Preferred Ion Diffusion Pathways and Activation Energies for Ag in the Crystal Structure of Stephanite, Ag5sbs4
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Mineralogical Magazine, February 2009, Vol. 73(1), pp. 17–26 Preferred ion diffusion pathways and activation energies for Ag in the crystal structure of stephanite, Ag5SbS4 1,2 2 3, M. LEITL ,A.PFITZNER AND L. BINDI * 1BASF Construction Chemicals GmbH, Dr.-Albert-Frank-Straße 32, D-83308 Trostberg, Germany 2Institut fu¨r Anorganische Chemie, Universita¨t Regensburg, Universita¨tsstrasse 31, D-93040, Regensburg, Germany 3Museo di Storia Naturale, Sezione di Mineralogia, Universita` degli Studi di Firenze, Via La Pira, 4, I-50121, Firenze, Italy [Received 21 January 2009; Accepted 26 March 2009] ABSTRACT The crystal structure of stephanite fromthe type locality, Freiberg District, Saxony, Germany,was refined in the space group Cmc21, up to a final R index of 0.0427. Unit-cell parameters are: a 7.8329(6) A˚ , b 12.458(1) A˚ , c 8.5272(7) A˚ , V 832.1(1) A˚ 3; Z = 4. The previously reported structural model is confirmed, but a higher-precision refinement was achieved herein by the introduction of third- order non-harmonic Gram-Charlier tensors for one Ag atom. In the structure of stephanite, Sb forms isolated SbS3 pyramids, which typically occur in sulphosalts, and Ag occupies sites with coordination ranging fromtriangular to almosttetrahedral. Both the Sb ÀS and AgÀS bond distances closely match the values commonly observed in the structures of other Ag sulphosalts and sulphides. The use of non-harmonic parameters for Ag allowed a better description of the electron density related to Ag, which is usually difficult to refine in good ionic conductors. A careful analysis of the energy barriers between the Ag sites defines preferred ion-diffusion pathways within the crystal structure of stephanite. The diffusion of Ag ions occurs preferentially along the sites Ag1 and Ag2, giving rise to two-dimensional nets of Ag atoms in which the ion conduction probably takes place. KEYWORDS: stephanite, crystal-structure refinement, non-harmonic approach, Ag, diffusion pathway, ionic conductivity. Introduction 1994; Gaudin et al., 1997) and ion-conducting BINDI and Evain (2007) showed that the non- phases (Kuhs and Heger, 1979; Boucher et al., harmonic approach, based upon a Gram-Charlier 1992, 1993; Haile et al., 1997; Evain et al., 1998; development of the atomic displacement factors, Haile and Wuensch, 2000a,b,c). Recently, it has can be useful in mineral sciences for the been used to solve complex structures of natural determination of unknown structures. Such an and synthetic sulphosalts and the pearceite- approach is used to refine already known polybasite mineral family: (Evain et al., structures with suspiciously high R values and/ 2006a,b; Bindi et al., 2006a,b, 2007); fettelite, or high isotropic displacement parameters for Ag (Bindi et al., 2009); synthetic skinnerite, (Pfitzner, or Cu atoms. The non-harmonic approach has 1998); synthetic tetrahedrite, (Pfitzner et al., been used successfully over the past twenty years 1997). to solve numerous structures of non-conducting We have reinvestigated the crystal structure of materials (van der Lee et al., 1993; Boucher et al., stephanite, Ag5SbS4, which was determined previously by Riba´r and Nowacki (1970) in the space group Cmc21. Although their structural model is correct, Riba´r and Nowacki reported an * E-mail: [email protected] R value of 9.4% (photographic methods) and Biso DOI: 10.1180/minmag.2009.073.1.17 values of 3.82, 4.49 and 3.33 A˚ 2 for the Ag1, Ag2 # 2009 The Mineralogical Society M. LEITL ET AL. and Ag3 positions, respectively (approximately Starting with the model obtained for the up to three times the values observed for Sb and structure of stephanite by Riba´r and Nowacki for the S atoms). The non-harmonic approach, (1970), the refinement in the Cmc21 space group based upon a Gram-Charlier development of the smoothly converged to a residual R = 0.0538 value atomic displacement factors, has been applied for 998 reflections [I >3s(I)] and 62 parameters. here to determine whether or not the crystal- To mimic the spread of electrons associated with structure refinement previously reported by Riba´r Ag along diffusion paths, third-order non- and Nowacki (1970) can be improved upon and to harmonic Gram-Charlier tensors for the Ag2 provide information on the diffusion pathways of atomwere used for the Debye-Waller description Ag, which are related to the fast ion conduction (Johnson and Levy, 1974; Kuhs, 1984). All character of stephanite. stephanite crystals are systematically twinned on {110}, which are repeated to formpseudo- hexagonal groups (e.g. Gaines et al., 1997). A X-ray crystallography and crystal-structure schematic visualization of this partially mero- ref|nement hedric twinning is given in Fig. 1. For the The two samples containing the stephanite refinement, the twin matrix |0.43 1.43 0/0.56 crystals that were used in the present study À0.43 0/0 0 À1| was used. The refinement showed (sample STP_01: Museo di Storia Naturale, that the ratio of the second twin domain was only Sezione di Mineralogia, Universita` di Firenze, 9%. This small twin fraction is one of the reasons Italy – catalogue number 2363/G; sample for the good quality of the X-ray diffraction data STP_02: Mineralogische Staatssammlung, set and the successful absorption correction, which Mu¨nchen, Germany – catalogue number 51164) is usually critical in the case of twinned crystals. are fromFreiberg, Saxony, Germany,a well At the last stage, the residual value settled at R = known source of Ag-bearing minerals. In both 0.0427 for 998 independent observed reflections samples, stephanite occurs as black anhedral to [3s(I) level] and 62 parameters, and at R = 0.0466 subhedral grains up to 400 mmlong and shows a for all 1041 independent reflections. grey-black to black streak. The other mineral spatially associated with stephanite is calcite. The crystal STP_01 was analysed by means of an Oxford Diffraction Xcalibur 3 diffractometer (Mo-Ka radiation, l = 0.71073 A˚ ) fitted with a Sapphire 2 CCD detector, whereas STP_02 was analysed using a STOE-IPDS diffractometer using graphite-monochromatized Mo-Ka radia- tion. Nearly identical unit-cell dimensions were found for the two crystals investigated. For this reason, crystal STP_02, which displayed a better diffraction quality, was chosen for subsequent studies. In anticipation of the presence of possible twinning, which is common in stephanite, special care was taken on the choice of the fraction of reciprocal space covered. A relatively high sin(y)/ l cut off and a high redundancy were chosen in the recording setting design. Intensity integration and standard Lorentz-polarization correction were performed with the X-RED programpackage (Stoe and Cie, 1997). Subsequent calculations were conducted with the Jana2000 programsuite (Petrˇ´cıˇek et al., 2000), except for the optimization of the crystal shape and dimension, which were performed with X-shape (Stoe and Cie, 1997), FIG. 1. Schematic visualization in the reciprocal space of based on the Habitus program(Herrendorf, 1993). the twinning of stephanite. The twin parts are indexed by Full-matrix refinements were carried out on F2, 1 and 2. The discontinuous line shows the twinning with all reflections included. plane. 18 DIFFUSION PATHWAYS FOR AG IN THE STRUCTURE OF STEPHANITE Crystal characteristics, data collection and crystal fragments used for the structural study, did reduction parameters, and refinement results are not indicate the presence of elements (Z > 9) other given in Table 1. Atomic parameters are reported in than Ag, Sb and S. Since the unit-cell parameters Tables 2, 3 and 4, whereas structure factors of the two crystals were nearly identical, the (Table 5) have been deposited with the Principal chemical composition was then determined on the Editor of Mineralogical Magazine and are available sample STP_01, which is the larger and better fromwww.minersoc.org/pages/e_journals/ polished crystal, using wavelength dispersive dep_mat_mm.html. analysis (WDS) by means of a Jeol JXA-8600 electron microprobe. Major and minor elements were determined at an accelerating voltage of Chemical composition 20 kV and a probe current of 40 nA, for 30 s A preliminary chemical analysis using energy count time. The following X-ray lines were used dispersive spectrometry, performed on the same for the WDS analyses: Ag-La, Sb-Lb, and S-Ka. TABLE 1. Crystallographic data and experimental details for STP_02. Molar (mass/gmolÀ1) 789.1 Crystal colour Grey Crystal systemOrthorhombic Space group Cmc21 (Nr. 36) Lattice parameters a (A˚ ) 7.8329(6) b (A˚ ) 12.458(1) c (A˚ ) 8.5272(7) Volume (A˚ 3) 832.1(1) Z 4 À3 rcalc (g cm ) 6.3 Diffractometer STOE-IPDS Radiation Mo-Ka, l =0.71073 A˚ Monochromator Graphite crystal Angles (º), Dj (º) 0.0À280.5, 1.5 Absorption correction numeric, X-RED and X-SHAPE (Stoe and Cie, 1997) m(Mo) (mmÀ1) 15.65 Temperature (K) 293 2y range (º) 3.8 À 56.3 hkl range À10 4 h 4 10; À16 4 k 4 16; À11 4 l 4 11 Number of reflections 5362 Independent reflections 1041 Independent reflections [I >3s(I)] 998 Rs 0.0344 Rint 0.0632 Refinement Full-matrix least-squares on F2 Software Jana2000 (Petrˇ´cıˇek et al., 2000) Weighting scheme s, 0.03 Extinction coefficient 0.068(6) (Becker and Coppens, 1974) R1 [I >3s(I)] 0.0427 wR2[I >3s(I)] 0.1106 R1 (all) 0.0466 wR2 (all) 0.1125 Refined parameters 62 Goodness of Fit [I >3s(I)] 1.53 Goodness of Fit (all) 1.54 Twin ratio 0.91(1):0.09(1) ˚ À3 rmax (eA ) 2.24 ˚ À3 rmin (eA ) À1.64 19 M. LEITL ET AL. ˚ 2 TABLE 2. Wyckoff positions, atomic coordinates and isotropic displacement parameters Ueq (A ) for STP_02.