001)-M surfaces and showed that the parallel adsorption structure is the most stable on Fe sites compared to Cu sites, with energies of −39.7 and −16.1 kcal mol⁻¹, respectively. Bader charge analysis was used to examine the charge transfer from the Fe and Cu sites to the O₂ molecule. The analysis showed that Fe and Cu atoms are predicted to carry more positive charge, unlike the S atom, which does not exhibit a significant charge change. Additionally, Liu et al. (2023), in a recent work, identified six possible locations for O₂ adsorption on the (112) surfaces of chalcopyrite, again indicating Fe sites as more favourable compared to copper (Liu et al., 2023).

In general, the surface has a substantial impact on both adsorption and the site of adsorption. However, all reported studies using various approaches agree that iron is the most favourable.

4.1.2. Dissociative

Dissociative adsorption of O₂ on the chalcopyrite surface also occurs, primarily on Fe atoms rather than Cu atoms. During this process, the O—O bond in the O₂ molecule breaks, forming individual O atoms bonded to the mineral surface. Studies have shown that the Fe site is the most thermodynamically favourable location for this interaction, compared to Cu sites (Xiong et al., 2018). Using DFT calculations at the PBE+U/plane waves level and slab models, Xiong et al. (2018) obtained adsorption energies of −137.0 and −159.5 kcal mol⁻¹ on the (001)-M and (112)-M surfaces, respectively (Table 1). For surfaces terminated by sulfur, the values were −92.7 and −95.4 kcal mol⁻¹ for the (001)-S and (112)-S surfaces, respectively. Comparing these adsorption energies to those for non-dissociation, they confirm that the dissociative configuration is the most stable and that Fe sites are preferred for this type of adsorption.

This is further supported by Wei et al. (2019), who suggests that dissociation can occur in one or two steps (Fig. 5). In both cases, the Fe site is more favourable than the Cu site. One-step dissociation has a barrier energy, obtained by the NEB/CI (nudged elastic band/climbing image) method, of 27.0 kcal mol⁻¹ at the Fe site and 29.5 kcal mol⁻¹ at the Cu site. For the two-step process, the barrier energies are 31.6 and 10.6 kcal mol⁻¹ at the Fe site, and 10.6 and 18.7 kcal mol⁻¹ at the Cu site. These findings imply that O₂ dissociation on Fe atoms often occurs in a single step, whereas Cu sites prefer a two-step pathway. Additionally, they showed that after adsorption on the (112)-M surface, electrons are transferred from the Fe atoms to the O atoms (3d orbitals of iron to 2p orbitals of oxygen) (Wei et al., 2019). The overlap between these orbitals ranges from −7.0 to −1.4 eV for the parallel non-dissociation configuration and from −6.64 to −1.2 eV for the dissociative configuration. This confirms a stronger interaction between Fe and O atoms in the dissociative configuration compared to the non-dissociation parallel configuration. Similar results were obtained for the (001)-M surface, with overlap values ranging from −5.54 to −2.26 eV. Notably, no overlap was found between the orbitals involved in the non-dissociative parallel configuration. So, dissociative adsorption is the most likely scenario, with Fe atoms being more susceptible to O₂ adsorption and subsequent oxidation.

Considering both thermodynamics and kinetics, O₂ adsorption on Fe sites appears to follow a thermodynamically favoured one-step route, while O₂ adsorption on Cu sites might exhibit a kinetically favoured two-step dissociation process (Xiong et al., 2018). This suggests that the products formed during dissociation depend on whether the process is controlled by thermodynamics or kinetics.

4.2. Water adsorption

Understanding the interaction between the chalcopyrite surface and water is critical since oxidation occurs often in aqueous solutions. Notably, in the literature, there are two possibilities for water adsorption: before and after O₂ adsorption (Liu et al., 2023; de Lima et al., 2011; Xiong et al., 2018). This dual scenario highlights the potential in flotation and hydrometallurgical processes. Consequently, elucidating these adsorption mechanisms is essential for optimizing the industrial applications.

In Table 2, we highlight the water adsorption energy on different chalcopyrite surfaces. Recent research by Liu et al. (2023) used theoretical calculations to show that isolated water molecules adsorb most favourably on Fe atoms compared to Cu and S atoms on the (112)-M surface of chalcopyrite. They found adsorption energies, calculated with a PW91/plane waves/dispersion correction, of −10.4, −2.6 and −0.68 kcal mol⁻¹ for Fe, Cu and S sites, respectively.

Table 2
Water adsorption energy (kcal mol⁻¹) in different chalcopyrite surfaces

Surface	Theory level	Adsorption site	Adsorption energy	Reference
(112)-M	PW91/plane waves/	Fe	−10.4	Liu et al. (2023)
	dispersion correction	Cu	−2.6
		S	−0.68
(112)-S	PW91/plane waves	Fe	−10.0	Wei et al. (2019)
			−5.1^a
		S	16.1
			36.8
(001)-M	PW91/plane waves	Fe	−36.8	Wei et al. (2019)
			−66.2^a
	PBE	Fe	−35.5	Xiong et al. (2018)
(001)-S	PBE	Cu	−2.8	de Lima et al. (2011)
		Fe	−22.8
		Cu	−17.0
		S	−13.4
	W91/plane waves	S	43.8	Wei et al. (2019)
Note: (a) dissociated.

Wei et al. (2019) investigated the (001)-S, (112)-S, (001)-M and (112)-M surfaces, and showed a preference for adsorption on the Fe sites. They reported adsorption energies of 43.8, 16.1, −36.8 and −10.0 kcal mol⁻¹, respectively. Based on these results, they concluded that metal-terminated surfaces are more favourable for water adsorption compared to sulfur-terminated surfaces. Their findings contrast from those of de Lima et al. (2011), who expected that adsorption in (001)-S would be more advantageous than adsorption in (001)-M. DFT calculations on wet chalcopyrite surface oxidation by Xiong et al. (2018) further support the results obtained by Wei et al. (2019). They found that water preferentially adsorbs on Fe sites in a non-dissociated configuration, with adsorption energies of −35.5 and −2.8 kcal mol⁻¹ for Fe and Cu atoms, respectively, on the (001)-M surface.

H₂O adsorption via a dissociation pathway is not expected because a weak S—H bond is formed in place of the stronger original O—H bond. The non-dissociative configuration exhibits high exothermicity (releases heat), making it more stable compared to the dissociative configuration, which is thermodynamically less favourable (Xiong et al., 2018; de Lima et al., 2011).

Studies have shown that the oxidized surface of CuFeS₂ becomes more hydrophilic (Fairthorne et al., 1997a ; Luo et al., 2022; Miki et al., 2017 ). This can be attributed to two main factors. First, the oxidation process replaces some S atoms with O atoms, resulting in additional Fe—O bonds that promote favourable interactions with water, resulting in a more polar surface. Second, the S—H bonds formed between water and the remaining S atoms on the surface are weaker than the O—H bonds found within water molecules, resulting in an energetically beneficial interaction between the oxidized surface and water. However, Liu et al. (2023) suggest that the hydrophilicity of oxidized CuFeS₂ surfaces may be more nuanced. The presence of metallic hydroxides formed during oxidation can further enhance hydrophilicity. Conversely, the dissolution of Fe²⁺ and Cu²⁺ ions can contribute to a hydrophobic character. Therefore, the overall hydrophilicity of the oxidized CuFeS₂ surface likely results from a complex interplay of these factors. There is a strong correlation between the hydrophilic characteristics of the CuFeS₂ surface and the degree of its oxidation. The presence of H₂O/O₂ alters the surface interactions, leading to changes in hydrophilicity and the formation of different chemical species.

4.3. Co-adsorption of water and O₂

Water dissociation is triggered by O₂ dissociation. In the presence of water, O₂ dissociation becomes more exothermic, leading to increased surface reactivity (Xiong et al., 2018). Experimental and theoretical studies have shown that water dissociation on a `clean' surface (i.e. before O₂ dissociation) is unfavourable. Water alone cannot oxidize the S atoms in chalcopyrite. Therefore, water molecules are more likely to react and potentially dissociate on the chalcopyrite surface only after it has been pre-oxidized by O₂. This pre-oxidation by O₂ increases surface reactivity, making water molecules more susceptible to dissociation and participation in further oxidation reactions (Wei et al., 2019).

$[{\rm CuFeS_2 + O_2 + 4H^+ \rightarrow Cu^{2+} + Fe^{2+} + 2S^0 + 2H_2O} \eqno(11)]$

$[{\rm CuFeS_2 + 4O_2 \rightarrow Cu^{2+} + Fe^{2+} + 2SO_4^{2-}} \eqno(12)]$

Equations (11) and (12) show how O₂ reacts with the surface, promoting its oxidation. A study by Wei et al. (2019) concluded that the order of adsorption for H₂O and O₂ on the CuFeS₂ surface is primarily determined by their adsorption energies, not simply by the concentration of water or oxygen in the solution. This finding emphasizes the importance of surface energetics in these adsorption processes. In Table 3, we reported the water and oxygen co-adsorption energy.

Table 3
Adsorption energy (kcal mol⁻¹) of H₂O and O₂ co-adsorption on different chalcopyrite surfaces

Surface	Theory level	Adsorption site	Adsorption energy	Reference
(112)-M	PW91/plane waves/	H₂O–Cu/O₂–Fe	−81.7	Liu et al. (2023)
	dispersion correction	H₂O–Cu/O₂–Fe	−80.9
	PW91/plane waves	Fe	43.4^a	Wei et al. (2019)
			32.4^a,b
(112)-S	PW91/plane waves	S	−6.61^a
			−12.4^a,b
(001)-M	PW91/plane waves	Fe	−22.0^a
	PBE	Fe	−40.9^a,b
			−92.5	Xiong et al. (2018)
Notes: (a) water on oxidized oxygen surfaces; (b) dissociated.

The formation of sulfoxy species is beneficial for CuFeS₂ dissolution. However, these species only exist if O₂ dissociation happens, because S—O bonds are formed under the dissociative O₂ configuration, as demonstrated by Wei et al. (2019). Xiong et al. (2018) showed that after oxidation, H₂O and O₂ preferentially adsorb and dissociate at the Fe site on the CuFeS₂ surface. Further results demonstrate that transferring hydrogen from H₂O to a surface O atom provides additional stabilization (3.2 kcal mol⁻¹), with a very small energy barrier (around 2.3 kcal mol⁻¹). Interestingly, when H₂O reacts with the Cu site, an even lower energy barrier (around 0.46 kcal mol⁻¹) is predicted for dissociation, which is also slightly exothermic.

Wei et al. (2019) found energy barriers of 52.8 and 97.0 kcal mol⁻¹ for O₂ dissociation on dry CuFeS₂ (112)-M and (112)-S surfaces, respectively. These results, along with previous studies, suggest that the dissociation is not expected in the absence of water on these surfaces. H₂O can also dissociate to form H and OH species. Wei et al. (2019) proposed that the formation of Fe—O bonds makes the surface more electropositive for neighbouring Fe and S sites due to electron transfer from Fe to O atoms. This mechanism was confirmed for the (001)-M surface (Wei et al., 2019). However, on the (112)-M surface, H₂O needs to overcome a higher energy barrier (37.6 kcal mol⁻¹) before adsorption on the Fe site. This higher barrier likely leads to H₂O dissociation into OH and H, resulting in the formation of FeOOH/FeOH species.

Bader charge analysis indicates that electron transfer occurs from the Fe site to the O atom during H₂O dissociation. Additionally, the difference in bond strength between O—H and S—H due to transferring hydrogen from H₂O to a surface O atom is thermodynamically and kinetically more favourable than transferring it to a surface S site (Xiong et al., 2018).

5. Modelling the interaction of chalcopyrite with collectors for flotation process

Flotation is a widely used method for concentrating minerals. It involves the addition of molecules called collectors, which selectively interact with the surface of the target mineral. These collectors are made to have a dual functionality: a polar group that binds to the mineral surface and a non-polar group that increases the attachment to air bubbles at the air–water interface (Bulatovic, 2007 ; Ives, 1983 ). This interaction enhances the hydrophobicity of the mineral particles, enabling them to adhere to air bubbles and rise to the froth layer of separation from the bulk aqueous phase. The mining industry is becoming more and more dependent on the development of selective collectors for effective mineral separation as the supply of high-grade ores declines. To this end, a variety of collector molecules have been investigated (Liu et al., 2017; Yuan et al., 2024 ; Huang et al., 2023 ).

Xanthates, ROCS₂M (R = organic radical and M = metal or H), have emerged as a prominent class of collectors for chalcopyrite. However, a comprehensive understanding of the mineral's surface chemistry remains elusive (Fairthorne et al., 1997a,b ), hindering the development of highly selective and efficient collectors. To address this challenge, computational simulations have been employed alongside advanced experimental techniques to elucidate the interaction between chalcopyrite and xanthate molecules (Zhang et al., 2024 ). While theoretical studies have extensively explored the structure, charge distribution and frontiers orbitals of collectors to elucidate their reactivity (Zhao et al., 2013 ; Ma et al., 2021), comparatively less attention has been devoted to understanding the specific interactions between these molecules and the mineral surfaces.

Ma et al. (2017 ) investigated the interaction of S-benxoyl-O-isobutil xanthate (BuIBX) (Fig. 6), a promising collector exhibiting higher efficiency than traditional sulfide collectors, with the chalcopyrite surface. XPS and FT–IR analyses suggested chemisorption of BuIBX on the surface of the mineral via the C=S and C=O groups. DFT calculations using the B3LYP functional (Becke, 1993 ; Lee et al., 1988 ) and the 6-311+G(d) basis set were employed to analyse the molecule's electronic structure. The calculations revealed a higher concentration of negative charge at the proposed bonding sites (C=S and C=O). Additionally, frontier orbital analysis indicate that the highest occupied molecular orbital (HOMO) was primarily localized on the S atom, facilitating electron transfer to the metal centre of chalcopyrite. Conversely, the lowest unoccupied molecular orbital (LUMO) exhibited some contribution of the S atom, suggesting the possibility of backdonation from the metal to the collector molecule (Ma et al., 2017).

Figure 6
Chemical structures of xanthate molecules used as collectors in the froth flotation process.

Building upon the established effectiveness of xanthates for chalcopyrite flotation, Huang et al. (2019a ,b ) designed a novel collector, S-hydroxyethyl-O-isobutyl xanthate (HEIBX) (Fig. 6), by modifying widely used sodium isobutyl xanthate (SIBX) (Fig. 6) with a hydroxyethyl group. This modification aimed to introduce both hydroxyl and thione functionalities, targeting the selective separation of chalcopyrite from pyrite, as non-ionic xanthates have shown promise in this application (Fairthorne et al., 1997b).

Experimental characterization supported the enhanced selectivity of HEIBX. UV–Vis spectroscopy indicated a stronger interaction with chalcopyrite compared to pyrite, while contact angle measurements revealed a significant increase in the hydrophobicity for chalcopyrite particles with minimal effect on pyrite. Microflotation experiments further confirmed the superior selectivity of HEIBX toward chalcopyrite (Huang et al., 2019a,b).

To elucidate the mechanism behind this improved selectivity, DFT calculations were employed to compare the reactivity of HEIBX and SIBX. The authors analysed the molecular electrostatic potential and frontier orbitals for both molecules at the B3LYP/6-311+G(d) level of theory. The electrostatic potential map suggested a higher electron density around the C=S and –OH groups in HEIBX. Additionally, frontier orbital analysis indicated a greater number of reactive sites in HEIBX compared to SIBX. Based on this combined data, Huang et al. (2019a,b) proposed an adsorption mechanism for HEIBX on the chalcopyrite surface involving bidentate coordination through the C=S and –OH groups, a mode not feasible for SIBX.

However, it is important to note that, while the study utilized computational methods to understand the intrinsic reactivity of the collectors, the investigation did not directly address the interaction of these molecules with the mineral surface itself.

Huang et al. (2019a,b) investigated the addition of a thioester moiety as a means of improving collector hydrophobicity. They compared the performance of O-benzythioethyl xanthate (SBEX) (Fig. 6), derived from sodium phenylethyl xanthate (SPEX) (Fig. 6), with SPEX and sodium isobutyl xanthate (SIBX) using flotation experiments. SBEX exhibited superior performance compared to the other collectors.

DFT calculations at the B3LYP/6-311+G(d) level were carried out to analyse the frontier orbitals and collector interactions with Cu^I ions. The authors explained that SBEX performed better than SPEX because they had different HOMO and LUMO energies. However, the reported HOMO energy difference (0.0003 a.u.) falls within the range of typical DFT errors, casting doubt on its significance for electron donation. Conversely, the LUMO energy of SBEX was slightly lower than that of SPEX, suggesting a potentially higher electron-accepting capacity for SBEX (Huang et al., 2019a,b).

Furthermore, the study modelled the interaction of SBEX and SPEX with chalcopyrite by simulating their interaction with isolated Cu^I ions, based on XPS data, suggesting Cu^I as the coordination point. Binding energies were calculated using Equation (13), where the energies of the complex, the Cu^I ion and the collector correspond to E_complex, E_Cu and E_collector, respectively, and indicated a stronger interaction between SBEX and Cu^I compared to SPEX (Huang et al., 2019a,b).

$[E_{\rm binding} = E_{\rm complex} - \left( E_{\rm Cu} + E_{\rm collector} \right) \eqno(13)]$

However, this simplified model neglects the complete coordination environment of Cu^I in the chalcopyrite lattice, potentially leading to overestimated binding energies due to an incomplete coordination sphere in the modelled complex.

Yang et al. (2018 ) investigated azolethione derivatives (Fig. 7) as potential collectors for chalcopyrite. DFT calculations at the B3LYP/6-311+G(d,p) level were employed to analyse the reactivity indices of various molecules: 5-heptyl-1,3,4-oxadiazole-2-thione (HpOT), 5-heptyl-1,3,4-thiadiazole-2-thione (HpST), 5-heptyl-1,2,4-triazole-3-thione (HpNT), 4-amino-5-heptyl-1,2,4-triazole-3-thione (HpATT) and 6-heptyl-1,2,4,5-tetrazine-3-thione (HpNNT). These molecules share an azolethione group with an exocyclic S atom potentially suitable for coordinating with Cu atoms on the chalcopyrite surface.

Figure 7
Chemical structures of azolethione molecules used as collectors in the froth flotation process.

The study revealed a trend of increasing HOMO energy in the order HpOT < HpST < HpATT < HpNT < HpNNT, which the authors correlated with enhanced affinity towards copper minerals. Conversely, the LUMO energy followed the trend HpST < HpATT < HpOT < HpNT < HpNNT, suggesting a greater propensity for backdonation in HpST and HpATT. Analysis of various chemical parameters, including Mülliken charges, dipole moments, absolute hardness and frontier orbitals, led the authors to conclude that azolethione collectors can interact with metal ions via the exocyclic S atom and endocyclic N3 and N2 atoms. The interaction between these azolethione compounds and Cu^II and Cu^I ions was investigated by considering the formation of different azolethione–Cu complexes. The calculated binding energies were around −35 kcal mol⁻¹ (Yang et al., 2018). However, similar to previous studies, this approach neglected the complexities of the chalcopyrite surface, potentially limiting the accuracy of the results.

Jia et al. (2019) examined the performance of thiohexanamide (THA), a new collector for sulfide ores, in comparison to O-isopropyl-N-ethyl thiocarbamate (IPETC) and SIBX, two well-known collectors. In microflotation, bench-scale flotation and adsorption tests, THA demonstrated greater affinity and selectivity for chalcopyrite in a mixture comprising galena and pyrite.

DFT simulations were used at the B3LYP/6-311+G(d) level to examine the frontier orbitals and electrostatic potential maps of each of the three collectors to clarify the interaction process. The findings suggested that the C=S group in both the THA and IPETC molecules was the main site of coordination with the mineral surface since regions of high electron density were clustered around this group. Moreover, this region was also the location of the HOMO and LUMO orbitals, supporting a binding process involving electron donation and backdonation. The authors postulated a reactivity trend of THA < SIBX < IPETC based on the HOMO–LUMO energy gap (Jia et al., 2019).

The studies reviewed herein have mostly focused on the intrinsic features of collector molecules, analysing their potential based primarily on frontier orbitals and charge distributions. In some instances, simplified models were employed to simulate collector–mineral interactions, often considering only isolated ions. However, recent advances in theoretical methodologies provide a broader choice of options for creating more realistic models of collector molecule interactions with mineral surfaces (Alizadeh Sahraei et al., 2023 ; Zhang et al., 2024).

Sarvaramini & Larachi (2017 ) studied the interaction between diethyl dithiophosphate (DEDTPA), diethyl dithiophosphinate (DEDTPI), diethyl monothiophosphate (DEMTPA) and diethyl monothiophosphinate (DEMTPI) (Fig. 8) with the (110) and (100) chalcopyrite surfaces. These thiophosphorus-like chelating agents have emerged as alternatives to xanthates for selective flotation of chalcopyrite and galena from pyrite mixtures (Güler et al., 2006 ).

Figure 8
Chemical structures of thiophosphorus-like molecules used as collectors in the froth flotation process.

The study used DFT calculations at the RPBE/DND level. The authors modelled both surfaces by constructing (1 × 2) supercells with a huge 40 Å vacuum to eliminate spurious interactions (Sarvaramini & Larachi, 2017). As reported previously, these reconstructed surfaces differ significantly from bulk-terminated surfaces (de Oliveira et al., 2012). Such reconstructions can influence the reactivity of chalcopyrite and should be considered when modelling collector interactions.

Analysis of the frontier orbitals for the thiophosphorus molecules revealed that the HOMO predominantly consists of p orbitals localized on the S and O atoms, suggesting these atoms as the primary interaction sites with the surface.

The (100) surface exposes both metal [(100)-M] and sulfur [(100)-S] atoms. Consistent with the findings of de Oliveira et al. (2012), the authors observed a significant reconstruction of the (100)-M surface, with extensive metal–metal bonding and exposed S atoms on the top layer. The increased stability of these metal-rich alloy-like structures, coupled with the repulsive electrostatic potential from the surface S atoms, disfavoured chemical adsorption of any of the studied collectors.

In contrast, all collectors chemisorbed onto the (100)-S surface, forming a chemical bond between their S atoms and a surface S atom. The calculated adsorption energies [using an equation similar to Equation (13)] indicated the strongest adsorption for DEDTPI on the (100)-S surface (Sarvaramini & Larachi, 2017).

The interaction with the (110) surface differed, with all collectors forming bidentate chemical bonds. This observation highlights the dependence of collector–surface interactions on the exposed chalcopyrite surface.

Chi et al. (2020 ) carried out DFT calculations using the PBESol/plane waves approach to simulate the interaction of O-butyl-S-(1-choroethyl) carbonodithionate (GC-I) with the (101) plane of chalcopyrite and pyrite. Their calculations point to a substantially stronger interaction between GC-I and the chalcopyrite surface, with an adsorption energy of −202.4 kcal mol⁻¹. This value is substantially higher compared to the interaction energy of butyl xanthate with chalcopyrite (−146.7 kcal mol⁻¹). In contrast, the adsorption energy of GC-I on pyrite is considerably weaker (−11.0 kcal mol⁻¹), representing only about 5% of the interaction strength observed with chalcopyrite. Notably, the interaction of butyl xanthate with pyrite (−14.4 kcal mol⁻¹) is also stronger than that of GC-I with this mineral surface. These results suggest a high selectivity of GC-I for chalcopyrite flotation over pyrite (Chi et al., 2020).

Molecular modelling offers a powerful tool to investigate collector–mineral interactions. However, many studies have focused solely on the properties of isolated collector molecules, neglecting the crucial influence of the mineral surface. While such analyses can provide preliminary insights into potential interaction mechanisms, recent advancements offer a wider range of methodologies capable of generating more robust data (Alizadeh Sahraei et al., 2023). The development of increasingly selective collectors for processing low-grade ores necessitates a combined approach that integrates flotation experiments, spectroscopic techniques and advanced computational modelling.

6. Conclusion

Density functional theory (DFT) calculations with periodic boundary conditions and slab models have emerged as powerful tools for investigating chalcopyrite surfaces, complementing experimental data and providing insights into their structure and reactivity. The absence of a well-defined preferential cleavage plane presents a modelling challenge, pushing researchers to explore various surfaces (de Oliveira et al., 2012; Thinius et al., 2018). A recurring observation is the preferential exposure of S atoms on the topmost reconstructed surface layer. Furthermore, studies consistently report the formation of disulfide groups (S₂²⁻) on pristine defect-free sulfur-terminated surfaces, accompanied by the reduction of Fe³⁺ to Fe²⁺ (de Oliveira et al., 2012; Wei et al., 2019). In contrast, the presence of defects appears to favour the formation of polysulfides (Nasluzov et al., 2019).

Despite extensive modelling efforts, the mechanism of chalcopyrite surface oxidation remains unclear. All studies consistently identify Fe sites as favourable adsorption locations for both oxygen and water molecules, independent of surface termination (de Lima et al., 2011; Wei et al., 2019; Xiong et al., 2018). However, discrepancies exist regarding the relative reactivity of sulfur and metal surfaces. While the dissociation of oxygen molecules on the surface is thermodynamically favourable with a low kinetic barrier, particularly on Fe sites (Wei et al., 2019), water-molecule dissociation is deemed unlikely due to the preferential stability of its molecularly adsorbed state. The key steps involved in chalcopyrite oxidation by water and oxygen remain elusive.

Computer modelling has the potential to provide valuable insights into collector–chalcopyrite surface interactions. However, the current research focus on the isolated properties of collector molecules limits our understanding of their interactions with the chalcopyrite surface. Future investigations that explore these interactions in more detail are warranted.

Acknowledgements

FAPEMIG, CNPq and CAPES are acknowledged for their financial support.

Funding information

Funding for this research was provided by: Fundação de Amparo à Pesquisa do Estado de Minas Gerais (grant Nos. APQ-00519-21 and RENOVAMin).

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