American Mineralogist, Volume 95, pages 148–152, 2010

The crystal-structure and vacancy distribution in 6C pyrrhotite
Johan P.R. de VillieRs1,* and daVid C. liles2
1

Department of Materials Science and Metallurgical Engineering, University of Pretoria, Pretoria, 0002 South Africa
2
Department of Chemistry, University of Pretoria, Pretoria, 0002 South Africa

abstRaCt
The crystal structure of a 6C pyrrhotite from Mponeng Mine, South Africa, has been refined using starting atomic parameters postulated by Koto et al. (1975). This pyrrhotite is monoclinic and is
described in the non-standard space group Fd, so that the metrically orthorhombic unit-cell shape ispreserved. The cell symmetry is monoclinic with dimensions a = 6.897(2), b = 11.954(3), c = 34.521(7),and with β = 90.003(4)°. The structure has been refined with anisotropic displacement parameters to
R = 0.029 using 1493 observable reflections with I > 2σ(I) and R = 0.034 for all 1800 reflections. Theinternal Rint is 0.023 for the symmetrically equivalent reflection data. The composition of the crystal,as determined by electron microprobe analysis is Fe10.91Ni0.05S12.
The crystal structure resembles that of the 5C pyrrhotite in that the atomic positions of the Fe and S
atoms are arranged in a very similar fashion, the only real difference being the arrangement of partiallyoccupied iron sites. The coordination of the iron atoms is octahedral and short Fe-Fe distances along
the c-axis are also encountered in this structure.
The vacancy distribution is similar to that postulated by Koto et al. (1975) and is characterized
by the stacking of two approximately half-occupied sites, followed by an essentially fully occupied
layer. This is however a simplification and results in a composition that is too metal-rich. Two otherslightly defect sites with occupancies of 0.90 and 0.87 are also present in the structure, and all layers
contain both fully occupied and partially occupied sites. Refinement of the occupancies of all thesesites gives rise to an atomic distribution that resembles the measured composition most closely, andis refined as Fe10.99S12.
The powder diffraction pattern of this structure is compared to the very similar pattern of the 5C
structure. The crystal structure is also given in the more conventional Cc setting so as to be compatible
with the available crystallographic software that cannot normally accommodate the Fd space group.
Keywords: Pyrrhotite-6C, crystal structure, non-stoichiometry, iron sulfide, superstructure

intRoduCtion
Pyrrhotite is one of the most common sulfide minerals andis present as an accessory mineral in most rocks. It is a common
mineral in most sulfide ore deposits, especially in those that
contain Ni, Cu, and Pt group elements. To study the behavior of
pyrrhotite in extraction processes, it is important to adequately
characterize the members of this group of minerals.
Pyrrhotites, together with troilite, occur as minerals with various superstructures in nature. It is typically non-stoichiometricin composition with general formula Fe1–xS, with x varying
between 0 and 0.125. The minerals occur as the ordered 4C, 5C,
and 6C varieties, where C represents the NiAs unit cell that is
the subcell on which the structures of the group are based. These
superstructures are not true polytypes because the occupancies ofthe layers differ in each superstructure, which is a consequenceof the specific vacancy distribution.
The composition of the magnetic 4C structure, is ideally Fe7S8
with a Fe/S ratio of 0.875, but with a substantial compositional
range from a Fe/S of 0.855 to 0.885, and is described in the
non-standard F2/d space group (Tokonami et al. 1972). It is also
* E-mail: johan.devilliers@up.ac.za
0003-004X/10/0001–148$05.00/DOI: 10.2138/am.2010.3266

148

described in the conventional C2/c space group setting by Powell
et al. (2004) in their neutron diffraction study of the magnetic
properties of this pyrrhotite. The structure consists of alternating
layers of filled Fe-S octahedra and layers containing one-thirdvacant Fe sites and two-thirds filled Fe-S octahedra. It must
be mentioned that the above structure defines a stoichiometriccomposition (Fe7S8) and does not allow for a variable composition as is found in nature.
The structure of 5C pyrrhotite was determined by de Villiers
et al. (2009), and this again shows a compositional range with
Fe/S that spans across the ideal Fe9S10 composition (Fe/S = 0.90)
from 0.885 to 0.91. The structure contains two layers containing
vacant Fe sites and all other layers consist of a mixture of sites
with variable Fe occupancy together with fully occupied sites.
The so-called “hexagonal pyrrhotite” is non-magnetic and is actually orthorhombic with space group Cmce (formerly Cmca) as
described originally by Morimoto et al. (1975), in their review ofthe pyrrhotites. The crystallography of the pyrrhotites is reviewed
in more detail in the paper by de Villiers et al. (2009).
The structure of the 6C pyrrhotite was correctly postulated
by Koto et al. (1975) as well as the broad details of the vacancy
arrangement. Unfortunately, however, they did not give a fullstructure determination with unit cell, space group, and a list ofDE VIllIERS AND lIlES: 6C PyRRhOTITE

refined atomic positions. They give the composition as Fe11S12with a monoclinic, but metrically orthorhombic cell and thenon-standard Fd space group. Again the compositions span arange across the ideal composition (Fe/S = 0.917) with Fe/S
from 0.91 to 0.94.
The determination of the pyrrhotite structures forms partof a broader study of the electrochemical and flotation properties of pyrrhotite. Proper characterization and examination ofpure samples of these superstructures are therefore essential
for the understanding of their behavior. In addition, becauseof the similarity of the powder X-ray diffraction patterns of
the non-magnetic (NC) pyrrhotites, which vary from Fe9S10 to
Fe11S12, their structural characterization is essential for the interpretation of the patterns and for their possible quantification.
This study describes the structure of the 6C pyrrhotite and its
vacancy distribution and compares it to that of the 4C and 5C
superstructures.

exPeRimental methods
A sample of 6C pyrrhotite from the Mponeng gold mine was obtained from
Bruce Cairncross of the University of Johannesburg, and this consisted of large (1× 1 × 0.1 cm3) hexagonally shaped single crystals. A subsample was crushed anda small fragment was found to be suitable for single-crystal analysis. A fragmentof the same single crystal was analyzed by a Cameca SX100 electron microprobe
at the University of Pretoria, run at 20 kV accelerating voltage and 20 nA probe
current. The average analysis for the crystal is 38.35 mass% for S, 60.71% for Fe,
and 0.32% for Ni, which gives a composition Fe10.91Ni0.05S12.
The unit cell was determined and diffraction data were collected using the
Fd setting suggested by Koto et al. (1975) to retain the metrically orthorhombic
setting. Data were collected on a Bruker (Siemens) P4 diffractometer equippedwith a Bruker SMART 1K CCD detector using graphite-crystal monochromatized
MoKα radiation by means of a combination of φ and ω scans. Data reduction was
performed using SAINT+ (Bruker 2001), and the intensities were corrected forabsorption by multiple scans of symmetry equivalent reflections using SADABS(Bruker 2001). The intensities of 3186 reflections were measured to obtain the 1800
unique reflections used in the refinements and the internal discrepancy factor of
Rint = 0.023 was obtained, which was considered to be acceptable. Refinement was

Table 1.

Crystal data and structure refinement for pyrrhotite-6C

Identification code
Empirical formula
Formula weight
Temperature
Wavelength
Crystal system
Space group
Unit-cell dimensions

Pyrrhotite-6C
Fe11S12999.07293(2) K
0.71073 Å
Monoclinic
Fda = 6.8973(15) Å
α = 90°b = 11.954(3) Å
β = 90.003(4)°c = 34.521(7) Åγ = 90°Volume2846.2(11) Å3
Z
8
Density (calculated)
4.663 Mg/m3
Absorption coefficient12.585 mm–1
F(000)
3824
Crystal size
0.12 x 0.12 x 0.12 mm
Theta range for data collection
3.46 to 26.36°
Index ranges–8 ≤ h ≤ 7, –12 ≤ k ≤ 14, –42 ≤ l ≤ 20
Reflections collected
3186
Independent reflections
1800 [Rint = 0.0234]
Completeness to theta = 25.00°
98.2%
Refinement method
Full-matrix least-squares on F2
Data/restraints/parameters
1800/2/222
Goodness-of-fit on F2
1.084
Final R indices [I > 2σ(I)]R1 = 0.0288, wR2 = 0.0706
R indices (all data)
R1 = 0.0371, wR2 = 0.0772
Absolute structure parameter0.32(15)
Largest diff. peak and hole
0.551 and –0.656 e·Å–3
Note: Standard errors in the tables are in parentheses and represent the lastsignificant numbers.

149

done using ShElX97 (Sheldrick 1997), and the crystal data are given in Table 1.
CIF1 files are on deposit.
Refinement proceeded with the ideal starting positional parameters of theiron and sulfur atoms as suggested by Koto et al. (1975). Initially overall isotropic atomic displacement parameters for the iron and sulfur atoms, respectively,
were used while refining positional parameters of all atoms and occupancies
for the iron atoms. The occupancies of those iron atoms that refined close tounity were fixed as such and occupancies of four atomic sites were further
refined. Individual isotropic displacement parameters were then introduced,
and finally, anisotropic displacement parameters (ADPs). Final refinement
consisted of a scale factor, a twin refinement with transformation matrix(1 0 0, 0 –1 0, 0 0 –1) and positional parameters and ADPs, together with occupancies of four Fe atoms, refined simultaneously. Final R-values of 0.029 using 1493
reflections with I > 2σ(I) and R = 0.034 for all 1800 reflections were obtained.
The goodness of fit value was S = 1.084 for the refinement of 222 parameters. The
calculated composition obtained from the refinement was Fe10.99S12 with a standard
deviation of 0.06 in the Fe composition as compared to the analyzed composition of
Fe10.91Ni0.05S12. The standard deviation in (Fe+Ni) is 0.11 for the analyzed crystal.
The model of Koto et al. (1975) with two iron atoms having half occupancies
and all others fully occupied was also tested and gave R = 0.035 for 1493 reflections with I > 2σ(I) and 0.0432 for all 1800 reflections, refining 220 parameters.
Using the hamilton significance test, (hamilton 1965) the ratio of R-factors forthe two models, using all data, is 1.16 as compared to F2,1578,0.005 = 1.003 for 1800
reflections, (dimension = 2, degrees of freedom = 1578). Therefore, the hypothesisthat only two vacant sites are present can be rejected at the 0.005 level. In addition,
the calculated composition using this model, refined to a formula of Fe89.21S96 or
Fe11.15S12. This does not correspond to the analyzed composition of Fe10.91Ni0.05S12,
although it still is within the range of compositions defined by the standard deviation of the microprobe analyses.
Therefore, the structure of the 6C pyrrhotite will be reported as having four
partially occupied sites in the structure instead of two. The atomic positional andanisotropic displacement parameters are given in Tables 2 and 3, with the standard
errors in parentheses.
Table 4 gives the bond lengths, octahedral angular variance (OAV) and polyhedral quadratic elongation (PQE) as defined by Robinson et al. (1971), for thedifferent octahedra surrounding the iron atoms. The latter two parameters were
Deposit item AM-10-005, CIF files. Deposit items are available two ways: Fora paper copy contact the Business Office of the Mineralogical Society of America(see inside front cover of recent issue) for price information. For an electronic
copy visit the MSA web site at http://www.minsocam.org, go to the American
Mineralogist Contents, find the table of contents for the specific volume/issue
wanted, and then click on the deposit link there.
1

Table 2.

Atomic coordinates, occupancies, and equivalent isotropic
displacement parameters for pyrrhotite-6C (space group Fd)

x
y
z
Occ
Ueq
Fe1
0.1360(5)0.1296(7)0.0002(1)1.000
0.028(1)Fe2
0.1154(7)0.1324(5)0.0840(1)1.000
0.023(1)Fe30.1451(7)0.1128(3)0.1668(1)1.000
0.019(1)Fe4
0.1173(10)0.1288(6)0.2507(1)1.000
0.029(1)Fe5
0.1162(8)0.1291(3)0.3351(1)1.000
0.018(1)Fe6
0.1395(10)0.1241(3)0.4193(1)0.898(6)0.026(1)Fe7
0.1196(10)0.1223(7)0.5034(2)0.661(4)0.028(2)Fe80.1421(12)0.1292(6)0.5810(2)0.556(5)0.015(2)Fe9
0.1096(8)0.1231(3)0.6649(1)1.000
0.022(1)Fe10
0.1325(10)0.1220(5)0.7501(1)1.000
0.026(1)Fe110.1363(8)0.1353(4)0.8335(1)0.874(6)0.018(1)Fe120.1151(8)0.1125(3)0.9164(1)1.000
0.020(1)S10.3761(8)0.0408(3) –0.0422(2)1.000
0.010(1)S2
0.3756(9)0.0408(3)0.1215(1)1.000
0.012(1)S3
0.3781(9)0.0419(2)0.2926(2)1.000
0.012(1)S4
0.3778(8)0.0417(3)0.4610(2)1.000
0.016(1)S5
0.3762(9)0.0415(3)0.6257(2)1.000
0.014(1)S6
0.3752(9)0.0433(2)0.7925(2)1.000
0.011(1)S7
0.3750(7)0.2075(3)0.426(2)1.000
0.013(1)S8
0.3788(7)0.2076(3)0.2096(2)1.000
0.014(1)S90.3753(9)0.2084(4)0.3752(2)1.000
0.009(1)S10
0.3782(7)0.2100(3)0.5401(2)1.000
0.013(1)S11
0.3770(7)0.2079(3)0.7057(2)1.000
0.014(1)S120.3756(8)0.2085(4)0.8782(2)1.000
0.011(1)Notes: Ueq is defined as one third of the trace of the orthogonalized Uij tensor.

150

DE VIllIERS AND lIlES: 6C PyRRhOTITE

calculated by the program XtalDraw (Downs and hall-Wallace 2003). Again, as in
the case of the 5C pyrrhotite (deVilliers et al. 2009), the shortest Fe-Fe distances
are along the c-axis, i.e., between face-sharing octahedra.
Part of the crystal was ground in a mortar and pestle, deposited on a lowbackground sample holder and examined with a PANalytical X’Pert PRO diffractometer equipped with an X’celerator detector and variable incident anddiffracted beam slits. Refinement using CoKα was done using the commercial
TOPAS academic software (Coelho 2007), modified by Coelho for refinement in
the non-standard Fd space group.
The structure as described in the non-standard Fd setting is useful for thecomparison of the different pyrrhotite structures because of the orthogonal geometry of their unit cells. however, it is not compatible with the most commonlyused programs using crystallographic information, such as Rietveld refinement,
electron microscopy, and materials modeling programs. The non-standard setting
was therefore transformed to the conventional Cc setting, which also included atransformed twin relation to correspond to this setting. The Cc structure is related
to the Fd structure by the transformation matrix: (1 0 0, 0 1 0, –½ 0 ½), with twin
relation (1 0 0, 0 –1 0, –1 0 –1). Refinement of the conventional Cc structure gives
an identical R-value of 0.029. The transformed unit cell and structural parameters
are given in Table 5, and the atomic parameters and anisotropic displacement
parameters in Tables 6 and 7.

desCRiPtion of the stRuCtuRe
The structure of the 6C pyrrhotite is essentially that describedby Koto et al. (1975). On the examination of the superstructurereflections they proposed a structure consisting of two halfoccupied iron sites together with fully occupied sites. The ironatoms are octahedrally coordinated with sulfur atoms arranged ina hexagonal close packed arrangement. They proposed an orderedarrangement where two layers containing half-occupied sites
alternate with a fully occupied layer. The sequence is represented
as: FDaDaFDbDbFDcDcFDdDdFDaDaF…, where Da, Db,
Dc, and Dd represent defect-containing layers where the a,b,c,dsites are half-filled. This is shown in Figure 1. The outline of
the structure shown in the figure is different from that used by
Tokonami et al. (1972) and Koto et al. (1975) in that the originof the structures are shifted by ¼, ¼, 0. This shift, first used by
Wang and Salveson (2005), allows the 4C and 6C pyrrhotite
Table 3.

Anisotropic displacement parameters (Å 2 × 10 3) for
pyrrhotite-6C

U11
U22
U33
U23
U13
U12
Fe1
26(2)
50(2)
9(1)
–2(1)
–1(2)
1(2)
Fe2
21(2)
32(2)
14(1)
0(1)
5(2)
7(2)
Fe3
23(2)
21(2)
14(1)
–3(1)
2(1)
3(1)
Fe4
35(3)
41(2)
10(1)
–2(1)
0(2)
–9(2)
Fe5
24(2)
17(1)
14(1)
–3(1)
2(1)
–7(2)
Fe6
36(3)
29(2)
13(2)
7(1)
1(2)
–12(3)
Fe7
29(3)
22(2)
32(3)
0(2)
–1(3)
9(3)
Fe8
15(3)
14(2)
16(3)
–6(2)
8(2)
–7(2)
Fe9
21(2)
24(2)
19(1)
7(1)
–3(2)
7(2)
Fe10
37(3)
26(2)
16(2)
–1(1)
–4(2)
7(2)
Fe11
27(3)
22(2)
6(1)
–4(1)
3(2)
–1(2)
Fe12
25(3)
24(1)
11(1)
–3(1)
–3(1)
7(2)
S1
10(2)
11(1)
8(2)
1(1)
2(2)
–1(2)
S2
15(2)
10(2)
10(2)
1(1)
4(2)
–1(2)
S3
9(2)
10(1)
16(2)
0(2)
3(2)
–3(2)
S4
9(2)
7(2)
33(2)
0(1)
6(2)
1(2)
S5
12(2)
8(2)
22(2)
–2(1)
7(2)
3(2)
S6
9(2)
11(1)
12(1)
1(2)
2(2)
–3(2)
S7
12(3)
9(2)
17(2)
–2(1)
6(2)
4(1)
S8
11(2)
10(2)
20(2)
0(1)
3(3)
1(2)
S9
10(2)
7(2)
10(2)
0(1)
2(2)
1(2)
S10
10(3)
12(2)
18(2)
1(1)
6(2)
6(1)
S11
9(2)
13(2)
18(2)
3(1)
6(2)
3(2)
S12
11(2)
7(2)
14(2)
0(1)
3(2)
0(2)
Note: The anisotropic displacement factor exponent takes the form: –2π2[h2a*2U11+ ... + 2 h k a*b*U12].

figuRe 1. Vacancy distribution of iron in the different layers in 6C
pyrrhotite as proposed by Koto et al. (1975) and refined with two partial
occupancies. Two layers containing approximately half-occupied Fe sites
alternate with a layer containing fully occupied sites (filled circles). The
adjacent half-occupied sites always project on top of each other.
Table 4.
Atom
Fe1

Metal-sulfur bond lengths (in angstroms) of the octahedra
in 5C pyrrhotite
Bond
S1
S3
S4
S7
S10
S11
Fe2
Fe12

Lengths Atom Bond Lengths Atom Bond Lengths
2.451(7) Fe2 S22.469(7)Fe3S2
2.391(7)2.520(8)S32.526(6)S4
2.399(6)2.471(7)S52.444(8)S52.486(7)2.392(7)S72.460(7)S82.463(7)2.446(7)S10
2.415(7)S11 2.552(7)2.478(8)S122.439(7)S12 2.522(6)2.896(3)Fe1
2.896(3)Fe2 2.876(5)2.905(4)Fe32.876(5)Fe4 2.911(3)Ave. M-S
2.460
2.459
2.469
OAV
6.118
11.67824.762PQE
1.00211.0035
1.0074Fe4S3
2.531(8) Fe5 S32.550(8)Fe6S1
2.463(7)S42.458(7)S52.474(7)S42.398(9)S62.430(7)S62.446(7)S52.488(7)S72.433(7)S72.445(6)S8
2.447(6)S8
2.482(7)S92.450(8)S92.445(8)S112.462(8)S122.421(7)S12 2.519(9)Fe32.911(3)Fe42.914(4)Fe5 2.909(4)Fe52.914(4)Fe6
2.909(4)Fe7 2.908(7)Ave. M-S
2.466
2.464
2.460
OAV
5.266
4.660
6.952
PQE
1.00171.00161.0022Fe7
S1
2.498(9) Fe8 S22.540(9)Fe9S12.459(6)S4
2.498(8)S52.468(10)S22.413(8)S62.396(8)S62.456(7)S52.484(8)S72.391(8)S72.454(9)S82.435(7)S82.534(8)S92.472(8)S92.441(6)S10
2.426(9)S102.360(9)S11 2.532(7)Fe62.908(7)Fe72.864(5)
Fe8 2.909(7)Fe82.684(5)Fe92.909(7)
Fe10 2.946(3)Ave. M-S
2.457
2.459
2.461
OAV
6.851
12.06011.187PQE
1.00241.00381.0034Fe10
S12.434(7) Fe11 S2
2.481(7)Fe12 S1
2.454(7)S32.480(8)S32.531(7)S22.401(6)S62.413(8)S62.435(7)S42.402(7)S82.464(8)S92.465(7)S92.464(8)S102.437(7)S10
2.380(7)S11 2.451(6)S112.502(8)S122.423(7)S12 2.507(7)Fe92.946(3)
Fe10 2.881(4)Fe1 2.905(4)Fe11 2.881(4)Fe12 2.878(4)Fe11 2.878(5)Ave. M-S
2.455
2.452
2.462
OAV
4.365
14.14120.734PQE
1.00151.0043
1.0062
Notes: The octahedral angular variance (OAV) is in degrees squared and thepolyhedral quadratic elongation (PQE) is dimensionless. The shortest metalmetal distances are also given.

DE VIllIERS AND lIlES: 6C PyRRhOTITE

structures to be directly compared with the 5C pyrrhotite.
The above structure refines to an R-factor of 0.035 anddeserves consideration despite the fact that refinement of theoccupancies of four Fe sites gives a lower R-factor, which issignificant at the 0.005 level, and that the composition refines to
one that corresponds better with the analyzed composition. The
occupancies of the two sites [Fe7 = 0.643(8) and Fe8 = 0.564(7)]refined in the structure proposed by Koto et al. (1975) are shownin Figure 1. These occupancies refine to values >0.5 and theoverall composition to Fe11.15S12, which is more metal-rich thanthe microprobe analysis (Fe10.91Ni0.05S12).
The structure where the four atomic sites are refined isshown in Figure 2. The structure is essentially the same as theone discussed above, but with two additional partially occupied
sites with occupancies of 0.90 and 0.87. Apparent here is thefact that the adjacent partially occupied sites always project on
top of each other. This is also the case in the 5C structure. Two
Table 5.

Crystal data and structure refinement for pyrrhotite-6C(space group Cc)

Identification code
Empirical formula
Formula weight
Temperature
Wavelength
Crystal system
Space group
Unit-cell dimensions
VolumeZ
Density (calculated)
Absorption coefficientF(000)
Crystal size
Theta range for data collection
Index ranges
Reflections collected
Independent reflections
Completeness to θ = 25.00°
Absorption correction
Max. and min. transmission
Refinement method
Data/restraints/parameters
Goodness-of-fit on F2
Final R indices [I >2σ(I)]R indices (all data)
Absolute structure parameter
Extinction coefficient
Largest diff. peak and hole

Pyrrhotite 6C-Cc
Fe11S12999.07293(2) K
0.71073 Å
Monoclinic
Cc
a = 6.8973(15) Å
α = 90°b = 11.954(3) Å
β = 101.302(4)°c = 17.602(4) Å
γ = 90°1423.1(5) Å3
4
4.663 Mg/m3
12.585 mm–1
1912
0.12 × 0.12 × 0.12 mm33.46 to 26.36°–8 ≤ h ≤ 7, –12 ≤ k ≤ 14, –21 ≤ l ≤ 123186
1800 [Rint = 0.0234]
98.2%
Semi-empirical from equivalents
0.221 and 0.210
Full-matrix least-squares on F2
1800/2/222
0.971
R1 = 0.0288, wR2 = 0.0726
R1 = 0.0368, wR2 = 0.0801
0.516(4)00.514 and –0.696 e·Å–3

151

possible models were proposed by Koto et al. (1975) for thisphenomenon that involved the random stacking of two layers
in the structure, one containing vacancies, and one containing
fully occupied sites, giving rise to the partial occupancies of
0.5. Confirmation of these models will have to wait for studies
utilizing transmission electron microscopy and materials modeling techniques. These will be attempted after crystallographic
studies on other pyrrhotites.
The layer occupancies of the 6C structure are also calculated
and compared with the 4C and 5C layer occupancies calculated
from the structures described by Tokonami et al. (1972) and deVilliers et al. (2009) respectively. This is given in Figure 3.
A comparison of the calculated powder diffraction patterns of
the 5C and 6C structures is given in Figure 4. It can be seen thatthey are almost indistinguishable. This means that distinction andquantification of the two NC pyrrhotites is presently not likely
using conventional X-ray powder diffraction methods. This was
confirmed by the refinement of 6C pyrrhotite diffraction datausing either the 5C or the 6C structural data. Using TOPAS, both
structures gave excellent refinements using the 6C diffraction
data. For the 6C structure with the 6C diffraction data, Rwp =0.017 and RBragg = 0.0121, and for the 5C structure with the 6C

figuRe 2. The vacancy distribution of sites in the different layers in
6C pyrrhotite. Four sites are partially occupied, with two sites that arealmost fully occupied and two sites that are approximately half-filled.
layers 1, 4, 7, and 10 contain two sets of vacant sites. Fully occupied
sites are shown as spheres.

figuRe 3. A comparison of layer occupancies in 4C, 5C, and 6C pyrrhotites. The 4C structure is the only one containing ordered vacant sites.
layers 0 and 8 in 4C, 0 and 10 in 5C, and 0 and 12 in 6C pyrrhotite are identical.

152
Table 6.

DE VIllIERS AND lIlES: 6C PyRRhOTITE
Atomic coordinates (×104) and equivalent isotropic displacement parameters (Å2 × 103) for pyrrhotite-6C (spacegroup Cc)

x
y
z
Occ
Ueq
Fe1
0.1226(5)0.1315(6)0.0015(2)1.00
0.024(1)Fe20.2264(7)0.1314(5)0.1692(2)1.00
0.026(1)Fe3
0.2813(6)0.1125(3)0.3345(2)1.00
0.021(1)Fe4
0.3925(8)0.1299(5)0.5020(2)1.00
0.026(1)Fe50.4715(10)0.1265(3)0.6707(2)1.00
0.022(1)Fe6
0.5354(9)0.1242(3)0.8390(2)0.892(6)0.024(1)Fe7
0.6402(14)0.1211(6)0.0078(4)0.667(4)0.032(2)Fe8
0.6983(10)0.1293(5)0.1632(4)0.555(5)0.013(1)Fe90.8125(8)0.1211(3)0.3301(2)1.00
0.021(1)Fe10
0.8683(10)0.1257(4)0.5005(2)1.00
0.026(1)Fe110.9557(10)0.1348(5)0.6679(2)0.875(6)0.017(1)Fe120.0604(8)0.1128(3)0.8336(2)1.00
0.021(1)S10.3409(9)0.0416(4)0.9240(4)1.00
0.015(1)S2
0.5060(9)0.0408(4)0.2528(3)1.00
0.013(1)S3
0.6723(9)0.0436(3)0.5866(4)1.00
0.012(1)S4
0.8380(9)0.0416(4)0.9180(4)1.00
0.010(1)S5
0.0040(9)0.0409(4)0.2449(3)1.00
0.012(1)S6
0.1710(9)0.0419(3)0.5856(4)1.00
0.012(1)S7
0.4180(7)0.2089(4)0.0824(3)1.00
0.012(1)S8
0.5860(8)0.2077(4)0.4118(3)1.00
0.013(1)S90.7580(8)0.2086(4)0.7571(3)1.00
0.011(1)S10
0.9234(8)0.2090(4)0.0874(3)1.00
0.014(1)S11
0.0899(8)0.2089(4)0.4209(3)1.00
0.014(1)S12
0.2574(7)0.2077(4)0.7523(3)1.00
0.009(1)Notes: Ueq is defined as one third of the trace of the orthogonalized Uij tensor.

Table 7.

Anisotropic displacement parameters (Å 2 × 10 3) for
pyrrhotite-6C (space group Cc)

U11
U22
U33
U23
U13
U12
Fe1
22(2)
41(2)
8(1)
–2(1)
1(2)
1(2)
Fe2
28(3)
37(2)
14(1)
1(1)
5(2)
3(2)
Fe3
19(2)
26(2)
16(2)
–5(1)
1(2)
–10(1)
Fe4
26(2)
43(2)
9(1)
1(1)
1(2)
11(2)
Fe5
29(3)
22(1)
14(2)
–3(1)
5(2)
2(2)
Fe6
28(3)
30(2)
12(2)
7(1)
0(2)
12(2)
Fe7
39(4)
28(2)
29(3)
–2(2)
6(3)
11(3)
Fe8
7(3)
11(2)
19(3)
–1(2)
1(2)
6(3)
Fe9
26(2)
19(2)
20(2)
4(1)
11(2)
–2(2)
Fe10
36(2)
24(2)
17(2)
–2(1)
1(2)
–10(2)
Fe11
26(3)
17(1)
6(1)
0(1)
–1(2)
0(2)
Fe12
32(2)
21(1)
11(1)
–5(1)
8(2)
–8(2)
S1
7(2)
7(2)
32(2)
–4(2)
5(2)
–2(2)
S2
9(2)
9(2)
22(2)
–1(2)
4(3)
–2(2)
S3
8(2)
12(1)
15(2)
–1(2)
–1(2)
6(2)
S4
11(2)
10(2)
9(2)
0(2)
0(2)
1(2)
S5
14(2)
8(2)
13(2)
–1(1)
–2(2)
4(2)
S6
9(2)
8(1)
19(2)
–3(2)
1(2)
0(2)
S7
7(2)
12(2)
13(2)
2(1)
–5(2)
–2(2)
S8
12(3)
14(2)
11(2)
3(1)
–1(2)
0(2)
S9
7(2)
10(2)
16(2)
2(2)
1(3)
–3(2)
S10
11(2)
9(2)
21(2)
0(1)
4(3)
0(2)
S11
8(2)
9(2)
24(2)
3(1)
0(3)
3(2)
S12
13(3)
7(2)
8(2)
3(1)
3(2)
–1(2)
Note: The anisotropic displacement factor exponent takes the form: –2π2[h2a*2U11+ ... + 2hka*b*U12].

figuRe 4. (a) Calculated powder XRD patterns of 5C (solid line) and 6C (crosses) pyrrhotite. The two patterns are almost identical except forminor peaks below 25 °2θ. (b) Expanded XRD pattern below 25 °2θ. The very weak unique peaks can be seen.

diffraction data Rwp = 0.0188 and RBragg = 0.0097.
Presently, the only reliable methods for their distinction are
careful electron microprobe analysis or single-crystal X-ray
methods. Rietveld methods will therefore only distinguish between 4C and NC pyrrhotites.

aCknowledgments
Donation of the single crystal by Bruce Cairncross of the University of Johannesburg is acknowledged with thanks. Because of the scarcity of good singlecrystal material, this sample is especially valuable. Microprobe analysis of thesample by Peter Gräser is gratefully acknowledged. Thanks also to Alison Tulingfor expert assistance with graphic challenges. Alan Coelho modified TOPAS toaccommodate the non-standard space groups into the program. Thanks to him forpatience and expertise.

RefeRenCes Cited
Bruker (2001) SAINT+ Version 6.45, SADABS Version 2.10. BRUKER AXS
Inc., Madison, Wisconsin.
Coelho, A. (2007) Technical Reference. TOPAS ACADEMIC, Version 4.1, July
2007.
de Villiers, J.P.R., liles, D.C., and Becker, M. (2009) The crystal structure of anaturally occurring 5C pyrrhotite from Sudbury, its chemistry, and vacancy
distribution. American Mineralogist, 94, 1405–1410.
Downs, R.T. and hall-Wallace, M. (2003) The American Mineralogist crystal

structure database. American Mineralogist, 88, 247–250.
hamilton, W.C. (1965) Significance tests on the crystallographic R factor. Acta
Crystallographica, 18, 502–510.
Koto, K., Morimoto, N., and Gyobu, A. (1975) The superstructure of the intermediate pyrrhotite. I. Partially disordered distribution of metal vacancy in the 6C
type, Fe11S12. Acta Crystallographica, B31, 2759–2764.
Morimoto, N., Gyobu, A., Mukaiyama, h., and Izawa, E. (1975) Crystallography
and stability of pyrrhotites. Economic Geology, 70, 824–833.
Powell, A.V., Vaqueiro, P., Knight, K.S., Chapon, l.C., and Sanchez, R.D. (2004)
Structure and magnetism in synthetic pyrrhotite Fe7S8: A powder neutron diffraction study. Physical Review B, 70, 014415.
Robinson, K., Gibbs, G.V., and Ribbe, P.h. (1971) Quadratic elongation: A
quantitative measure of distortion in coordination polyhedra. Science, 172,
567–570.
Sheldrick, G.M. (1997) ShElX97—Programs for Crystal Structure Analysis(Release 97-2). Institüt für Anorganische Chemie der Universität, Göttingen,Germany.
Tokonami, M., Nishiguchi, K., and Morimoto, N. (1972) Crystal structure of a
monoclinic pyrrhotite (Fe7S8). American Mineralogist, 57, 1066–1080.
Wang, h. and Salveson, I. (2005) A review on the mineral chemistry of thenon-stoichiometric iron sulfide, Fe1–xS (0 ≤ x ≤ 0.125): polymorphs, phaserelations and transitions, electronic and magnetic structures. Phase Transitions, 78, 547–567.
Manuscript received March 31, 2009
Manuscript accepted septeMber 10, 2009
Manuscript handled by Guoyin shen