Pirquitasite, Ag2ZnSnS4

Pirquitasite, ideally Ag2ZnSnS4 (disilver zinc tin tetrasulfide), exhibits tetragonal symmetry and is a member of the stannite group that has the general formula A2BCX 4, with A = Ag, Cu; B = Zn, Cd, Fe, Cu, Hg; C = Sn, Ge, Sb, As; and X = S, Se. In this study, single-crystal X-ray diffraction data are used to determine the structure of pirquitasite from a twinned crystal from the type locality, the Pirquitas deposit, Jujuy Province, Argentina, with anisotropic displacement parameters for all atoms, and a measured composition of (Ag1.87Cu0.13)(Zn0.61Fe0.36Cd0.03)SnS4. One Ag atom is located on Wyckoff site Wyckoff 2a (symmetry -4..), the other Ag atom is statistically disordered with minor amounts of Cu and is located on 2c (-4..), the (Zn, Fe, Cd) site on 2d (-4..), Sn on 2b (-4..), and S on general site 8g. This is the first determination of the crystal structure of pirquitasite, and our data indicate that the space group of pirquitasite is I-4, rather than I-42m as previously suggested. The structure was refined under consideration of twinning by inversion [twin ratio of the components 0.91 (6):0.09 (6)].

The structure was refined using both I42m and I4, with the R factor for I4 (R = 0.027) significantly lower than for I42m (R = 0.051). The structure of pirquitasite is a derivative of the cubic sphalerite structure that displays cubic closest packed (CCP) layers of S stacked along [111]. Because pirquitasite has a doubled c cell dimension, its stacking direction is [221].
Half of the tetrahedral sites are occupied by Ag, (Zn,Fe), and Sn cations, forming metal layers described by Hall et al. (1978), and it is the arrangement of Ag, (Zn,Fe), and Sn within these layers that differentiates the I4 kësterite structure from the I42m stannite structure.
Stannite and kësterite were originally recognized as distinct species because of different Fe-Zn compositional ratios and different optical properties (Orlova, 1956;Hall et al. 1978). Structural and chemical analyses by Hall et al. (1978) and Kissin and Owens (1979) not only showed a miscibility gap between the pure Fe end-member stannite and the pure Zn end-member kësterite, but found the two minerals differed in symmetry from I42m (stannite) to I4 (kësterite). In I42m, Cu atoms are ordered to the Wyckoff 4d site, (Fe,Zn) atoms are ordered to Wyckoff 2a, Sn is ordered to 2b (Hall et al. 1978). For comparison, the I4 symmetry has Cu atoms ordered to two sites: 2a and 2c, (Zn,Fe) ordered to 2d, Sn ordered to 2b (Hall et al. 1978). As pointed out by Hall et al. (1978), two distinct metal layers perpendicular to [001] result from this ordering in each mineral. Stannite exhibits one layer of Cu atoms only, with the other layer consisting of ordered Fe and Sn atoms, while kësterite exhibits one layer of ordered Cu and Sn atoms and one layer of ordered Zn and Cu atoms (Hall et al. 1978). This is illustrated for pirquitasite versus stannite in Fig. 1, which shows the pirquitasite structure ( Fig.   1a) with one layer containing ordered Ag and Sn, the second containing ordered Zn and Ag. For comparison, the two stannite metal layers consist of one layer of Fe and Sn atoms and a second layer containing only Cu atoms (Fig. 1 b). The The mineral hocartite (tetragonal Ag 2 FeSnS 4 ) is reported to exhibit space group I42m (Johan and Picot, 1982), but its structure is as yet unreported. It is likely that the hocartite-pirquitasite series follows the same systematics as the stannitekësterite series.

Ag-Sn layers in pirquitasite and
An interesting feature is the distortion displayed by the AgS 4 tetrahedra, with tetrahedral angle variance of 8.86° displayed by Ag1S 4 and 25.40° displayed by Ag2S 4 . M-S bond lengths are 2.539 Å and 2.497 Å for the Ag1S 4 and Ag2S 4 tetrahedra, respectively. As our sample contains approximately 13% apfu Cu, this Cu appears to be located in the Ag2 site because the bond lengths are smaller and the tetrahedron can accomodate the distortion. Bond valence calculations gave sums of 1.28 valence units (VU) and 1.35 VU for Ag1 and Ag2, respectively, corroborating that Cu is ordered to the Ag2 site. In a study of the mechanism of incorporation of Cu, Fe, and Zn in the stannite-kësterite series, Bonazzi et al. (2003) studied synthetic crystals, quenched from 1023 Kelvin, of composition Cu 2 Fe 1-X Zn X S 4 (X = 0, 1/5, 1/2, 0.7, 0.8, 1), which showed decreasing tetrahedral angle distortion with increasing Zn content across the stannite-kësterite compositions.

Experimental
The pirquitasite specimen used in this study comes from the type locality, the Pirquitas deposit, Jujuy Province, Argentina and is in the collection of the RRUFF project (http://rruff.info/R061016). The chemical composition, (Ag 1.87 Cu 0.13 ) (Zn 0.61 Fe 0.36 Cd 0.03 )SnS 4 , was determined with a CAMECA SX100 electron microprobe. The composition was normalized to four cations.

Special details
Geometry. All e.s.d.'s (except the e.s.d. in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell e.s.d.'s are taken into account individually in the estimation of e.s.d.'s in distances, angles and torsion angles; correlations between e.s.d.'s in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell e.s.d.'s is used for estimating e.s.d.'s involving l.s. planes. Refinement. Refinement of F 2 against ALL reflections. The weighted R-factor wR and goodness of fit S are based on F 2 , conventional R-factors R are based on F, with F set to zero for negative F 2 . The threshold expression of F 2 > σ(F 2 ) is used only for calculating R-factors(gt) etc. and is not relevant to the choice of reflections for refinement. R-factors based on F 2 are statistically about twice as large as those based on F, and R-factors based on ALL data will be even larger.  (3)