AGaSnS4 (A = Rb, Cs): Three sulfides and their structure diversity

Journal Pre-proof AGaSnS4 (A = Rb, Cs): Three sulfides and their structure diversity Qian-Qian Liu, Xin Liu, Ling Chen, Li-Ming Wu PII:

S0022-4596(20)30063-3

DOI:

https://doi.org/10.1016/j.jssc.2020.121233

Reference:

YJSSC 121233

To appear in:

Journal of Solid State Chemistry

Received Date: 8 December 2019 Accepted Date: 2 February 2020

Please cite this article as: Q.-Q. Liu, X. Liu, L. Chen, L.-M. Wu, AGaSnS4 (A = Rb, Cs): Three sulfides and their structure diversity, Journal of Solid State Chemistry (2020), doi: https://doi.org/10.1016/ j.jssc.2020.121233. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2020 Published by Elsevier Inc.

Graphic abstract The Eg and structure relationships among three AGaSnS4 compounds, the latter explains the F boundary defining the symmetry change of the all known layered members in the AM M Q4 family.

Graphical Legend Figure 1. Powder XRD patterns of o-CsGaSnS4 (a), m-RbGaSnS4 (b) and c-CsGaSnS4 (c). The star in c indicates that from the Sn2S3 impurity. Figure 2. (a) Single crystal structure of o-CsGaSnS4 viewed down the b (left) and a (right) axis. (b) The local coordination of M(Sn, Ga) in o-CsGaSnS4 with bond length marked. (c) The layer structure comparison between o-CsGaSnS4 and m-RbGaSnS4. Green: the Sn-rich M1 and M2; purple, the Ga-rich M3 in o-CsGaSnS4 and M3, M4 in m-RbGaSnS4.

Figure 3. Single crystal structure of c-CsGaSnS4 viewed along the [111] direction. Figure 4. Experimental band gaps of AGaSnS4 Figure 5. Electronic band structures and density of states of o-CsGaSnS4 (a and b, respectively), m-RbGaSnS4 (c and d, respectively), c-CsGaSnS4 (e and f, respectively).

AGaSnS4 (A = Rb, Cs): three sulfides and their structure diversity Qian-Qian Liu,1 Xin Liu,2 Ling Chen,*,1 Li-Ming Wu*,2 1. Beijing Key Laboratory of Energy Conversion and Storage Materials, College of Chemistry, Beijing Normal University, Beijing 100875, P. R. China 2. Key Laboratory of Theoretical and Computational Chemistry of Ministry of Education, College of Chemistry, Beijing Normal University, Beijing 100875, People′s Republic of China * Corresponding authors: E-mail address: [email protected], [email protected] Dedicated to the occasion of the 70th Birthday of Prof. Kenneth Poeppelmeier

Abstract: Three sulfides in the AMⅢMⅢQ4 family are prepared via the solid-state flux synthesis method and characterized by single-crystal X-ray diffraction data for the first time. Their structures represent two classes: layered type including monoclinic RbGaSnS4 (m-RbGaSnS4, P21/c), and orthorhombic CsGaSnS4 (o-CsGaSnS4, Pnma), and 3D type (cubic CsGaSnS4 (c-CsGaSnS4, Pa3), isostructural with BaGa2S4). The former features a layer motif constructed by the MQ4 tetrahedron chains linked with dimeric M2Q6 and shows slight in-layer distortion on going from Rb to Cs. Interestingly, for all the known layered AMⅢMⅢQ4 members to date, a structure mismatch factor (F) defines well the monoclinic to orthorhombic symmetry change at the boundary F = 1.5. These compounds show similar Eg of about 2.9 eV. By DFT calculations, the valence and conduction band components and the reason why they have similar Eg are both revealed. Keywords: Metal chalcogenide; Crystal growth; Crystal structure; Optical property 1. Introduction Metal chalcogenides have attracted great attention due to their rich chemistry and diverse structures. In particular, involving the different building blocks composed of the third or fourth main group elements M (M = Al, Ga, In, Ge, Sn, Pb) and chalcogen elements Q (Q = S, Se, Te) enriches their properties, and opens new application opportunities in fields such as thermoelectric, nonlinear optical, catalytic and so on and so forth. [1-5]. Particularly, the [MQ4] tetrahedral block, as a common structure building unit, can construct diverse structures by different connecting motifs, such as corner sharing, edge sharing, or face sharing. For example, the corner-sharing motif of the [MQ4] has been reported in PbGa2GeSe6 [6], Li2BaGeS4 [7], LixA1-xGaS2 [8], Sn2Ga2S5 [9, 10], and so on, while the edge-sharing of [MQ4] is found in Li2Cs2Cl[Ga3S6] [11], Cs2HgSn3Se8 [12], Cs2MnGe3Se8 [13] and others. In the previous work, the AMⅢMⅢQ4 (A = alkali metal; MⅢ = Al, Ga, In; MⅢ = Ge, Sn, Pb; Q = S, Se, Te) family, have shown great diverse structures including triclinic, monoclinic, orthorhombic, tetragonal, and cubic 1

structures. Three major structure characteristics are distinct in the AMⅢMⅢQ4 family as followed: (Ⅲ) The polymorphism is common. For example, only with different cooling ramp, KInSnS4 can crystallize in either a tetragonal I4/mcm (α-KInSnS4) structure if cools at 10 K/min, or a monoclinic P21/c (β-KInSnS4) one if cools at 600 K/min, or a cubic Pa3 (γ-KInSnS4) one when the α- or β-phases were annealed at 923 K. Their energy gaps were determined to be Eg(α, 2.40 eV) > Eg(β, 1.80 eV) > Eg(γ, 1.49 eV) as the increase of the structural dimensionality from chain to layer and to three dimensional characteristics.[14] Similarly, the KGaSnS4 [15, 16] crystallizes either in Pa3 at 1123 K, or P1 space group at 1173 K, and the I4/mcm or P21/c symmetry of KGaSnSe4 [17] can convert to the cubic form at 923 K. (Ⅲ) The symmetry of a compound can be controlled by adjusting the stoichiometry of some certain element. Such as, Na1.263Ga1.262Sn0.737S4 [15] belongs to the AgGaGeS4-structure type, crystallizing in non-centrosymmetric orthorhombic Fdd2 space group, and NaGaSnS4 crystallizes in centrosymmetric cubic Pa3 space group that seems to be related to the occupancy changes on the co-shared Sn/Ga sites, from 0.5/0.5 in the cubic phase to 0.454/0.546 or 0.099/0.401 in the orthorhombic phase. Or, Na7.36Ga7.24Sn4.78Se24 [17] crystallizes in a non-centrosymmetric monoclinic C2 space group with a much lower Sn/Ga occupancy. (Ⅲ) The structure is sensitive to the size of the cation. Although sharing the similar layered motif that is constructed by chains linked by the edge-shared [MS4] pairs, with different size of In or Ga atom, KInGeS4 and KGaGeS4 end up with different symmetries (P1 for the former vs P21/a for the latter).[16] In addition, AGaSnSe4 (A = K, Rb, Cs) [17] possess similar layered motif that is constructed by the side-by-side linked [MSe4] chains, as size increasing from K to Cs, KGaSnSe4 and RbGaSnSe4 crystallize in monoclinic symmetry, and CsGaSnSe4 in orthorhombic symmetry instead showing an increasing of the energy gap of Eg(K, 1.73 eV) < Eg(Rb, 1.88 eV) < Eg(Cs, 1.97 eV). Besides, AInMⅢS4 (A = K, Rb, Cs; MⅢ = Sn, Ge) [18] may crystallize in one of the three different structures: three-dimensional BaGa2S4-type, layered- or spinel structure. In this paper, for the first time, we report three AGaSnS4 (A = Rb, Cs) compounds obtained by a solid-state flux method. Revealed by the single-crystal X-ray diffraction data, RbGaSnS4 crystallizes in P21/c (denoted as m-RbGaSnS4 hereafter), and CsGaSnS4 shows polymorphism crystallizing as either Pnma (o-CsGaSnS4) or 3D Pa3 (c-CsGaSnS4) structure. (note: the unit cell parameters of c-CsGaSnS4 had been previously report but with no detailed crystallographic data are available owing to lacking of single crystals [15]). Interestingly, the mismatch factor (F), we previously proposed for the A2MⅢMⅢ3Q8 family, also works well for the layered members in the AMⅢMⅢQ4 family, by which a boundary between the lower monoclinic symmetry and the higher orthorhombic structure is well defined at F = 1.5 for all the layered members known to date. The energy gaps of the title compounds have been studied experimentally and theoretically. 2

2. Experimental 2.1. Crystal growth. Raw materials including CsCl (99.9 %), RbCl (99.5 %), Ga2S3 (99.99 %), Sn (99.9 %), S (99.999 %) were purchased from Aladdin or Alfa and stored in a dry argon-filled glovebox. The o- and c-CsGaSnS4 crystals are light-yellow or orange sheet- or block-shaping crystals. and m-RbGaSnS4 crystals are light-yellow sheet-like crystals. High quality crystals were obtained by the following described high-temperature flux reactions. The crystals of o-CsGaSnS4 was surprisingly obtained in a mixture of CsCl, Ga2S3, Sn, Mn and S with the molar ratio of 2 : 1 : 1 : 1.6 : 4 at 1053 K. Subsequently, the experimental condition was optimized as followed: a mixture of CsCl, Ga2S3, Sn, and S in a molar ratio of 2 : 1 : 1 : 4 was weighed with a gross weight of 400 mg, and then loaded into a graphite crucible that was put into an outer silica tubing, and finally the whole assembly was sealed under a vacuum of 10-3 Pa. The sealed assembly was heated to 1083 K in 40 h, and maintained for 60 h, followed by a slow cooling to 573 K before turning off the furnace. The product was washed with distilled water and CS2 in ultrasonic cleaner to remove the by-products; the air-stable light-yellow crystals were obtained. Similarly, c-CsGaSnS4 was obtained at 973 K, and m-RbGaSnS4, at 1053 K. Very interestingly, c-CsGaSnS4 with higher symmetry was obtained at 973 K instead, lower than the 1083 K for the o-CsGaSnS4 with lower symmetry. This is unusual because the low symmetry compound is usually obtained at relatively higher reaction temperature. We consider that the some not-yet-identified by-product in the reaction system may actually provide a flux condition that favors and helps to stabilize and crystallize the o-CsGaSnS4 with lower symmetry at 1083 K. 2.2. Single-crystal X-ray diffraction (SXRD). The high-quality single crystal was selected and fixed on a glass fiber with vaseline, on which the single crystal X-ray diffraction data were collected with the aid of a Bruker APEX2 diffractometer with Mo Kα radiation at room temperature. The absorption correction was done by the multi-scan method. The data was reduced in APEX III, and the structure was refined and determined by the direct method and full matrix least-squares fitting on F2 with the SHELXS program. [19] The relevant crystallographic data and refinement details are shown in Table 1. The atomic coordinates and occupancies are summarized in Tables 2-4, and the selected bond lengths and angles are shown in Table S1-S3 in the SI.

3

Table 1. Crystallographic date and structural refinements for AGaSnS4 (A = Cs, Rb). c-CsGaSnS4

o-CsGaSnS4

m-RbGaSnS4

formula weight

449.56

449.56

402.12

crystal system

cubic

orthorhombic

monoclinic

space group

Pa3 (No. 206)

Pnma (No. 62)

P21/c (No.14)

a (Å)

13.3729(2)

17.5707(11)

7.2522(12)

b (Å)

—

7.3788(4)

12.377(2)

c (Å)

—

12.4338(8)

17.570(3)

β (deg)

—

—

96.554(6)

V (Å3)

2391.54(11)

1612.05(17)

1566.7 (5)

Z

12

8

8

Dcalc (g/cm–3)

3.746

3.705

3.410

µ (mm–1)

11.951

11.820

13.755

F(000)

2400

1600

1456

Completeness to θ (%)

100.0

99.7

99.9

GOF on F2

1.300

1.074

1.068

R1, wR2 (I>2σ (I)) a

0.0322, 0.0703

0.0311, 0.0728

0.0403, 0.0751

R1, wR2 (all data)

0.0350, 0.0712

0.0374, 0.0769

0.0593, 0.0819

extinction coefficient

0.00164(13)

0.00106(13)

—

diff peak, hole (e/Å3)

0.708, -0.689

1.219, -1.584

1.019, -1.091

a

R1 = ∑||F0| − |Fc||/∑|F0|, wR2 = {∑w[(F0)2 − (Fc)2 ]2 / ∑w[(F0)2 ]2 }1/2.

2.3 Powder X-ray diffraction (PXRD) The PXRD data were collected by a Bruker D8 Advance Powder X-ray diffractometer with monochromatized Cu-Kα radiation (λ = 1.54056 Å). The measure condition is 40mV, 40mA at 25Ⅲ, in the range of 2θ = 5–70°, with the scanning speed of 2s per step. The XRD patterns of o-CsGaSnS4 and m-RbGaSnS4 (Figure 1) are well indexed with the strong peak at 14° assigned as the (002) diffraction, so does the experimental c-CsGaSnS4 pattern, in which a small impurity peak around 16° is coming from those of the binary Sn2S3 impurity.

4

Figure 1. Powder XRD patterns of o-CsGaSnS4 (a), m-RbGaSnS4 (b) and c-CsGaSnS4 (c). The star in c indicates that from the Sn2S3 impurity.

2.4 UV-visible diffuse reflectance spectroscopy The UV-vis diffuse reflectance spectroscopy date was obtained by Spec-3700DUV in the wavelength range 200-800 nm. BaSO4 was used as a reference with a reflectance of 100%. The F(R) value was calculated via the Kubelka-Munk function: F(R) = (1-R)2/2R, where R is the measured reflectance. The energy value (E) was calculated via the function: E = 1240/λ, in which λ is the wavelength. 2.5 Theoretical calculations By using the pseudopotential method in the VASP package and the density functional theory (DFT) [20], the first principle calculations were carried out. With the help of the generalized gradient approximation (GGA) [21] method and the Perdew-Burke-Ernzerhof (PBE) functional, structure was optimized. The following pseudopotentials were used to simulate the ion electron interaction of all the constituent elements: Cs 5s25p66s1, Rb 4s24p65s1, Ga 4s24p1, Sn 5s25p2, S 3s23p4. A kinetic energy cutoff of 500 eV was chosen with Monkhorst-Pack k-point meshes spanning less than 0.05/Å3 in the Brillouin zone. And then we use the optimized structures to calculate the static self-consistency, the density of state and energy band with a dense 0.02/Å3 k-point spacing mesh.

3. Results and discussion 3.1 Structures of o-CsGaSnS4 and m-RbGaSnS4

5

Figure 2. (a) Single crystal structure of o-CsGaSnS4 viewed down the b (left) and a (right) axis. (b) The local coordination of M(Sn, Ga) in o-CsGaSnS4 with bond length marked. (c) The layer structure comparison between o-CsGaSnS4 and m-RbGaSnS4. Green: the Sn-rich M1 and M2; purple, the Ga-rich M3 in o-CsGaSnS4 and M3, M4 in m-RbGaSnS4.

As shown in Table 1, m-RbGaSnS4 crystallize in the monoclinic P21/c space group (No. 14) with a = 7.2522 Å, b = 12.377 Å, c = 17.570 Å, β = 96.554°, which is different from the cubic phase reported [15] before, and o-CsGaSnS4 crystallize in the orthorhombic Pnma space group (No. 62) with a = 17.5707 Å, b = 7.3788 Å, c = 12.4338 Å. The m-RbGaSnS4 and o-CsGaSnS4 possess similar unit cell parameters, but belong to different space groups. Despite their different symmetries, m-RbGaSnS4 and o-CsGaSnS4 share a similar layered structure with the major difference lying in the slight distortion within the layer. Taking CsGaSnS4 as an example, there are two crystallographically independent Cs, three M(Sn, Ga) and six S atoms in a unit, in which Sn and Ga are co-occupied at all the M sites. The M3, S4 and S6 atoms located at the Wyckoff 8d positions, the other atoms are all located at the 4c sites. As shown in Figure 2a, all the M atoms of o-CsGaSnS4 are coordinated with four S atoms to form a [MS4] tetrahedron, then the edge-sharing [M2S6] dimer connects the [MS4] chains by corner-sharing to form a layer perpendicular to the c axis and the Cs atoms are distributed between the layers. Although Sn and Ga are 1 : 1 in o-CsGaSnS4, the occupancies of Sn and Ga are different in the three independent [MS4] building block, which further lead to different connections. The occupancy of Sn/Ga in M1, M2 and M3 are 6

0.645/0.355, 0.59/0.41 and 0.382/0.618, respectively, as shown in Table 2. As the occupied proportion of Sn decreases, the [MS4] tetrahedron becomes less distorted and the bond distances of M-S are gradually shortened (Figure 2b). The M1-S, M2-S and M3-S bond distances are of 2.3332–2.3981, 2.3264–2.3670 and 2.3218–2.3306 Å, respectively, which are close to those reported, such as Ba3CdSn2S8 (2.340-2.3977 Å for Sn-S) [22], Sr3MnSn2S8 (2.344-2.399 Å for Sn-S) [23], BaGa4S7 (2.231-2.338 Å for Ga-S) [24] and Ba4Ga4SnS12 (2.252-2.339 Å for (Sn, Ga)-S) [25]. As Figure S1 shows, two crystallographic independent Cs atoms adopt distorted 9-fold polyhedral coordination with S atoms. Among the nine Cs-S bonds, two bonds have a longer distance of 3.9427 Å for the Cs1 and 3.9940 Å for the CS2, whereas the left seven bonds distance range from 3.6095-3.7742 Å for the Cs1 and 3.5568-3.6953 Å for the Cs2 (Table S1). Table 2. Atomic coordinates (× 104) and equivalent isotropic displacement parameters (Ueq, Å2 × 103) and occupancies of o-CsGaSnS4. Atom

Wyck.

x

y

z

Ueq/ Å2

Occu.

Cs1

4c

3496(1)

2500

-678(1)

40(1)

1.0

Cs2

4c

574(1)

-2500

1105(1)

35(1)

1.0

Sn1

4c

1820(1)

2500

2034(1)

24(1)

0.645(5)

Ga1

4c

1820(1)

2500

2034(1)

24(1)

0.355(5)

Sn2

4c

168(1)

2500

3091(1)

21(1)

0.59(5)

Ga2

4c

168(1)

2500

3091(1)

21(1)

0.41(5)

Sn3

8d

3490(1)

-58(1)

2508(1)

20(1)

0.382(3)

Ga3

8d

3490(1)

-58(1)

2508(1)

20(1)

0.618(3)

S1

4c

3456(1)

2500

3594(2)

28(1)

1.0

S2

4c

1491(1)

2500

-1315(1)

23(1)

1.0

S3

4c

1403(1)

2500

3844(2)

30(1)

1.0

S4

8d

2410(1)

-138(2)

1421(1)

29(1)

1.0

S5

4c

566(1)

2500

1272(1)

26(1)

1.0

S6

8d

4553(1)

-150(2)

1387(1)

26(1)

1.0

7

Table 3. Atomic coordinates (× 104) and equivalent isotropic displacement parameters (Ueq, Å2 × 103) and occupancies of m-RbGaSnS4. Atom

Wyck.

x

y

z

Ueq/ Å2

Occu.

Sn1

4e

2614(1)

7935(1)

1829(1)

22(1)

0.658(5)

Ga1

4e

2614(1)

7935(1)

1829(1)

22(1)

0.342(5)

Sn2

4e

2816(1)

6862(1)

185(1)

21(1)

0.644(5)

Ga2

4e

2816(1)

6862(1)

185(1)

21(1)

0.356(5)

Sn3

4e

-4681(1)

7513(1)

3591(1)

20(1)

0.384(5)

Ga3

4e

-4681(1)

7513(1)

3591(1)

20(1)

0.616(5)

Sn4

4e

172(1)

7489(1)

3448(1)

19(1)

0.313(5)

Ga4

4e

172(1)

7489(1)

3448(1)

19(1)

0.687(5)

Rb1

4e

7543(1)

9044(1)

542(1)

46(1)

1.0

Rb2

4e

-2238(1)

5685(1)

1652(1)

48(1)

1.0

S1

4e

-2235(2)

6311(1)

3559(1)

24(1)

1.0

S2

4e

-7254(2)

6391(1)

3489(1)

27(1)

1.0

S3

4e

318(3)

6188(1)

-624(1)

27(1)

1.0

S4

4e

-249(2)

8348(2)

2257(1)

29(1)

1.0

S5

4e

5701(3)

6539(2)

-250(1)

30(1)

1.0

S6

4e

2502 (3)

8691(1)

565(1)

28(1)

1.0

S7

4e

5090(3)

8744(1)

2585(1)

29(1)

1.0

S8

4e

2891(3)

6125(1)

1431(1)

29(1)

1.0

Compared with o-CsGaSnS4, the m-RbGaSnS4 crystallize in monoclinic P21/c space group. As shown in Figure 2c, due to the smaller size of Rb than that of Cs, the [MS4] chains tilt along the [001] direction and the β angle increases to 96.554° in order to make the space of Rb smaller. In the asymmetric unit of m-RbGaSnS4, there are two Rb, four M(Sn, Ga), and eight S atoms crystallographically independent, and all atoms located at the Wyckoff positions 4e. The occupancy of Sn/Ga at the M1, M2, M3 and M4 sites are 0.658/0.342, 0.644/0.356, 0.384/0.616 and 0.313/0.687, respectively (Table 3). In addition, the M(Sn, Ga) coordinate with four S atoms, and the M1-S, M2-S, M3-S, M4-S bond lengths are 2.3341-2.4023, 2.3265-2.3779, 2.3156-2.3387, 2.3000-2.3348 Å, respectively 8

(Table S2, Figure S2). The Rb1, Rb2 atom coordinate with seven or eight S atoms with the bond distances of 3.360-3.687 and 3.339-3.823 Å, respectively. (Table S2, Figure S3) The structures o-CsGaSnS4 and m-RbGaSnS4 are similar with those of Cs2ZnGe3S8 [12], Cs2MnGe3Se8 [13], AGaSnSe4 [17] and TlInSiS4 [26]. All of them have a two-dimensional layered structure that is constructed by the neighboring corner-sharing [M1M2Q7] chains linked via edge-shared [M2Q6] dimers, although they eventually crystallize in different space group. Previously, for the A2MⅢMⅢ3Q8 family (A = alkali metal, MⅢ = divalent metal; MⅢ = tetravalent metal; Q = chalcogenide), we have put forward a structure mismatch factor that is defined as F = rMⅢ + rMⅢ + 2 rQ2- - 2 rA+, in which r is the effective ionic radius taken from Shannon [27]. Such a F factor successfully describes the structure distribution map of the A2MⅢMⅢ3Q8 family members.[13] Very nicely, such a factor F = rMⅢI + rMⅢ + 2 rQ2- - 2 rA+, works fine for the AMⅢMⅢQ4 family as well. For all the known members of the AMⅢMⅢQ4 family up to date, when F < 1.5, compounds prefer to crystalize in high symmetry Pnma space group; when F > 1.5, lower symmetry monoclinic space will be adopted. (Table 4)

Table 4. The space group and the structure factor F for all the known members with layered structure type in the AMⅢMⅢQ4 family Compound

a

Space group

r(A)/ Å

r(MⅢ)/ Å

r(MⅢ)/ Å

r(Q)/ Å

F = rMⅢI + rMⅢ + 2 rQ2- - 2 rA+

KInSnSe4[14]

P21/c

1.46

0.62

0.55

1.98

2.21

KGaSnSe4[17]

P21/c

1.46

0.47

0.55

1.98

2.06

RbGaSnSe4[17]

P21/c

1.585a

0.47

0.55

1.98

1.81

m-RbGaSnS4

P21/c

1.585a

0.47

0.55

1.84

1.53

KGaGeS4[16]

P21/a

1.51

0.47

0.39

1.84

1.52

CsGaSnSe4[17]

Pnma

1.78

0.47

0.55

1.98

1.42

CsInGeSe4[28]

Pnma

1.78

0.62

0.39

1.98

1.41

o-CsGaSnS4

Pnma

1.78

0.47

0.55

1.84

1.14

CsInGeS4[18]

Pnma

1.78

0.62

0.39

1.84

1.13

The coordination number of the two crystallographically independent Rb atoms are seven, eight, respectively.

Therefore, an average ionic radius is used in this case. b

AInSnS4 (A = Na, In, Rb, Tl) [18] are not discussed herein, because their layered structure is totally different.

9

3.2 Structure of c-CsGaSnS4

Figure 3. Single crystal structure of c-CsGaSnS4 viewed along the [111] direction. The c-CsGaSnS4 prefers to crystallize in the cubic Pa3 space group with a = b = c = 13.3729 Å at lower reaction temperature, adopting the AGaSnS4-type (A = Na, K, Rb, Cs) that is isostructural with BaGa2S4 [29] and cubic-KInSnSe4 [14]. (Figure 3) In the c-CsGaSnS4 unit, there are two crystallographically independent Cs, one M(Sn, Ga) and two S atoms, in which Sn and Ga is half/half co-occupied. Two Cs atoms are located at Wyckoff positions 8c, 4a, respectively, and all other atoms are located at the 24d sites, as shown in Table 5. The M atom is coordinated with four S atoms in a distorted [MS4] tetrahedron with M-S distances of 2.3258, 2.3263, 2.3324, 2.3365Å, respectively. The [MS4] connects with each other by sharing corner to build a three-dimensional structure. The Cs atom is distributed among the intervals adopting slightly different local coordination. The Cs1 coordinates with nine S atoms with Cs1-S distances of 3.4801, 3.6384 and 3.8239 Å. The Cs2 coordinates with twelve S atoms with bond distances of 3.7513 and 3.9246 Å (Table S3). Table 5. Atomic coordinates (× 104) and equivalent isotropic displacement parameters (Ueq, Å2 × 103) and occupancies of c-CsGaSnS4. Atom

Wyck.

x

y

z

Ueq/ Å2

Occu.

Cs1

8c

8700(1)

3700(1)

1300(1)

28(1)

1.0

Cs2

4a

5000

0

5000

38(1)

1.0

Sn1

24d

6181(1)

1923(1)

1530(1)

14(1)

0.5

Ga1

24d

6181(1)

1923(1)

1530(1)

14(1)

0.5

S1

24d

7751(1)

1157(1)

1488(1)

17(1)

1.0

S2

24d

7690(1)

4880(1)

-788(1)

26(1)

1.0 10

3.3 UV-visible diffuse reflectance spectroscopy

Figure 4. Experimental band gaps of AGaSnS4 The energy gaps of AGaSnS4 were measured by using UV-visible diffuse reflectance spectroscopy and calculated according to the Kubelka-Munk formula. As showed in Figure 4, the energy gaps (Eg) of o-CsGaSnS4 (3.02 eV), m-RbGaSnS4 (2.96 eV), and c-CsGaSnS4 (2.92 eV), respectively. The Eg of c-CsGaSnS4 agrees in principle to that reported one (2.75 eV). [15] Besides, the Eg difference on going from m-RbGaSnS4 to o-CsGaSnS4 is only 0.06 eV, because the alkali metal cation makes trivial contribution to the Eg. (Figure 5) Such a phenomenon has been repeatedly observed in many other systems, such as Cs2MnGe3S8 (2.93 eV) vs Rb2MnGe3S8 (3.01 eV) [13], BaHgGeSe4 (2.49 eV) vs SrHgGeSe4 (2.42 eV) [30], Li2BaGeS4 (3.66 eV) [31] vs Na2BaGeS4 (3.70 eV) [32]. 3.4 Theoretical calculations As shown in the Figure 5, the electronic structure calculations give o-CsGaSnS4, m-RbGaSnS4 and c-CsGaSnS4 direct band gaps of 1.97, 2.16 eV and 1.78 eV, respectively. The calculated band gaps are in principle consistent with the experimental results, the discrepancy between the theoretical and experimental results may originated from the Ga/Sn disorder in the structure. Besides, the calculated values are usually underestimated due to the insufficient description of the eigenvalues of the electronic states for GGA [33,34]. The total and projected densities of states (TDOS, PDOS) analyses shown in Figure 5 b, d, f display that even the structure symmetry or the composition are in difference, the TDOS and PDOS are surprisingly similar in shape. The valence bands (VB) lower than -7.5 eV (VB-3) mostly consist of the Cs 5s or Rb 4s states. The VB-2 region is predominately derived from the Ga 3s and S 3s states. The VB-1 is the main part of the valence band in the bonding process, which originates mainly from the S 3p, Ga 3p and Sn 4p states. The conductive bands (CB) is mainly composed of the Cs 4d/ Rb 3d, Ga 4s, and Sn 5s states, mixing with small amounts of Ga 4p, Sn 5p states. The electron transition from the S 3p non-boding states to 11

the Sn 5s anti-bonding states leads to the optical absorption. The PDOS of the S 3p and Sn 5s states are almost clearly separated on both sides of EF, meaning that S acts as an electron acceptor and Sn, an electron donor.

Figure 5. Electronic band structures and density of states of o-CsGaSnS4 (a and b, respectively), m-RbGaSnS4 (c and d, respectively), c-CsGaSnS4 (e and f, respectively). 4. Conclusions In this work, three compounds AGaSnS4 (A = Cs, Rb) representing two structure classes, layered- and 3Dstructures are synthesized by solid-state flux reaction and characterized for the first time. The CsGaSnS4 exhibits 12

polymorphism with cubic- and orthorhombic phases, i.e., the high symmetric Pa3 c-CsGaSnS4 obtained at the lower reaction temperature of 973 K, and the low symmetric Pnma o-CsGaSnS4 obtained at the higher reaction temperature of 1083 K. And m-RbGaSnS4 crystallizes in the monoclinic P21/c. Very interesting, all the known layered members of the AMⅢMⅢQ4 family to date, including o-CsGaSnS4, m-RbGaSnS4 reported herein obeys an empirical rule of the structure mismatch factor (F) boundary at F = 1.5, below which, the monoclinic structure will be adopted; whereas above which, the orthorhombic structure will be adopted. The energy gaps of o-CsGaSnS4, m-RbGaSnS4 and c-CsGaSnS4 are measured to be 3.02, 2.96 and 2.92 eV, respectively. The electronic structures with the aid of DFT calculations reveal that the S 3p non-boding states and the Sn 5s anti-bonding states dominate the top of the valence band and the bottom of the conduction band, respectively.

Acknowledgements This work was supported by the National Natural Science Foundation of China under Projects 21971019, 21975032, 21571020 and 21671023.

Appendix A. supporting material The supporting information to this work is available free of charge online at http://doi.org/. The CSD for c-CsGaSnS4, o-CsGaSnS4 and m-RbGaSnS4 are 1970282, 1970283, 1970284, respectively. References [1] N. Ma, L. Xiong, L. Chen, L. M. Wu, Vibration uncoupling of germanium with different valence states lowers thermal conductivity of Cs2Ge3Ga6Se14, Sci. China. Mater. 62 (2019) 1788–1797. https://doi.org/10.1007/s40843-019-1192-y. [2] I. Chung, M. G. Kanatzidis, Metal chalcogenides: a rich source of nonlinear optical materials, Chem. Mater. 26 (2014) 849–869. https://doi.org/10.1021/cm401737s. [3] Y. Y. Wu, L. Xiong, F. Jia, L. Chen, Cs2Ge3In6Se14: a structure transformation driven by the size preference and its properties, Inorg. Chem. 57 (2018) 4667–4672. https://doi.org/10.1021/acs.inorgchem.8b00400. [4] L. Y. Nian, K. Wu, G. J. He, Z. H. Yang, et al, Effect of element substitution on structural transformation and optical performances in I2BaMⅢQ4 (I = Li, Na, Cu, and Ag; MⅢ = Si, Ge, and Sn; Q = S and Se), Inorg. Chem. 57 (2018) 3434–3442. https://doi.org/10.1021/acs.inorgchem.8b00220. [5] Y. Wu, H. Wang, W. G. Tu, S. Y. Wu, et al, Effects of composition faults in ternary metal chalcogenides (ZnxIn2S3+x, x = 1–5) layered crystals for visible-light-driven catalytic hydrogen generation and carbon dioxide 13

reduction, Appl. Catal. B: Enviro. 256 (2019) 117810. https://doi.org/10.1016/j.apcatb.2019.117810. [6] Z. Z. Luo, C. S. Lin, H. H. Cui, W. L. Zhang, et al, PbGa2MSe6 (M = Si, Ge): two exceptional infrared nonlinear optical crystals, Chem. Mater. 27 (2015) 914–922. https://doi.org/10.1021/cm504195x. [7] K. Wu, B. Zhang, Z. Yang, S. L. Pan, New compressed chalcopyrite-like Li2BaMⅢQ4 (MⅢ = Ge, Sn; Q = S, Se): promising infrared nonlinear optical materials, J. Am. Chem. Soc. 139 (2017) 14885–14888. https://doi.org/10.1021/jacs.7b08966 [8] H. M. Zhou, L. Xiong, L. Chen, L. M. Wu, Dislocations that decrease size mismatch within the lattice leading to ultrawide band gap, large second-order susceptibility, and high nonlinear optical performance of AgGaS2, Angew. Chem. Int. Ed. 58 (2019) 9979–9983. https://doi.org/10.1002/anie.201903976. [9] M. Y. Li, B. X. Li, H. Lin, Z. J. Ma, et al, Sn2Ga2S5: a polar semiconductor with exceptional infrared nonlinear optical properties originating from the combined effect of mixed asymmetric building motifs, Chem. Mater. 31 (2019) 6268–6275. https://doi.org/10.1021/acs.chemmater.9b02389 [10] Z. H. Shi, Y. Chi, Z. D. Sun, W. L. Liu, et al, Sn2Ga2S5: a type of IR nonlinear-optical material, Inorg. Chem. 58 (2019) 12002–12006. https://doi.org/10.1021/acs.inorgchem.9b02021. [11] B. W. Liu, X. M. Jiang, B. X. Li, H. Y. Zeng, et al, Li[LiCs2Cl][Ga3S6]: unprecedented tetrahedra-built nanoporous framework with excellent nonlinear optical performance, Angew. Chem. 131 (2019) 1–5. http://dx.doi.org/10.1002/anie.201912416. [12] C. D. Morris, H. Li, H. Jin, C. D. Malliakas, et al, Cs2MⅢMⅢ3Q8 (Q = S, Se, Te): an extensive family of layered semiconductors with diverse band gaps, Chem. Mater. 25 (2013) 3344–3356. https://doi.org/0.1021/cm401817r. [13] X. N. Hu, L. Xiong, L. M. Wu, Six new members of the A2MⅢMⅢ3Q8 family and their structural relationship, Cryst. Growth Des. 18 (2018) 3124–3131. https://doi.org/10.1021/acs.cgd.8b00247. [14] S. J. Hwang, R. G. Iyer, P. N. Trikalitis, A. G. Ogden, et al, Cooling of melts: kinetic stabilization and polymorphic transitions in the KInSnSe4 system, Inorg. Chem. 43 (2004) 2237–2239. https://doi.org/10.1021/ic0351545. [15] P. WU, Y. J. LU, J. A. IBERS, Solid-state synthesis, structural variants and transformation of three-dimensional sulfides, AGaSnS4 (A = Na, K, Rb, Cs, Tl) and Na1.263Ga1.262Sn0.737S4, J. Solid State Chem. 97 (1992) 383–39. https://doi.org/10.1016/j.jssc.2007.04.017. [16] A. Kumari, K. Vidyasagar, Synthesis and Structures of the Quaternary Sulfides KGaSnS4, KlnGeS4, and KGaGeS4, J. Solid State Chem. 180 (2007) 2013–2019. https://doi.org/10.1016/0022-4596(92)90047-Y. [17] S. J. Hwang, R. G. Iyer, M. G. Kanatzidis, Quaternary selenostannates Na2-xGa2-xSn1+xSe6 and AGaSnSe4 14

(A=K, Rb, and Cs) through rapid cooling of melts. Kinetics versus thermodynamics in the polymorphism of AGaSnSe4, J. Solid State Chem. 177 (2004) 3640–3649. https://doi.org/10.1016/j.jssc.2004.06.019. [18] J. P. Yohannan, K. Vidyasagar, Syntheses, structural variants and characterization of AInM'S4 (A = alkali metals, Tl; M' = Ge, Sn) compounds; facile ion-exchange reactions of layered NaInSnS4 and KInSnS4 compounds, J. Solid State Chem. 238 (2016) 291–302. https://doi.org/10.1016/j.jssc.2016.03.045. [19] G. M. Sheldrick, A short history of SHELX, Acta Crystallogr. Sect. A: Found. Crystallogr. 64 (2008) 112–122. https://doi.org/10.1107/S0108767307043930. [20] G. Kresse, J. Furthmuller, Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set, J. Phys. Rev. B 54 (1996) 11169. https://doi.org/10.1103/PhysRevB.54.11169. [21] J. P. Perdew, Y. Wang, Accurate and simple analytic representation of the electron-gas correlation energy, Phys. Rev. B 45 (1992) 13244. https://doi.org/10.1103/PhysRevB.45.13244. [22] N. Zhen, K. Wu, Y. Wang, Q. Li, et al, BaCdSnS4 and Ba3CdSn2S8: syntheses, structures, and non-linear optical

and

photoluminescence

properties,

Dalton

Trans.

45

(2016)

10681–10688.

https://doi.org/10.1039/c6dt01537a. [23] C. Liu, D. J. Mei, W. Z. Cao, Y. Yang, et al, Mn-Based tin sulfide Sr3MnSn2S8 with a wide band gap and strong nonlinear optical response, J. Mater. Chem. C 7 (2019) 1146–1150. https://doi.org/10.1039/c8tc05904g. [24] X. S. Lin, G. Zhang, N. Ye, Growth and characterization of BaGa4S7: a new crystal for mid-IR nonlinear optics, Cryst. Growth Des. 9 (2009) 1186–1189. https://doi.org/10.1021/cg8010579. [25] R. H. Duan, P. F. Liu, H. Lin, S. X. Huang-Fu, et al, Syntheses and characterization of three new sulfides with large band gaps: acentric Ba4Ga4SnS12, centric Ba12Sn4S23 and Ba7Sn3S13, Dalton Trans. 46 (2017) 14771–14778. https://doi.org/10.1039/c7dt03267f. [26] Y. Nakamura, A. Aruga, I. Nakai, K. Nagashima, The crystal structure of a new thiosilicate of thallium, TlInSiS4, Bull. Chem. Soc. Jpn. 57 (1984) 1718–1722. https://doi.org/10.1246/bcsj.57.1718. [27] R. D. Shannon, Revised effective ionic radii and systematic studies of interatomic distances in halides and chalcogenides, Acta Cryst. A32 (1976) 751. https://doi.org/10.1107/S0567739476001551. [28] M. D. Ward, E. A. Pozzi, R. P. V. Duyne, J. A. Ibers, Syntheses, structures, and optical properties of the indium/germanium selenides Cs4In8GeSe16, CsInSe2, and CsInGeSe4, J. Solid State Chem. 212 (2014) 191–196. https://doi.org/10.1016/j.jssc.2014.01.023. [29] T. E. Peters, J. A. Baglio, Luminescence and structural properties of thiogallate phosphors. Ce+3 and Eu+2 -activated phosphors. Part I, J. Electrochem. Soc. 119 (1972) 230–236. https://doi.org/10.1149/1.2404167. 15

[30] Y. W. Guo, F. Liang, W. L. Yin, Z. Li, et al, BaHgGeSe4 and SrHgGeSe4: two new Hg-based infrared nonlinear optical materials, Chem. Mater. 31 (2019) 3034–3040. https://doi.org/10.1021/acs.chemmater.9b01023. [31] K. Wu, B. B. Zhang, Z. H. Yang, S. L. Pan, New Compressed Chalcopyrite-like Li2BaMⅢQ4 (MⅢ = Ge, Sn; Q = S, Se): promising infrared nonlinear optical materials, J. Am. Chem. Soc. 139 (2017) 14885–14888. https://doi.org/10.1021/jacs.7b08966. [32] K. Wu, Z. H. Yang, S. L. Pan, Na2BaMQ4 (M = Ge, Sn; Q = S, Se): infrared nonlinear optical materials with excellent performances and that undergo structural transformations, Angew. Chem. Int. Ed. 55 (2016) 6713–6715. https://doi.org/10.1002/anie.201602317. [33] K. M. S. Etheredge, R. Mackay, G. L. Schimek, S. J. Hwu, Ba3CuBr3(P2O7): the first copper(Ⅲ) halide pyrophosphate, Inorg. Chem. 35 (1996) 7919. https://doi.org/10.1021/ic960461e. [34] R. W. Godby, M. Schluter, L. J. Sham, Trends in self-energy operators and their corresponding exchange-correlation potentials, Phys. Rev. B 36 (1987) 6497. https://doi.org/10.1103/PhysRevB.36.6497.

16

Highlights •Three sulfides of AGaSnS4 (A = Cs, Rb) were prepared by high-temperature solid-state flux reactions for the first time. •The layered m-RbGaSnS4 and o-CsGaSnS4 structures together with all the known layered AM M Q4 members to date, obey an empirical rule of the structure mismatch factor (F) boundary at F = 1.5 that defines well the monoclinic to orthorhombic symmetry change. •The energy gaps are measured to be 3.02, 2.96 and 2.92 eV for o-CsGaSnS4, m-RbGaSnS4 and c-CsGaSnS4, respectively, which agree well with the DFT calculation results.

Declaration of interests ☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. ☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: