New cation-disordered quaternary selenides Tl₂Ga₂TtSe₆ (Tt=Ge, Sn)

1 Introduction

The family of binary TlX (X=S, Se, Te) compounds and their derivatives is well known as optical and semiconducting materials [1]. Ordered ternary representatives TlTtX₂ (Tt=Al, Ga, In) also exist featuring two crystallographic sites with different coordination environments, but the existence of solid solutions for different chalcogenides cannot be excluded [2], [3], [4], [5], [6]. The light atoms in those structures usually exhibit the oxidation state +3, while the heavy ones rather adopt the oxidation state +1. This fact provoked further investigation towards formation of solid solutions or quaternary compounds in the series TlTtX₂–Tt′X₂ (Tt′=Si, Ge, Sn) exhibiting aliovalent metal substitutions.

It should be noted that a few representatives of the Tt″TtX₂–Tt′X₂ systems are known with Tt″=Li, Na, Cu, Ag having approximate stoichiometry Tt″₂Tt₂Tt′X₆. For instance, lithium-containing systems with gallium include the Li₂Ga₂GeS₆ compound that crystallizes in the non-centrosymmetric orthorhombic space group Fdd2 which is a promising non-linear optical material [7]. The substitution of In for Ga results in a series of compounds Li₂In₂Si(Ge)S₆(Se₆) that crystallize in a monoclinic structure, space group Cc [8], [9]. Isostructural sodium-containing compounds Na₂In₂Si(Ge)S₆(Se₆) and Na₂CdGe₂S₆(Se₆) have also been reported [10], [11], [12], [13]. It has been found that Na₂Ga₂GeS₆ crystallizes in the orthorhombic structure (space group Fdd2), while Na₂In₂SiS₆ and Na₂In₂GeS₆ have monoclinic structures (space group Cc). Na₂Ga₂SnS₆ is dimorphic and crystallizes in both of the above structures.

The formation of the 2-2-1-6 compounds is also common in silver-containing systems. They all crystallize in either of two structures. The monoclinic structure (space group Cc) is typical of indium-containing compounds (Ag₂In₂Si(Ge)S₆ [14], Ag₂In₂SiSe₆ [15], Ag₂In₂GeSe₆ [16]), while compounds with Ga (Ag₂Ga₂SiS₆ [17], Ag₂Ga₂SiSe₆ [18]) crystallize in the tetragonal structure (space group I4̅2d). Finally, unique cases of this composition are known in a copper-containing system Cu₂In₂SiS₆ (space group Cc) [19] and in a combination with thallium, Tl₂In₂SnSe₆ (space group I4/mcm) [20].

For that reason, the TlGaSe₂–SnSe₂ system has been investigated in more detail, followed by iso-compositional representatives with Ge. At ambient conditions TlGaSe₂ has a monoclinic crystal structure [10] (structure type KInS₂ [21]), whereas a tetragonal structure (high-temperature inherent variant, α-TlSe type [6]) has been observed within the TlGaSe₂–SnSe₂ cross-section. The composition, defined by energy-dispersive X-ray spectroscopy (EDX), indicated the existence of a new quaternary compound. In this work we present the results of structural, spectroscopic and theoretical investigations of the nonstoichiometric Tl_1−xGa_1−xTt_xSe₂ series.

2 Experimental

2.4 X-ray powder diffraction

Experimental diffraction data for the isostructural compounds Tl₂Ga₂GeSe₆ and Tl₂Ga₂GeSe₆ were obtained on a DRON 4-13 diffractometer (45 kV and 30 mA, CuKα radiation, Bragg-Brentano geometry) and analyzed with the WinCSD program package [28].

Phase analysis showed that the XRD pattern of Tl₂Ga₂GeSe₆ was similar to that of the tetragonal II-TlGaSe₂ phase (high temperature-high pressure modification) [6] with slightly different unit cell parameters. In the first stage of the treatment of the crystal structure was refined as TlGaSe₂ using the initial atomic coordinates of HT-TlGaSe₂ [6]. After accounting for the predominant orientation factor (texture) along the 0 0 1 direction, refinement of isotropic displacement parameters for Tl, Ga and Se atoms showed significantly increased values of the latter, especially for the Tl and Ga sites. Taking into account the EDX results for the elemental composition, a statistical mixture M=0.65 Ga+0.35 Ge was restrained. The R_B and B_iso values for the M and Se positions were reduced, but for Tl B_iso they increased. Refinement of the 4a site occupancy (G) by thallium atoms resulted in G=0.66. Finally both the 4a and 4b occupancies and, afterwards, the isotropic displacement parameters for all Tl, M, and Se atoms were refined. Experimental, calculated and difference powder XRD profiles of the Tl₂Ga₂GeSe₆ sample are shown in Fig. 1. Details of the refinement are listed in Table 5, atomic coordinates and their displacement parameters in Table 6. High correlation of the refined composition with the elemental analysis was observed, despite comparatively higher B_iso values for Tl, caused by structural features of this structure type, since Tl atoms are localized in Se tunnels along the 0 0 1 direction (see Fig. 3a). Unfortunately, anisotropic displacement parameters could not be refined reliably from powder XRD due to a poor data to parameter ratio.

Fig. 1:

Observed (dots) and calculated (line) profiles and their difference plot (bottom) of the XRD patterns of the Tl₂Ga₂GeSe₆ sample. Peak positions are marked by short vertical bars.

Table 5:

Details of data collection and refinement of the crystal structure of Tl₂Ga₂GeSe₆.

Refined composition	Tl1−xGa1−yGeySe2, x=0.343(5), y=0.35(2)
Space group	I4/mcm (no. 140)
Structure type	α-TlSe
Pearson symbol and Z	tI16, 4
Unit cell parameters
a, Å	8.0770(4)
c, Å	6.2572(5)
V, Å3	408.20(7)
Calculated density, g·cm−3	5.91
Diffractometer	DRON 4-13
Radiation/λ, Å	CuKα/1.54185
Mode of refinement	Full with fixed elements per cycle
2θ range/step, °	10.0–100.0/0.02
(sinθ/λ)max, Å−1	0.497
Detector	NaI(Tl) scintillation counter
Scanning time (in s) per step of 0.02° in 2θ	20
No. of reflections	69
No. of parameters (all/free)	24/5
Scale factor	0.0682(1)
Goodness-of-fit	2.46
RB(I)/RP/RPw, %	8.4/4.1/5.8

Table 6:

Refined atomic coordinates and isotropic displacement parameters for Tl₂Ga₂GeSe₆.^a

Atom	Wyckoff position	G (site occupancy)	x	y	z	Biso (Å2)
Se	8h	1	0.1577(2)	x+½	0	1.18(7)
M	4b	1	0	½	¼	2.87(12)
Tl	4a	0.657(5)	0	0	¼	3.48(9)

1. ^aM=0.65(2) Ga+0.35(2) Ge.

CCDC 1960737 (Tl₂Ga₂SnSe₆) and 1960739 (Tl₂Ga₂GeSe₆) contain the supplementary crystallographic data for this paper. These data can be obtained free of charge from The Cambridge Crystallographic Data Centre via www.ccdc.cam.ac.uk/data_request/cif.

3 Results and discussion

The crystal structure of Tl₂Ga₂SnSe₆ is closely related to the structures of the stoichiometric 2-2-1-6 compounds and contains three main building units – MSe₄ tetrahedra, SeM₂Tl₄ trigonal prisms and Tl@Tl₂Se₈ bi-capped tetragonal antiprisms (Fig. 2). Atomic coordination numbers and selected interatomic distances are summarized in Table 4. The simplest structural representation appears in the form of chains of edge-sharing [MSe₄] tetrahedra along [001], connected in the ab plane with Tl⁺ cations occupying the channels (Fig. 3a). This structural arrangement is related to the one in the tetragonal quaternary selenide Ag₂Ga₂SiSe₆ (Fig. 4f), that exhibits a three-dimensional framework composed of corner-sharing [(Ga/Si)Se₄] and [AgSe₄] tetrahedra with empty cavities [17]. In the disordered crystal structure of Ag₂Ga₂SiSe₆ the Ga and Si atoms form a statistical mixture, while the Ag atoms partially occupy the 4b site. The crystal structure of the monoclinic quaternary selenide Na₂In₂GeSe₆ (Fig. 3d), exhibits a three-dimensional framework composed of corner-sharing [InSe₄] and [GeSe₄] tetrahedra with Na⁺ cations occupying the voids [11]. The basic building unit of the Na₂In₂GeSe₆ framework is a [In₄Ge₂Se₁₆] block comprised of two smaller [In₂GeSe₉] units. The latter in turn consists of two [InSe₄] tetrahedra and one [GeSe₄] tetrahedron linked to each other via Se vertex-sharing. The [In₄Ge₂Se₁₆] blocks are connected to each other via corner-sharing to generate the three-dimensional framework.

Fig. 2:

Filled unit cell (atoms are shown as their anisotropic ellipsoids with 95% probability) and atomic coordination polyhedra (ions are shown as circles with color distinguishing sectors, indicating partial or mixed site occupancy) of Tl₂Ga₂SnSe₆.

Fig. 3:

Packing of tetrahedra of selenium and sulfur atoms in the crystal structures of Tl₂Ga₂SnSe₆ (a), K₂Sn₂ZnSe₆ (b) and Na₂Ge₂ZnSe₆ (c), Na₂In₂GeSe₆ (d), Li₂Ga₂GeS₆ (e), and Ag₂Ga₂SiSe₆ (f).

Fig. 4:

Band structure and projected densities of state (DOS) for an idealized model of Tl₂In₂SnSe₆.

The lithium sulfide Li₂Ga₂GeS₆ crystallizes in the non-centrosymmetric orthorhombic space group Fdd2 [7]. The crystal structure is built of [GeS₄] tetrahedra linked by corners to other four identical units to create a three dimensional framework with tunnels along the c axis, in which the Li⁺ ions are located (Fig. 3e). The Li atoms in distorted tetrahedral coordination (Li@S₄) form an infinite chain parallel to the c axis by vertex-sharing. K₂Sn₂ZnSe₆ and Na₂Ge₂ZnSe₆ ([11], Fig. 3b and c) crystallize in the space groups P4/ncc and I4/mcm, respectively. In these structures [SnSe₄] or [GeSe₄] and [ZnSe₄] edge-sharing tetrahedra appear in similar chains. Two [Sn(Ge)Se₄] tetrahedra are first connected to each other by sharing two Se atoms to form the [Sn(Ge)₂Se₆] block, which is further linked via edge-sharing two other Se atoms with one [ZnSe₄] tetrahedron to build up a [Sn(Ge)₂ZnSe₆] infinite chain along [001]. The chains are separated from each other by K⁺ or Na⁺ cations occupying the voids. All K⁺ and Na⁺ cations are coordinated by eight Se atoms in tetragonal antiprismatic arrangement. The unit cell expansion is in good agreement with the atomic sizes of Na/Ge vs. K/Sn [32].

Observed interatomic distances indicate that in Tl₂Ga₂SnSe₆ thallium is monovalent (ionic radius [33] r(Tl⁺)=1.49 Å), gallium trivalent (r(Ga³⁺)=0.62 Å) and selenium divalent (r(Se²⁻)=1.91 Å) showing a reasonable correlation of their coordination polyhedra (Fig. 2) and earlier evaluations for β-TlGaSe₂ [6]. The shortest interatomic distances are those between the M and Se atoms indicating stronger chemical bonding between them. From the viewpoint of the charge balance each Sn atom introduced to the structure leads to simultaneous exclusion of both a Ga and a Tl atom according to Tl1−x+Ga1−y3+Sny4+Se22− (x=y=0.345(5)), in agreement with the observed interatomic distances (Table 4). Substitution of gallium atoms by larger tin atoms leads to an only minor expansion of the unit cell compared to the TlGaSe₂ analogue [6] due to partial compensation by Tl deficiency. This is further confirmed by the more visible unit cell contraction of the Ge compound (Table 5).

Electronic structure calculations were performed for a couple of slightly modified models of Tl₂Ga₂SnSe₆ because of the difficulties in the treatment of partially occupied sites. TlGaSe₂, TlInSe₂ and TlSnSe₂ have been examined in order to estimate changes in the electronic structure with regard to the atomic size, electronegativity and valence electron concentration. All three models revealed qualitatively identical results with reasonable variation of the monitored output parameters as a good approximation for the observed disordered structure. Expectedly, the fully occupied Sn position led to the shift of the Fermi level into the areas with non-zero densities of states. The proper adjustment to the corresponding valence electron count revealed a comparable gap in the electronic structure (Fig. 4). The electronic densities of state (DOS) exhibit broad valence s, p bands reaching 8 eV below the Fermi level including large contributions from mostly Se-4p bands located 1–2.5 eV below E_F. In this region they exhibit the largest overlap with the Ga-4p and Tl-6s,6p bands. The contributions from the Ga and Tl bands are significantly smaller being comparable to each other in the range from –5 to 2 eV. This agrees well with the formally cationic roles of both metals in this compound. The Tl-6s bands dominate at –5 to –6.5 eV while the Ga-4s bands appear around –7 eV.

The maximum of the valence band is located at the Z point, while the pronounced minimum of the conduction band is found between the X and P points. Consequently, the model suggests an indirect band gap semiconductor with a calculated band gap size varied between the Ga and Sn model from 0.74 to 0.93 eV. These values are considerably lower than the expected range based on the samples’ color and optical appearance. Since the size of the band gap is usually underestimated by the DFT methods, UV/Vis diffuse reflectance measurements were performed to obtain more accurate values. The UV/Vis diffuse reflectance spectra, recorded at room temperature, show an intense broad band with an absorption edge at 728 nm for 1 and at 779 nm for 2 (Fig. 5). These spectral features correlate well with the red-brown color of the compounds. The UV/Vis data were then employed to determine the band gap of the compounds. The values of the energy band gap (E_g) were estimated by linear extrapolation of the Tauc plot [34] [(αhν)² vs. hν] to (αhν)²=0. The values of E_g are 2.15(3) eV for 1 and 2.05(5) eV for 2, which is consistent with the transparency of the crystals and the color of the compounds. However, the band gap of 2 is smaller compared with that of 1. A similar observation can be made in the case of other quaternary selenides, like BaGa₂GeSe₆ (2.22 eV) [35] and BaGa₂SnSe₆ (1.95 eV) [36]. It can be concluded that the heavier the employed group 14 elements is, the narrower is the band gap observed in this series of compounds. This can be explained in terms of differences in electron binding capacities of the various ions. Nuclei of heavier tetravalent ions are larger and exhibit weaker electron binding capacities than those of lighter ones. Therefore, the valence orbitals of the heavier tetravalent ions contribute to the bottom of the conduction bands to a larger extent, resulting in smaller band gaps.

Fig. 5:

UV/Vis diffuse reflectance spectra and energy band gap of 1–2.

4 Conclusions

In summary, two new quaternary selenides Tl1−x+Ga1−y3+Tty4+Se22− (Tt=Ge, Sn; x=y=0.345(5)) have been synthesized from self-flux allowing growth of large single phase samples. They crystallize tetragonally in the space group I4/mcm and represent a pseudoternary positionally ordered variant of the α-TlSe structure type. Intercalation of a tetrel element into the crystal structure leads to a partial substitution of the triel position and simultaneously to an equimolar exclusion of thallium. First-principle calculations and optical measurements indicate these materials to be narrow gap semiconductors suggesting further examination of their heat transport and thermoelectric performance.