1481
The Canadian Mineralogist
Vol. 41, pp. 1481-1501 (2003)

CRYSTAL STRUCTURES AND CRYSTAL CHEMISTRY OF MEMBERS
OF THE CUPROBISMUTITE HOMOLOGOUS SERIES OF SULFOSALTSDAN TOPA§
Geological Institute, University of Salzburg, Hellbrunnerstr. 34/III, A–5020 Salzburg, Austria

EMIL MAKOVICKY§ AND TONČI BALIĆ-ŽUNIĆ§
Geological Institute, University of Copenhagen, Østervoldgade 10, DK–1350 Copenhagen K, Denmark

ABSTRACT
Crystal structures of natural cuprobismutite, Cu8.05 (Bi12.83Ag0.96Pb0.15Cd0.08)14.02 S23.93, from Felbertal, Austria, with a
17.590(4), b 3.922(1), c 15.177(3) Å,  100.710(4)°, space group C2/m, Z = 1, and of two samples of hodrushite: (1)(Cu7.48Fe0.45)7.93 (Bi11.54Ag0.40Pb0.08)12.02 S22.05, also from Felbertal, with a 17.562(1), b 3.920(1), c 27.150(2) Å,  92.561(1)°,space group C2/m, Z = 2, and (2) (Cu8.08Fe0.28)8.36 (Bi11.51Ag0.03Pb0.08Sb0.03Cd0.08)11.73 S21.91, from Swartberg, South Africa,
with a 17.535(4), b 3.900(1), c 27.109(4) Å,  92.333(9)°, space group C2/m, Z = 2, were refined from single-crystal X-ray data.
Eight samples of cuprobismutite homologues were analyzed with an electron microprobe. All homologues consist of PbS-likeaccretional (a) slabs of two distinct thicknesses (kupčíkite-like N = 1 slabs and cuprobismutite-like N = 2 slabs) interleaved with(b) slabs combining paired coordination pyramids of Bi with Cu tetrahedra. Bismuth occurs in four distinct types of coordination
polyhedra, from regular octahedra to capped prismatic polyhedra; copper occurs in trigonal planar and tetrahedral coordination.
Silver substitutes for Bi in the central octahedron of cuprobismutite-like slabs, and Pb possibly as well, whereas Fe3+ substitutes
for Cu along the boundaries of kupčíkite-like slabs. In the hodrushite from Swartberg, Cu substitutes for octahedrally coordinatedBi, as is the case in synthetic cuprobismutite. Multiple correlations among substitution trends were observed.
Keywords: cuprobismutite, hodrushite, kupčíkite, single-crystal X-ray diffraction, electron-microprobe data, cuprobismutite homologous series, substitution trends, crystal chemistry.

SOMMAIRE
Les structures cristallines de la cuprobismutite naturelle, Cu8.05 (Bi12.83Ag0.96Pb0.15Cd0.08)14.02 S23.93, provenant de Felbertal,en Autriche, a 17.590(4), b 3.922(1), c 15.177(3) Å,  100.710(4)°, groupe spatial C2/m, Z = 1, et de deux échantillons dehodrushite: (1) (Cu7.48Fe0.45)7.93 (Bi11.54Ag0.40Pb0.08)12.02 S22.05, aussi de Felbertal, a 17.562(1), b 3.920(1), c 27.150(2) Å, 
92.561(1)°, groupe spatial C2/m, Z = 2, et (2) (Cu8.08Fe0.28)8.36 (Bi11.51Ag0.03Pb0.08Sb0.03Cd0.08)11.73 S21.91, provenant de
Swartberg, en Afrique du Sud, a 17.535(4), b 3.900(1), c 27.109(4) Å,  92.333(9)°, groupe spatial C2/m, Z = 2, ont été affinéesà partir de données en diffraction X prélevées sur monocristal. Huit échantillons d’homologues de la cuprobismutite ont été
analysés avec une microsonde électronique. Tous les homologues sont faits de panneaux accrétionnels de type PbS (a) de deuxépaisseurs différentes (de type kupčíkite, N = 1, et de type cuprobismutite, N = 2) interstratifiés avec des panneaux (b) contenantdes pyramides de tétraèdres à Bi et Cu en paires. Le bismuth se présente en quatres types de polyèdre de coordinence, variantd’octaèdre régulier à polyèdre prismatique chapeauté; le cuivre se présente en coordinence trigonale en plan et en coordinence
tétraédrique. L’argent remplace le Bi dans l’octaèdre central des panneaux de type cuprobismutite, et même le Pb, tandis que leFe3+ remplace le Cu le long des bordures des panneaux de type kupčíkite. Dans la hodrushite de Swartberg, le Cu remplace le Bi
en coordinence octaédrique, tout comme dans la cuprobismutite synthétique. De multiples corrélations parmi les vecteurs de
substitution sont présentes.
(Traduit par la Rédaction)
Mots-clés: cuprobismutite, hodrushite, kupčíkite, diffraction X sur monocristal, données de mirosonde électronique, série deshomologues de la cuprobismutite, vecteurs de substitution, cristallochimie.

§

E-mail addresses: dan.topa@sbg.ac.at, emilm@geo.geol.ku.dk, tonci@geo.geol.ku.dk

1482

THE CANADIAN MINERALOGISTINTRODUCTION
Cuprobismutite, hodrushite, and kupčíkite are thethree known members of the cuprobismutite homologous series of Cu–Bi sulfosalts (Makovicky 1989).
Cuprobismutite was described by Hillebrand (1884) as
an unnamed mineral of ideal composition 3(Cu,Ag)2S•
4Bi2S3. Dana (1892) assigned it the current name.
Nuffield (1952) obtained a monoclinic unit-cell with a
17.65, b 3.93, and c 15.24 Å,  100.5°, space group
C2/m from the type material. He managed to synthesize
silver-free cuprobismutite, tentatively assigned it a formula CuBiS 2, and considered it dimorphous with
emplectite. The crystal structure of synthetic cuprobismutite was determined by Ozawa & Nowacki (1975);
these authors found a composition of Cu10.4Bi12.6S24,
with some Bi sites largely filled by Cu.
Hodrushite was described by Koděra et al. (1970);
electron-microprobe data were reported by Makovicky& MacLean (1972), and the structure determination, by
Kupčik & Makovicky (1968). Its composition wasquoted as Cu8.12Bi11.54 Fe0.29S22, with unspecified, small
amounts of Pb. The unit cell, a 27.21, b 3.94, and c 17.58
Å,  92.9°, space group A2/m, indicated its relationshipto cuprobismutite. This relationship was defined in
Koděra et al. (1970) by reference to the results ofKupčik & Makovicky (1968): the structure of hodrushite
is a regular intergrowth of cuprobismutite-like slabs
with slabs of a hitherto undescribed Cu–Bi sulfosalt.
This relationship was confirmed and refined by
Mariolacos et al. (1975), who synthesized the “missingslab” as an independent phase. Its composition wasgiven by them as Cu4Bi5S10 with a 17.54, b 3.93, c 12.85
Å,  108°, space group C2/m. Nobody else managed tosynthesize this phase, but Sugaki et al. (1981) synthesized “phase Z”, to which they assigned the composition Cu 8.4 Fe 1.2 Bi 10.8S 22 , analogous to hodrushite,
although its unit-cell parameters are practically identical to those of Cu4Bi5S10. Topa et al. (2003) described
the natural occurrence of such a phase, Cu3.4Fe0.6Bi5 S10,
as kupčíkite, and determined its structure.
Two structure types are related to the cuprobismutite
homologous series, synthetic Cu4Bi4S9 (Takéuchi &Ozawa 1975, Bente & Kupčik 1984) and the isostructural Cu4Bi4Se9 (Makovicky et al. 2002) on the one
hand, and paderaite Ag1.2Cu5.8Pb1.3Bi11.5S22 (Mumme
1986) on the other. Both of them share many featureswith cuprobismutite homologues, but differ from themin several substantial “non-homologous” features; they
are “plesiotypic” with respect to this homologous series(Makovicky 1997).
All three members of the cuprobismutite homologous series contain minor elements, Ag, Fe and Pb, invariable amounts. For some of them, the presence of Cufor-Bi substitution was inferred from electron-microprobe data, as was observed by Ozawa & Nowacki(1975). Makovicky (1989) stated that “among the members of an accretional series, the composition changes

regularly and by increments; therefore the electron-microprobe data for the microscopic grains of such phases
can be used to evaluate the order number of the homologue.” Unfortunately, such a procedure is in principle
not applicable to the cuprobismutite homologues because of the unknown extent of the Cu-for-Bi substitution and its influence on stoichiometry. Moreover,assignments of minor elements to Cu or Bi sites hasremained problematic.
In present paper, we seek to amend this situation bymeans of determinations of the exact structure of preanalyzed crystals from well-characterized samples. The
present determinations of the structures (including thaton kupčíkite by Topa et al. 2003) not only confirm thestructural schemes for individual members of the series,
but also allow an assessment of the extent of the Cufor-Bi substitution in the natural homologues as well as
an assignment of minor elements to individual structuralsites. This approach leads to a revised structural formulafor the entire series which, with the exception of samples
with extensive Cu-for-Bi substitution (rare in nature),
automatically leads to a correct assignment of the homologue order number N (i.e., mineral determination)from results of the chemical analysis alone.
We do not attempt to collect literature data on potential cuprobismutite homologues and re-evaluate
them. This exercise requires a time-related re-assessment of the reliability of all the electron-microprobe data
accumulated since about 1968 (cf. problems with the
ZAF correction cited by Makovicky & MacLean 1972),
among other factors, and is relegated to other publications.

PROVENANCE OF THE SAMPLESElectron-microprobe analyses were performed on
samples from five localities: Felbertal (Austria),
Hodrusha (Slovakia), Swartberg (South Africa), as wellas Bǎit˛ a Bihor and Ocna de Fier (Romania). As part ofthis project, crystal structures were determined for
cuprobismutite (Felbertal), hodrushite (Felbertal andSwartberg), for comparison with results on kupčíkite
from Felbertal (Topa et al. 2003).
In the Felbertal scheelite deposit, Hohe Tauern, Austria, cuprobismutite homologues are known only in the
orebodies K7 and K8 (Topa 2001, Topa et al. 2002,
2003). These orebodies lie in amphibolite with lenses
of leucocratic gneisses and quartz masses. The ore isbelieved to be related to Variscan magmatic events andwas reworked during Alpine metamorphism.
Cuprobismutite homologues occur associated withmakovickyite (pavonite homologue 4P), cupromakovickyite (modified 4P) and bismuthinite derivatives,with 50–96 mol.% of the aikinite end-member. Simple
and multiple parallel intergrowths of kupčíkite–
hodrushite (Topa et al. 2003, Fig. 5) and hodrushite–
cuprobismutite (Figs. 1a, b) display sharp, straightboundaries between the intergrown components. The

THE CUPROBISMUTITE HOMOLOGOUS SERIES OF SULFOSALTS

1483

FIG. 1. Typical aggregates of cuprobismutite homologues and associated phases from: a) and b) Felbertal, K8 ore body, Austria,c) Bǎiţa Bihor, Romania, and d) Swartberg, South Africa. Where not indicated, bar length is 100 m. Abbreviations: cup:
cuprobismutite, kup: kupčíkite, hod: hodrushite, emp: emplectite, pad: paděraite, tet: tetradymite, bdxx: bismuthinite derivative, with the percentage of the aikinite end-member indicated.

association kupčíkite–cuprobismutite is characterized
by the replacement of the latter by the former. Native
Bi is a late product of decomposition.
The Cu–(Ag)–Pb–Bi sulfosalt assemblages from
Triassic skarn deposits at Bǎiţa Bihor, Apuseni Mountains, Romania (Cioflica & Vlad 1973, Žák et al. 1994)
consist of bismuthinite derivatives with 50–89 mol.%of the aikinite end-member, makovickyite, cupromakovickyite, hodrushite, kupčíkite, paděraite and tetradym-

ite. The specimen studied contains a parallel intergrowthof hodrushite and kupčíkite with indistinct signs of a
replacement texture, and with emplectite as the final
product (Fig. 1c). A bismuthinite derivative with 83
mol.% of aikinite end-member replaces both phases;
grains of tetradymite are scattered in the aggregates.
In the sample from Swartberg, South Africa(Ciobanu & Cook 2002), composite crystals of
hodrushite are lined by splintery crystals of paděraite,

1484

THE CANADIAN MINERALOGIST

probably an older phase. The intermediate spaces arefilled by a bismuthinite derivative decomposed into acoarse intergrowth of a derivative with 10 mol.% and aderivative with 34 mol.% of aikinite end-member.
Emplectite replaces primarily hodrushite and paděraite(Fig. 1d). A description of the Swartberg occurrence aswell as the Ocna de Fier deposit will be given by Cooket al. (in prep.).

EXPERIMENTAL

TeL), n-Sb2S3 (SbL) and pure metal for AgL. Raw
data were corrected with the on-line ZAF–4 procedure.
Standard deviations (error in wt.%) of elements soughtfor the cuprobismutite series are: Bi 0.17, Pb, Cd and S
0.06, Cu 0.04, Ag 0.03, Sb 0.02 and Fe 0.01. Results ofthree to five point-analyses obtained from a homogeneous grain or an individual phase in an aggregate wereaveraged. Chemical data for the material structurally
investigated, as well as for mineral assemblages presented in Figure 1, are compiled in Table 1.

Chemical analysis

Single-crystal X-ray diffraction

Quantitative chemical analyses were performed witha JEOL JXA–8600 electron microprobe controlled by a
LINK–eXL system, operated at 25 kV, and 30 nA, with
20 s counting time for peaks and 7 s for background.
The following natural (n) and synthetic (s) standards and
X-ray lines were used: n-CuFeS2 (CuK, FeK), sBi2S3 (BiL, SK), n-PbS (PbL), s-CdTe (CdL,

Fragments of cuprobismutite with an irregular shapeand a diameter of 0.03–0.07 mm from Felbertal andfragments of hodrushite from Felbertal and Swartberg
were measured on a Bruker AXS four-circle diffractometer equipped with a CCD area detector using graphite monochromated MoK radiation. Crystal data for thegrains studied are listed in Table 2. The SMART

THE CUPROBISMUTITE HOMOLOGOUS SERIES OF SULFOSALTS(Bruker AXS, 1998) system of programs was used forunit-cell determination and data collection, SAINT+(Bruker AXS, 1998) for the calculation of integrated
intensities, and XPREP (Bruker AXS, 1998) for empirical absorption correction based on pseudo -scans. The
centrosymmetric space-group C2/m, proposed by the
XPREP program, was chosen and is consistent with themonoclinic symmetry of the lattices and intensity statistics. The structures were solved by direct methods(program SHELXS, Sheldrick 1997a) that revealed mostof the cation positions. In subsequent cycles of the refinement (program SHELXL, Sheldrick 1997b), cation
positions were deduced from difference-Fourier syntheses by selecting from among the strongest maxima at
appropriate distances. Thus, the new structure solutions
were independent of the published results. As can be

1485

seen in Table 1, the results of the structure refinement
for cuprobismutite do not match those on the hodrushite
and kupčíkite samples. Even the best fragment ofcuprobismutite available displays a slightly domain-liketexture with spurious amounts of other sulfides
intergrown (bismuthinite derivative).
Results of the refinement are given in Table 2, fractional coordinates, isotropic and anisotropic displacement parameters of the atoms are listed in Tables 3a–c,
and selected Me–S bond distances are presented in Table
4. Selected geometrical parameters, calculated with
IVTON program (Balić-Žunić & Vicković 1996), related to individual coordination polyhedra are given in
Table 5. The structures of cuprobismutite homologues
are presented in Figures 2–5, which show the site labeling for cuprobismutite and hodrushite structures. Tables

1486

THE CANADIAN MINERALOGIST

FIG. 2. The crystal structure of cuprobismutite Cu8.05 (Bi12.83Ag0.96Pb0.15Cd0.08)14.02 S23.93 from Felbertal. Projection along[010], a axis 17.59 Å, c axis 15.177 Å. Shaded and void circles indicate two levels of y, approximately 2 Å apart. Bi1
represents a mixed Ag (yellow), Bi (grey) position. Two thin layers (grey-shaded) and two cuprobismutite-like layers (yellow-shaded), are indicated.

THE CUPROBISMUTITE HOMOLOGOUS SERIES OF SULFOSALTS

of structure factors may be obtained from the Depository of Unpublished Data, CISTI, National ResearchCouncil, Ottawa, Ontario K1A 0S2, Canada.

1487

DESCRIPTION OF THE STRUCTURES
Modular elements
The crystal structures of the cuprobismutite homologous series can be interpreted (Makovicky 1989) as aregular 1:1 intergrowth on the unit-cell scale of two
types of slabs: (a) (311)PbS slabs of a galena-like structure (cuprobismutite-like or kupčíkite-like layers orboth), and (b) complex slabs with columns of paired
BiS5 pyramids and paired CuS4 coordination tetrahedra(thin layer) (Fig. 2). The (a) slabs consist of BiS6 coordination octahedra, coordination pyramids BiS5 flanking them, and of the fitting parts of the trigonal
coordination bipyramids of Cu(Fe). The (b) layers are
identical in all homologues, i.e., homologous accretion
takes place in the galena-like portions. In kupčíkite, N =1, two coordination pyramids of Bi2 attach themselvesto the appropriate sides of the Bi1 coordination octahedron; in cuprobismutite, N = 2, there are pairs (Bi2 andBi3) of such pyramids. The PbS-like slab is then two
and three octahedra (or pyramids) wide, respectively.
Hodrushite is a regular 1:1 combination of these two
slabs thicknesses, N = 1; 2.
The Bi sites

FIG. 2a. Atom positions in cuprobismutite. Axes and orientation as indicated.

On the polyhedron level, the structures of the
cuprobismutite homologous series are distinguished by
the presence of regular Bi coordination octahedra, a feature shared, so far, only by the structures of the pavonite
homologous series (Makovicky 1989). These octahedra
form two groups: (a) the unsubstituted Bi octahedra, Bi1

1488

THE CANADIAN MINERALOGIST

THE CUPROBISMUTITE HOMOLOGOUS SERIES OF SULFOSALTS

1489

FIG. 3. The crystal structure of kupčíkite (Cu6.58Fe1.28)7.86 (Bi9.87Ag0.03Sb0.03Cd0.09)10.02 S20.13 from Felbertal (Topa et al.
2003). Projection along [010], a axis 17.512 Å, c axis 12.869 Å. Shaded and void circles indicate two levels of y, approximately 2 Å apart. Cu2 (green) represents a mixed Cu,Fe position. Two thin layers (grey-shaded) and one kupčíkite-like layer(unshaded), are indicated.

1490

THE CANADIAN MINERALOGIST

FIG. 4. The crystal structure of hodrushite (Cu7.48Fe0.45)7.93 (Bi11.54Ag0.40Pb0.08)12.02 S22.05 from Felbertal. Projection along[010], a axis 17.562 Å, c axis 27.15 Å. Shaded and void circles indicate two levels of y, approximately 2 Å apart. Cu1A
(green) represents a mixed Cu,Fe position, and Me2 a mixed Bi (grey), Ag (yellow) position. Three thin layers (grey-shaded),
one kupčíkite-like layer (unshaded), and one cuprobismutite-like layer (yellow-shaded), are indicated.

in cuprobismutite and Me1(Bi) in hodrushite, with larger
volumes of polyhedron or circumscribed sphere (93.2 ≤Vs ≤ 93.9 Å3; for explanations see Appendix), and (b)the Bi octahedra partly substituted by Ag or, in thehodrushite from Swartberg, by Cu with smaller volumes(Vs = 90.2 Å3). For the first group (a), smaller differences in Bi–S bonds are typical (Bi–S 2.80  2 and
2.82–2.83  4 Å), whereas for the second group (b),larger differences and the opposite bond-length distribution (elongate octahedra, Bi–S 2.76  4 and 2.82–
2.85  2 Å) (Fig. 6) are found.
The next group of Bi polyhedra are BiS5 coordination pyramids completed to become asymmetricoctahedra by an additional Bi–S bond (Bi2 in cuprobismutite, Bi5 in hodrushite). These are attached to theabove Bi octahedra only in the thicker, cuprobismutitelike layers. The additional bond is not the longest one in
the octahedron: the ratio of shortest bond to additionalbond varies from 2.68 Å : 2.95 Å in cuprobismutite to
2.65 Å : 2.97 Å in Cu–Bi-substituted hodrushite. At thesame time, the ratio of bonds in the base of the pyramidvaries from 2.74 Å : 3.03 Å to 2.71 Å : 3.05 Å.

The last group of Bi polyhedra in the PbS-like layers are the marginal BiS5 pyramids completed by two
additional, equally long bonds to monocapped trigonal
prisms (Bi2 in kupčíkite, Bi3 in cuprobismutite, and Bi1
and Bi4 in hodrushite). The asymmetry of Bi2 coordination in kupčíkite is close to that in the corresponding
Bi1 in hodrushite; the same holds for the asymmetry of
the Bi3 coordination in cuprobismutite in relation to thatof Bi4 in hodrushite (Table 5).
There are systematic differences between kupčíkite
and cuprobismutite in the coordination of bismuth incolumns of paired pyramids in the (b) slabs (Bi3 andBi4 in the above order). Bi4 in cuprobismutite has agreater asymmetry of coordination, e.g., the ratio of the
pyramid height to the longest bonds below the pyramidis 2.61Å : 3.48Å in kupčíkite, whereas it is 2.59Å :3.67Å in cuprobismutite. Remarkably, this trend ismaintained in hodrushite. Pyramids of Bi2 situated next
to the kupčíkite-like slabs tend toward a configurationof kupčíkite type, and those of Bi3 adjacent tocuprobismutite-like slabs assume cuprobismutite-like
configurations (Table 4, Figs. 3, 4).

THE CUPROBISMUTITE HOMOLOGOUS SERIES OF SULFOSALTS

FIG. 4a.

1491

Atom positions in hodrushite. Axes and orientation as indicated.

The above trends in configuration can best be expressed by the volume-based eccentricity (see the Appendix and Table 5) of Bi polyhedra: 0.0 for the regularcoordination octahedra [e.g., Me1(Ag,Bi) and Me2(Bi)in hodrushite], 0.24–0.26 for the attached asymmetricoctahedra (such as Bi5 in hodrushite), 0.41–0.42 for themarginal monocapped trigonal prisms of Bi (e.g., Bi4
in hodrushite), 0.55 for the cuprobismutite-likemonocapped-prismatic configuration in the columns ofpaired coordination pyramids of Bi (Bi3 in hodrushite),and 0.5 for the kupčíkite-like configuration in the latter(Bi2 in hodrushite).
Further details of the coordination of Bi can be seenin the diagrams of volume-based sphericity versus volume-based eccentricity of the coordination polyhedra of
Bi (Fig. 7a), and of the hyperbolic correlation of the
opposing Bi–S bonds distances (Fig. 8). In general, there
is an inverse correlation between eccentricity and sphericity of the bismuth polyhedra in Figure 7a, violated
only by the shapes of partly substituted bismuth octahedra denoted as Bi1 in cuprobismutite and Me2 inhodrushite (the two lowermost values of sphericity atzero eccentricity in Fig. 7a). The polyhedra with greatest eccentricity thus also deviate most from regularity.

The types of bismuth polyhedron defined above areclearly distinguished in Figure 7a, whereas there is coincidence of these properties for the same site in different homologues. Differences between the kupčíkite-likeand cuprobismutite-like environments for Bi coordinations in the double-pyramid columns of the (b) slabs are
more pronounced than those between the marginal Bi
atoms in the (a) slabs and in the (b) slabs.
The same clear-cut distribution of polyhedron types
is found in the diagram of volumes Vp of coordination
polyhedra versus volumes Vs of spheres circumscribedby least-squares fitting to these polyhedra (Fig. 7b).
Regular or asymmetrical octahedra offer considerably
smaller volumes to Bi and its lone-pair electrons thando capped trigonal prisms; the degree of the Ag-for-Bi
substitution is reflected in the reduced volume of thesubstituted octahedra. Volumes of prisms increase fromcuprobismutite-like slabs, through kupčíkite-like slabs
to those in paired columns. Interestingly enough, thelargest volumes are those for paired prisms close tocuprobismutite columns, which also display the largest
distortion.
Coordination polyhedra of the bismuth in cuprobismutite homologues follow closely a hyperbolic correla-

1492

THE CANADIAN MINERALOGIST

FIG. 5. The crystal structure of Cu-enriched hodrushite (Cu7.72Fe0.28)8.00 Cu0.36 (Bi11.51Ag0.03Pb0.08Sb0.03Cd0.08)11.73 S21.91 from
Swartberg, South Africa. Projection along [010], a axis 17.535 Å, c axis 27.109 Å. Shaded and void circles indicate two levelsof y, approximately 2 Å apart. Cu1A (green) represents a mixed Cu,Fe position. Cu5 (blue) and Me2(Bi) (dark grey) denotethe new split position.

tion of opposing bonds, investigated originally by
Trömel (1981) for Sb3+, Te4+, I5+ bonds with oxygen,and by Berlepsch et al. (2001) for bismuthinite derivatives (meneghinite homologues). Bismuth Bi3+ is the
only case among Group-V elements for which an octahedral coordination with a 1:1 ratio of opposing bonds
exists. The unsubstituted Bi octahedra cluster tightly
around the hyperbola, whereas the values above or below the hyperbola belong to the partly substituted octahedra (Fig. 8). Numerical data for the hyperbola fitted
to the bond lengths in the three substituted structures
are presented in Table 6, together with those obtainedby Berlepsch et al. (2001) for literature data on
bismuthinite derivatives.
Irrespective of their orientation in the PbS-like (a)slabs, or of their position in the (b) layers, pairs of opposing Bi–S distances in kupčíkite (N = 1) and thekupčíkite-like module in hodrushite lie closer to the hyperbola than do those from cuprobismutite (N = 2)
and the cuprobismutite-like portions of the hodrushite.
The values for the cuprobismutite-like slab (Bi4 and Bi5
in hodrushite) accompany the hyperbola from bothsides; the trends for the bond pairs oriented across the
PbS-like slabs and those for the bond pairs oriented
nearly parallel to the slabs cross on the 1:1 point (Fig. 8).
This cross-correlation of the Bi–S bond scheme suggeststhat a compensation of strains and stresses across andalong the slabs may be present in the thicker, cuprobismutite-like slabs of the cuprobismutite homologues.
These phenomena are largely absent from the thinner,
kupčíkite-like slabs.
The Cu sites
In all structures, the tetrahedral coordination of copper is asymmetrical, transitional to trigonal-planar or,considering more distant ligands, trigonal-bipyramidal(Figs. 2, 3). The trend of coordination asymmetry forcopper tetrahedra in the (b) slab is opposite that for Bi
in paired pyramids. The asymmetry of coordination isgreater for the kupčíkite-like configuration (the volumebased eccentricity for Cu1 in kupčíkite is 0.12, and in
the range 0.16–0.19 for Cu2 in hodrushite), whereas it
is smaller for cuprobismutite-like configurations (the ec-

THE CUPROBISMUTITE HOMOLOGOUS SERIES OF SULFOSALTS

FIG. 6.

1493

Bi and Cu coordination polyhedra in cuprobismutite.

centricity value for Cu2 in cuprobismutite is 0.08, andin the range 0.05–0.06 for Cu3 in hodrushite).
In all structures, the galena-like slabs are flanked bytrigonal bipyramidal voids accommodating copper ±iron. The latter could be refined as split position in thecase of kupčíkite-like slabs, whereas refinements
yielded only single positions for the cuprobismutite-likeslabs. As discussed by Topa et al. (2003) for kupčíkite,splitting of the position is not automatically a consequence of Fe-for-Cu substitution: this splitting also isfound in Cu 4 Bi 4 S 9 (Bente & Kupčik 1984) andCu4Bi4Se9 (Makovicky et al. 2002) in a completely
analogous situation.
Both in kupčíkite and in kupčíkite-like N = 1 slabsof the hodrushite structure, the splitting produces anearly triangular planar position (Cu3 in kupčíkite and
Cu1B in hodrushite) and a distorted tetrahedral position(Cu2 and Cu1A, respectively). In the trigonal bipyramidal void of kupčíkite, distances to the distal vertices
are 2.93 Å and 3.21 Å for Cu3, whereas they are 2.48 Å
versus 3.66 Å for Cu2. The Cu–S distances (Table 4)
indicate clearly CN = 3 and CN = 4, respectively. Topaet al. (2003) placed Fe3+ in kupčíkite at the tetrahedral
Cu2 position; the same can be assumed for the Cu1A
site in hodrushite.

The single site Cu1 in cuprobismutite is closer to thetriangular planar site seen in the split configuration; thesame is true for the Cu4 position of cuprobismutite-likeslabs in hodrushite, especially in the Cu-enriched variety (Table 4). The augmented displacement-factor U11
suggests pronounced displacements of these atoms inthe direction perpendicular to the triangular plane. The
differences in coordination between the triangular andtetrahedral sites are best seen in the eccentricity valuesof the tetrahedra in Table 5.

THE SUBSTITUTING ELEMENTS
Silver is concentrated in cuprobismutite (Tables 1,2) at the Bi1 position, which contains 0.292 Bi + 0.708
Ag. Silver has been placed on (0,½,0) overlapping with
Bi without altering its displacement factors (Table 3a).
In hodrushite, with less Ag, the corresponding Me2 position contains 0.58Bi + 0.42Ag (Table 3b); the influence on the coordination has already been described.
In Cu-enriched hodrushite, this polyhedron consistsof 0.75Bi, flanked by triangular Cu5 on the two freefaces of the Bi octahedron; the composite occupancy is
0.5 Cu, and the bonds correspond well to triangular Cu
when taking into account that the S sites in three quar-

1494

THE CANADIAN MINERALOGIST

FIG. 7. Polyhedron characteristics of Bi coordination polyhedra in cuprobismutite homologues. (a) Volume-based eccentricity
versus volume-based sphericity, (b) polyhedron volume versus circumscribed-sphere volume. Symbols: cuprobismutite (䊐),hodrushite (䉫), kupčíkite (䊊).

ters of cases belong to the Bi octahedron and not to Cu
triangles (Table 4).
As already mentioned above, iron has been ascribedto the distorted tetrahedrally coordinated sites situatedin the split trigonal bipyramidal sites. Assigning lead tothe bismuth sites is most difficult. With about 0.10–0.15
Pb apfu (atoms per formula unit) in kupčíkite andhodrushite, and ~0.25 Pb apfu in cuprobismutite, thistask is virtually impossible.

COMPOSITIONAL VARIATIONSAND CRYSTAL CHEMISTRY
Calculation of N, the order of the homologue
Calculation of the order N of a cuprobismutite homologue (see Appendix) in a way similar to the calculation of N in the lillianite homologous series(Makovicky & Karup-Møller 1977) only becomes possible now, on the basis of results of structural refine-THE CUPROBISMUTITE HOMOLOGOUS SERIES OF SULFOSALTS

1495

FIG. 8. Hyperbolic correlation of opposing Bi–S bond distances in cuprobismutite homologues. Symbols distinguish the phases studied as well as the kupčíkite-like,cuprobismutite-like (a) slabs (module), and the composite (b) slabs (thin layer) interleaved with them. Symbols: blue circle: kupčíkite – kupčíkite modules, blue diamond:
hodrushite – kupčíkite modules, green diamonds: hodrushite – cuprobismutite modules, green squares: cuprobismutite – cuprobismutite modules, red circle: kupčíkite thinlayer, red diamond: hodrushite thin layer, red square: cuprobismutite thin layer.

ments for kupčíkite (Topa et al. 2003), cuprobismutite
and hodrushite (current work). The reasons are twofold.
a) The ratio of Cu sites versus Bi sites in the structure. Wherever the structure requires partial substitutionof Bi by Cu in order to reduce the total cation charges(as typified by synthetic cuprobismutite: Ozawa &Nowacki 1975), the Cu:Bi ratio does not reflect the ratio of fundamentally distinct Cu and Bi sites, and erroneous values of N result. The substitution is governedby a combination of the charge-balance requirementwith steric problems encountered in the structure, so thata ratio of 3Cu for 1Bi cannot be expected to occur. The
stoichiometry of N = 1, synthetic Cu4Bi5S10 (Mariolacos
et al. 1975), suggests that even some Cu2+ may bepresent in the structures in addition to Cu+, i.e., a priori
assumptions cannot always be made about the valenceof Cu.
b) Until the recent determinations of the structures,the structural role of two principal substituting elements,
Fe and Ag, and the degree of Cu-for-Bi substitution innatural phases, were not known.
The structural-site formula for kupčíkite, N = 1, is‘Cu 8’‘Bi 10’S 20; that for cuprobismutite, N = 2, is‘Cu8’‘Bi14’S24, resulting in a general formula ‘Cu8’‘Bi10+4(N–1)’S4N+16. For N based on metal ratios, this for-mula yields N = 2•(‘Bi’/‘Cu’) – 1.5, where ‘Bi’ and ‘Cu’
can be atom percentages or atoms per (a suggested)
formula unit, with ‘Bi’ = Bi + Sb + Ag + Pb + Cd and‘Cu’= Cu + Fe, i.e., we take into account the site occupancies without regard to element valences. The successful tests of these calculations, including the cases
confirmed by structure determination (Fig. 9), suggest
a general validity of the proposed substitutions and thevirtual absence of important Cu-for-Bi substitution in
the samples studied. Only one natural case, hodrushite
from Swartberg, South Africa, contains importantamount of Cu substituting for Bi. This results in an erroneously low N value for this sample (N = 1.27), in
contradiction of the N = 1.5 confirmed by structure determination. If a chemical N is calculated for synthetic
cuprobismutite, Cu10.44Bi12.4S24 with considerable substitution of Cu for Bi at several positions, (Ozawa &Nowacki 1975), the resulting value is N = 0.9, insteadof the expected 2.0.
Compositional variations
The three known phases of the series are clearly
separated in the three-component discrimination diagrams shown in Figures 10a–c, although in two of these

1496

THE CANADIAN MINERALOGIST

FIG. 9. Calculated values of homologue order N for the members of the cuprobismutite
homologous series studied (based on microprobe data). N = 1 is kupčíkite, N = 1.5,
hodrushite, and N = 2, cuprobismutite. Anomalous results for hodrushite from Swartberg
are explained in the text. Symbols: green triangles: kupčíkite from Felbertal, blue triangles: kupčíkite from Bǎiţa Bihor, green diamonds: hodrushite from Felbertal, blue diamonds: hodrushite from Bǎiţa Bihor, brown diamonds: hodrushite from Swartberg,
black diamonds: hodrushite from Hodrusha, green squares: cuprobismutite fromFelbertal, magenta squares: cuprobismutite from Ocna de Fier.

they span only a small area. These diagrams work very
well for the substituted phases, whereas the Cu-enrichedhodrushite (and with it all potential unsubstituted
phases) is a notable exception. The (Cu + Fe) – (Bi +Ag + Pb) – S diagram (Fig. 10a) describes the site ratios
in these homologues. It demonstrates that additional Cu
sites are present in the phases with limited extents of
Fe, Ag, and Pb substitution for the principal elements,
such as the Cu-enriched hodrushite just mentioned. The
Fe–Pb–Ag diagram (Fig. 10b) describes the ratios ofprincipal substituting elements (i.e., ratios of principal
charge-balancing processes). The (Cu + Fe) – (Bi +0.5Pb) – (Ag + 0.5Pb) plot (Fig. 10c) combines the properties of the two above diagrams.
Our crystallographic studies indicate that four typesof cation substitutions are present in the cuprobismutite
homologues: (a) Cu-for-Bi, (b) Ag-for-Bi, (c) Pb-forBi, and (d) Fe3+-for-Cu. The details of the complicatedcrystal chemistry of the cuprobismutite homologous
series are best resolved in a series of binary diagrams(Figs. 11a–h) combined with the Fe–Pb–Ag diagram(Fig. 10b). The binary diagrams are based on number ofatoms per respective formula units. They combine
changes in the formulae with substitutional trends.
The (Cu + Fe) versus Bi diagram (Fig. 11a) shows
displacement of Bi values from the ideal values of 10,

12, and 14 apfu, respectively. These displacements correlate well with the Ag and Pb substitutions in the individual compounds (Figs. 11d, f); these substitutions
increase from kupčíkite to cuprobismutite. The formulae used for calculation of atomic percent values in Figures 11a–h should ideally deliver 8(Cu + Fe) apfu.
Hodrushite has (Cu + Fe) contents balanced about thevalue of 8 apfu, whereas cuprobismutite has a slightsurplus above 8 apfu, with the increase in Cu matchedby a decrease in Bi, an indication of a small degree of
Cu-for-Bi substitution. Copper-enriched hodrushite
shows a decrease in Bi contents and a substantial increase in Cu content in comparison with the Fe–Ag–
Pb-substituted variety of hodrushite. Kupčíkite shows asmall deficit in (Cu + Fe) (Fig. 11a), apparently due to
0.1 Pb substituting for Bi in the Felbertal material, andalso to higher content of Fe3+ (Fig. 11c). A charge-balance calculation shows that both kupčíkite samples analyzed show excellent charge-balance if Cu+ and Fe3+ are
assumed to be present.
The presence of only minor Cu-for-Bi substitution
in the Ag–Fe–Pb-substituted homologues is confirmedby the closeness of the calculated values of N to the ideal
ones (Fig. 9) and by a well-expressed clustering of compositional points in Figure 10a.

THE CUPROBISMUTITE HOMOLOGOUS SERIES OF SULFOSALTS

1497

FIG. 10. a) Ratios of the occupants of the three principal kindsof sites in the structures of cuprobismutite homologues withelement roles as found by results of crystal-structure analysis (modification by the Cu-for-Bi substitution is dealt within the text). Microprobe data (results of individual analyses). b) Ratios of substituting elements in the members of
the cuprobismutite homologous series studied. c) Composition of cuprobismutite homologues in the modified cation
diagram with Pb removed owing to 2Pb
Ag + Bi.

Figure 10b shows that the amounts of Fe-for-Cu andAg-for-Bi substitutions are balanced in the hodrushite
samples, whereas only a single type of substitution plays
an appreciable role in the members with N = 1 and N =2. Figures 11b and 10b show that hodrushite aggregatesfrom Felbertal and Bǎiţa Bihor show compositional
trends toward the unsubstituted hodrushite, with the increasing role of Fe-for-Cu and Pb-for-Bi substitutions
correlated with a decreasing role of Ag-for-Bi substitution. The Ag-enriched type of hodrushite material from
Hodrusha does not follow this trend. For cuprobismutite,N = 2, the outlines of the composition field in Figure
11b indicate trends similar to those of hodrushite fromFelbertal. Only in cuprobismutite is a distinctly negative correlation between Bi and Ag contents observed(Fig. 11d).
All four types of substitution show mutual correlations. The weakest correlation takes place between Pb(+
Cd) and Fe (Fig. 11h). More pronounced trends are: (a)negative correlations between Ag and Cu + Fe contents
in hodrushite and cuprobismutite (an interplay between
the Ag-for-Bi and Cu-for-Bi substitutions) in Figure11b; (b) a fan of trends for hodrushite in the Ag versus
Fe diagram (Fig. 11e), with the majority of cases following an approximate 2Ag:1Fe line (a consequence ofthe fact that the increase in the extent of Fe-for-Cu
substitution must be compensated by the Ag-for-Bi substitution). The other potential mechanism of compensation, (c) the Pb(+ Cd)-for-Bi substitution, is discernible
for hodrushite (Fig. 11f). (d) The indistinct negative 1:1
correlation between Pb and Ag contents (Fig. 11g) suggests that Pb(+ Cd) and Ag compete for the same sites
in hodrushite and cuprobismutite. For hodrushite, the
2:1 trend, i.e., the Ag + Bi
2Pb substitution, is suggested by certain groups of data within the broad cluster of data points in Figure 11g. This factor explains thelack of correlation between the Bi and Ag contents in
hodrushite in Figure 11d, which is at variance with thecase for cuprobismutite.
The observed trends are not limited to a combination of data from different localities; the richest spectrum of trends and correlations is observed within one
locality, the Felbertal deposit (Figs. 11a–h), where it
expresses the variations within single grains and theiraggregates.
Summarizing these data for individual phases,
kupčíkite from Felbertal displays a small (0.1 apfu) deficit in Bi, related to a weak Pb-for-Bi and very weak Agfor-Bi substitution. A high level of Fe 3+ -for-Cu
substitution (~1.2 Fe apfu) was observed (Fig. 11c), in1498

THE CANADIAN MINERALOGIST

FIG. 11. Element-correlation diagrams for the members of the cuprobismutite homologous series studied. The number of atoms
per formula unit were calculated from electron-microprobe data (details in the text). Symbols and colors as in Figures 9
and 10.

comparison with kupčíkite from Bǎiţa Bihor (~0.9 Feapfu). It correlates with a small deficit in Cu (Fig. 11a).
Cuprobismutite only exceptionally has measurable
contents of Fe (Fig. 11c). The extent of Ag-for-Bi substitution reaches 1 apfu, although values as low as 0.75
apfu also are common (Fig. 11d). Pb(+ Cd)-for-Bi substitution plays an important role, Ag and Pb(+ Cd) competing for the sites in the PbS-like layers. Negative
correlations exist between Pb(+ Cd), Ag, and (Cu + Fe)
versus Bi. The broad negative correlation between Ag
and (Cu + Fe) suggests a competition between the (Cu+ Fe)-for-Bi and Ag-for-Bi mechanisms.
Hodrushite combines the trends observed in N = 1
and N = 2 homologues. Negative correlation between
Bi and (Cu + Fe) is weak, best observable for the Pb(+Cd)- and Ag-free varieties; the negative correlation is
distinct in the plot Pb(+ Cd) versus Bi, but not in theplot of Ag versus Bi, suggesting an important role of
the Ag + Bi
2Pb substitution in the Felbertal andBǎiţa Bihor materials. The extent of replacement of Bi

by other cations is substantial, reducing the number of
Bi apfu from 12 to below 11.6. The Cu-for-Bi substitution competes with the Ag-for-Bi substitution. The extent of the Fe-for-Cu substitution increases in parallelwith that of the Ag-for-Bi substitution. Although lessdistinctly, it decreases with the Pb(+ Cd)-for-Bi substitution. The type hodrushite from Hodrusha is relatively
enriched in Ag and modestly so in Pb (matching the Cuenriched variety from Swartberg in its Pb contents); only
average Fe contents and non-negligible Cu-for-Bi substitution are observed in this sample.

CONCLUSIONS(1) Crystal structures of natural cuprobismutite andtwo types of hodrushite were refined and chemicalvariations for eight samples of cuprobismutite homologues from five localities were determined. The newdata allow a crystal-chemical evaluation of element substitutions observed in natural samples.

THE CUPROBISMUTITE HOMOLOGOUS SERIES OF SULFOSALTS(2) The crystal structures of cuprobismutite homologues are composed of accretional PbS-like (a) slabs
in two distinct thicknesses (kupčíkite-like N = 1 andcuprobismutite-like N = 2 slabs) interleaved by (b) slabs
composed of columns of paired Bi pyramids and Cu
tetrahedra.
(3) Four types of Bi polyhedra are present incuprobismutite homologues: central Bi octahedra in the
PbS-like slabs, asymmetrically distorted octahedra andcapped trigonal prisms in these slabs as well as paired
capped trigonal prisms in the (b) slabs. These groups
have very distinct coordination properties, polyhedronvolumes and eccentricities.
(4) Copper occurs in paired coordination tetrahedrain (b) slabs and as split trigonal planar or tetrahedral
coordination in trigonal bipyramidal spaces lining the(a) slabs.
(5) Silver substitutes for Bi in coordination octahedra of the cuprobismutite-like (N = 2) layers; minor
amounts of Pb probably do as well; Fe3+ substitutes fortetrahedrally coordinated Cu along the boundaries ofkupčíkite-like (N = 1) (a)-type slabs. In hodrushite from

1499

Swartberg, IIICu substitutes for a part of VIBi in the
thicker slabs. Multiple correlations among these substitutions are documented by electron-microprobe data.

ACKNOWLEDGMENTS
This project was supported by grants of the State
Research Council of Denmark and by a grant to D. Topaby the University of Salzburg. The manuscript benefitted from comments of P. Goodell and an anonymousreferee, as well as from the editorial care of Robert F.
Martin.

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THE CANADIAN MINERALOGISTBENTE, K. & KUPČÍK, V. (1984): Redetermination and refinement of the structure of tetrabismuth tetracopper enneasulphide, Cu4Bi4S9. Acta Crystallogr. C40, 1985-1986.
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APPENDIX
The parameters used for the description of coordination polyhedra were defined by Balić- Žunić &Makovicky (1996) and Makovicky & Balić- Žunić
(1998). In the first stage of the procedure, a circumscribed sphere is fitted to all the ligands of the central
atom by a least-squares procedure. Sphere radius rs andsphere volume Vs are typical for the chemical elements
involved and the coordination number (CN). The standard deviation r of the radius is used to define “linear
sphericity” SPHL = (1 – r/r), or “volume-based sphericity” SPHv = (1 – 3r/r), the latter derived by the error-propagation formula from the formula for thevolume of a sphere. Sphericity is a measure of “goodness-of-fit” of the polyhedra observed to the sphere.
Eccentricity describes the displacement of the central atom from the ideal center of the circumscribed
sphere, the “centroid”. The centroid – central atom distance is used either to define a “linear eccentricity”
ECCL = /r or a “volume-based eccentricity” ECCv = 1– [(rs – )/rs]3. The latter was obtained by comparisonof the volumes of the spheres with a radius equal to rs
and (rs – ), respectively.
A measure of the volume-based distortion is calculated as follows: = (Vi – Vp)/Vi, where Vp is the volume of the polyhedron observed, and Vi is the volume
of such polyhedron with the ideal shape, both with thesame circumscribed sphere. The volume of the polyhedron Vp is calculated from the structure, together withVs, whereas the formula of Vi for the observed CN canbe looked up in Makovicky & Balić-Žunić (1998); Vi isthen calculated for the given value of rs. Another expression of this polyhedron distortion is the position of
the polyhedron in the Vp versus Vs plot: for the given
CN, distorted polyhedra have lower values of Vp than
the ideal ones (= Vi).

The scatter of the ligands about the least-squaresfitted circumscribed sphere (resulting in the value of r)
is a function of the shape of the coordination polyhedron. It is not identical to the uncertainty in the value ofthe sphere radius or of the calculated sphere or polyhedron volume, because of standard errors of the atom
positions.
As demonstrated by Trömel (1981) and illustrated
in detail for sulfosalts by Berlepsch et al. (2001), in thecoordination polyhedra of lone-pair cations, the opposing bonds (or cation–ligand distances) follow a hyperbolic correlation trend, specific for a given element.
Besides explaining details of coordination, this analysis
allows one to recognize cation disorder and substitution
at individual sites.
The notion of archetype and homologous series isuseful for compact structures with larger volumes (rods,
slabs, blocks) of fairly uniform coordination polyhedra
sharing vertices, edges and, in some cases, faces. A
homologous series is a series of compounds with structures built of the same type of building blocks (in mostcases slabs) cut out along the same planes (hkl) of agiven archetypal structure. These blocks are joined together by action of structure-building operations, suchas unit-cell twinning on mirror or glide planes, crystallographic shear or intergrowths on a unit-cell scale.
Members of the series differ in the size of these blocks;
the blocks grow incrementally by addition of new layers of coordination polyhedra. The order N of a homologue is determined by the number of polyhedra acrossa suitable diameter of the building block. Each homologue has its own unit cell, chemical composition andstructure although all of these follow the same incremental general principles. More detailed definitions, andthe relation to a polysomatic description, are given in
Makovicky (1989, 1997) and Ferraris et al. (2004).