Prediction of Solubility and Miscibility Parameters of Bismuth-Arsenic Complex and Amorphous Mineral Compounds Using Molecular Dynamics Simulation

Abstract

Bismuth is one of the most difficult impurities to remove in mining concentrates and low concentrations generate problems in silver and copper refineries. Therefore, financial penalties are established when concentrations exceed 0.05%. Some researchers had used arsenic to remove bismuth with results of up to 52% of extraction. Unfortunately, this mechanism is not yet fully understood. The objective of this research was to obtain the solubility parameters of amorphous mineral compounds, including bismuth-based compounds, through computational simulation using molecular dynamics. The composition of the mineral sample was determined by X-ray diffraction and the crystalline species were obtained and modeled using Materials Studio software. The nanostructures were optimized by an energy minimization methodology using the Broyden-Fletcher-Goldfarb-Shanno algorithm and were validated using the figure of merit equation and density. Simulations were performed using the Universal Force Field at constant pressure and temperature. The results of the minerals identified in the sample were compared with arsenic trioxide, indicating miscibility between As2O3and Bi2O3, possible miscibility with 10 other minerals, and immiscibility with the rest. The results indicate that As2O3 can be successfully used for the removal of Bi2O3 without a negative effect on the recovery of other minerals of higher commercial value.

1. Introduction

In many metals’ extraction processes, the ore extracted from the mines usually undergoes a particle reduction or purification process, where high amounts of amorphous phases can be generated [1]. The presence of impurities (non-desired compounds) affects properties, such as electrical conductivity and ductility [2]. Bismuth (Bi), a very difficult element to remove from copper minerals, is practically insoluble in such minerals because of its melting point of 271°C, compared to 1083°C for copper, and tends to localize at the edges of copper crystals, causing rod cracking and poor drawability [3]. Regularly, high commercial value metals with bismuth concentrations higher than those established by the buyer result in penalties, thus decreasing the final price, so the elimination of such impurities in the extraction processes has become a key problem faced mainly by mining companies [4]. A negative setback is the lack of detailed research on its removal.

Previously Xiao et al. [1] developed a method using arsenic trioxide to form a complex that precipitates and which can be later removed. Xiao and Zheng found that As(III) ion as As₂O₃ played a significant role in the removal of antimony (Sb) and Bi impurities from copper electrolytes [1, 5, 6]. When As(III) is added to the electrolyte, the removal rate of antimony and bismuth increases significantly [5, 7], reaching up to 52% of extraction effectiveness. However, despite being an effective method, this mechanism is not yet fully understood, so it is desirable to further evaluate it and a key consideration is to know the miscibility between the compounds of interest.

One technique that allows a detailed and profound understanding of this mechanism is by using a computational simulation by molecular dynamics (MD), where a molecular structure and its behavior can be represented and analyzed over time, by considering intramolecular and intermolecular forces, such as van der Waals forces, electrostatic forces, covalent and non-covalent bonds, among others. From the simulation, different physicochemical properties of the system can be calculated, such as the solubility parameter of the substance, which, according to the principle of similarity, if two substances have similar values it indicates that they are miscible, hence it could predict whether two substances are miscible or not [8, 9].

Therefore, in this research, a computational simulation by molecular dynamics was used through Materials Studio 8.0 software to obtain the solubility parameters of simulated amorphous cells of arsenic trioxide (As₂O₃) and different minerals that compose a sample of mining concentrate, among them bismuth oxide (Bi₂O₃), thus indicating the miscibility and affinity between them for the formation of bismuth-arsenic complexes.

2. Materials and methods

The mineral sample was obtained from a local mine located in the Sierra Madre Occidental region of Durango, Mexico, and it was grinded and sieved using a 200 mesh.

2.1 X-ray diffraction

X-ray diffraction (XRD) of the powdered mineral sample was carried out on a Mini Flex 300 equipment in a 2θ angular range between 5° and 90° at a step size of 0.02°. The obtained diffraction pattern was refined using the Rietveld method and the crystalline composition was determined. The crystal structures were also obtained from the open database of crystallography (COD) [10, 11, 12, 13, 14].

2.2 Molecular dynamics simulation

BIOVA Materials Studio software version 8.0 (Accelrys, San Diego, CA) was used to perform the molecular dynamics simulations. The crystals were created using the latency data previously obtained from the XRD technique, from which the amorphous cells were obtained with the amorphous cell module; 10 cubic boxes were created, containing 100 repetitions of each of the molecules at 298 K. Geometric optimization was performed using the FORCITE module using the Universal Force Field (UFF) and the Quasi-Newton Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm using the sum of atoms method for nonderivative van der Waals and electrostatic interactions, which were truncated using a group distance less than half the box length. The Andersen thermostat and barostat were used to maintain temperature and pressure, respectively. The box with the lowest energy was used to perform dynamics using constant number of molecules, constant pressure, and constant temperature (NPT) of 1 atm and 298 K, respectively, and for a time of 200 ps with a time step of 1 fs. Finally, the cohesive energy densities and the solubility parameters were obtained.

3. Results

The XRD results are shown in Figure 1, where silicon oxide or quartz (Si₂O) predominates since the sample was not previously processed. Silver and gold, among others, were also found. Bismuth was detected as an element of interest, since it is considered an impurity and is the object of study of the research, due to the economic interests of the mining industry.

Figure 1.

Diffractogram of the mineral sample and its crystalline composition.

The Mini Flex 300 comes equipped with a program and a crystal database that provides crystallographic data, such as lattice parameters, crystal type, and space group, among others (Table 1). Subsequently, the composition of each mineral in the sample was determined, as shown in Figure 2.

Name	Formula	Space group	Crystal type	Lattice parameters
				a (Å)	b (Å)	c (Å)	β (°)	γ (°)
Silver	Ag	225: Fm-3m	Cubic	4.09	4.09	4.09	90.00	90.00
Argentite	Ag2S	229: Im-3m	Cubic	4.88	4.88	4.88	90.00	90.00
Lenaite	AgFeS2	122: I-42d	Tetragonal	5.94	5.94	10.17	90.00	90.00
Gold	Au	194: P63/mmc	Cubic	2.35	2.35	4.00	90.00	120.00
Kusachiita	Bi2CuO4	130: P4/ncc	Tetragonal	8.56	8.56	5.79	90.00	90.00
Bismite	Bi2O3	14: P21/c	Monoclinic	5.85	8.17	7.51	112.58	90.00
Bismuthine	Bi2S3	62: Pnma	Orthorhombic	11.04	4.25	10.33	90.00	90.00
Malachite	Cu2(CO3)(OH)2	14: P121	Monoclinic	9.41	10.85	2.92	95.90	90.00
Chalcocite	Cu2S	194: P63/mmc	Monoclinic	3.57	3.57	6.29	90.00	120.00
Chalcopyrite	CuFeS2	122: I-42d	Tetragonal	5.28	5.28	10.41	90.00	90.00
Covellite	CuS	194: P63/mmc	Hexagonal	4.00	4.00	16.00	90.00	120.00
Iron	Fe	225: Fm-3m	Cubic	2.83	2.83	2.83	90.00	90.00
Pyrrhotite	Fe(1-X)S	147: P-3	Monoclinic	6.14	6.14	57.40	90.00	120.00
Hematite	Fe2O3	167: R-3c	Hexagonal	5.02	5.02	13.78	90.00	120.00
Goethite	Fe^3+O(OH)	62: Pbnm	Orthorhombic	4.50	9.80	2.90	90.00	90.00
Marcasite	FeS2	58: Pnnm	Orthorhombic	4.52	5.43	3.38	90.00	90.00
Galena	PbS	225: Fm-3m	Cubic	6.20	6.20	6.20	90.00	90.00
Quartz	SiO2	154: P3221	Hexagonal	4.91	4.91	5.40	90.00	120.00
Lepidocrocite	ϒ-FeO(OH)	63: Cmcm	Orthorhombic	3.13	12.37	3.98	90.00	90.00

Table 1.

Crystallographic data of the mining sample.

Figure 2.

Qualitative analysis of the mining sample (weight percentage of the crystalline components).

These data obtained from XRD were supplied to the Materials Studio 8.0 program for the creation of the in silico crystals (Figure 3).

Figure 3.

Crystals created by simulation in Materials Studio.

Initially, the crystal structures detected were obtained from the open crystallography database (COD) (Figure 3) [10, 11, 12, 13, 14]. Subsequently, all the created crystals were modeled in an amorphous form by eliminating the crystal parameters and keeping the positions of the atoms; thus, the amorphous cell was created (Figure 4). The molecular dynamics technique was used to model the molecular structure of minerals and their behavior was analyzed as a function of time, considering the intramolecular forces known as force fields. The accuracy of a properly balanced molecular simulation is determined by the ability of the parameters and equations describing the atomic interactions (force fields) to reproduce reality [15]. The force field used was the Universal Force Field (UFF), which has complete coverage of the periodic table and is relatively accurate in predicting geometries and conformational energy differences of metal complexes and is expressed by Eq. (1) [16, 17].

Figure 4.

Creation of the amorphous cell from (1) AgFeS₂ crystal, (2) AgFeS₂ molecular structure without lattice parameters, (3) AgFeS2 unit amorphous cell, (4) amorphous cell with 100 units of AgFeS₂ repetitions, (5) AgFeS₂ unit amorphous cell with 100 units of AgFeS₂ repetitions, and (6) AgFeS₂ unit amorphous cell with 100 units of AgFeS₂ repetitions.

$$E_{\mathit{pot}}=E_R+E_{\theta }+E_{\varphi }+E_{\omega }+E_{\mathit{vdW}}+E_{\mathit{el}}$$E1

where E_R = bond-stretching energy, E_θ = valence angle bending energy, E_Φ = dihedral torsion energy, E_ω = inversion energy, E_vdW = van der Waals interaction energy, and E_el = electrostatic energy.

The chosen force field was developed to be used with all the elements of the periodic table to obtain appropriate parameters. In this force field, the first three terms parameterize the short-range bound interactions, the fourth is the energy required to transform a molecule from one spatial form to another, while the last two terms parameterize the unbound inter and intramolecular interactions [16].

Normally the initial structures that are created in the simulators have much higher energies than a real structure would have, for this reason, algorithms are used to calculate the positions and forces, to minimize them and make them more realistic. The minimum points on the potential energy surface corresponding to the steady states of the system were then analyzed and a geometric optimization using the Quasi-Newton method with the Broyden-Fletcher-Goldfarb-Shanno algorithm (BFGS) was performed to achieve the crystal relaxation and improve its stability and efficiency [18]. BFGS accumulates information about the Hessian matrix and the shape of the enthalpy surface around the minimum [19].

Figure 5 shows (a) the amorphous cell of arsenic trioxide in its initial form where the total energy is above 12 million kcal/mol, and, in image (b), the same cell after optimization at 298 K where the energy is 6707.6 kcal/mol, indicating that it is a structure closer to its minimum energy state, and, therefore, more stable and likely to be found in reality.

Figure 5.

Energy-minimized structure of As₂O₃ at (a) its initial configuration at 298 K, and (b) the end of the geometry optimization.

The rationality of the simulation system was verified by comparing the simulated density with the experimental reference density from the Mining Handbook published by the Mineralogical Society of America [20], as shown in Table 2, since density is one of the most basic physical properties. Gupta mentions that close agreement between simulated and experimental density values means effective optimization of intermolecular interactions and hence accurate prediction [21]. All density values remained within the correct ranges, except for Kusachiite and Argentite, which showed a discrepancy of 1.16 and 1.67%, respectively.

Name	Formula	Density g/cm^3
		Simulated	Experimental
Silver	Ag	10.50	10.1–11.1
Argentite	Ag2S	7.08	7.2–7.4
Lenaite	AgFeS2	4.60	4.6
Claudetite	As2O3	4.17	3.9–4.2
Arsenolite	As2O3	3.87	3.86–3.88
Gold	Au	18.40	16–19.3
Kusachiita	Bi2CuO4	8.60	8.5
Bismite	Bi2O3	9.37	8.5–9.5
Bismuthine	Bi2S3	6.81	6.8–7.2
Malachite	Cu2(CO3)(OH)2	4.00	3.6–4
Chalcocite	Cu2S	5.74	5.5–5.8
Chalcopyrite	CuFeS2	4.19	4.1–4.3
Covellite	CuS	4.63	4.6–4.8
Iron	Fe	7.87	7.3–7.9
Pyrrhotite	Fe(1-X)S	4.62	4.6–4.7
Hematite	Fe2O3	5.30	5.2–5.3
Goethite	Fe^3+O(OH)	4.27	3.3–4.3
Marcasite	FeS2	4.88	4.8–4.9
Galena	PbS	7.37	7.2–7.6
Quartz	SiO2	2.65	2.6–2.7
Lepidocrocite	ϒ-FeO(OH)	4.00	4

Table 2.

Comparison of simulated and experimental densities.

The density calculated in the simulation is obtained using Eq. (2) [22].

$${\rho }_{\mathit{\text{calc}}}=\frac{N_{\mathit{at}}\bullet M}{V_{\mathit{cel}}\bullet N_A}$$E2

where Ρ_calc = calculated density, N_at = number of atoms per cell, M = atomic mass, V_cel = volume of the cell, and N_A = Avogadro’s number = 6.022 140 857(74) × 10²³ 1/mol.

For validation, the experimental and simulated XRD patterns were used, and, using Eq. (3), which corresponds to the figure of merit (FoM) [23], the similarity between them was evaluated using the total number of coincident peaks, as well as the intensities and values at their highest peaks (Table 3).

Name	Formula	FoM
Arsenolite	As2O3	0.94
Bismite	Bi2O3	0.91
Bismuthine	Bi2S3	0.91
Galena	PbS	0.85
Lenaite	AgFeS2	0.98
Quartz	SiO2	0.89
Chalcopyrite	CuFeS2	0.98
Covellite	CuS	0.92
Gold	Au	0.98
Kusachiita	Bi2CuO4	0.96
Marcasite	FeS2	0.98
Hematite	Fe2O3	0.97
Lepidocrocite	ϒ-FeO(OH)	0.95
Goethite	Fe^3+O(OH)	0.96
Iron	Fe	0.99

Table 3.

Comparison of results of simulated and experimental XRD patterns.

$$\mathit{FoM}=\sqrt{\frac{{\mathit{FoM}}_{\mathit{db}}\bullet \left(w_{\theta }\bullet {\mathit{FoM}}_{\theta }+w_I\bullet {\mathit{FoM}}_I+w_{\mathit{ph}}\bullet {\mathit{FoM}}_{\mathit{ph}}\right)}{w_{\theta }+w_I+w_{\mathit{ph}}}}$$E3

where FoM_db is the contribution due to the associated database peak intensities and its percentage, FoM_θ coming from 2θ is the difference between the experimental database peaks, FoM_I is the difference between the experimental database peak intensities, FoM_ph is the contribution due to the associated experimental peak intensities and its percentage, and w_θ, w_I, and w_ph are weighting factors.

The patterns of the simulated crystals coincided consistently with the real ones in the database, those values greater than 0.8 are considered acceptable for identification. The patterns of As₂O₃ and Bi₂O₃ are shown in Figure 6.

Figure 6.

Comparison of simulated XRD pattern with the experimental one for (a) As₂O₃ and (b) Bi₂O₃.

Hildebrand [24] introduced the concept of solubility parameter (δ_hil), defined as the square root of the cohesive energy density (CED) (Eq. (3)), which is the energy required to break intermolecular bonds per unit volume. Those compounds with similar solubility parameters are miscible in most proportions, while values with a greater difference are considered immiscible. Greenhalgh et al. [25] and Forster et al. [26] mention that those values with differences less than 2 would be miscible, values between 2 and 7 would possibly be miscible and, on the other hand, values greater than 7 would be immiscible. The solubility parameter is calculated by Eq. (4) [27].

$${\delta }_{\mathit{hil}}=\sqrt{\mathit{CED}}=\sqrt{\frac{E_{\mathit{coh}}}{V}}$$E4

where E_coh is cohesive energy and V is the molar volume of the substance.

Table 4 shows the difference in crystal parameters concerning arsenic trioxide, obtaining values of 24.33 (J/cm³)^0.5 and 22.65 (J/cm³)^0.5 for Bi₂O₃ and As₂O₃, respectively. On the other hand, minerals such as iron, gold, and silver obtained higher differences with values below 11.00 (J/cm³)^0.5.

Name	Formula	δHildebrand	(|δArsenolite–δMineral|)	Miscibility with As2O3
Arsenolite	As2O3	22.65	—	—
Bismite	Bi2O3	24.33	1.68	Miscible
Marcasite	FeS2	20.49	2.15	Possibly miscible
Quartz	SiO2	24.91	2.26	Possibly miscible
Bismuthine	Bi2S3	25.86	3.21	Possibly miscible
Galena	PbS	27.64	4.99	Possibly miscible
Malachite	Cu2(CO3)(OH)2	17.23	5.42	Possibly miscible
Lenaite	AgFeS2	16.96	5.69	Possibly miscible
Kusachiita	Bi2CuO4	16.42	6.23	Possibly miscible
Argentite	Ag2S	16.21	6.44	Possibly miscible
Covellite	CuS	15.90	6.75	Possibly miscible
Pyrrhotite	Fe(1-X)S	15.60	7.05	Possibly miscible
Chalcopyrite	CuFeS2	15.53	7.12	Immiscible
Lepidocrocite	ϒ-FeO(OH)	14.78	7.87	Immiscible
Goethite	Fe^3+O(OH)	14.78	7.87	Immiscible
Chalcocite	Cu2S	12.82	9.83	Immiscible
Hematite	Fe2O3	12.55	10.09	Immiscible
Silver	Ag	10.31	12.34	Immiscible
Gold	Au	10.00	12.65	Immiscible
Iron	Fe	6.95	15.70	Immiscible

Table 4.

Solubility parameters in MPa^0.5 from the simulation of amorphous mineral cells compared to As₂O₃.

4. Conclusions

The composition of the mineral sample from the Avino mine consisted of 19 identified crystals, with three of them containing bismuth in the form of B_iO₃, Bi₂S₃, and Bi₂CuO₄: representing 2% of the total composition of the sample, while also contributing to 1.65% of bismuth weight, exceeding the allowable limit of 0.05% for bismuth by far. The structures of the simulated minerals were effectively corroborated to match the real structures by comparing the diffraction patterns obtaining similarities higher than 9. The solubility parameters indicate an affinity in the miscibility between As₂O₃ and Bi₂O₃, possible miscibility with 10 other minerals, and an immiscibility with the rest of the minerals in which gold, silver, and copper stand out. The results indicate that As₂O₃ can be used for the removal of Bi₂O₃ at ambient pressure and temperature conditions without having a negative effect on the recovery of other minerals of higher commercial value. The mining industry could benefit from the results obtained from this research since the economic penalties because of the presence of bismuth in concentrates might be reduced by using arsenic trioxide. The molecular simulation could serve as a resourceful tool in metal recovery processing by avoiding time investment and the use of reagents.

Acknowledgments

This work was supported in part by the USDA National Institute of Food and Agriculture, Hatch grant (1010849) “Food Bioengineering Technology of Agro-industrial Products.”

Conflict of interest

The authors declare no conflict of interest.