Physico-Chemical Interaction in the Ag₂Se–Zn(Cd, Hg, Pb)Se–SnSe₂ Systems ^†

Abstract

The quaternary compounds A^I₂B^IIC^IVX₄, where A^I–Cu, Ag; B^II–Zn, Cd, Hg; C^IV–Si, Ge, Sn; and X–S, Se, Te, crystallize in non-centrosymmetric structures and may be of interest for nonlinear optics. Here, we present in detail isothermal sections and physico-chemical equilibria in the Ag₂Se–Zn(Cd, Hg, Pb)Se–SnSe₂ systems where some of these compounds were found. The crystal structure of Ag₂ZnSnSe₄ was determined for the first time as the tetragonal symmetry, S.G. I$\overline{4}$2m, lattice parameters a = 0.60434(2), c = 1.13252(5) nm. No quaternary compounds were found in the Ag₂Se–PbSe–SnSe₂ system. Ag₈SnSe₆–PbSe is the triangulating section in this system.

1. Introduction

The formation of quaternary compounds in the A^I₂X–B^IIX–C^IVX₂ systems where A^I–Cu, Ag; B^II–Zn, Cd, Hg; C^IV–Si, Ge, Sn; and X–S, Se, Te is known for seven component combinations [1]. The most common are the phases with the equimolar ratio of all three binary compounds described by the A^I₂B^IIC^IVX₄ formula. These quaternary compounds crystallize in non-centrosymmetric structures and may be of interest for nonlinear optics. Ag-containing compounds may be of interest due to the possible formation of compounds with high ionic conductivity [2,3].

The boundary sides of the presented systems Ag₂Se–Zn(Cd, Hg, Pb)Se–SnSe₂ feature only two compounds, Ag₈SnSe₆ (Ag₂Se–SnSe₂ system) and Hg₂SnSe₄ (HgSe–SnSe₂ system). High-temperature modification of Ag₈SnSe₆ crystallizes in fcc structure (S.G. P4₂32); the crystal structure of the low-temperature Ag₈SnSe₆ was investigated using X-ray powder diffraction. This modification crystallizes in the orthorhombic unit cell (S.G. Pmn2₁) and is isostructural to β’-Ag₈GeSe₆. Hg₂SnSe₄ crystallizes in the thiogallate structure (defect chalcopyrite, S.G I$\overline{4}$).

The Ag₂Se–ZnSe–SnSe₂ and Ag₂Se–CdSe–SnSe₂ systems contain only one intermediate quaternary compound each, Ag₂ZnSnSe₄ and Ag₂CdSnSe₄ [4]. Each compound has at 670 K a minor homogeneity region stretched along the Ag_33.3Sn_16.7Se₅₀–Zn(Cd)Se sections. Due to the absence of a ternary compound, the sections are non-quasi-binary in the range of 0–50 mol.% Zn(Cd)Se. The crystal structure of the Ag₂CdSnSe₄ compound was determined in the orthorhombic symmetry, S.G. Cmc2₁, a = 0.42640(2), b = 0.73170(3), c = 0.69842(4) nm, R_I = 0.0782) [4]. The Ag₈SnSe₆–Zn(Cd)Se sections of these systems are quasi-binary, of the eutectic type, with large solid solution ranges of end compounds [5].

The Ag₂Se–HgSe–SnSe₂ system [6,7,8] features at 670 K three intermediate phases, Ag₂HgSnSe₄, Ag₄Hg₃Sn₂Se₉ (Ag_2.66Hg₂Sn_1.34Se₆) and Ag₆HgSnSe₆. Ag₂HgSnSe₄ crystallizes in the orthorhombic S.G. Pmn2₁, with lattice periods a = 0.8461(1), b = 0.7340(1) and c = 0.69901(6) nm [6,8]. The Ag₄Hg₃Sn₂Se₉ compound crystallizes in an orthorhombic unit cell (S.G. Imm2, a = 1.2795(2), b = 0.42631(6) and c = 0.58207(4) nm) [7]. This compound has a homogeneity region that is stretched to the ternary compound Hg₂SnSe₄ (the Ag₂Se content is 15–28 mol.%) and is negligible along the Ag_33.3Sn_16.7Se₅₀–HgSe section. The unit cell periods decrease within the homogeneity region to a = 1.2665(3), b = 0.4222(1) and c = 0.5739(1) nm. The structure of Ag₆HgSnSe₆ has not been investigated.

2. Materials and Methods

The alloys for investigation were prepared from high purity elements and the previously synthesized mercury selenide. The alloys were synthesized in evacuated quartz containers placed in a shaft-type furnace. The ampoules were heated to 1100 K at the rate of 50 K/h, kept for 6 h, then cooled at the rate of 10 K/h to 670 K. The alloys were annealed at this temperature for 500 h followed by quenching in air. Obtained ingots were compact and black.

The alloys were studied by differential thermal analysis (computer-controlled set-up of Thermodent T-04 furnace, Pt/Pt-Rh thermocouple) and powder X-ray diffraction (DRON 4-13 diffractometer, CuKα radiation).

3. Results and Discussion

3.1. Phase Equilibria in the Ag₂Se–PbSe–SnSe₂ System

Isothermal sections at room temperature of the title systems Ag₂Se–Zn(Cd, Hg, Pb)–SnSe₂ are presented in Figure 1. The systems with B^II–Zn, Cd and Hg were discussed in in the introduction and are shown here for visual comparison.

No quaternary compounds were found in the Ag₂Se–PbSe–SnSe₂ system. The alloys in the Ag₈SnSe₆–PbSe–SnSe₂ sub-system are four-phase since the PbSe–SnSe₂ section is non-quasi-binary [9]. Thus, the isothermal section consists of two three-phase fields, Ag₂Se + Ag₈SnSe₆ + PbSe and PbSe + SnSe₂ + Se (along the PbSe–SnSe₂ line), one four-phase field Ag₈SnSe₆ + PbSe + SnSe₂ + Se and contains four two-phase equilibria.

Ag₈SnSe₆–PbSe is the only triangulating section in this system (Figure 2). The section is quasi-binary, features a eutectic at 885 K and 67 mol.% PbSe and is quite similar to the previously referenced Ag₈SnSe₆–Zn(Cd)Se sections [5].

3.2. Crystal Structure of the Quaternary Compound Ag₂ZnSnSe₄

The crystal structure of the Ag₂ZnSnSe₄ compound was determined by X-ray powder method. The set of the experimental intensities of diffraction reflections was recorded in the 2Θ range 10–100° with scan step 0.05° and 20 s exposure in each point at a DRON 4-13 diffractometer (CuKα radiation). The diffraction pattern of the obtained compound was indexed well in the tetragonal structure of the Cu₂FeSnS₄ stannite type with the parameters listed in

Table 1. Results of the crystal structure determination of the Ag₂ZnSnSe₄ compound.

Compound	Ag2ZnSnSe4
Number of formula units per unit cell	2
Space group	$I\overline{4}$2m
Pearson symbol	tI16
a (nm)	0.60434(2)
c (nm)	1.13252(5)
c/a	1.874
Cell volume (nm3)	0.41363(5)
Number of atoms in the cell	16.0
Calculated density (g/cm3)	5.7454(6)
Absorption coefficient (1/cm)	884.93
Radiation and wavelength	CuKα 0.154178 nm
Diffractometer	Powder DRON 4–13
Mode of refinement	Full profile
Number of atomic sites	4
Number of free parameters	7
2Θ and sinΘ/λ (max)	99.80 and 0.496
RI and RP	0.0570 and 0.1277

. The refinement of profile and structure parameters of Ag₂ZnSnSe₄ in isotropic approximation yielded in the selected model the fit factors R_I = 0.0570 and R_P = 0.1277.

Experimental and theoretical X-ray diffraction patterns of the Ag₂ZnSnSe₄ compound and their differences are plotted in Figure 3. Atomic coordinates, site occupation and isotropic parameters of temperature displacement of the atoms in the structure of this quaternary chalcogenide are listed in

Table 2. Atomic coordinates and isotropic temperature displacement factors for the Ag₂ZnSnSe₄ structure.

Atom	Wyckoff Site	x/a	y/b	z/c	Biso × 102, nm2
Ag	4(d)	0	1/2	1/4	1.21(9)
Zn	2(a)	0	0	0	3.5(3)
Sn	2(b)	0	0	1/2	0.31(9)
Se	8(i)	0.2432(4)	x	0.1129(3)	1.51(8)

. According to the obtained results, the structure formula of the quaternary compound is identical to the stoichiometric Ag₂ZnSnSe₄.

The location of the atoms in the unit cell, coordination surrounding and the interatomic distances in the structure of the investigated compound are shown in Figure 4. All atoms are characterized by tetrahedral surrounding. Interatomic distances in the quaternary compound are consistent with the sum of the effective ionic radii.

The second coordination surrounding (SCS) [10] of selenium atoms shown in Figure 5 has the shape of a cuboctahedron within which the atoms of metallic components occupy four tetrahedral cavities. Comparing the crystal structure of Ag₂ZnSnSe₄ and the components and compounds of the Ag₂Se–ZnSe–SnSe₂ system, it should be noted that in terms of SCS and its content, the Ag₂ZnSnSe₄ compound is related to the sphalerite structure of room-temperature ZnSe [11]. Therefore, the crystal structure of Ag₂ZnSnSe₄ can be derived from the cubic sphalerite structure by doubling the unit cell along the c axis and ordering the sites of the atoms of the metallic components. SCS of selenium atoms in the structure of Ag_0.67Sn_0.33Se [12] is also of the sphalerite type where the atoms of the statistical mixture of cations occupy octahedral cavities within the SCS. Conversely, in the binary tin selenide SnSe₂ [13], the wurtzite-type SCS is in the form of the hexagonal analog of a cuboctahedron, where tin atoms also occupy octahedral cavities. As for the binary silver selenide Ag₂Se at room temperature [14], Ag1 atoms occupy tetrahedral voids and Ag2 atoms occupy octahedral voids within the wurtzite-type SCS.

Thus, in the quaternary compound, only zinc atoms occupy the same sites as in the binary selenide, whereas silver and tin atoms occupy atypical octahedral voids within an atypical SCS, which is abnormal for them and can produce interesting physical properties in materials based on Ag₂ZnSnSe₄.