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Article

Synthesis, Crystal Structures, Optical Properties and Theoretical Calculations of Two Metal Chalcogenides Ba2AlSbS5 and Ba2GaBiSe5

by
Xiaowen Wu
1,
Xiaofeng Gu
1,
Hui Pan
1,
Yi Hu
1 and
Kui Wu
2,*
1
College of Chemistry and Chemical Engineering, Xinjiang Normal University, Urumqi 830017, China
2
Xinjiang Technical Institute of Physics & Chemistry of CAS, Urumqi 830011, China
*
Author to whom correspondence should be addressed.
Crystals 2018, 8(4), 165; https://doi.org/10.3390/cryst8040165
Submission received: 19 March 2018 / Revised: 8 April 2018 / Accepted: 9 April 2018 / Published: 13 April 2018
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Abstract

:
Two quaternary metal chalcogenides, Ba2AlSbS5 and Ba2GaBiSe5, were successfully synthesized by solid-state reaction in sealed silica tubes. Both of them crystallize in the same orthorhombic space group Pnma, but they appear with obviously different construction features. For example, Ba2AlSbS5 exhibits [SbS3]3− units and zero-dimensional (0D) [AlSbS5]4− clusters, which is different from those ([BiSe6]3− units and 1D ∞[GaBiSe5]4− chains) of Ba2GaBiSe5. We also systematically investigated the entire series of Ba2MIIIMIII’Q5 (MIII = Al, Ga, In; MIII’ = As, Sb, Bi; Q = S, Se, Te) compounds, and the results showed that the interconnection of MIIIQ4 and MIII’Qn (n = 3, 5, 6) units can form three different structural types, including 0D [MIIIMIII’Q5] clusters, single [MIII’Q3] chains and isolated [MIIIQ4] units, or [MIIIQ3]n and [MIII’Q3]n double chains, which may be induced by the flexible coordination and on-link modes of MIII’ atoms. Spectral investigation shows that their bandgaps are about 2.57 eV for Ba2AlSbS5 and 2.14 eV for Ba2GaBiSe5. Theoretical calculation was also used to analyze their structure-property relationships, and the results indicate that the title compounds exhibit larger birefringences (Δn > 0.10), thus having potential as the IR birefringent materials.

Graphical Abstract

1. Introduction

Metal chalcogenides have been used as critical materials in the development of modern science and technology because of their structural complexities and fascinating properties [1,2,3,4,5,6,7,8,9,10,11,12]. Among them, many trivalent cations (such as MIII’: As, Sb, or Bi) containing chalcogenides have been discovered and shown to have various application prospects. With stereochemically active lone-pair electrons, the above trivalent cations exhibit a flexible coordination environment for the formation of MIII’Qn units (n = 3~6; Q = chalcogen), which offers an opportunity to affect their crystal structures and physicochemical properties [13,14,15,16,17,18,19,20,21,22,23,24]. For example, AAsQ2 (A = Li, Na; Q = S, Se) [15] and A3Ta2AsS11 (A = K, Rb) [13] compounds feature [AsS3]3- pyramids and show strong second harmonic generation (SHG) responses; BaBiTe3, AgBi3S5 and A2Bi8Se13 (A = Rb, Cs) compounds exhibit small bandgaps and have promising potential as thermoelectric materials [22,23,24]; Ba2GaAsSe5 shows novel [AsGaSe5]4− anions and high visible-light-induced photocatalytic reactivity [17]. In addition, overall literature research indicates that the above MIII’Qn units can bridge other functional units to form a variety of extended structures [16]. Moreover, Ba atoms have flexible coordination numbers (6 to 10) with chalcogens, owing to their large ionic radii, which can also produce distinctive structures in combination with MIII’Qn units. So far, many efforts have been focused on the Ba-MIII–MIII’-Q system, and several compounds with the Ba2MIIIMIII’Q5 (MIII = Ga, In) formula have been discovered [17,18,19,20,21]. Unfortunately, their structural changes and theoretical calculations have not been systematically studied. Herein, we have focused our attentions on the (MIII = Al, Ga; MIII’ = Sb, Bi) system and two metal chalcogenides, Ba2AlSbS5 and Ba2GaBiSe5, were successfully synthesized. Note that Ba2AlSbS5 was the first discovered compound in the Ba-Al-Sb-S system. We have also systematically investigated the structural changes in the series of Ba2MIIIMIII’Q5 (MIII = Al, Ga, In; MIII’ = As, Sb, Bi; Q = S, Se, Te) compounds and analyzed the effect of interconnection between MIIIS4 and MIII’Sn units. Theoretical calculations were used to analyze their structure-property relationships.

2. Materials and Methods

2.1. Synthesis

The raw materials, including the Ba block (99.9%), Al slice (99.99%), Ga block (99.9%), Sb block (99.99%), Bi powder (99.99%), S powder (99.99%) and Se powder (99.99%), were purchased from Shanghai Aladdin Biochemistry Technology Co., Ltd. (Shanghai, China). All preparations were completed in a glovebox with Ar atmosphere. Raw materials with stoichiometric proportion were loaded into the silica ampoules with diameter 10 mm and length 100 mm, evacuated under high-vacuum (10−3 Pa), and flame-sealed.

2.1.1. Ba2AlSbS5

The raw mixture with 2 mmol Ba, 1 mmol Al, 1 mmol Sb and 5 mmol S powders were loaded into the silica ampoules, sealed under vacuum, and then placed into the muffle furnace to complete the solid-state reaction. The temperature control curve was set as following: firstly, it was heated to 1273 K over 30 h (kept at this temperature for 50 h), cooled to 673 K at a rate of 3 K/h, and finally cooled to room temperature by switching off the furnace. N,N-dimethylformamide (DMF) was used to remove the other impurity phases in an ultrasonic cleaner. Many yellow Ba2AlSbS5 crystals were finally discovered, and were stable for several months.

2.1.2. Ba2GaBiSe5

The preparation process of Ba2GaBiSe5 is similar to that of Ba2AlSbS5. The raw mixture with stoichiometric ratio was loaded into the silica ampoule, evacuated, flame-sealed and then placed into the muffle furnace for heating. The temperature control curve was set as following: firstly, it was heated to 1173 K over 30 h, then left at this temperature about 100 h, cooled to 573 K at a rate of 5 K/h, and finally cooled to room temperature by switching off the furnace. Red Ba2GaBiSe5 crystals were found after repeatedly washing with DMF solvent, and these were also stable in air.

2.2. Structure Determination

Selected single-crystals were used for data collection with a Bruker SMART APEX II 4K CCD diffractometer (Bruker Corporation, Madison, WI, USA) using Mo Kα radiation (λ = 0.71073 Å) at room temperature. The multi-scan method was used for absorption correction [25]. All the crystal structures were solved by the direct method and refined using the SHELXTL program package (Shelxtl 1997) [26]. The final structures were carefully checked with the PLATON software (Glasgow, UK), and no other symmetries were found. We measured the element contents in the title compounds with an EDX-equipped Hitachi S-4800 SEM (Tokyo, Japan). The measurement results for single crystals of Ba2AlSbS5 confirmed the Ba/Al/Sb/S molar ratio of 2.14:1:0.92:4.90, which was in good agreement with the stoichiometric proportions from single-crystal X-ray structural analysis. Similarly, the EDS elemental analysis of single crystals of Ba2GaBiSe5 confirmed the Ba/Ga/Bi/Se molar ratio of 1.93:1.15:1.09:4.81, which is also in good agreement with the stoichiometric proportions. Table 1 shows the crystal data and structure refinement of the title compounds.

2.3. Powder XRD Measurement

A Bruker D2 X-ray diffractometer (Madison, WI, USA) with Cu Kα radiation (λ = 1.5418 Å) was used to measure the powder X-ray diffraction (XRD) patterns of the title compounds at room temperature. The measured range was 2 theta = 10–70° with a step size of 0.02°. Note that the calculated XRD patterns were derived from the respective single-crystal data. We carefully investigated the experimental XRD patterns of the title compounds and compared the extra peaks with those of other known related compounds. As for the impurity peaks, several small peaks can be attributed to the XRD peaks of BaSb2S4 and BaGa2Se4, respectively (Figure 1).

2.4. UV–Vis–NIR Diffuse-Reflectance Spectroscopy

Diffuse-reflectance spectra were measured by a Shimadzu SolidSpec-3700DUV spectrophotometer (Shimadzu Corporation, Beijing, China) in the wavelength range of 200−2600 nm at room temperature. The absorption spectra were converted from the reflection spectra via the Kubelka-Munk function.

2.5. Raman Spectroscopy

Hand-picked crystals were firstly put on an object slide, and then a LABRAM HR Evolution spectrometer (HORIBA Scientific, Beijing, China) equipped with a CCD detector by a 532 nm laser was used to record the Raman spectra. The integration time was set to be 5 s.

2.6. Theoretical Calculation

On the basis of ab initio calculation implemented in the CASTEP package (version 6.1), the density functional theory (DFT) was used to obtain electronic structures [27]. The Perdew-Burke-Ernzerhof (PBE) was used to calculate the exchange−correlation effects in the generalized gradient approximation (GGA) [28]. The following orbital electrons were regarded as valence electrons; Ba: 5s25p66s2; Al: 3s23p1, S: 3s23p4; Se: 4s24p4; Sb: 5s25p3; Ga: 4s24p1; Bi: 6s26p3. The energy cutoff of the plane-wave basis set was 700.0 eV within Normconserving pseudopotential (NCP), and the Monkhorst−Pack scheme (3 × 3 × 4) for the Brillouin Zone was chosen [29,30]. As an important parameter for optical crystals, refractive index was also calculated. Owing to the discontinuity of exchange correlation energy, the experimental value is usually larger than that of calculated band gap. Thus, scissors operators are always used to make the conduction bands (CBs) agree with the experimental values [31].

3. Results and Discussion

3.1. Crystal Structure

The title compounds crystallize in the same orthorhombic space group Pnma, but there are obvious differences in their structures. As for Ba2AlSbS5, its asymmetrical unit is composed of one Ba, one Al, one Sb, and four S atoms. As can be seen from its structure, the Al atoms are linked with four S atoms to form AlS4 tetrahedra with d(Al-S) = 2.189(3)–2.2599(17) Å, and the Sb atoms connect with three S atoms to compose SbS3 units with d(Sb-S) = 2.4294(19)–2.5191(13) Å. The above two units (AlS4 and SbS3) interconnect with each other to form the isolated [AlSbS5]4− clusters (0D) (Figure 2a–c). The Ba atoms are connected with eight S atoms to form typical BaS8 dodecahedra. Additionally, the BaS8 units connect together to form the wavelike layers that can be clearly found along the b-axis (Figure 2e,f). Then, these layers further interconnect by sharing their corners or edges to form a 3D framework structure (Figure 2d). Thus, its whole structure can also be depicted as the interconnection of 0D [AlSbS5]4− clusters and BaS8 units.
Ba2GaBiSe5 exhibits a different structure from Ba2AlSbS5, and it exhibits a 3D framework structure consisting of infinite 1D ∞[GaBiSe5]4− chains with d(Ga-Se) = 2.3409(18)–2.4304(13) Å and d(Bi-Se) = 2.6517(14)–3.1918(11) Å and Ba cations located between the chains for charge balance; in other words, the obvious structural difference between the title compounds is the (0D) [AlSbS5]4− clusters in Ba2AlSbS5 versus 1D ∞[GaBiSe5]4− chains in Ba2GaBiSe5 (Figure 3). Moreover, an overall literature investigation shows that dozens of quaternary compounds have been found in the Ba2MIIIMIII’Q5 (MIII = Al, Ga, In; MIII’ = As, Sb, or Bi; Q = S, Se, Te) formula [17,18,19,20,21]. Detailed analysis on their structures shows that all of them crystallize in two different space groups: Pnma and Cmc21. The comparison of their structures shows that the interconnection of MIIIS4 and MIII’Sn (n = 3, 5, 6) units can form three different structural types, including isolated 0D [MIIIMIII’Q5] cluster, single [MIII’Q3] chains and isolated [MIIIQ4] units, or [MIIIQ3]n and [MIII’Q3]n double chains, which may be induced by the flexible coordination and on-link modes of MIII’ atoms (Table 2). Note that they are inclined to form 0D dimers, while MIII and MIII’ are smaller-sized atoms, such as Al and Sb or Ga and As atoms; otherwise, they tend to compose 1D chains due to the larger-sized atoms that exist in the structure, such as In, Bi or Te atoms. A topological approach has also been applied to better understand their structural differences, and the BaS8 units are simplified as the nodes. As a result, from Figure 4, it is clear that BaS8 units form a topological honeycomb-like tunnel framework in the Pnma space group, whereas they compose the topological layers in the Cmc21 space group.

3.2. Optical Properties

Diffuse-reflectance spectra of the title compounds were measured in the wavelength range of 200−2600 nm at room temperature (Figure 5). Through an absorption edge and the linear part of absorption plot, the band gaps of Ba2AlSbS5 and Ba2GaBiSe5 were deduced by a straightforward extrapolation method [32] as 2.57 and 2.14 eV, respectively, which are values much larger than those of a series of commercial IR materials, such as ZnGeP2 (1.65 eV) and AgGaSe2 (1.75 eV) [33,34]. Moreover, we also measured their Raman spectra (Figure 6). Note that there were no obvious absorption bands above 400 cm−1 in Ba2AlSbS5 or 300 cm−1 in Ba2GaBiSe5, which shows that they may have wide IR transmission ranges. As for Ba2AlSbS5, the absorption bands above 200 cm−1, such as 242, 304, and 352 cm−1, can be can be assigned to the characteristic absorptions of the Al-S and Sb-S modes, which are similar to those of other related compounds, such as Al-S (375 cm−1) in K(AlS2)(GeS2) [35], Sb-S (360, 300, 340, and 270 cm–1) in A2Sb2Sn3S10 (A = K, Rb, Cs) [36]. Additionally, owing to the heavier Se atoms, the Bi-Se and Ga-Se vibrations occur at lower bands of 193 and 230 cm−1 in Ba2GaBiSe5, which are also similar to those in Ba4CuGa5Se12 (Ga-Se, 185–262 cm−1) [37] and (Bi4Se4)[AlCl4]4 (Bi-Se, 189 and 183 cm−1) [38]. In addition, the absorption bands located at 70 and 98 cm−1 primarily correspond to the Ba−S in the Ba2AlSbS5, and the bands at 63, 83, 95, and 129 cm−1 correspond to Ba-Se vibration in Ba2GaBiSe5, and are similar to those in Na2BaSnS4 and Na2BaSnSe4 [6].

3.3. Theoretical Studies

To further investigate the relationship between the structure and performance, the DFT method was chosen to complete the relative calculation. The calculated band structures for the title compounds are plotted in Figure 7, and show a pair of bonding and anti-bonding orbitals separated by gaps. Ba2AlSbS5 and Ba2GaBiSe5 are the indirect band-gap compounds with energy gaps of 2.40 and 1.89 eV, respectively.
Herein, we focus our attention in the vicinity of Fermi level (FL), which counts for most of the bonding character, and is bound up with the optical parameters. For Ba2AlSbS5, the valence band (VB) near the FL can be divided into four regions: from −15 to −10 eV, S 3s states overlap completely with Ba 5p, showing strong Ba-S covalent interactions. Bands in the region −7.5 to −5.0 eV mainly come from Sb 5s and S 3p states, which shows some contributions to the Sb-S bonds. The upper part of VB, from −5 eV to FL, shows some hybridizations between Ba 5s, S 3p, Al 3p, Sb 5s, 5p orbitals, revealing a few chemical bonds between the Ba-S, Sb-S, and Al-S; but the top VB maximum is dominated by S 3p orbitals. In addition, for the CB bottom, it is dominated by the orbitals of all atoms, and the S 3p and Sb 5p orbitals determine the CB minimum of the Ba2AlSbS5 crystal. As for Ba2GaBiSe5, its PDOS diagram shows some differences with that of Ba2AlSbS5. The region between −15 and −7.5 eV mainly consists of Ba 5p, Bi 6s and Se 4s orbitals, showing the obvious interactions of Ba-Se and Bi-Se bonds. The VB (−6.0 to −4.0 eV) is mainly from the contributions of Bi 6p and Se 4p states with some of the Ga 4p orbitals, and for the bands in the region near the top of the VB (from −4.0 to FL), there is strong hybridization between the orbitals of Se 4p and other atoms, which show obvious hybridization of Bi-Se and Ga-Se bonds. The orbitals of all atoms originate from 1.89 to 10 eV of CB, and the Se 4p orbitals dominate the CB minimum of the Ba2GaBiSe5 crystal. Therefore, the calculated PDOS shows that both the upper part of the VB and the bottom area of the CB are mainly dominated by Se 4p and Bi 6p orbitals. To sum up, optical absorption for the title compounds is mainly determined by the MIII’Qn units. Additionally, based on the electronic structure, refractive indices are also obtained theoretically from the imaginary part of the dielectric function through a Kramers–Kronig transform [39]. The dispersion curves of the refractive indices calculated also display an obvious anisotropy, and their birefringences (Δn) are about 0.13 for Ba2GaBiSe5 and 0.11 for Ba2AlSbS5, with wavelengths of about 1 μm. The large birefringence can be elucidated from their microscopic structural feature; the coplanar and aligned manners of the isolated (0D) [AlSbS5]4− clusters or 1D ∞[GaBiSe5]4− chains are beneficial for their large birefringences. Therefore, the title compounds can be expected to be potential IR birefringent materials.

4. Conclusions

In this work, two metal chalcogenides, Ba2AlSbS5 and Ba2GaBiSe5, were successfully synthesized. Although they crystallize in the same Pnma space group, they exhibit obvious structural differences. In terms of their structures, 0D [AlSbS5]4− clusters exist in the structure of Ba2AlSbS5, whereas Ba2GaBiSe5 has 1D ∞[GaBiSe5]4− chains. After the systematic investigation of the series of Ba2MIIIMIII’Q5 (MIII = Al, Ga, In; MIII’ = As, Sb, Bi; Q = S, Se, Te) compounds, the interconnection of MIIIS4 and MIII’Sn (n = 3, 5, 6) units can form three different structural types, including 0D [MIIIMIII’Q5] cluster, single [MIII’Q3] chains and isolated [MIIIQ4] units, and [MIIIQ3]n and [MIII’Q3]n double chains, which may be induced by the coordination and on-link modes of MIII’ atoms. Their bandgaps are about 2.57 eV for Ba2AlSbS5 and 2.14 eV for Ba2GaBiSe5, respectively. Moreover, the title compounds exhibit larger birefringences (Δn > 0.10) and have potential as IR birefringent materials.

Supplementary Materials

The following are available online at https://www.mdpi.com/2073-4352/8/4/165/s1. Cifs and checkcifs for title compounds.

Acknowledgments

This work was supported by the National Natural Science Foundation of China (Grant No. 21763026), Scientific Research Program of the Higher Education Institution of Xinjiang (Grant No. XJEDU2016S063), Ten Thousand People Plan Backup Project (Grant No. QN2016YX0340), and Xinjiang Key Laboratory of Electronic Information Materials and Devices (Grant No. 2017D04029).

Author Contributions

Xiaowen Wu designed this study and wrote the manuscript. Xiaofeng Gu prepared the crystals. Hui Pan analyzed the crystal structures. Yi Hu carried out the properties characterization work. Kui Wu conceived and coordinated the project.

Conflicts of Interest

The authors declare no conflict of interest.

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Figure 1. Powder XRD patterns of title compounds.
Figure 1. Powder XRD patterns of title compounds.
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Figure 2. (a) Crystal structure of Ba2AlSbS5 with the Ba-S bonds omitted for clarity; (b) view of the crystal structure of Ba2AlSbS5 along the a-axis; (c) 0D [AlSbS5]4− cluster; (d) 3D framework structure composed of BaS8 units; (e) one wavelike layer composed of BaS8 units located at the bc plane; (f) view of wavelike layer along the b-axis.
Figure 2. (a) Crystal structure of Ba2AlSbS5 with the Ba-S bonds omitted for clarity; (b) view of the crystal structure of Ba2AlSbS5 along the a-axis; (c) 0D [AlSbS5]4− cluster; (d) 3D framework structure composed of BaS8 units; (e) one wavelike layer composed of BaS8 units located at the bc plane; (f) view of wavelike layer along the b-axis.
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Figure 3. (a) View of the crystal structure of Ba2GaBiSe5 along the c-axis; (b) isolated 1D ∞[GaBiSe5]4− chains.
Figure 3. (a) View of the crystal structure of Ba2GaBiSe5 along the c-axis; (b) isolated 1D ∞[GaBiSe5]4− chains.
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Figure 4. (a) Topological structure in Pnma space group with the BaS8 units regarded as the nodes; (b) topological structure in Cmc21 space group with BaS8 units regarded as the nodes.
Figure 4. (a) Topological structure in Pnma space group with the BaS8 units regarded as the nodes; (b) topological structure in Cmc21 space group with BaS8 units regarded as the nodes.
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Figure 5. Experimental bandgaps of title compounds.
Figure 5. Experimental bandgaps of title compounds.
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Figure 6. Raman spectra of title compounds.
Figure 6. Raman spectra of title compounds.
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Figure 7. Band structures and PDOS diagrams of title compounds.
Figure 7. Band structures and PDOS diagrams of title compounds.
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Table
Table 1. Crystal data and structure refinement for the title compounds.
Table 1. Crystal data and structure refinement for the title compounds.
Empirical FormulaBa2AlSbS5Ba2GaBiSe5
fw583.71948.18
crystal systemorthorhombicorthorhombic
space groupPnmaPnma
a (Å)12.140(3) 12.691(4)
b (Å)8.8911(17)9.190(3)
c (Å)8.9552(17)9.245(3)
Z, V (Å3)4, 966.6(4)4, 1078.2(6)
Dc (g/cm3)4.0115.841
μ (mm−1)11.92242.757
GOF on F21.0800.997
R1, wR2 (I > 2σ(I)) a0.0202, 0.04730.0273, 0.0499
R1, wR2 (all data)0.0225, 0.04850.0371, 0.0535
largest diff. peak and hole (e Å−3)1.351, −0.7801.570, −1.648
aR1 = Fo − Fc/Fo and wR2 = [w (Fo2 − Fc2)2/wFo4]1/2 for Fo2 > 2σ (Fo2).
Table
Table 2. Structural comparison among the series of Ba2MIIIMIII’Q5 (MIII = Al, Ga, In; MIII’ = As, Sb, or Bi; Q = S, Se, Te) compounds.
Table 2. Structural comparison among the series of Ba2MIIIMIII’Q5 (MIII = Al, Ga, In; MIII’ = As, Sb, or Bi; Q = S, Se, Te) compounds.
CompoundsCrystal SystemSpace GroupAnion Connection ModeRef.
Ba2GaSbS5orthorhombicPnma∞[SbS3]n chain and GaS4[20]
Ba2GaSbSe5orthorhombicPnma∞[SbSe3]n chain and GaSe4[18]
Ba2GaSbTe5orthorhombicPnma∞[SbTe3]n chain and GaTe4[18]
Ba2GaBiS5orthorhombicPnma∞[BiS3]n chain and GaS4[21]
Ba2GaBiSe5orthorhombicPnma∞[BiSe3]n chain and GaSe4[18], this work
Ba2GaBiTe5orthorhombicPnma∞[BiTe3]n chain and GaTe4[18]
Ba2InSbTe5orthorhombicPnma∞[SbTe3]n chain and InTe4[18]
Ba2InSbSe5orthorhombicCmc21[InS3]n and [SbS3]nchains[18]
Ba2InBiS5orthorhombicCmc21[InS3]n and [BiS3]nchains[21]
Ba2InBiSe5orthorhombicCmc21[InSe3]n and [BiSe3]nchains[19]
Ba2GaAsSe5orthorhombicPnma0D [GaAsSe5]4− cluster[17]
Ba2AlSbS5orthorhombicPnma0D [AlSbS5]4− clusterThis work

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Wu, X.; Gu, X.; Pan, H.; Hu, Y.; Wu, K. Synthesis, Crystal Structures, Optical Properties and Theoretical Calculations of Two Metal Chalcogenides Ba2AlSbS5 and Ba2GaBiSe5. Crystals 2018, 8, 165. https://doi.org/10.3390/cryst8040165

AMA Style

Wu X, Gu X, Pan H, Hu Y, Wu K. Synthesis, Crystal Structures, Optical Properties and Theoretical Calculations of Two Metal Chalcogenides Ba2AlSbS5 and Ba2GaBiSe5. Crystals. 2018; 8(4):165. https://doi.org/10.3390/cryst8040165

Chicago/Turabian Style

Wu, Xiaowen, Xiaofeng Gu, Hui Pan, Yi Hu, and Kui Wu. 2018. "Synthesis, Crystal Structures, Optical Properties and Theoretical Calculations of Two Metal Chalcogenides Ba2AlSbS5 and Ba2GaBiSe5" Crystals 8, no. 4: 165. https://doi.org/10.3390/cryst8040165

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