American Mineralosist
vol .57, pp. 1066-1080 (1972)

CRYSTAL STRUCTURE OF A MONOCLINIC(FezSs)PYRRHOTITE
Mesev,s.su TonoNAlrr,l K.q.rsuHrse Nrsrrrcucur' aNl Nosuo
MoRtr,toto,sInstitute of Scientifi,cand Industrial Research,
Osaka Uni"uersity, Suita, Osaha 565, Japan.
Assrnecr
The crystalstmctureof the monoilinic4C-type pyrrhotite (Fe'S")has beenrefinedusingthe three-dimensional
intensity data collectedwrth Zr filtered MoK"
radiationfrom an untwinnedcrystalfrom Kisbanya,Rumania.This crystalhas-{- 0.008,b = 6859 -F 0.005,c - 22.187+ 0.010
the cell dimensionsof a = 11.902
A, andp - 90"26'-{-3'. It wasrefinedin spacegroupFZ/d and the final weighted-R factoris 0.045for 487crystallographicallyindependent
reflections.
The structure obtained confirms the ordered arrangement of vacant positions
for iron atoms proposed by Bertaut (1953), and gives shifts of iron and sulfur
atoms from the atomic positions in the ideal NiAs-type structure. All iron atoms
lie between six sulfur atoms with octahedral arrangements and also between a few
iron atoms which must be considered to be the nea.restneighbors becauseof
short Fe-Fe distances.The mean Fe-S bond lengths in the four FeScoctahedra
are 2.446,2.456,2449,and,2.444A, and the Fe-Fe distancesare 2868, 2.911,and
2.956A along the c axis. In the iron layer normal to the c axis, one of the Fe-Fe
distance is 2944 A, though the others are more than 3.1 A. The group of seveniron atom3 along the c axis can be consideredas a collective unit in the 4C-typepyrrhotite as the triangular group in the troilite structure. Each iron group isconnected with two others through the short Fe-Fe bonds in the basal ironlayers.
T'he atomic arrangements around the vacant positions for iron atoms show
slight contraction of the vacant spacein comparisonwith the space around ironatoms.
INrnooucrroN
Pyrrhotite(Fer-"S)has been extensively

studied, because of theimportance and complexity of its phase relations, structures, andmagnetic properties. A detailed review on the studies of the properties
and structures of pyrrhotite has been given by Ward (1970). Five
different types of pyrrhotite have been conflrmed to be stable at room
temperature by studying single crystals of natural pyrrhotite (Morimoto, Nakazawa, Nishiguchi, and Tokonami, 1970; Morimoto, NakalPresent address: Fachbereich Geowissenschaften;Mineralogie, Kristallographie, Petrologie, Philipps-Universiilit, 355 Marburg/Lahn, Deutschhausstr.10,
Germany.
'Present address: Industrial Research Institute of Chiba Prefecture, Chiba
280,Japan.
" To whom all the corresnondenceshould be addressed.
1066

MONOCLINICPYRNHOTITE

1067

zawa, Tokonami, and Nishiguchi, 1971). The flve types are superstructures of the NiAs-type structure, with cell dimensions ,4., about
3.45 A; C about,5.8 A; and have essentially stoichiometric compositions, Fe,-1S, (n ) 8), with the structures of (n/2)C type for n evenand of nC Lype for n odd (Morimoto, Nakazawa, Nishiguchi, andTokonami, 1970). Three new types of pyrrhotite stable at high temperatures were also describedby Nakazawa and Morimoto (1971).
Monoclinic pyrrhotite of the 4C-type superstructure occurs innature at and near the composition FerSr, with a : 213A, b : 2A,
and c : 4C, and 0 : 90.4o. On the basis of geometry of the diffraction
patterns of trvinned crystals of this pyrrhotite, Bertaut (1953) proposedthat the superstructure contained ordered vacancies in alternate ironlayers normal to the c axis. The space group and cell dimensions determined by him, were recently confirmed by Corlett (1968) and Wuensch(Ward, 1970) using untwinned crystals. However, there was no report on
the crystal structure of the monoclinic 4C-type pyrrhotitebased on thecomparison of the observed and calculated structure factors, though
the structure of troilite (FeS) was determined by Bertaut (f956) andrefined by Evans (1970) and that of the hexagonal 3C-type was determined by Fleet (1971).
The present investigation has been initiated to describe the crystal
structure of the monoclinic 4Ctype pyrrhotiie using the three-dimensional counter-measured intensities and to elucidate the arrangementof vacant positions for iron atoms and the effects of the vacancies on
the shifts of iron and sulfur atoms from the ideal NiAs structure. The
characteristics of complex magnetic and electric properties of thepyrrhotite can be explained based only on the precise crystal structure.
ExpontlrpNt,uMany crystals of monoclinic pyrrhotite from various localities were examinedby the X-ray single crystal method to find single crystals for structure determination. The crystals examined were in twin relations by 60' or 120' rotation
about the pseudo-hexagonalc* axis. Cr5'g1r1*from Kisbanya, Rumania were also
examined, which had been describedby Corlett (1968) and given to us by her.
Though the crystals also showed the twin relations, a small platy fragment with
0.03 X 0.03 X 0.01mm was found to be untwinned, and used for intensity collection throughout in this study. AII attempts to obtain larger single crystals than
this specimenwere not successful.
If we assume symmetry centers in the structure of the pyrrhotite, the possible
space group is C2/c, which was conveniently expressedas F2/d'by Bertaut (1953)
to keep an approximate orthogonal relation between the axes. This centrosymmetricspace group was adopted during the structure determination and successfulrefinement of the structure confirmed this choice. The ceII dimensions were determinedfrom the goniometry of the reciprocalIattice points 12.4.0,6.6.0, and 0.0.32 using
the Rigaku four-circle automatic diffractometer with Mo-Kor radiation (I : 0.70929

1068

TOKONAMI,NISHIGUCHI,

AND MORIMOTO,E). Based on space grortp F2/d,, they are a : 1L.902 + 0.008, b : 6.859 + 0.005,
c : 22.787 + 0.010 A, and F : 90o26' :t 3' in good agreement with the values
obtained previously (Corlett, 1968; Wuensch,1969).The estimated standarddeviations of the cell dimensions were obtained by the relative errors derived from theequation, 2d, sir' 0 : /rtr, considering possible errors in reading of angles. The calcuIated density of this specimenis 4.62 B.cm-: for eight FezSaunits in the unit ceII,
which is in good agreement with the observed value of 4.56 g'cm-a (Palache,
Berman, and Frondel, 1955).
The integrated intensities were measuredusing the automatic diffractometerwith Zr-filtered MoKa radiation (0.7107A). The intensitiesof 487 crystallographically independentreflectionswere measuredwithin the range of sin a/I ( 0.5 by
the e20 scan technique. The specimen was so small that 75 reflectionshad theintensities equal to or less than the background values, and were regarded to be
zero in intensity. Reflections with sin 0/x > 0.5 were not measured. The intensity
data were converted into observed str-ucture factors by applying the standard
Lorcntz and polarization corrections.The absorption correction was not made,becausethe linear absorption coefficientwas 125 cm-' and the maximum Iength of
the specimenwas 0.003cm.
Srnucrunn DprnnrurNerroNeNr Rprrununxt
Bertaut (1953) proposed a crystal structure for the C-lype monoclinic pyrrhotite based on the space group FZ/d (Fig. 1), but he did not give explicitly any
atomic coordinatesof the structure. In order to describethe atomic coordinates,
the space group F2/d is maintained and expressedby the following coordinate
system (Fig. 2) throughout in this investigation:
origin at T on a 'diamond' glide plane d with a translation of (a I c) /a;
unique axis b;
coordinates of equivalent positions:(0,0,0; t, *, 0; i,0, L;0,4,\) *r, !1,z', L - r, A, L - zl i, !, 2; i I r, U, i I z.
The geometrical structure factors for this system are as follows:[h+t:+"

A : 16 cos2r(hr * le) cos 2rky, B : 0;

lh + lt :2n:4n+2{h+t :2nlh+h

A :-16 sln?n(hx f lz) sin 2rhy,B : 0; and:2n*I

fn+t or

1o*, : 2 n * l

A:B:0

According to this system,the atomic coordina,tesof iron atoms determined byBert"aut are described as in Table I by fixing one of the vacant positions at 1,/8,
l/8,7/8 (Fig. 1). The iron atoms in the filled layers are representedin this investigation by odd numbers [Fe(l) and Fe(3)] and those in the vacancy-containing
layers are by even numbers [Fe(2) and Fe(4)]. For this a.rrangementof ironatoms, two alterrative arrangements of sulfur atoms are possible, because there
are two possible positions for sulfur layers in the closest packing relation with theiron layers. The atomic coordinates of sulfur atoms in one of the arrangements

MONOCLINIC PYRRHOTITE

1069

c

Frc. 1. The ideal structure of ihe 4C-type pyrrhotite proposed by Bertaut(1953) based on space $oup FZ/d. Only iron layers are indicated and sulfur layers
are omitted for simplicity. Squa,resrepresent vacant sites.

r070

TOKONAMI, NISHIGUCHI,

AND MORIMOTO

Frc. 2. Spacegroup sJrmmetryand equivalent positions of F2/d.

a,relisted in Table 1, while those in the other can be obtained by replacing (r,U, z) for sulfur atoms by Q/A - n, a, e) in Table 1. The choice between these
two arrangements was carried out by comparison of F, and F" for hkl withh:
!2 (mod 6) and I - -+-4 (mod 16), because the contributions of sulfur
atoms to .F, of these reflections are same in absolute value but opposite in signfor these two altematives. Becausethe atomic coordinatesof zulfur atoms listed
in Table I gave better agreement between l', and F, for the reflections mentioned above, they were determined to be correct ones for this stmcture.
tr'ull matrix least-squares refinements of the structure were carried out on the
FACOM 230-60 of Kyoto University with the use of RStr'LS-4 of the UNICS
system (universal crystallographic computation system, crystallographic societyof Japan, 1967)modified by Sakurai from ORFLS written by Busing, Martin, and

table

1.

AtomicbasedonNumberequivaleDt
PeI
Fe2
Fe4
SI

s2
s4

coordinatEs
the

ideal

of
points

I6
l6
16
I
15
16
I5

of
structurethe

4C-type
proposeClSi tes)metry

xy

t
L
I
2
1
lt
I

3/e
3/8
3/8
3/8
s/24
3/24
s/24
3/24

3/8
3/8
3/8
3/8
3/8
3/8
3/A
3/e

pyrlhotirebyBertaut

0
t/8
2/8
3/8
-t/L6
I/16
3/16
5/!6

(Fe?58)(I953).

MON OCLIN IC P'' RRHOT IT E

1071

Levy (1962).The function minimized is 1/(o)"ll1,l - lf'.ll', where o represents
the estimated standard deviation computed from counting statistics' The estimated standard deviations of the weakest non-zero reflections were uscd for thereflections which were regarded.as zero intensity. Scattering factors were takenfrom MacGillavry and Rieck (1962), assuming that sulfur atoms are doubly
ionized and iron atoms are the mixture of 5/7 Fe'* and 2/7 Fe'*. Isotropic temperature factors were assumedas 1.0 for all atoms. Refinement was initiated using
the atomic coordinatesof the ideal stmcture (Table 1), with the arrangementof
sul{ur atoms describedabove, which gave ,R - 0.395.
The full matrix least-squares failed by divergence of the E coordinates when thex, y, and a coordinates were allowed to vary together. The first two cycles were,
therefore, carried out with the fixed g coordinates varying only the t and z coordinates. In the next two cycles, all the z, E, a coordinates were allowed to vary.
The final four cycles were carried out varying the atomic coordinates and isotropic
temperature factors. The final R factors for all reflections and for reflections excluding
zero intensity are 0.134 and 0.093, respectively. The final weighted E factor was
0.045. At this stage, the order of differencesbetween F. ar'd F have become almost"
equal to the order of oF, resulting in 1.69 for the quantity of error of fit,[Ir" {(f" - F")16F.'l/(N" - ,liro;trz,where ff" is the number of observedreflections and No the number of adjustable parameters. Any further refinement withincreased number of parameters is, therefore, likely to result in no significant
improvement. In fact, attempts to determine the ordering of ferric and ferrous ionsin the structure or the anisotropic temperature factors for the atoms in the stnrcture
were not successful.
The final atomic coordinates and the individual isotropic temperature factors
with the estimated standard deviations are given with the amount of displacements
of atoms from the ideal structure (Table 2). Fo and .F, values are on deposit.l
Dnscnrprrox
The

interatomic

oF THE Srnucrunn

distances and the bond angles (Table

3 and 4)

were computed wiih the program RSDA-4 of the UNICS system(1967) based on the final atomic coordinates (Table 2). The estimatedstandard deviations of the atomic coordinates were used to computethe standard deviations in the interatomic distances and the bondangles.
Deuiation from th"eid,eal structtae
The result of the refinement confirms the ideal structure proposedby Bertaut (1953). Sulfur atoms approximately occupy the nodes of
the hexagonal closest packing and iron atoms are regularly arranged
1To obtain a copy of this material,order NAPS DocumentNumber 01805.
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prrce.

1072

TOKONAMI,N ISHIGACH I, AN D MORI MOT,O

TabLe 2.
Finalatoniccooldinates
and isotlopic
temperatulefactors
for atons ln
plrrhotite(fe-S")(Fe,so)Pyrrnotrte
obtainedin thisstud.y.
Estinatedslandard
deviations
are"The coluns
in parentheses:of axll , b * l A vl ,l a n d c l A z l
Iacqent
in Angstron(195
froh-the-ideElsE r u c t u r e
by Bertaut

I rat
Fe3
Fe4

s2
s4

0 . 3 8 0 9( 3 )0 . 3 8 1 5( 4 )0 . 3 5 8 7( 3 )0.37500 . 2 0 6 1( s )0 . 5 4 1 8( 5 )0.2096(5)0 . s 4 2 8( 5 )0.070
0. 079
0.194
0,025
0.00L
0.015
0.013

0.35000 . 3 6 6 0I I
0.39750.35281 )0.36600.38330 . 3 8 5 8 l-5
0 . 36 4 5

O .I 7 I
0.062
0.154
0.r52
0.062
0.057
0.074
0.072

- 0. 0 0 6 3o,r2340r250I
0.3750-0.06r8
0.05980.I8050.308?

0.144
0.035
0.002
0.0r5
0.r60
0.087

0.94(r0
0.89 (B
0.7s(10
I.4r (130 . 7 8( 1 5
0.6r(140.50(r4
0 . 6 5( 1 5in the octahedral interstices of the sulfur atoms. The vacancies among
the iron sites are in ordered arrangement and conflned to alternate
layers of iron atoms and normal to the c axis (Fig. 1). These vacancies
result in slight displacements of iron and sulfur atoms from the positions in the ideal structure proposed by Bertaut (Table 1). The
amounts of displacement of atoms in the final structure are given in
Angstriim along the a,b, and c axes (Table 2).
Coordinations of iron and sullurr atoms
Because of the ordering of vacant sites for iron atoms and the displacements of iron and sulfur atoms from the ideal structure, coordinations of iron and sulfur atoms indicate some characteristics in the
structure under discussion in comparison with the structures of troilite(Evans, 1970) and of the 30-type pyrhotite (Fleet, 1921).
All the iron atoms lie between six sulfur atoms with octahedral
aruangements and also between other iron atoms, which are so closethat the iron atoms are coordinated both by sulfur atoms and by ironatoms as described later in detail.
The bond lengths and the bond angles around the iron atoms (Table3) indicate that the octahedra of sulfur atoms are not much distorted
in this structure. The mean distancesof Fe-S are 2.446,2.M9,2.486,
a n d 2 . 4 M A f o r t h e o c t a h e d r ao f F e ( l ) , F e ( 2 ) , F e ( 3 ) , a n d F e ( 4 ) ,respectively. These values a,re compared with the corresponding onesof 2.491 A in troilite (Evans, 1970) and 2.448 L in the BC-typepyrrhotite (Fleet, 1971).
All the Fe-Fe distances are more than 3.1 A in the basal iron layers
except the Fe(3)-Fe(3)distance with 2.94+ A in the filled layer(Table 4). This makes a clear contrast with the structure of troilite,
where the formation of triangular groups is characteristic in every
basal iron layer with the Fe-Fe distance of 2.glg A (Evans, lg70).
However, the Fe-Fe distances between the neighboring iron layers
are rather short along the c axis in the 4C-type structure, ranging from2.868 to 2.956 A (Table 3). They show systematic change along the c1073

M ONOC.LIN IC PYRRHOT] TE
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t074

TOKANAMI,NISHIGUCHI,

AND MORIMOTO

T3ble 4.
Fe-Fe
alistancesin the vacancy
containing
and fil,led
iron,
layers.
Estimated
standalddeviations
are in parentheses,
fheiron
atoms are.locatedby the following
Letterst f, x=L/8ig, x=3/8ij, y=!./eih, x=5/8,i, ye-L/8i
k, y=5/8ie, y=j/9.
Vacancy-containing
layer

Filledlayerz >3/8

Fe4 -Fe2hj
Fe4 -Fe2hk
Fe2hj -Fe2hk

3.263 (7)3.613 (7)3 . 4 3 4( 1 1 )Fe3-Felhk
Fe 3 -Fe 19 t.
reJ-!

efga

3 . 6 7 8( 6 )3 . 1 0 9( 9 )3 . 2 0 1( 6 )3 . 7 6 0( 9 )Fa1-Fa1FLFelhk-Petgl,Felfj -Felgi

9 2 6( 6 1
2 9 4 4( 6 1
3 4r8(6)3 s 1 4( 7 )axis: 2.868A for the central Fe (4)-Fe (3) distanceincreasesto 2.956A
f o r t h e F e ( 2 ) - F e ( 1 ) d i s t a n c et h r o u g h 2 . 9 1 1A f o r t h e F e ( 3 ) - F e ( 2 )distance (FiS. 3). The linear arrangement of iron atoms along the caxis in the ideal NiAs structure (Table 1) can be compared withthe slightly bent arrangement in this structure where the angles
Fe(1)-Fe(2)-Fe(3),Fe(2)-Fe(3)-Fe(a),and Fe(3)-Fe(a)Fe (3) are 174.06",166.05o,and 167.7lo,respectively.
Because a bonding interaction is expected between iron atoms withinteratomic distancesof about 3.0 A or less (Goodenough,1g62), Fe(l)is coordinated by one iron atom [Fe(2)l Fe(2), and Fe(4) by twoiron atmos [Fe(2) by Fe(3) and Fe(4), and Fe(a) bV two Fe(3)],and Fe(3) by three iron atoms fFe(2), Fe(3), and Fe (a)1, besides by the six sulfur atoms with octahedral arrangement describedabove (Figs. 3 and 4). The Fe-Fe bonding in this structure will be
discussedlater in more detail.
The sulfur atoms are eoordinated by five iron atoms which are on
the corners of a trigonal prism because of a vacant site on one of thecorners. Only S(a) is coordinated by six iron atoms as in troilite( F i s .3 ) .

The structure as a whole can be described to be built up of chain
elements of seven octahedra of sulfur atoms around iron atoms,
elongating along the c axis, in which the octahedra are united bysharing two opposite faces. The chain elements thus formed are connected sideways by sharing edges with the neighboring ones (Fig. B).
Atomic arrangement around, the uacant site
Vacant sites:for iron atoms are orderly distributed in the vacancycontaining basal layers, and are surrounded by six sulfur atoms andtwo iron atdms. It is of interest to examine the arrangement of theseneighboring atoms around the vacant sites. The amount of displacements of these neighbors from the positions in the ideal structure are

1075

MO N OCLIN IC PY RRH OT I I'E

z=#
z=H

z=i8
z=H
z-*
z= 116z,*-7 = 316z=*

1-7 = 16z=-*z--*
Frc. 3. Schematic drawing of the crystal structure of the 4C-type pyrrhotite.
A group of seven octahedra of sulfur atoms around iron atoms builds a collective unit along the c axis, in rvhich the octahedra are united by sharing two
opposite faces.

TOKONAXII. N ISHIGUCH I. AN D MORIMOTO

( 1I

tzt

(31

t4t

Frc. 4. The coordination schemesof iron atoms in the 4C-type pyrrhotite.

schematicallyshownin Figure 5, wherethe arrowsrepresentthe componentsof the displacements
alongthe a, b, andc axes.
In order to comparethe atomic arrangementaroundthe vacant sitewith that around the iron atoms in the structure, a hypothetical site(X) was determinedfrom the positions of octahedralsulfur atoms
aroundthe vacant site so that all the X-S distancesbecomeapproximately same. The coordinatesof the X site were obtained to be(0.3750,0.3668,-0.1250). The mean valuesfor the X-S, X-tr'e, and
S-S distancesaroundthe X site are comparedwith thosefor the Fe-S,
Fe-Fe, and S-S distancesaroundthe iron atoms (Table 5). The result
seemsto indicatethat the octahedraof sulfur atomsaroundthe vacantsitesare only slightly smallerin comparisonwith thosearoundthe ironatoms.The X-Fe distanceis, however,significantlysmallerthan the
Fe-Fe distances.
Drscussrorq
Becausethe vacant sites are distributed in the structure as far as
possiblefrom each other and the atoms around the vacant sites arelikely to morreto reducethe vacant space,the structureof the 4C-typepyrrhotite seemsto be essentiallyionic.
In order to obtain a clue to the distribution of Fe,* and Fe3*,thestabilization energieshave been calculatedfor different distributionsof Fes*and Fe2*on the basisof the refinedstmcture.The distributionsof Fe3* were limited into the following four typical models after
Bertaut (1953),

MONOCLINICPYRRHOTITE

L077

model 1 (distribution of Fe' '"* at, all the iron sites),model2 (distributionof Fe'* at the Fe(2) sites),model3 (distributionof Fe'* at the Fe(l) sites)andmodel 4 (distribution of Fe'* at the Fe(4) sites and a partof the Fe(l) sites).
The calculations were carried out by using a Madelung constantprogram (Unpublished report by Quintin Johnson of the Lawrence
Radiation Laboratory, 1965)adaptedto FACOM 230-60computerat
Kyoto University. The stabilization energiesare as follows:-276.3 kcal/mol,model 1-395.6 kcal/mol,model2-409.9 kcal/mol andmodel3-408.5 kcal/mol.
model4The conclusion that the model 3 is most stable among the four models
is different from that obtained by Bertaut (1953) based on his ideal
structure, which gave the sta.bilization energies of -495 kcalmol forhis model 4 and of -472 kcal/mol for his model 3. Our result seems
reasonable because the electric unbalance caused by the vacancies ofiron atoms can be compensatedby the additional charge of Fe(l)atoms which are the nearest cations of the vacant sites.

T"'aFrc. 5. Displacements of atoms around the vacant site from the positions in
the ideal structure prgposed by Berta,ut (1953). The a;ITowsrepresent the components of displacements along the a, b, and c axes.

1078

I'OKONAMI,

aaDre

).
and
are

NISHIGUCHI,(A)
The mean distances
thosefor Fe-s,
Fe-Fe andthoseof bonds considered.

arounal x

aroundx-s(6) 2.439
s-s (12) 2.450 s-s(12)s-s(3) 4.876 s-s(3)x-Fe(2) 2.708

Fel

for
s-S

AND MORIMOTO

the vacant
site
x-S,
x-Fe
and s-s aroundin parentheses
iron
atoms.
Nuber
aroundaroundFe2

2 . 4 4 6 F e 2 - s( 6 ) 2 . 4 4 9
3.458
3 . 4 5 0 s-s (12)4.876 s-s(3)4.889
Fe2-Fe(2)2.934

around
Pe3-s (6)s-s(r2)s-s(3)
Fe3-Fe(3)Fe3around(x)Fe4Fe3-s(6) 2.444
2.456
3.454
3.451 s-s(12)4.881
4.885 s-s (3)Fe4-Fe(2) 2.858
2.908

However, the \{6ssbauer spectra of the C-type pyrrhotite show nosign of Fet* even at, 4.2oK (Hafner and Kalvius, 1966; Levinson andTreves, 1968). This means that even at this low temperature the Fe'*and Fet* ions do not have separate existencefor a time longer than thatoccupied by the Mossbauer transition (10-?-10-8 sec.). These results
seem to reveal that the stability of pyrrhotite should be treated on thebasis of an ionic model not of Feu'*Fert*Sr'-, but of Fer22s+S82(model 1),
although its calculated stabilization energy is not favorable.
Furthermore the observation of the Mijssbauer spectra of the
4C-type pyrrhotite (Hafner and Kalvius, 1966; Levinson and Treves,1968) provides three different magnetic flelds at the sites of the ironatoms which are caused by the magnetic interactions between theiron neighbors in the structure. The application of an external
magnetic field and the intensity ratio for the various subspectra
indicate that the three different magnetic fields correspond to theFe(2) and Fe(4), Fe(1) and Fe(3) (Levinson and Treves, 1968).
Because the iron neighbors are different for these three kinds of ironatoms as explained above (Fig. 4) , the structure obtained in thisstudy explains well the results of the Miissbauer study.
According to Goodenough (1962), there are critical values ofcation-cation separation below which the d-electron must be treatedby means of collective system rather than localized one. In the Fe1-,Ssystem the critical separation is about 3.0 A, (Goodenough,1962).
Accepting this critical value for the Fe-Fe separation, the groupof seven iron atoms along the c axis ean be considered as a collective
unit, in the 40-type pyrrhotite (Fig. 3) like the triangular group in
the troilite structure. Each iron group is connected with two others
through the short Fe(3)-Fe(3) bonds in the filled iron layer, forming
an endless chain elongated along [101] (Fig. 6). The formation ofthese iron clusters possibly increases the stability of the apparent
ionic model of Ferz'zo+grz-.
The complicated structure of iron clustering found in the 4C-typepyrrhotite must be important for understanding of the long-rangeordering of vacant sites in the superstructures of pyrrhotite at various

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seveniron atomselongatedalongthe c axis.
temperatures and compositions (Morimoto, Nakazawa, Tokonami, andNishiguchi, 1971; Nakazawa and Morimoto, 1971).
ACKNoWLEDGMENTS

We expressour thanks to Dr. Mabel Corlett for providing us with the specimens from Kisbanya, Rumania, and to Dr. Quintin Johnson for providing us the
Madelung Constant Program. Thanks are also due to Drs. H. Nakazawa andH. Horiuchi for illuminating discustionsthroughout this work, to Mr. A. Gyobu
for drawing the figures, and to Miss M. Hirano for typing the manuscript.
Rr:rr:nnNcns
Benraut, E. F. (1953I Contribution ir, ll6tude des structures lacunaires' ,4cla
C r ystallogr.6,537-56^.
(1956) Structure de FeS stoichiometriqne. Bull. Soc. Franc. Mhnral.
Crg stallo gr. 79, 276-292.
BusrNc, w. R., K. O' MenuN,,rxn II. A. Lnvv (1962)ORFLS, A Fortran Crystallographic Least-SquaresProgram. U. 8. Nar. Tech".Info. Seru' Rep. ORNLTM-305.
Conr,nrr, Mennl, (1968) Low-iron polymorphs in the pyrrhotite group. Z. KristalIogr. 126,124-134.
EveNs, H. T., Jn. (1970) Lunar troilite: Crystallography. Science,767,621423.
Fr,nnr, M. E. (1971) The crystal structure of a pyrrhotite (Fe"S"). Acta CrgstalIogr. 827, 1864-1867.
Goooououcu, JonN B. (1962) Cation-cation three-membered ring formation.
J. AppL Phss. 33,1197-1199.

1080

TOKONAMI,N ISHIGACHI,

A.ND MORIMOTO

Herxnn, SrnnaN, eNn Mrcrranr, ILqlvrus (1966)'The Mrissba,uerresonance of FeF
in troilite (FeS) and pyrhotite (Feo*S). Z. Kristallogr. r2g, 44345&.
MecGrr,r,evnv, C. H., ello G. D. Rrncr (eds.) (1962) Inte,ntatinnal Tables Jor
X-ray Crystallography, Vol. 3, Kynoch Press, Birmingham.
LnvrrsoN, Lroxer, M., arvt D. Tnnves (1968) Miissbauer study of magnetic structure of Fe"Ss.,f. Phys. Chem. Solids, 29,2227-2231.
Monruoro, N., H. Narezewe, K. Nrsnrcucur, eNl M. Toroxerrr (1970) Pyrrhotites: Stoichiometric compounds with composition Fe-,S" (z ) 8). Science,
168.964-966.
-,-t
M. ToroNennr,ern K. Nrsnrcucrrr (1971) Pyrrhotites: Structure
type and composition. Soc. Mining Geol. Ja,p.,Spec. Issue, 2, 15-21. [Proc.
IMA-IAGOD Meeting'70. Joint-Symp. Vol.J
NerAzawe, E[., aNn N. Monrrroro (1g71) Phase relations and zuperstructuresof
pyrrhotite, Fer-,S.Mater. Res. BuIl.6, B4b-358.
Per,ecno, C., H. BnnlreN, eNn C. Fnorvnnr,(1g55) Dana's Sgstem ol M,i,neralogg,
Vol. t. John Wiley and Sons, New York, p. 2BB.
Wano, J. C. (1970) The structure and properties of some iron sulfides.Reu. Ptne
Appl. Chem.20, 175-W.
Mantncript receiuecl, February 11, 1972; accepted,lor publication, Febntnry pS,
1972.