**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 As2O3 and 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.

**Keywords:** molecular dynamics, solubility parameter, miscibility, amorphous mineral compounds, bismuth, arsenic trioxide

## **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 bismutharsenic 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°.

*Prediction of Solubility and Miscibility Parameters of Bismuth-Arsenic Complex… DOI: http://dx.doi.org/10.5772/intechopen.106316*

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) [10–14].

#### **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.

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

**Figure 1.** *Diffractogram of the mineral sample and its crystalline composition.*


#### **Table 1.**

*Crystallographic data of the mining sample.*

group, among others (**Table 1**). Subsequently, the composition of each mineral in the sample was determined, as shown in **Figure 2**.

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

Initially, the crystal structures detected were obtained from the open crystallography database (COD) (**Figure 3**) [10–14]. 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].

$$E\_{\rm pot} = E\_R + E\_\theta + E\_\phi + E\_{o\nu} + E\_{vdW} + E\_{el} \tag{1}$$

*Prediction of Solubility and Miscibility Parameters of Bismuth-Arsenic Complex… DOI: http://dx.doi.org/10.5772/intechopen.106316*

**Figure 2.**

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


#### **Figure 3.**

*Crystals created by simulation in Materials Studio.*

where *ER* = bond-stretching energy, *E<sup>θ</sup>* = valence angle bending energy, *E<sup>Φ</sup>* = dihedral torsion energy, *E<sup>ω</sup>* = inversion energy, *EvdW* = van der Waals interaction energy, and Eel = 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

#### **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.*

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

#### **Figure 5.**

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

*Prediction of Solubility and Miscibility Parameters of Bismuth-Arsenic Complex… DOI: http://dx.doi.org/10.5772/intechopen.106316*

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.

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.

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

$$
\rho\_{calc} = \frac{N\_{at} \bullet M}{V\_{cell} \bullet N\_A} \tag{2}
$$


#### **Table 2.**

*Comparison of simulated and experimental densities.*


#### **Table 3.**

*Comparison of results of simulated and experimental XRD patterns.*

where *Pcalc* = calculated density, *Nat* = number of atoms per cell, *M* = atomic mass, *Vcel* = volume of the cell, and *NA* = 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**).

$$FoM = \sqrt{\frac{FoM\_{db} \bullet \left(w\_{\theta} \bullet FoM\_{\theta} + w\_{I} \bullet FoM\_{I} + w\_{ph} \bullet FoM\_{ph}\right)}{w\_{\theta} + w\_{I} + w\_{ph}}} \tag{3}$$

where *FoMdb* is the contribution due to the associated database peak intensities and its percentage, *FoM<sup>θ</sup>* coming from 2*θ* is the difference between the experimental database peaks, *FoMI* is the difference between the experimental database peak intensities, *FoMph* is the contribution due to the associated experimental peak intensities and its percentage, and *wθ*, *wI*, and *wph* 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**.

Hildebrand [24] introduced the concept of solubility parameter (δhil), 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

*Prediction of Solubility and Miscibility Parameters of Bismuth-Arsenic Complex… DOI: http://dx.doi.org/10.5772/intechopen.106316*

#### **Figure 6.**

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


#### **Table 4.**

*Solubility parameters in MPa0.5 from the simulation of amorphous mineral cells compared to As2O3.*

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].

$$
\delta\_{hl} = \sqrt{\text{CED}} = \sqrt{\frac{E\_{coh}}{V}} \tag{4}
$$

where *Ecoh* 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/cm<sup>3</sup> ) 0.5 and 22.65 (J/cm<sup>3</sup> ) 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/cm<sup>3</sup> ) 0.5.
