Structural and Electronic Properties of Qatranaite

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Introduction
Qatranaite named after the village Al Qatrana (situated 15 km southeast from the Amman Aquaba Asia-Jordan Desert Highway) is considered as a natural analogue of synthetic calcium hexahydroxodizincate dehydrate [1,2]. e mineral, discovered in an altered pyrometamorphic spurrite rocks in the Daba-Siwaqa region of the Hatrurim complex located in Jordan [3][4][5][6], was for the first time described in 2016 by Stasiak et al. as CaZn 2 (OH) 6 ·OH 2 O [7]. Qatranaite crystallized in the temperature range 150 to 200°C, similarly as Se-bearing thaumasite or afwillite, in the form of flatten (010) crystals, growing up to 0.3 mm [7,8].
Qatranaite unit cell consists of octahedrally coordinated Ca 2+ ions linked to four hydroxy groups and two water molecules, whereas Zn 2+ ions are tetrahedrally coordinated with four OH − groups and form pyroxene-like chains [Zn 2 (OH) 6 ] 2− . e mineral may display charge deficiency in case all oxygen atoms participate in the formation of OH groups, which certainly affects electronic properties of this interesting material [8].
e potential application of calcium hexahydroxodizincate dehydrate-like systems sparked hope for improved charge/discharge reversibility in Zn battery electrodes. Furthermore, they are expected to restrict Znelectrode shape change and inhibit dendrite formation [1,2,[9][10][11]. Additionally, electrochemical properties of CaZn 2 (OH) 6 ·2H 2 O make it suitable for negative electrodes in rechargeable zinc-air batteries [12,13]. e energy gap of calcium hexahydroxodizincate dehydrate has been a subject of experimental investigations [2] from which the direct energy gap width of 3.1 eV has been concluded. Our UV-Vis measurements of qatranaite revealed that the spectrum can be equally well interpreted, assuming the presence of direct or indirect energy gap. In order to disclose the nature of the energy gap in the mineral, we carried out the quantum, DFTbased, electronic structure investigations by means of the pseudopotential method employed in the Quantum Espresso package [14]. To verify reliability of the calculations, we have also performed the structural optimization and compared the results with experimental data. An ab initio prediction for the energy band gap was compared with experimental results provided by UV-Vis measurements.

Computational and Experimental Details
An ab initio calculations were carried out using the Quantum Espresso code [14] by applying the scalar relativistic ultrasoft pseudopotentials [15] for Ca(3s 2 3p 6 4s 2 ), H(1s 2 ), and O(2s 2 2p 6 ) elements within both LDA and GGA calculations. For Zn, we used the same type pseudopotentials with (3d 9.7 4s 2 4p 0.3 ) and (3d 10 4s 2 ) valence state configuration for LDA and GGA, respectively. Calculations were performed for two approximations of exchange correlation (XC) energy functional. e LDA XC functional in the form parameterized by Perdew and Zunger [16] and the GGA XC functional proposed by Perdew et al. [17] were employed. e plane wave kinetic energy and charge density cutoff of 46 and 368 Ry, respectively, were applied within LDA, while in the case of GGA, the corresponding cutoff values equaled 53 and 368 Ry. e structure-optimization, following the Broyden-Fletcher-Goldfarb-Shanno (BFGS) scheme, was carried out within LDA and GGA approaches. e usage of the 12 × 12 × 12 Monkhorst-Pack mesh [18] in reciprocal space enabled us to achieve satisfactory convergence in the structural optimization. e total energy of the qatranaite unit cell was evaluated with an accuracy of 5 meV, while forces were calculated with uncertainty less than 0.08 and 5.21 meV/Å for LDA and GGA, respectively. To determine precisely the details of electronic density of states, the additional calculations using the 20 × 20 × 20 Monkhorst-Pack mesh were performed.
To study the energy gap of qatranaite, the ultravioletvisible spectroscopy (UV-Vis) was performed with the use of microspectrophotometer (CRAIC Technologies) equipped with standard halogen lamp and Zeiss 15x objective. e sample was prepared in the form of petrographic polished plate with the qatranaite crystals (diameter of 0.3 mm) embedded in the mineral matrix. e experiments were performed at room temperature and ambient pressure. To estimate the band gap width, we use the formula proposed by Wood and Tauc [19]: where α is the absorbance, h stands for the Planck constant, ] defines the photon's frequency, E g denotes the optical band gap energy, and n is a constant related to different kinds of electronic transitions. e n parameter equals 0.5, 2, 1.5, and 3 for direct, indirect, allowed, and forbidden transitions, respectively.  [20], which ensures the electric charge balance. Tables 1 and 2 summarize the results of ab initio structural optimization of qatranaite unit cell carried out with the use of two approximations for XC energy functional. e calculated results were compared with available experimental data. It is worth emphasizing that the output of DFT-LDA calculations is in well agreement with the previously reported diffraction data [7,8] (Table 1). e computed (LDA) and measured a, b, c lattice parameters and β angle differ less than 0.2, 2.3, 3.5, and 2.1%, respectively. GGA approach give slightly worse results (corresponding differences are 4.1, 2.9, 5.6, and 0.6%). It can be concluded that LDA XC functional better describes the nature of bonding in qatranaite.

Results and Discussion
In Table 2, we compare experimental and optimized coordinates of Wyckoff positions in the structure of CaZn 2 (OH) 6 ·2H 2 O mineral. To avoid the issue of high mobility of hydrogen atoms [21], their experimentally obtained coordinates were frozen during structural optimization. We are satisfied with the overall agreement between calculated and measured coordinates of Wyckoff positions [8]. e noticeable difference in Wyckoff position can be observed for oxygen atoms, which may be attributed to their relative high mobility [22].

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Based on structural data collected in Table 2, we also calculated an interatomic distances in tetrahedral ZnO 4 and octahedral CaO 6 clusters. e obtained results are presented in Table 3. e comparison of DFT structural results with experimental data con rms su cient reliability of our calculations.

UV-Vis Absorption Spectroscopy.
e results obtained from our DFT calculations demonstrated that qatranaite is the direct band gap material, and consequently, the n value of 0.5 have to be used in equation (1). e energy band gap, E g 3.9 eV, was estimated by tting equation (1) to the experimental points at the linear portion of the curve (Figure 4). e latter value exceeds the one deduced from DFT calculations (E g 3.2 eV). is con rms the common perception that DFT calculations frequently lead to . .

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underestimation of the band gap [23]. erefore, it may be concluded that the true energy gap in qatranaite should significantly exceed the calculated DFT value. Finally, the calculations and experimental results obtained for natural qatranaite were compared with previously published data for synthetic counterpart [2]. us, Xavier et al. measured the energy gap E g of 3.1 eV, the value significantly lower than the one obtained by our UV-Vis absorption spectroscopy measurements. Such a high discrepancy is due to disputable assumptions imposed by Xavier et al. [2], who fitted their absorption results in such a way that stipulates n � 2 (equation (1)). e differences between experimentally derived energy gap for qatranaite (3.9 eV) and synthetic CaZn 2 (OH) 6 ·2H 2 O (3.1 eV) [2] may stem from chemical and structure imperfections present in mineral qatranaite.

Conclusions
In sum, we have demonstrated the DFT calculations within LDA and GGA schemes accurately predict the atomic structure, which encourage the further study of qatranaite electronic properties. e calculated lattice parameters at the ground state conditions are in agreement with the experimental results. It is contend, therefore, that LDA is more appropriate for estimation of lattice parameters of qatranaite. e LDA (GGA) predicted direct band gap energy at Γ point of the first Brillouin zone provided the lower value 3.2 eV (3.3 eV) compared to our experimentally obtained 3.9 eV data. Moreover, it is worth noting that our theoretical and experimental results reveal the presence of direct gap in qatranaite mineral where available experimental data for its synthetic analogue pointed on indirect energy gap. We believe that the output of our calculations contains information being of importance to the modern electronic and photonic industries.
Data Availability e raw data from all implemented techniques (UV-VIS, DFT) used to support the ndings of this study are available from the corresponding author upon request.
Disclosure e authors would like to inform that a small part of their simulation results were previously published in a poster form.

Conflicts of Interest
e authors declare no con icts of interest regarding the publication of this paper. Advances in Materials Science and Engineering 5