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 Hassan and Grundy (1984)chose a Y). Shannon(1981) provides sulfidecrystal radii for some simple geometric model. As noted by the latter authors, of these,but not for a semimetal in a trigonal pyramidal the two approachesare essentiallyequivalent in their re- coordination or for metals in planar threefold coordina- sults. tion. Radii for these atoms were obtained by selecting The few data available for tetrahedrite make interpre- data from Edenharter (1976) that fit the above coordi- tation of the structural effects of composition difficult. nation restraints. The radii used in the modeling are list- Hence at present, modeling ofers the only means of de- ed in Table 1. termining the effects of composition in tetrahedrite. One of the assumptionsmade in using crystal radii in Therefore, it was decided to follow the approach of Has- this manner is that the atoms act as spheres.However, san and Grundy (1984) and to derive a geometric model Figure 7a shows that the lengths of the M(2)-Z and the for tetrahedrite. M(2)-Y bonds in tetrahedrite diverge as the Ag content For the sodalite model, two piecesof information are increases,indicating that threefold Ag is distinctly required: the T-O distance for the framework tetrahedra aspherical relative to threefold Cu. To improve the ac- and either the unit-cell dimension or the O-O distance curacy of the model, it was decided to use two radii for for the framework tetrahedra. In silicate and aluminosil- Ag. Becauseof this, neither the M(2):Z or the M(2fY icate frameworks, both the T-O and the O-O distances bond lengthsalone are adequatefor gagingthe expansion are reasonablyconstant for a given composition and can or contraction of the structure. As shown in Figure 7b, be predicted from the Shannonand Prewitt (1969) crystal the length of the spinner blade, measured from the Z radii. In the frameworks of tetrahedrite and the tetrahe- anion through the M(2) cation to a point midway between drite-series minerals, however, although the M-Y dis- the two Y anions, increaseslinearly as a function of Ag tance can be consideredconstant, the Y-Y distancecan- content and combines both the M(ZYZ and the M(2FY not. Therefore, for a tetrahedrite model, the unit-cell bonds. The calculated spinner-blade length is therefore dimension is required; for most compositions, this value used in place of either the M(2)-Z or the M(2)-Y bond can be predictedaccurately (Johnson et a1., 1987),and Iengths. for other compositions, a cell edge can be reasonably The high symmetry of tetrahedrite and the small num- closely interpolated from existing data. Furthermore, the ber of atoms in the asymmetric unit produce the result model is sufficiently insensitive to cell-edgevariations so that all the atoms lie on specialpositions in the structure. that errors in a predicted cell dimension as large as 0.05 Of l5 fractional coordinatesfor all the atoms in the asym- A do not adverselyaffect the results. metric unit, there are only four independent variables, Tetrahedritehas one more atom in the asymmetric unit which results in a systemoffour equations (one for each than does sodalite; hence it is necessaryto predict four of the bond lengths listed above) and four unknowns. bond lengths: the metal-Y anion distance in the frame- Therefore, a model structure can be calculatedgiven the work tetrahedra [M(lfY]; the metal-Z anion distancein unit-cell dimension and four predictedbond lengths.Once the Laves polyhedron I]0|4Q)a\ the metal-Y anion dis- the fractional coordinateshave been determined, the ro- JOHNSON ET AL.: CRYSTAL CHEMISTRY OF TETRAHEDRITE 393

Fig. 5. Internalstructure of tetrahedriteframework cavity. The centralZ anionis bondedto six M(2) cations,which are Fig. 6. One complete framework unit of the tetrahedrite thenbonded to theframework Y anions.XY, pyramidssit upon structure. the truncatedcorners (after Wuensch, 1964). tation angle d can be calculated,along with the amount pands, thereby decreasingthe amount ofrotation by ex- of tetragonal distortion of the framework tetrahedra rel- panding the framework from inside. This expansion is ative to ideal tetrahedra(Depmeier, 1984). much more pronounced than the contraction discussed The accuracyofthis approachwas testedby calculating above, and thesetwo effectsmay be usedto explain some the fractional coordinates,O, and tetragonaldistortion for natural compositional variations. In As-rich tetrahedrite, those tetrahedrite-seriesminerals whose structures have the framework is small and therefore expanded,so that been previously determined(Wuensch, 1964; Wuensch a large increasein the spinner-bladelength that would be et aI., 1966; Kalbskopf, 1972, 1974; Makovicky and needed to accommodate Ag substitution would expand Skinner, 1979; Kaplunnik et al., 1980; Johnson and the framework beyond its range of stability. Hence, As Burnham, 1985; Petersonand Miller, 1986). With the and Ag substitutions should generallybe mutually exclu- exception of those structures containing significant va- sive, which is in fact observedin natural minerals (John- cancies(Kalbskopf, 1974;Makovicky and Skinner, 1979), sonet al.. 1986). diferences betweenpredicted and actual valueswere less There are two corollaries to this idea: (l) according to than 4o/o. the modeled results, the effectsof Ag and Bi substitution on the tetrahedrite framework are similar in magnitude Rnsur,rs and direction and could possibly tend to offseteach other The results of the modeling for varying compositions and allow for greater mutual substitution than otherwise of tetrahedrite are found in Figures 8 and 9, which are possible and (2) there should be a critical angle for a plots of bond length versusframework rotation or percent framework of a given size, beyond which a framework distortion from ideality. Each point representsa specific structure is no longer the most stableconfiguration. Both composition, following the general formula for tetrahe- ofthese points are discussedfurther below. drite (Johnsonet al., 1986).As seenin Figure 8a, the effecton the framework of increasingthe M(l)-Y and the X-Y bond lengths is an increasein the rotation. The in- TABLE1. Crystalradii used in modelingequations creaseappears to be a linear function of both the semi- Radius(A) Atom Radius(A) metal radii and the metal radii. These increasesin can @ ,uFe 0 66 rrOu 0 55 be rationalized by considering that the framework in- *Cu 0 635 'Ag- 0.83 creasesin size as the M(IFY and the X-Y bond lengths tvzn 0.64 u'Ag.- 0.62 ,vcd rrAs increase,but the Laves polyhedron 0 84 0.56 does not. A frame- tvHg 0 84 'sb 0 76 work so increasedmust thereforerotate through a greater lvMn 0 725 rBi 0.89 illTe angle@ in order to maintain contact with the unexpanded s 1.70 0.71 Lavespolyhedron. Se 184 ' The opposite effect is displayed in Figure 8b; as the Usedfor M(2)-Y bond .- Usedfor M(2)-Z bond spinner-bladelength increases,the Laves polyhedron ex- 394 JOHNSON ET AL.: CRYSTAL CHEMISTRY OF TETRAHEDRITE

2.5

M2-Y bond

c o) c^ 2.3 €sl M2-Z bond g ! o c (E o dl 50

49 2.1 2.36 238 2.& 0 s 2.32 bond length(A) a) Ag atoms a) M1-Y

.t.0

o -48 5 3.e o o D (E g -o 8m b 3.8 c o. a

42L 3.6 3.7 3.8 4.0 4.1 0123456 b) Spinrcrblade length (A) b) Ag atoms Fig.7. (a)Plot of M(2)-ZandM(2)-Y bondlengths vs. num- Fig. 8. Plotsof frameworkrotation angle @ vs. bondlength: berof Ag atomsin the M(2) site.(b) Plot of spinner-bladelength (a)M(IFY bondlength. (b)M(z)-Z bond length. (equalsM(2)-Z plus [M(2)-Y]cos{/[Y-M(2FYI/ 2]) vs. number of Ag atomsin theM(2) site. respectto ideality, the Bi end-member curve displays an absoluteamount of distortion that is approximately twice Figure 9a displays the distortional effectson the frame- that of the Sb and As curves. This may indicate that a work tetrahedra of increasingthe M(lfY and X-Y bond pure Bi end-member tetrahedrite is not stable, a point lengths. The most distinct feature is that the polyhedral consistent with the absenceof reported natural Bi end- distortion is negligibly affectedby changesin the M(l)- member tetrahedrite(Johnson et al., 1986)and absence Y bond length compared to the effect of changesin the of a synthetic Bi end member (N. E. Johnson, unpub. length ofthe X-Y bond. This appearsto be reasonable, data). If such a Bi-rich tetrahedrite does occur, it may be becausethe position of the Y anion relative to the M(l) due to a stabilizing effect created by the presenceof Ag cation, which is the measure of distortion used here, is as discussedabove. more influencedby the X-Y bond than the M(l)-Y bond. The curves in Figure 9b, rather than trending parallel It should also be noted that whereasthe curves for Sb to the ideal line, intersectit, resulting in compositions for and As end members are approximately symmetric with which the framework tetrahedra show no distortion. This JOHNSON ET AL.: CRYSTAL CHEMISTRY OF TETRAHEDRITE 395

Drscussron The results of the modeling appear to be qualitatively correctfor all compositionsof tetrahedriteattempted, and at least semiquantitatively correct for many as well. The exceptionsto this are the magnitudesof rotation and dis- ?t tortion predicted for Ag-rich tetrahedrites. It seemsun- ;< Exlension likely that rangesof framework rotations greaterthan 10" e0 and polyhedral distortions of nearly 300/o(corresponding I physical o Compression to a changein dimension of a framework tetra- o hedron of I A) are reasonable.Possibilities for thesedis- s u ------crepanciesinclude too large crystal radii being used for Ag or that not all six of the M(2) sites are occupied by Ag. Cu Zn Fe Mn Cd,Hg The estimatesof the Ag radii appear to be reasonable, -10 basedon available data (Edenharter,1976), but as Shan- 2.32 2.36 2.U 2.40 non (1981)noted, sulfosalts,with their irregularcoordi- nation polyhedra, complicate efforts to obtain character- a) M1-Ybond lengh (A) istic metal-sulfur radii. More accurate modeling may simply require more accurateradii. It has recently been suggestedthat Fe andZn may pref- erentially substitute into the M(2) site in Ag-rich tetra- hedrite (Petersonand Miller, 1986)or that Ag may sub- stitute into the M(1) site (Pattrick and Hall, 1983;O'kary and Sack,1987). Attempts to test the first assertionwere Cu€ unsuccessfulas little data exist for the crystal radii of Cu-Se metals in planar threefold coordination, and the uncer- tainty in extrapolating threefold radii from tetrahedral radii masked any differencesin modeled structures.All E structure refinements of Ag-bearing tetrahedrite pub- c lished to date have found that Ag preferentially substi- -ro tutes into the M(2) site. None of thesestudies, however, €o .(, have examined tetrahedrites with greater that approxi- o mately four atoms of Ag per formula unit, the point at which it is suggestedthat tetrahedral Ag becomesimpor- tant (O'Leary and Sack, 1987). Ag is less common in tetrahedral than threefold coordination in sulfosalts,and the tetrahedra are usually highly distorted (Edenharter, -30 L 1976).Models utilizing tetrahedralAg werefound to show 3.6 3.7 3.8 3.9 4.0 4.1 less framework rotation but considerably greater distor- tion than those models with only threefold Ag. b) Spinnerbtade length (A) Taylor (1972) describeda mechanismto explain the Fig. 9. Plotsof frameworkrotation angleQ vs. percentdis- thermal expansion behavior of certain members of the tortionof frameworktetrahedra: (a) M(l)l-Y bondlength. (b) sodalite group. He proposed that the initial effect of in- M(2)J bondlength. creasedtemperature on the framework would be to ex- pand the framework by decreasingthe amount of rota- is consistentwith the above-mentionedconcept of a crit- tion. Once an ideal fully expanded state was achieved, ical angle; if a framework is not stable beyond a certain further thermal expansionwould occur by lengtheningof angle of rotation, then there must be an angle where the the bonds in the structure. A curve of thermal expansion framework has the highest stability, i.e., where the strain versus temperature would therefore contain a disconti- on structural elementsis minimized. The intersectionsof nuity, Zo, the point at which the framework first reached the distortion curves with the zero-distortion line differ the fully expanded state. Subsequentwork (Taylor and dependingon the Group VA metal occupying the X site: Henderson,1978; Hendersonand Taylor, 1978) found For As, the "ideal" spinner-bladelength and 6 are 3.59 such a discontinuity in some sodalite minerals but not in A and 51.1'; for Sb and Bi, the values are 3.76 A and others. This led to an interpretation that the frameworks 49.3'and 3.86 A and 48.0o,respectively. This "ideal" were further constrained by nonframework cations and framework angle should fall approximately halfway be- could expand by rotation to a certain point and no fur- tween a critical angle ofexpansion and a critical angle of ther, which is another approach to the concept that each collapse. framework had a critical value for the angle f. 396 JOHNSON ET AL.: CRYSTAL CHEMISTRY OF TETRAHEDRITE

Hazen (1977) noted that in silicate minerals, the struc- Henderson,CM.B., and Taylor, D (1978) The thermal expansionof tural effectsof changingpressure, temperature, and com- synthetic aluminosilicatesodalites, Ms(.416Si6O,4)Xr Physics and Chemistryof Minerals,2,337-347 position were There have no in- often analogous. been Johnson.M L (1982)The efect ofsubstitutionson the physicalproper- vestigations of the structure of tetrahedrite at pressures tiesof tetrahedritePh D. thesis,Harvard University, Cambridge, Mas- or temperatures above ambient conditions, and only a sachusetts preliminary attempt was made at low temperatures Johnson,M L., and Burnham,C.W (1985)Crystal structure refinement argentian tetrahednte. American Mineralogist, (Johnson,1982). However, it reasonable such of an arsenic-bearing seems that 70,165-170. studies could be successfullyinterpreted by application Johnson,N.E., Craig,J R , and Rimstidt, J.D. (1986)Compositional trends and extensionof the principles outlined here. If the com- in tetrahedrite Canadian Mineralogist, 24, 385-397. position of a tetrahedrite sample representsthe most sta- -(1987) Substitutionaleffects on the cell dimensionof tetrahedrite. -244 ble structural state at the temperature and pressure of CanadianMineralogist, 25, 237 Kalbskopl R (1972) Strukturverfeinerungdes freibergits. Tschermaks formation, and if re-equilibration after changesin tem- Mineralogischeund PetrographischeMitteilungen, I 8, 147-l 55. perature and pressureis sluggish,then the possibility ex- -(1914) Syntheseund Kristallstrukturvon Cu,, ,TeoS,r,dem Tel- ists for the development of a geothermometeror a geo- lur-endglied der Fahlerze Tschermaks Mineralogischeund Petrogra- barometer. phischeMitteilungen, 21, l-10 Pobedimskaya,E A, and Belov, N V (1980)Crystal The one existing low-temperature structure refinement Kaplunnik, L.N., structureof schwatzite(CuooHg,u)CuuSboS,2 Soviet Physics Doklady, (Johnson,1982) indicates that rotation of the framework 25,506-s07 is indeed affected by temperature; consistent with the Koch, E, and Hellner,E. (1981)The frameworksof sodalrte-likestruc- model developedhere, the framework rotation was great- tures and oftetrahedritelike structures.Zeitschrift fiir lcistallographie, er. Studies in the Cu-As-S and Cu-Sb-S systems(Maske t 54,95-t t 4 Machatschki,F. (1928a)Formel und Ikistallstruktur destetraedrites. Norsk and Skinner,1971; Skinner et al., 1972)haveshown that GeologischeTidsskrift, 10,23-32 the thermal stability of tetrahedrite is increasedby As. - (l 928b)Prilzisionsmessungen der Gitterkonslantenverschiedener This is inconsistentwith the model, as substitution of As Fahlerze Formel und struktur derselben Zeitschrift fiir Kristallogra- increasesthe framework rotation, which should then de- phie,68,204-222 B (1979) Studiesof the sulfosaltsof cop- the thermal Although the tetrahedrite Makovicky,E, and Skinner, J crease stability. per VII. Crystalstructures ofthe exsolutionproducts Cu,r3Sb.S13 and model does provide some insight into the effectsof sub- Cu,3rSboS,, of unsubstituted synthetic tetrahedrite Canadian Miner- stitution, it is clear that the usefulnessof modeling in alogist,17, 619-634 determining the effects of P-T-X on the tetrahedrite Maske,S., and Skinner,B.J. (1971)Studies ofthe sulfosaltsofcopper I. framework is limited and that there is room for a sreat Phasesand phaserelations in the systemCu-As-S Economic Geology, 66, 90l-9 I 8. deal more researchon such effects. Nowacki. W ( I 969) Zur Klassifikation und Kristallchemie der Sulfosalze. SchweizerischeMineralogische und PetrographischeMitteilungen, 49, Acxlqowr,BrcMENTS 109-l56. (1981)The relatedstructures of a-Mn, so- This paper benefitedfrom careful reviews by F D Bloss,G. V. Gibbs, Nyman, H, and Hyde, BG 437 I l-17 . P. B Moore, P H. Ribbe, and R. O. Sack The study was supported in dalite,SbrTf , etc.Acta Crystallographica, , (1981) reaction between part by the Department of the Interior's Mining and Mineral Resources O'Leary, M J., and Sack, R.O Fe-Zn exchange Contributions to ResearchInstitute's (MMRRI) programadministered by the Bureauof tetrahedrite and sphaleritein natural environments Mines underallotment grant number G I l64l 5I . Mineralogy and Petrology,96, 415-425 Pattrick,R A D, and Hall, A.J (1983)Silver substitutioninto synthetic RprpnnNcns crrnn zinc, cadmium and iron tetrahedntesMineralogical Magazine, 47,441- 450. Beagley,B , Henderson,C.M.B., and Taylor,D. (1982)The crystalstruc- Pauling, L. (1930) The structure of sodalite and helvite. Zeitschrift fiir tures of aluminosilicate-sodalites:X-ray diffraction studies and com- Kristallographie,74, 2 13-225. puter modeling. Mineralogical Magazine,46, 459464 Pauling,L., and Neumann,E.W (1934)The crystalstructure of binnite, Belov, N.V., and Pobedimskaya,EA. (1969) Covelline (klockmannite), (Cu,Fe),rAsnS,.,and the chemicalcomposition and structureof min- chalcocite (acanthite, stromeyerite, bornite), fahlerz Soviet Physics erals in the tetrahedritegroup Zeitschrift fiir ltuistallographie,88, 5't- Cryslallography,13, 843-847 oL. Dempsey,M.J, and Taylor, D. (1980)Distance least squares modelling Peterson,R.C, and Miller, I (1986)Crystal structure and cation distri- of the cubic sodalite structure and of the thermal expansion of bution in freibergiteand tetrahedrite.Mineralogical Magazine, 50,717- Nar(AluSiuOr.)Ir.Physics and Chemistryof Minerals,6, 197-208 721 Depmeier,W. (1984)Tetragonal tetrahedra distortions in cubic sodalite Ross,V. (1957)Geochemistry, crystal structure and mineralogyof the frameworks Acta Crystallographica,840, I 85-1 9 l. sulfidesEconomic Geology, 52, 755-77 4. Edenharter,A (1976) Fortschritte auf dem Gebiete der Kristallchemie Sack,R O., and Loucks,R R. (1985)Thermodynamic properties oftetra- der Sulfosalze. SchweizerischeMineralogische und Petrographische hedrite-tennantites:Constraints on the interdependenceof the Ag + Mitteilungen,56, 195-217 Cu,Fe + Zn and As = Sb exchangereactions. American Mineralogist, Hassan,I., and Grundy, H.D. 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