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Crystal Chemistry of Tetrahedrite

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Crystal Chemistry of Tetrahedrite American Mineralogist, Volume 73, pages 389-397, 1988 Crystal chemistry of tetrahedrite N. E. JonNSoN, J. R. Cnq'Ic, J. D.Rrmsrror Department of Geological Sciences,Virginia Polytechnic Institute and State University, Blacksburg,Virginia 24061, U.S.A. AssrRAcr The crystal chemistry of tetrahedrite can be rationalized by considering the structure, commonly written asr"M(l)uIIIM(2)6ftrXI"Y3l4"'Z[where M(l) : Cu, Fe, Zn,Mn, Hg, Cd; M(2) : Cu, Ag; X : Sb, As, Bi, Te; Y and Z : S, Sel, to be generallyanalogous to sodalite, i.e., a framework of corner-connectedM(l)Y" tetrahedra forming a seriesof cavities that contain ZM(2)6 octahedra rather than an interframework cation or anion as in sodalite. Adaptation of modeling techniques originally applied to sodalite-group minerals allows for the interpretation ofthe structural effectsofcomposition on tetrahedrite that has been previously hindered by the lack ofstructural studies. Framework rotation (@)is causedby the rotation of the framework tetrahedra about their 4 axes and is increased by increasesin the M(IFY and X-Y bond lengths, but decreasedby increasesin the spinner-bladelength. Distortion of framework tetrahedra is negligibly affectedby the M(l)-Y bond length and greatly afected by the X-Y bond length. Increasesin the spinner-bladelength causethe distortion to decrease,then increase,im- plying a state of no distortion to the framework polyhedra at particular values of the spinner-bladelength and @. Becausethe structural effectsof temperature, pressure,and composition are somewhat analogousin minerals, these results indicate that natural tetrahedrite composition may provide some indication of the thermal and baric conditions at the time of formation. tures previously considered complex, including tetrahe- INrnooucrroN drite, could be related quite easily to the well-understood Tetrahedrite, the most common representativeof the silicate-frameworkstructure of sodalite(Hellner and Koch, sulficsaltgroup. is a frequentminor constituentin many 1981;Koch and Hellner,l98l;Nyman and Hyde, 1981). types of ore deposits worldwide and often carries signif- However, no studies have appearedextending this con- icant amounts of Ag. Becausewell-developed crystals are cept and adapting researchon silicate-framework struc- not uncommon, it was among the first minerals to be tures to nonsilicate frameworks. Tetrahedrite is uniquely examined as the scienceof crystal-structureanalysis de- suited for such an approach, becauseit acceptsa latge veloped. rangeof substitutions(Johnson et al., 1986)without se- Initial solution of the tetrahedrite structure was by Ma- riously distorting the structure; thus it has been referred chatschki(1928a, 1928b) who noted a marked similarity to as a "sulfide amphibole" (Sackand Loucks, 1985). of the tetrahedrite and sphalerite powder patterns. Fol- The concept of tetrahedrite as a framework analogous lowing this, Pauling and Neumann (193a) solved the to sodalite is not altogether new. Belov and Pobedim- structure by using Laue and oscillation photographsand skaya (1969) clearly referred to this but attributed the described a complicated relationship between the tetra- original insight to Pauling, following his solutions of the hedrite and sphalerite structures.This interpretation led sodalite and tetrahedrite structures(Pauling, 1930; Paul- to the description of the tetrahedrite structure as a "com- ing and Neumann, 1934).However, as noted by Nyman plex defect derivative" of the sphalerite structure (Ross, and Hyde (1981),no mention of this relationshipcan be 1957).Despite the results and discussionsof Wuensch found in either of the two studies by Pauling' (Wuensch,1964; Wuensch et al., 1966), which clearly The purpose ofthis paper is to clearly define how tet- indicate that this is at best misleading, the sphaleritede- rahedrite is based on a framework of corner-connected rivative view is still prevalent in current mineralogical tetrahedra and to apply the crystallochemicaltechniques literature (Wuensch,1974; Johnson, 1982; Pattrick and developed for sodalite to model the structural effectsof Hall, 1983). the observed compositional variations. For consistency Recent researchinto the theoretical geometriesof crys- with previouswork on the subject(Johnson et al., 1986, tal structures(Smith and Bennett, 1981, 1984; Haw- 1987), the following structural formula will be used: thorne, 1983)have begunto make senseout ofthe enor- 'uM(1)uu'M(2)u["'X'"Yr]ou'2,where M(l) : C.u,Fe, Zn, mous array of mineral and intermetallic structures.One Mn, Hg, and Cd, M(2) : Cu and Ag, X : Sb, As, Bi, and suchline of inquiry led to the realization that many struc- Te, and Y andZ: S and Se. 0003-004x/88/0304-o389$02.00 389 390 JOHNSON ET AL.: CRYSTAL CHEMISTRY OF TETRAHEDRITE Fig. 1. Interpretation ofrotation ofcorner-connectedtetrahedral framework: (a) Idealized fully expandedframework. (b) Ideal- ized partially collapsedframework. THB srnucruRE oF TETRAHEDRITE rotate, the symmetry decreasesto 143m. Figure 2 dem- Framework of M(l)Y. tetrahedra onstrateshow the degreeofrotation can be quantified, as the angle is calculated directly from the fractional co- Figure l, modified from Taylor (1972), displays the @ ordinates of the tetrahedral corners. This approach fol- relationship between two types of corner-connectedtet- lows that of Nyrman and Hyde (1981), who tabulated rahedral frameworks. In Figure la, the framework tetra- rotations for severalcompounds, including tetrahedrite. hedra are all oriented so that the tetrahedraledges normal They found that intermetallic compounds tend toward to the 4 axes are at right anglesrelative to one another smallrotations (< 15"),silicate minerals toward moderate and to the unit-cell dimensions.In this orientation,the rotations (10-30), and sulfidestoward large rotations cavity createdby the framework has the maximum vol- (>45'). ume possible, and the framework is referred to as fully Figure 3 consists of two views of a fully expanded expanded.Figure lb showsthe sameframework, but with framework, and two views of a framework rotated 50', the tetrahedrarotated away from the ideal positions. The which is approximately the amount of rotation for tetra- net result ofthis rotation is to decreasethe unit-cell size hedrite and other minerals of the tetrahedrite series.The and shrink the framework cavity; this orientation is re- most obvious differencebetween the two can be found in ferred to as a collapsedframework. The symmetry of the the linked six-membered rings of the framework. In the ideal expandedframework is Im3m, but as the tetrahedra ideal case,these rings are hexagonal,but for tetrahedrite, the hexagonhas collapsedto a triangular shape. Cavity polyhedron The geometry as well as the size of the cavity formed by the framework changeswith the angle of rotation. Connectingthe framework Y atoms inside the cavity pro- duces an imaginary Archimedian semiregular polyhe- dron; for the expandedframework, this polyhedron takes the shapeofa truncated octahedron(Fig. 4a), whereasfor Tetrahedroncenter : 1140 112 Tetrahedroncenter : 1t4 O 1lz a framework rotated 45', the polyhedron is a truncated Telrahedroncorner:x x'l/2 TetEhedroncomer:x x1l2-z tetrahedron(Fig. ab) (Nyman and Hyde, 1981).The trun- cated tetrahedron is also referred to as a Laves poly- ,.- _/1 | hedron (Belov and Pobedimskaya,1969). /^-tl l1t2.z Unlike sodaliteor galkhaite,the tetrahedritecavity does not contain a singlelarge anion, but insteadhosts a ZM(2)u ranl=(12-zllx octahedron.The M(2) cationsare also bondedto two of S = tanr ((1/2- z) / x) the framework Y anions, forming a triangular "spinner Fig. 2. Schematicdrawing showing how the framework ro- blade" as describedby Wuensch(1964). Y anionsat the tation angle@ is related to the translation ofthe tetrahedralcor- adjacent corners of these blades describe the truncated ner (Y) anions. corners ofthe Laves polyhedron (Fig. 5). JOHNSON ET AL.: CRYSTAL CHEMISTRY OF TETRAHEDRITE 391 Fig. 3. Crystal-structuredrawings ofcorner-connectedtetrahedral frameworks: (a) Ideal expanded,viewing direction slightly otr (100).(b) Tetrahedrite,slightly off(100). (c) Ideal expanded,slightly off(111). (d) Tetrahedrite,slightly otr(111). XY, pyramid extend away from the framework toward the hexagonal cav- A Group VA metal pyramid is one of the characteristic facesofLaves polyhedra contained within adjacent structuralattributes of sulfosaltminerals (Nowacki, 1969). rtles. In tetrahedrite, the semimetal is bonded to the three ad- MoDEL jacent Y anionsofthe Lavespolyhedron, forming a py- Trrn rrrn.lrtEDRITE ramidal cap that sits upon the truncated corner (Fig. 5). Severalstudies have modeled the sodalite structure in All four of these corners are so occupied, and the pyra- order to interpret the effects of thermal expansion and mids extend out of the six-memberedrings of the frame- compositional variation on the framework of silicate and work (Fig. 6). Lone pairs of the semimetal atoms then aluminate tetrahedra. Taylor and Henderson (1978), 392 JOHNSON ET AL.: CRYSTAL CHEMISTRY OF TETRAHEDRITE a Fig. 4. Internal Archimedian semiregularpolyhedra formed by the cavities of frameworks: (a) Truncated octahedronin frame- works rotated less than 45'. (b) Truncated tetrahedron, also referred to as a Laves polyhedron, in frameworks rotated more than 45.. Dempseyand Taylor (1980), and Beagleyet al. (1982) tance connecting the Laves polyhedron and the frame- have all used iterative computer proceduresto model the work [M(2fY]; and the semimetal-Y anion distance(X- framework,whereas
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