2.1. Synthesis

The sample was synthesized by the melt and anneals technique. Highly pure components (silver 99.98%, manganese 99.97%, tin 99.99%, and sulphur 99.99) of 1 g sample were sealed under vacuum (≈10-5 Torr) in a small quartz ampoule, and then the components were heated up to 200°C and kept for about 1-2 h. The temperature was then raised to 500°C using a rate of 40°C/h, and held at this temperature for 14 hour. After, the sample was heated from 500°C to 800°C at a rate of 30°C/h and kept at this temperature for another 14 hours. Then it was raised to 1150°C at 60°C/h, and the components were melted together at this temperature. The furnace temperature was brought slowly (4°C/h) down to 600°C, and the sample was annealed at this temperature for 1 month. Finally, the sample was slowly cooled to room temperature using a rate of about 2°C/h.

2.2. Chemical Analysis

The stoichiometric relation of the sample was investigated by SEM technique, using a Hitachi S2500 microscope equipped with a Kedex EDX accessory. Three different regions of the ingot were scanned and the average atomic percentages are as follows: Ag (25.2%), Mn (11.1%), Sn (11.3%) and S (52.4%). The error in standardless analysis was around 5%. These values are in good agreement with the ideal composition 2:1:1:4.

2.3. Differential thermal analysis (DTA)

Phase transition temperatures were obtained in the temperature range between 20 to 1150°C, using a Perkin-Elmer DTA-7 with aluminum and gold used as reference materials. The charge was of powdered alloy of approximately 100 mg weight. Both heating and cooling runs were carried out on each sample. The average rates of these runs being approximately 10°C/min. The error in determining these temperatures is of about ±10°C.

2.4. X-ray powder diffraction (XRPD)

For the X-ray analysis, a small quantity of the sample, cut from the ingot, was ground mechanically in an agate mortar and pestle, and sieved to a grain size of less than 10 µm. The XRPD data was collected at 293(1) K, in θ/θ reflection mode using a Siemens D5005 diffractometer equipped with an X-ray tube (CuKα radiation: λ=1.5418 Å; 40 kV, 30 mA). The specimen was scanned from 10°-80° 2θ, with a step size of 0.02° and counting time of 10 s. Quartz was used as an external standard.

3.1. Differential thermal analysis

DTA runs were carried out on the sample as indicated above. The transition temperatures as well as the type of melting were obtained from the peaks on the DTA heating and cooling curves. Each transition temperature was determined from the base intercept of the tangent to the leading edge of the peak in the differential signal. The value of the melting point temperature, denoted as TM, obtained from the peaks on the DTA curve, is given in Fig. 2, which shows the thermogram for Ag₂MnSnS₄.

Figure 2 DTA thermogram for Ag₂MnSnS₄. The direction of heating run, or cooling run, is indicated by the corresponding arrow 

Three transitions are observed in both heating and cooling runs. These appear at about 477, 640 and 790°C, and at about 973, 700 and 592°C, in these curves, respectively. It can also be seen, that the compound melts congruently at about 973°C. Hence, the effect observed at 973°C corresponds to the transition from (L + β1) to the liquid state L. Here, β1 is a zinc-blende (ZB) structure high-temperature modification. The effect observed at 790°C corresponds to the liquid-line, i.e., to the peritectic decomposition of the Ag₂MnSnS₄ from β (other ZB phase high temperature modification) to L + β1. On the other hand, the peaks at 640 and 700°C, in the heating curve, are related to the peritectic decomposition of the compound from α1, which is a wurtz-stannite phase high temperature modification, to β+α1, and to the solid-solid transformation from β+α1 to β, respectively. In addition, the peaks at 592 and 640°C correspond to the peritectic decomposition of the Ag₂MnSnS₄, from α1+α to solid α1, and to the transition from α1 to β+α1, respectively. The transition at about 477°C, observed in heating curve, corresponds to the peritectic decomposition of the room temperature α-Ag₂MnSnS₄ phase with wurtz-stannite (Pmn21) structure, to α+α1. Finally, the sequence of phase relations for this compound from low to high temperatures should be: α→α+α1→α1→α1+β→β→β1+L→L.

3.2. X-ray powder diffraction analysis

Figure 3 shows the resulting X-ray powder diffractogram for the Ag₂MnSnS₄ compound. The X-ray powder pattern show a single phase. The 20 first peak positions were indexed using the program Dicvol04⁴², which gave a unique solution in an orthorhombic cell with parameters a=8.1701 Å, b=6.9401 Å, and c=6.6501 Å. The lack of systematic absence condition h+k+l, in the general reflections of the type hkl, indicated a P-type cell. By analyzing the crystallographic characteristics of Ag₂MnSnS₄ with those of other I₂-II-IV-VI₄ related compounds, taking in account the sample composition, cell parameters and lattice-type, it is found that this material is isomorphic with Ag₂CdGeS₄²⁹ which crystalize with wurtzite-stannite structure (space group Pmn21)¹³. So, in order to refine the structural parameters of Ag₂MnSnS₄, the space group Pmn21 (N° 31) and the atomic position parameters of Ag₂CdGeS₄ were taken as the starting values.

Figure 3 Final Rietveld plot showing the observed, calculated and difference pattern for the Ag2MnSnS4 compound. The Bragg reflections for both phases are indicated by vertical bars. 

The Rietveld refinement⁴³ was performed using the Fullprof program⁴⁴. The indexed unit cell results were taken as starting parameters. The angular dependence of the peak full width at half maximum (FWHM) was described by the Cagliotti’s formula⁴⁵. The parameterized Thompson-Cox-Hastings pseudo-Voigt profile function⁴⁶ was used for the simulation of the peak shapes. The background of the XRD data was refined with a polynomial with six coefficients. The thermal motion of the atoms was described by one overall isotropic temperature factor. A total of 23 parameters of the Ag₂MnSnS₄ compound, including peak shape, scale factor, cell, atomic coordinates, isotropic displacement and full-width at half-maximum (FWHM) parameters, were refined. The final Rietveld refinement led to agreement factors of: R_p = 10.3%, R_wp = 11.8%, R_exp = 9.6%, and S = 1.2, for 4001 step intensities and 145 independent reflections.

The results of the Rietveld refinement are summarized in Table I. Figure 3 shows the observed calculated and difference profile for the final cycle of the refinement. Atomic coordinates, occupancy factors and isotropic temperature factor are given in Table II. Bond distances and angles are given in Table III. Figure 4 shows the unit cell diagram for Ag₂MnSnS₄.

Figure 4 Unit cell diagram of Ag₂MnSnS₄ viewed in the ba plane of the space group Pmn2₁. 

Ag₂MnSnS₄ crystallize with orthorhombic symmetry, space group Pmn21, and unit cell parameters: a=8.17055Å, b=6.94135 Å, c=6.65325 Å , and V=377.335 Å3 in a wurtzite-stannite structure. This structure can be described as a hexagonal, closest-packed array of sulfur anions with Ag⁺, Mn⁺² and Sn⁴⁺ occupying tetrahedral holes, and is characterized by a three-dimensional arrangement of slightly distorted AgS₄, MnS₄ and SnS₄ tetrahedra connected by corners. All S atoms are surrounded by two Ag atoms and by one Mn and one Sn atom, and each cation is coordinated by 4 anions. This array is expected for adamantane compounds¹.

The tetrahedrons containing the Sn atoms [mean S… S distance 3.67(2) Å] are slightly smaller than those containing the Mn atoms [means S… S distance 4.16(2) Å] and Ag atoms [mean S…S distance 4.22(2) Å] respectively. The interatomic distances are shorter than the sum of the respective ionic radii (rAg⁺ = 1.14, rMn²⁺ = 0.80, rSn⁴⁺ = 0.69, rS^2- = 1.70 Å) for structures tetrahedrally bonded⁴⁷.

The mean bond distance values for Ag-S, Mn-S and Sn-S, given in Table III, agree well with the distances observed in other adamantane compounds as Ag₂CdSnS₄⁹, Ag₂CdGeS₄²⁹, Ag₂CdSnS₄³⁰, Ag₂ZnSiS₄³², AgCd₂GaS₄⁴⁸, Ag₂ZnGeS₄⁴⁹, MnIn₂S₄⁵⁰, AgInS₂ and AgIn₅S₈⁵¹.

In addition, the Debye temperature θD, which is an important parameter in the understanding of thermal and electrical properties of semiconducting materials, can be estimated for this compound by using the Lindemann’s expression θD≈C(TM/W¯)1/2(1/ae) ⁵². Here, W¯=W/n, W is the molecular weight, n is the number of atoms per molecule (n = 8 for Ag₂MnSnS₄), C is a constant (C≈300 for I₂-II-IV-VI₄ tetrahedral bonded quaternary compounds ²⁴), and ae is the effective lattice parameter ae=(V/Z)1/3, where V is the volume of unit cell (in ų) and Z the number of molecules per cell (Z = 2). For Ag₂MnSnS₄, from the calculated value ae=5.7354 Å, we obtain θD212 K. This value is in good agreement with those reported for the related Cu₂Mn-IV-VI₂ semimagnetic semiconductor compounds, which vary from 185 to 310 K²⁴.