# Probing the Local Atomic Structure of In and Cu in Sphalerite by XAS Spectroscopy Enhanced by Reverse Monte Carlo Algorithm

^{1}

^{2}

^{3}

^{4}

^{5}

^{*}

## Abstract

**:**

^{2+}↔2In

^{3+}+ □, where □ is a Zn vacancy. The coordination spheres of In remain undistorted. Formation of the solid solution in the case of (In, Cu)-bearing sphalerites follows the charge compensation scheme 2Zn

^{2+}↔Cu

^{+}+ In

^{3+}. In the solid solution, splitting of the interatomic distances in the 2nd and 3rd coordination spheres of In and Cu is observed. The dopants’ local atomic structure is slightly distorted around In but highly distorted around Cu. The DFT calculations showed that the geometries with close arrangement (clustering) of the impurities—In and Cu atoms, or the In atom and a vacancy—are energetically more favorable than the random distribution of the defects. However, as no heavy In atoms were detected in the 2nd shell of Cu by means of EXAFS, and the 2nd shell of In was only slightly distorted, we conclude that the defects are distributed randomly (or at least, not close to each other). The disagreement of the RMC-EXAFS fittings with the results of the DFT calculations, according to which the closest arrangement of dopants is the most stable configuration, can be explained by the presence of other defects of the sphalerite crystal lattice, which were not considered in the DFT calculations.

## 1. Introduction

^{+}and does not depend on the presence of other impurities. The difference in the “formal” oxidation states of In

^{3+}and Zn

^{2+}implies the substitution scheme 3Zn

^{2+}↔2In

^{3+}+ □, where □ is a Zn vacancy. In most natural sphalerites, enrichment in In is associated with elevated concentrations of Cu. According to our previous data, in the presence of In, the oxidation state of Cu is 1+, which means that the formation of the In-Cu-bearing sphalerite solid solution follows the scheme 2Zn

^{2+}↔Me

^{+}+ In

^{3+}. In the solid solution state, the local atomic environment of Cu derived by EXAFS spectra fitting is close to the one of pure ZnS. However, we found that the 2nd and 3rd coordination shells of Cu are considerably distorted—the atoms in each shell form two subshells, which implies significant deformation of ZnS crystal structure near Cu impurity. According to quantum chemical Density Functional Theory (DFT) calculations, such deformation can be observed in the case of the close arrangement of impurities (In and Cu), or the atom of In and the vacancy. Nonetheless, the conventional method of EXAFS spectra approximation, realized in the IFEFFIT software package [3], usually provides less accurate results for the disordered or amorphous materials than for the structures of high symmetry [4,5]. To improve the quality of the EXAFS spectra fittings, we employed the reverse Monte Carlo (RMC) method, which is highly informative in exploring the distortion of crystal structure around impurities [6,7].

## 2. Materials and Methods

#### 2.1. Sample Preparation and Characterization

_{2}.

#### 2.2. X-ray Absorption Spectroscopy (XAS) Measurements

#### 2.3. Density Functional Theory (DFT) Calculations

^{2+}↔2In

^{3+}+ □ and 2Zn

^{2+}↔In

^{3+}+ Cu

^{+}. In the present study, the formation energy of In- and In-Cu-bearing sphalerite solid solutions was calculated by means of Density Functional Theory (DFT). Besides, inthis way, the distortion of the local atomic geometry around dopants was explored.

^{−9}Ry was applied in the electronic structure calculations. The optimizations of the crystal structure and supercell parameters were performed using the Broyden-Fletcher-Goldfarb-Shanno algorithm for the atomic coordinates with convergence threshold 10

^{−3}Ry/a.u. for the forces and 10

^{−4}Ry for the energy. The relaxation of the atomic positions and cell parameters were applied for a 3 × 3 × 3 supercell, which contained 108 Zn and 108 S atoms, with periodic boundary conditions. In all cases, the large unit cell allowed gamma point approximation to be employed. Our previous investigations [1,12,13] demonstrated the high accuracy of this approach to DFT calculations in the case of sphalerite-type structures. The discrepancy between the calculated interatomic distances and EXAFS results was 0.02, 0.01, and 0.04 Å for the 1st, 2nd, and 3rd coordination shells, respectively.

_{FE}, [12,14]) were obtained using the calculated total energies. We considered the following models: two In atoms substitute for two Zn atoms in ZnS crystal structure; two In atoms substitute for two Zn atoms in ZnS crystal structure with the formation of a vacancy at Zn position; one In and one Cu atom substitute for two Zn atoms in ZnS crystal structure. Accordingly, the E

_{FE}values per impurity atom after geometry relaxation were calculated as defined by the following equations:

_{FE}= E(Zn

_{106}S

_{108}In

_{2}) + 2E(ZnS) + E(S) − E(Zn

_{108}S

_{108}) − E(In

_{2}S

_{3})

_{FE}= E(Zn

_{105}S

_{108}In

_{2}) + 3E(ZnS) − E(Zn

_{108}S

_{108}) − E(In

_{2}S

_{3})

_{FE}= E(Zn

_{106}S

_{108}InCu) + 2E(ZnS) − E(Zn

_{108}S

_{108}) − E(CuInS

_{2})

_{2}), and E(In

_{2}S

_{3}) are the energies calculated by DFT for pure sphalerite, roquesite, and In

_{2}S

_{3}crystal structures; E(S) is calculated for the isolated S atom placed in a vacuum box. The structures with lower E

_{EF}are more stable.

#### 2.4. Reverse Monte Carlo (RMC) EXAFS Spectra Fitting

_{0}shift was determined for each EXAFS spectrum by fitting the first peak of Fourier transform magnitude.

_{0}

^{2}was fixed at values estimated for the references in [1]: S

_{0}

^{2}(Zn) = 0.85, S

_{0}

^{2}(Cu) = 0.75, S

_{0}

^{2}(In) = 0.95.

#### 2.5. XANES Spectra Calculation

## 3. Results

#### 3.1. DFT Calculations

_{DFT}= 5.439 Å, which is slightly bigger than the experimental XRD value of a

_{XRD}= 5.410 Å, with relative deviation of 0.5%. This accuracy level is high enough to model the local atomic geometry and compare it to the structural parameters derived from EXAFS spectra.

_{EF}obtained in all calculations implies endothermic character of the substitution reactions. Embedding two In atoms in ZnS without a vacancy creation does not obey the charge compensation scheme and is characterized by high value of E

_{EF}. Therefore, this configuration is not stable. Comparison of E

_{EF}calculated for different arrangements of In atom and a vacancy in the cationic sublattice shows that the location of In and a vacancy in the nearest cationic positions is energetically favorable. The same conclusion can be reached for Cu and In atoms: the close position of these dopants is more stable because of low values of E

_{EF}.

#### 3.2. EXAFS Spectra Analysis (RMC-EXAFS)

#### 3.3. XANES Spectra Simulation

#### 3.3.1. In K-Edge

#### 3.3.2. Cu K-Edge

## 4. Discussion

_{S}= 4), from 3.85 to 3.91 Å in the 2nd coordination shell (N

_{Zn}= 12), and are close to the Me-S distance in the pure sphalerite in the 3rd coordination shell (N

_{S}= 12, R

_{In-S}= 4.48 Å). The In Radial Distribution Function (RDF) consists of three distinct peaks, which correspond to the first three coordination shells. We observe no splitting of the coordination shells of In into subshells when In is the only dopant. The presence of Cu in sphalerite distorts the local atomic surrounding of In, and the distortion extent of the In-Zn coordination shell depends on the concentration of impurity atoms. In Sample 4108 (concentration of In and Cu is less than 0.1 mol%), the shape of In-Zn RDF is close to the one of In-Zn for the sphalerite with only In dopants. An increase in concentrations of In and Cu causes the splitting of In-Zn RDF into three contributions.

^{3+}→Zn

^{2+}results in the formation of a positively charged site located on the dopant. On the contrary, the Cu

^{+}→Zn

^{2+}substitution results in the formation of a negatively charged site. The DFT calculations show that the close arrangement of In and Cu is more energetically favorable than random distribution of dopants, which can be explained by the local charge balance. The DFT shows significant distortion in ZnS crystal structure around the dopants (In and Cu). The splitting of interatomic distances, calculated by means of DFT, reaches 0.10 Å for the 2nd shell around Cu and 0.12 Å for the In 2nd shell. This coordination shell splitting should be observed by means of EXAFS, even in the samples with low concentrations of In and Cu. Analysis of the experimental EXAFS spectra shows considerable deformation of ZnS geometry around Cu, which doesnot depend on the concentration of Cu or In. In the case of In, the local atomic distortion depends on the concentration of impurities, and its extent correlates with the amount of dopants in sphalerite. This implies that Cu and In impurities in sphalerite with low concentration of dopants are placed at a significant distance from each other. The apparent disagreement between the results of the DFT calculations and experimental EXAFS spectra fittings can stem from the oversimplified model of doped sphalerite structure used in the DFT calculations. In the calculations, we employed the simplest models with defects localized at the atoms of In, Cu, or vacancy. The real structure of doped sphalerite can be more complicated and contain defects, which were not considered in our calculations.

## 5. Conclusions

## Supplementary Materials

_{2}[4] (Adopted from Trofimov et al. [2]). Bottom: Crystal structures of sphalerite (doubled cell is shown to make comparison with CuInS

_{2}easier) and roquesite [4], Figure S2: The RMC fit results of Cu K-edge EXAFS spectra of samples 4108 and 4186 (the 2nd coordination shell of Cu is described by Zn + In atoms). Panel A: experimental WT image; panel B: fitted WT image; panel C: calculated RDF for first three coordination shells around absorbing atom; panel D: experimental (black dotted line) and fitted (red solid line) EXAFS signal χ(k)*k2; panel E: Fourier transform magnitudes of experimental (black dotted line) and fitted (red solid line) χ(k)*k2 function; panel F: close view of Cu-Zn and Cu-In RDF. The RDFs fitted by Gaussians are shown by solid lines, Figure S3: Comparison of Cu-Zn and In-Zn RDFs with Zn-Zn RDF derived from RMC EXAFS fits. The model assumes In atoms in the 2nd coordination shell of In and Cu, Figure S4: Comparison of Cu-Zn and Cu-(Zn + In) RDFs for Cu K-edge EXAFS fitting with and without In in the 2nd coordination shell of Cu. Note that the shapes of the curves representing the two models (11Zn + In and 12Zn) are very close to each other which means that incorporation of In atom in the 2nd sphere of Cu is not necessary for the accurate approximation of the experimental data, Table S1: Interatomic distances in sphalerite with and without dopants determined by DFT calculations. Literature data on the interatomic distances of unrelaxed pure sphalerite structure are given at the bottom of the table. Data for the systems ZnS + In was obtained in the present study, all other data are adopted from [1,2]. The method of the calculations is described in [1].

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**The RMC fit results of ZnS EXAFS spectra. Panel (

**A**): experimental WT image; panel (

**B**): fitted WT image; panel (

**C**): calculated RDF for first three coordination shells around absorbing atom; panel (

**D**): experimental (black dotted line) and fitted (red solid line) EXAFS signal χ(k)*k

^{2}; panel (

**E**): Fourier transform magnitudes of experimental (black dotted line) and fitted (red solid line) χ(k)*k

^{2}function; panel (

**F**): close view of Zn-Zn RDF. The RDFs fitted by Gaussians are shown by solid lines.

**Figure 2.**The RMC fit results of In K-edge EXAFS spectra for Samples 3757 (doped with In), 4108, and 4186 (doped with In and Cu). Panel

**A**: experimental WT image; panel

**B**: fitted WT image; panel

**C**: calculated RDF for first three coordination shells around absorbing atom; panel

**D**: experimental (black dotted line) and fitted (red solid line) EXAFS signal χ(k)*k

^{2}; panel

**E**: Fourier transform magnitudes of experimental (black dotted line) and fitted (red solid line) χ(k)*k

^{2}function; panel

**F**: close view of In-Zn RDF. The RDFs fitted by Gaussians are shown by solid lines.

**Figure 3.**The RMC fit results of Cu K-edge EXAFS spectra for Samples 4108, and 4186 (doped with In and Cu). Panel

**A**: experimental WT image; panel

**B**: fitted WT image; panel

**C**: calculated RDF for first three coordination shells around absorbing atom; panel

**D**: experimental (black dotted line) and fitted (red solid line) EXAFS signal χ(k)*k

^{2}; panel

**E**: Fourier transform magnitudes of experimental (black dotted line) and fitted (red solid line) χ(k)*k

^{2}function; panel

**F**: close view of Cu-Zn RDF. The RDFs fitted by Gaussians are shown by solid lines.

**Figure 4.**Comparison of Cu-Zn and In-Zn RDFs in doped sphalerites (green curves) with Zn-Zn RDF in pure sphalerite (red curve) derived from RMC-EXAFS fits.

**Figure 5.**Comparison of experimental (Sample 3757) and calculated In K-edge XANES spectra. The calculation was performed for different models of In-bearing sphalerite obtained by DFT: (

**a**) 2Zn

^{2+}↔Cu

^{1+}+ In

^{3+}substitution; (

**b**) 2Zn

^{2+}↔In

^{3+}+ □ substitution; (

**c**) 2Zn

^{2+}↔2In

^{3+}substitution. Black lines are used to plot the experimental spectra of Sample 3757; red lines—calculated spectra for structures with impurities and/or vacancy placed far from each other; green lines—calculated spectra for the structures with impurities and vacancy placed in the nearest positions.

System | E_{EF}, eV |
---|---|

ZnS + Cu + In (In and Cu atoms are in neighboring sites) | 0.18 |

ZnS + Cu + In (In and Cu atoms are placed far from each other) | 0.28 |

ZnS + 2In, (2 In atoms are placed far from each other | 2.99 |

ZnS + 2In, (2 In atoms are in the nearest positions) | 3.06 |

ZnS + 2In + □, (In atoms and vacancy are placed far from each other) | 0.89 |

ZnS + 2In + □, (In atoms and Zn vacancy are placed in the nearest positions) | 0.35 |

**Table 2.**Structural parameters derived from RMC-EXAFS fitting (all RDF peaks are fitted with one Gaussian function). Coordination numbers of sphalerite structure were fixed for all samples. Results of the present study (RMC) are compared with values derived by conventional EXAFS analysis performed using IFFEFIT software [2].

Experiment | Fitting Procedure | Coordination Spheres Around Absorbing Atoms | |||||||
---|---|---|---|---|---|---|---|---|---|

S | Zn | In | S | ||||||

R,Å | σ^{2}*10^{3}, Å^{2} | R,Å | σ^{2}*10^{3}, Å^{2} | R,Å | σ^{2}*10^{3},Å^{2} | R,Å | σ^{2}*10^{3},Å^{2} | ||

ZnS, Zn K-edge | RMC | 2.34 | 5.3 | 3.83 | 14.4 | - | - | 4.50 | 16.1 |

IFEFFIT, [2] | 2.34 | 5.0 | 3.85 | 17.0 | - | - | 4.46 | 15.0 | |

Sample 3757, In K-edge | RMC | 2.45 | 3.3 | 3.91 | 13.0 | - | - | 4.48 | 13.7 |

IFEFFIT, [2] | 2.45 | 4.0 | 3.91 | 14.0 | - | - | 4.48 | 14.0 | |

Sample 4108, In K-edge | RMC | 2.46 | 2.0 | 3.91 | 13.7 | - | - | 4.49 | 12.3 |

IFEFFIT, [2] | 2.46 | 3.0 | 3.91 | 15.0 | - | - | 4.49 | 11.0 | |

Sample 4186, In K-edge | RMC | 2.45 | 3.4 | 3.91 | 13.8 | - | - | 4.49 | 14.2 |

IFEFFIT, [2] | 2.46 | 4.0 | 3.91 | 16.0 | - | - | 4.47 | 12.0 | |

Sample 4108, Cu K-edge | RMC, with In in 2nd shell | 2.28 | 4.3 | 3.84 | 21.3 | 3.87 | 8.8 | 4.47 | 14.6 |

Sample 4108, Cu K-edge | RMC, no In in 2nd shell | 2.28 | 4.3 | 3.84 | 21.0 | - | - | 4.47 | 14.7 |

IFEFFIT, [2] | 2.30 | 5.0 | 3.81 | 7.0 | - | - | 4.44 | 11.0 | |

4.01 | |||||||||

Sample 4186, Cu K-edge | RMC, with In in 2nd shell | 2.29 | 7.5 | 3.84 | 22.5 | 3.88 | 24.3 | 4.46 | 13.4 |

Sample 4186, Cu K-edge | RMC, no In in 2nd shell | 2.30 | 7.9 | 3.84 | 24.0 | - | - | 4.47 | 22.5 |

Sample 4186, Cu K-edge | IFEFFIT, [2] | 2.31 | 6.0 | 3.76 | 11.0 | - | - | 4.31 | 9.0 |

3.92 | - | - | 4.52 |

**Table 3.**Structural parameters derived from Cu-Zn and In-Zn RDF decomposition. Results of the present study (RMC) are compared with values derived by conventional EXAFS analysis performed using IFFEFIT software [2].

Parameter | 3757 In K-Edge | 4108 In K-Edge | 4186 In K-Edge | 4108 Cu K-Edge | 4186 Cu K-Edge | |||||
---|---|---|---|---|---|---|---|---|---|---|

RMC | [2] | RMC | [2] | RMC | [2] | RMC | [2] | RMC | [2] | |

Centroid position, Å | 3.90 4.05 | 3.91 | 3.88 4.04 | 3.91 | 3.73 | 3.91 | 3.66 | 3.81 4.01 | 3.61 | 3.76 3.92 |

3.89 | 3.82 | 3.79 | ||||||||

4.03 | 4.00 | 3.97 | ||||||||

Gaussian variance × 10^{3}, Å^{2} | 11.2 1.7 | 14.0 | 9.9 5.3 | 15.0 | 3.7 | 16.0 | 8.8 | 11.0 | 5.4 | 7.0 |

4.4 | 7.2 | 7.6 | ||||||||

2.8 | 6.5 | 8.9 | ||||||||

Coordination number | 11.8 0.2 | 12 | 11.0 1.0 | 12 | 1.4 | 12 | 2.8 | 6.4 5.6 | 1.0 | 5.4 6.6 |

7.8 | 6.2 | 5.6 | ||||||||

2.8 | 3.0 | 5.3 |

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**MDPI and ACS Style**

Trigub, A.L.; Trofimov, N.D.; Tagirov, B.R.; Nickolsky, M.S.; Kvashnina, K.O. Probing the Local Atomic Structure of In and Cu in Sphalerite by XAS Spectroscopy Enhanced by Reverse Monte Carlo Algorithm. *Minerals* **2020**, *10*, 841.
https://doi.org/10.3390/min10100841

**AMA Style**

Trigub AL, Trofimov ND, Tagirov BR, Nickolsky MS, Kvashnina KO. Probing the Local Atomic Structure of In and Cu in Sphalerite by XAS Spectroscopy Enhanced by Reverse Monte Carlo Algorithm. *Minerals*. 2020; 10(10):841.
https://doi.org/10.3390/min10100841

**Chicago/Turabian Style**

Trigub, Alexander L., Nikolay D. Trofimov, Boris R. Tagirov, Max S. Nickolsky, and Kristina O. Kvashnina. 2020. "Probing the Local Atomic Structure of In and Cu in Sphalerite by XAS Spectroscopy Enhanced by Reverse Monte Carlo Algorithm" *Minerals* 10, no. 10: 841.
https://doi.org/10.3390/min10100841