American Mineralogist, Volume 96, pages 1686–1702, 2011 The crystal structure of franckeite, Pb21.7Sn9.3Fe4.0Sb8.1S56.9 E. MAKOVICKY,1,* V. Petříček,2 M. DušEK,2 AND D. TOPA3 1Department of Geography and Geology, University of Copenhagen, Østervoldgade 10, DK1350 Copenhagen, Denmark 2Institute of Physics, Czech Academy of Sciences, Na Slovance 2, CZ-18040 Prague 8, Czech Republic 3Department of Material Research and Physics, University of Salzburg, Hellbrunnerstrasse 34, A-5020 Salzburg, Austria ABSTRACT The layer-like crystal structure of franckeite from the mine of San José, Bolivia, exhibits a pro- nounced one-dimensional transversal wave-like modulation and a non-commensurate layer match in two dimensions. It consists of alternating pseudohexagonal (H) layers and pseudotetragonal (Q) slabs and forms a homologous pair with cylindrite, which has thinner Q slabs. The Q slabs in franckeite are four atomic layers thick. The two components have their own lattices and a common modulation. The 2+ 2+ Q slab of the refined franckeite structure, Pb21.74Sn9.34Fe3.95Sb8.08S56.87, is an MS layer (M = Pb , Sn , Sb3+) four atomic planes thick, with a = 5.805(8), b = 5.856(16) Å, and the layer-stacking vector c = 17.338(5) Å. The lattice angles are α = 94.97(2)°, β = 88.45(2)°, γ = 89.94(2)°; the modulation vector q = –0.00129(8) a* + 0.128436(10) b* – 0.0299(3) c*. The H layer is a single-octahedron MS2 layer (M = Sn4+, Fe2+) with a = 3.665(8), b = 6.2575(16), c = 17.419(5) Å, α = 95.25(2)°, β = 95.45(2)°, γ = 89.97(2)°; the modulation vector is q = –0.00087(8) a* + 0.13725(16) b* – 0.0314(4) c*. The a and b vectors of both subsystems are parallel; the c vectors diverge. (3+2)D superspace refinement was performed in the superspace group C1, using 7397 observed reflections. It resulted in the overall R(obs) value equal to 0.094. The Q slabs are composed of two tightly bonded double-layers, separated by an interspace hosting non-bonding electron pairs. Average composition of cations on the outer surface was refined as Pb0.74(Sn,Sb)0.26, whereas that of cations, which are adjacent to the interspace with lone electron pairs, with a configuration analogous to that observed in orthorhombic SnS, corresponds to 4+ (Sn,Sb)0.73Pb0.27. Iron is dispersed over the octahedral Sn sites in the H layer. Transversal modula- tion of the Q slab is achieved by local variations in the Pb:(Sn,Sb) ratios at its surface and interior. Its purpose is to re-establish a one-dimensional commensurate contact along [010] between the curved Q and H surfaces to the greatest extent possible. Layer-stacking disorder and divergence of the Q and H stacking directions, and the divergence between modulation wave-front and these stacking directions are typical for the composite structures of franckeite and cylindrite. Because of the increased rigidity of the Q component, franckeite usually forms masses of curved crystals rather than cylindrical ag- gregates. The existence of this family depends critically on the radius ratios of the cations involved, especially those involving (Pb2+, Sn2+) and Sn4+. Their replacement by a Pb2+:Bi3+ combination leads to misfit layer structures of a very different type, typified by cannizzarite. Keywords: Franckeite, Pb-Sn-Sb-Fe sulfide, modulated layer-misfit crystal structure, 2D–non- commensurate layer structure, San José, Bolivia INTRODUCTION AND HISTORY OF INVESTIGATION a Patterson function of franckeite but the work apparently did Franckeite is a complex sulfide of Pb, Sn2+, Sn4+, Sb, and Fe, not proceed any further. Extensive HRTEM and electron diffrac- described first by Stelzner (1893) from Bolivia. Until the 1970s it tion study of franckeite was performed by Williams and Hyde aroused little attention, mostly of field mineralogists (Bonshtedt- (1988) and Williams (1989). Models of the crystal structure of Kupletskaya and Chukhrov 1960), but after the interesting results franckeite in a projection along the non-modulated direction of a of studies on related cylindrite (Makovicky 1970, 1974; Mozgova layer were constructed using the HRTEM data by these authors et al. 1975) became known, attention was directed to franckeite as and by Wang (1989) and Wang and Kuo (1991). A STM study well. X-ray crystallography of Sn-rich franckeite was described of a cleavage surface of franckeite was performed by Ma et al. by Makovicky (1976), whereas that of Pb-rich franckeite by (1997), whereas Henriksen et al. (2002) made a detailed study Wolf et al. (1981). They were described under the names incaite by STM and AFM. The classical chemical analyses of franckeite and potosiite, respectively. Li (1990) quotes additional crystal- were summarized by Bonshtedt-Kupletskaya and Chukhrov lographic studies by Wang (1989); these data are summarized by (1960). Further contributions to the chemistry of franckeite were Makovicky and Hyde (1992). Organova et al. (1980) published made by Makovicky (1974), Wolf et al. (1981), Williams (1989), and especially by Mozgova et al. (1975) and Bernhardt (1984), using electron microprobe. Synthetic studies performed by Li * E-mail: [email protected] (1984) confirmed the idea, derived from chemical analyses, that 0003-004X/11/1112–1686$05.00/DOI: 10.2138/am.2011.3814 1686 MAKOVICKY ET AL.: CRYSTAL STRUCTURE OF FRANCKEITE 1687 franckeite is a broad solid-solution series with an extensive Pb et al. (1975), was not pursued further. Trying to reconcile the for Sn2+ substitution. crystallographic and electron microprobe data Makovicky (1976) Franckeite is a natural layer-misfit structure with two-dimen- and Makovicky and Hyde (1981) suggested that the Q slabs in sional non-commensurability of component layers, the second incaite might have layer thickness 1.5 times that of cylindrite. such structure after cylindrite. The purpose of the current study is to Organova et al. (1980) performed a partial crystal structure determine and refine the crystal structure of franckeite from X-ray determination on franckeite from Huanuni, Bolivia. Based on diffraction data by means of superspace refinement as a clue to its the published Patterson synthesis, they suggested that franckeite remarkable properties and highly variable crystal chemistry. (layer stacking period equal to 17.4–17.7 Å) has four atomic lay- ers thick pseudotetragonal slabs as the principal difference from PREVIOUS CRYSTALLOGRAPHIC STUDIES cylindrite, which has two atomic layers thick Q slabs according In the first single-crystal diffraction experiment on franckeite, to Makovicky (1974). They suggested that incaite should have Coulon et al. (1961) found only one component [the pseudote- the same structure. At least a partial structure study was neces- tragonal component of Makovicky (1974)], and they determined sary because, as demonstrated by Williams and Hyde (1988), the the monoclinic unit-cell parameters a = 5.82(4), b = 8 × 5.86(1), four-layer model cannot be selected from among other possible c = 17.3(5) Å, and β = 94.66(25)° (in the orientation used in this models based on purely metric differences of franckeite and paper). Makovicky (1974) stated that “incaite”, a Sn-rich vari- cylindrite. As for the problem of incaite, we can suggest that ety of franckeite, shows similar diffraction and compositional the original electron microprobe data obtained by Makovicky features (Table 1) as cylindrite, i.e., two component lattices (1974) from thin replacement shells of “incaite” in the cylinders described as a pseudotetragonal (T, later altered to Q) and a of cylindrite might have been influenced by remnants of original pseudohexagonal (H) component lattice. It has a longer layer- cylindrite in these shells although none were detected by X-ray stacking c vector (our orientation) than cylindrite (17.29 Å for diffraction or, alternatively, the early electron-microprobe cor- the Q component compared to 11.73 Å of cylindrite), which rection programs had problems with compositions combining indicates thicker Q slabs. Makovicky’s remark that the major- heavy and light elements. ity of franckeites show d001 spacing (our orientation) of ∼17.3 The interpretation based on two component lattices became Å, based especially on the powder diffraction data of Mozgova standard in all subsequent works on franckeite, and they were TABLE.1 Selection of published unit-cell data for franckeite Compound Q component H component Coincidence data Reference “Incaite” a = 5.79 Å a = 3.66 Å along [010] Makovicky (1976) FePb3.3Ag0.3Sn3.6Sb2S13 b = 5.83 Å b = 6.35 Å 2 × 34.98 ÅQ with c = 17.29 Å c = 17.25 Å 69.85 ÅH α = 94.14o α = 91.13o 12Q:11H β = 90o β = 90o γ = 90o γ = 90o A2, Am, or A2/m A2, Am, or A2/m “Potosiite” a = 5.84 Å a = 3.70 Å along [010] Wolf et al. (1981) Pb24.0Ag0.2Sn8.8Sb7.8Fe3.7S55.6 b = 5.88 Å b = 6.26 Å 188.06 Å c = 17.28 Å c = 17.28 Å about 32Q:30H α = 92.2o α = 92.2o β = 90o β = 90o γ = 90° γ = 90° A1 or A1 A1 or A1 Franckeite (natural) a = 5.84 Å a = 3.68 Å 16Q:15H Wang (1989) b = 5.90 Å b = 6.32 Å c = 17.3 Å c = 17.3 Å α = 95o α = 96o β = 88o β = 88o γ = 91° γ = 91° Franckeite (natural) a = 5.82 Å a = 3.62 Å 16Q:15H Wang (1988) b = 5.92 Å b = 6.30 Å c = 17.5 Å c = 17.5 Å α = 95.46o α = 95o β = 91.46o β = 90o γ = 90o γ = 90° A-centered A-centered Franckeite a = 5.815 Å a = 3.672 Å along [010] present work b = 5.873 Å b = 6.275 Å modulation 45.80 Å c = 17.366 Å c = 17.447 Å match α = 94.98 Å α = 95.26o 15.5Q:14.5H β = 88.43o β = 95.45o at 91.1 Å γ = 89.97o γ = 89.97o A-centered A-centered Coiraite a = 5.862 Å a = 3.660 Å 14Q:13H Paar et al.