4 N a 2 S O 4 . 2 D 2 0 2.

NaC1 917

Table 2. Bond lengths (A) and angles (°)

X-ray
data*
)7 ×
S(1)-O(1) 1.448 (9) 1.44 (1)
S(1)-O(2) 1.500 (6) 1.47 (1)
S(1)-O(3) 1.505 (9) 1.47 (I)
0 ( 4 ) - 0 ( 4 ~) 1.37 (1) 1.33 (2)
D(1)-O(4) 0.96 (1) -

O(1)-S(l)-O(2) 111.4 (4) 110.4 (3) (a) (b)

O(I)-S(1)-O(3) 110.9 (6) 110.0 (6) Fig. 1. View of the D202 molecules. Each molecule has a site
O(1)-S(1)-O(2 H) 111.4 (4) 110.4 (3) occupancy of 0.5. The hydrogen-bonding scheme 0 ( 4 ) -
O(2)-S(1)-O(3) 108.1 (4) 109.0 (3) D( l). . . 0(3) is shown. (a) Projection on to (001). The centre of
O(2)-S(1)-O(2") 106.8 (5) 107.9 (5) the diagram is at x = 0.5, y -- 0.0. (b) Projection on to (100).
O(3)-S(1)-O(2 u) 108.1 (4) 109.0 (3) The centre of the diagram is aty = 0.0, z = 0.25.

The dihedral angle for D202 is 100.1 (6) ° 0 ( 4 ) . . . O(1TM) 2.85(1) A. It is likely from these figures
that 0 ( 4 ) . . . 0 ( 3 ) is the hydrogen bond since the
Symmetry code
0 ( 4 ) . . . O ( W I) distance is close to the van der Waals
(i) 1 - x, -y, z (x) ½-x, ½+Y, ½-z diameter for an O atom. In addition the D atom lies
(ii) x, y, - z (xi) ½--x,--l+Y, ½--z
(iii) x , l + y , z (xii) ½- x, l + Y, - l + z close to the line between 0(4) and 0(3). We have
(iv) 1-x,l-y,z (xiii) ½ - x, - ½ + y, ½ + z O(4)-D(1) 0.95 (1), D(1).-.O(3) 1.62 (1) A, 0 ( 4 ) -
(v) 1-y,x,z (xiv) ½+x, ½ - y , ½ - z D(1)...O(3) 163 (1) °.
(vi) 1½--x,½+Y, ½--z (xv) -½ + x, ½- y, ½- z
(vii) ½+ y, ½+ x, ½-- z (xvi) y, 1 - x, z We thank Laporte Industries for the gift of the 87 %
(viii) ½+ x, ½- y, --½ + z (xvii) 1 +x,l +y,z hydrogen peroxide and the Science Research Council
(ix) -½ + x, ½- y, ½ + z
for support during the data collection.
* Adams & Pritchard (1978).
References
Table 3. Coordination around the cations ADAMS, J. M. & PRITCHARD, R. G. (1978). Acta Cryst. B34,
1428-1432.
Na(l)-O(3 t'l) 2.485 (8) A Na(2)-O(2 v'll) - )
Na(1)-O(41") 2.707 (13)+-'1 O(2Jx) BUSING, W. R. & LEVY, H. A. (1965). J. Phys. Chem. 42,

t
Na(l)-O(l v) 2.290 (7) | 0(2 x) 3054-3059.
Na(1)-O(2 vl) 2.347 (7) ! 0(2 x') 2.557 (3) A German patent (1975). No. 2 530 539, filed 9th July 1975.
Na(I)--O(2 vii) 2.316 (7) or O(2Xl~) Kao Soap Ltd., and Nippon Peroxide Co. Ltd.
Na(I)-O(4 viI) 2.249 (11) ~ 0(2 ~l'l)
Na(1)-CI(1 ~vu) 3.029 (7) 0(2 ~') HEWAT, A. W. (1973a). Rutherford Report R R L 73/239.
0(2 ~) The Rietveld computer program for the profile refinement
hydrogen-bonding scheme. In the previous X-ray study of neutron diffraction powder patterns modified for
anisotropic thermal vibrations.
(Adams & Pritchard, 1978) it was shown that the
HEWAT, A. W. (1973b). J. Phys. C, 6, 2559-2572.
peroxide 0(4) was close to the sulphate 0(3) and HEWAT, A. W. & BAILEY, A. (1976). NucL Instrum.
O(1TM) and it was therefore possible that the hydrogen Methods, 137, 463-471.
bond could be to either of these O atoms since the International Tables for X-ray Crystallography (1974). Vol
O . . . O distances were similar, 2.71 (2) and 2.68 (2),/k IV. Birmingham: Kynoch Press.
respectively. We have found in the neutron study that PEDERSEN, B. F. (1969). Structural Aspects of Perhydrates.
the O . . . O distances are less similar than those for the Oslo: Universitetsforlaget.
non-deuterated compound: 0 ( 4 ) . . . 0 ( 3 ) 2.51 (1) and RIETVELD, H. M. (1969). J. Appl. Cryst. 2, 65-71.

Acta Cryst. (1981). B37, 917-920

The Structure of Magnetite

BY MICHAEL E. FLEET

Department of Geology, University of Western Ontario, London, Ontario, Canada N6A 5B7

(Received 4 November 1980; accepted 2 January 1981)

Abstract. Fe30 4, cubic, Fd3m, a = 8.3941 (7)A. The temperature on a single-crystal diffractometer with Mo
structure has been refined to a weighted R of 0.033, Ka (4 = 0.7107/k) radiation. The oxygen positional
using 147 unique averaged reflexions collected at room parameter (u) is 0.2549 (1). The observed M--O bond
0567-7408/81/040917-04501.00 © 1981 International Union of Crystallography
918 MAGNETITE

distance and electron density distribution in the vicinity (~2 × 10 4 S m -1) through continuous exchange of
of the O atom are consistent with a common Fe 3+ electrons between Fe 2+ and Fe a+ in the octahedrally
nucleus for M site atoms. Residual electron density at coordinated position. This fast electron-hopping hy-
equipoint position 8(b) is assigned to interstitial Fe 3+ in pothesis is also supported by M6ssbauer spectra of
a second tetrahedrally coordinated position. Thus magnetite above the Verwey phase transition, which
natural magnetite at room temperature has a defect indicate a single six-line hyperfine spectrum for M site
structure with an interstitial-vacancy couple similar to atoms (Bauminger, Cohen, Marinov, Ofer & Segal,
that reported for ferrous oxide. 1961; Ito, Ono & Ishikawa, 1963). The relaxation time
for fast electron hopping is assumed to be appreciably
less than that expected for Fe2+-O and F e a + - o bonds,
Introduction. Magnetite has the inverse-spinel struc- and M site Fe 2+ and Fe 3+ should appear in X-ray
ture with space group Fd3m (Bragg, 1915; Claasen, structure analysis as one atom. Certainly, modern
1926; Verwey & de Boer, 1936; Shull, Wollan & theories on the electronic structure of magnetite predict
Koehler, 1951). The O atoms, at equipoint position a common Fe 3+ nucleus for M site Fe atoms, with an
32(e), form an approximate cubic close-packed array, itinerant 3d electron either having a fast electron-
with one Fe 3+ per formula unit at a tetrahedrally hopping role (Lotgering & van Diepen, 1977) or
coordinated position, equipoint 8(a), and Fe 2+ and the delocalized within a conduction band (Evans, 1975). At
remaining Fe 3+ randomly distributed at an octa- the outset of the present investigation it was intended to
hedrally coordinated position, equipoint 16(d) (Fig. 1). ascertain whether the thermal parameters and residual
The single positional parameter (u) locates the O atom. electron density, particularly of the O atom, were
The structure was most recently refined by Hamilton consistent with a common nucleus for M site atoms, or
(1958), using neutron diffraction data, to give u = with an average structure of short-range ordered
0.2548 (2). Due to their remarkable solid-state proper- discrete Fe 2+ and Fe a+ atoms.
ties, magnetite and related spinel ferrites have been The present investigation was made on natural
extensively examined by scientists of diverse magnetite occurring as euhedral octahedra in a
specialities, and this has resulted in some confusion in magnetite-chlorite schist (No. 633, Dana Collection,
structural terminology. In the present paper, tetra- University of Western Ontario). This material was
hedral and octahedral metal positions will be referred to thoroughly characterized by polished-section petro-
either explicitly or as T and M sites respectively. The graphic examination, electron microprobe analysis, and
familiar 'A' and 'B' notation is not adopted as these single-crystal X-ray diffraction procedures as single-
symbols are already used in the general chemical phase, essentially end-member magnetite. Observed
formula, AB204. reflexions on precession and Weissenberg films are
The inverse-spinel configuration was originally sug- consistent with space group Fd3m. Sporadic, very
gested by Verwey & de Boer (1936) to account for the weak hk0 reflexions with h + k = 4n + 2 (e.g. 420),
anomalously high electrical conductivity of magnetite observed on long-exposure films, were confirmed as
multiple reflexions (Samuelsen, 1974) by varying the
conditions of diffraction. Least-squares refinement of
17 centred reflexions measured on a four-circle
diffractometer with graphite-monochromatized Mo Ka
(2 = 0.7107 A) radiation gave a = 8.3941 (7) A, which
is in good agreement with published data for Fe304
e ~ i ~,.~o,, ~ O ~ M (Hamilton, 1958).
The crystal selected for the structure refinement was
an approximately equidimensional single-crystal frag-
ment bounded by (100), (010), (112) and (112), with a
calculated volume of 1.8 x 10 -3 mm a. The X-ray
intensity data were collected at room temperature on a
Picker FACS 1 four-circle diffractometer system by the
0-20 scan technique: 40 s stationary background
.l'
counts, peak-base widths of 2 ° 20 and a scanning rate
of 2 ° min -~. All hkl and hkl reflexions with h + k,
k + l, l + h = 2n out to 20 = 90 ° were measured. The
X resulting data were processed with program DA TAP77
(SUNY at Buffalo) and corrected for background,
Fig. 1. Crystal structure of magnetite within x = 0 to ½,y = 0 to ½, Lorentz and polarization effects, and absorption.
z = 0 to ½, showing location of residual electron density at T(2)
site (small open circles) and in the vicinity of 7", M and O sites Transmission factors for the absorption correction
(dots). were calculated by Gaussian integration with a 12 × 12
 MAGNETITE 919

Table 1. Positional and thermal (/k 2) parameters f o r magnetite

Anisotropic thermal parameters (x 105) are calculated from T = exp [-I(B~ h2a .2 + B22k2b.2 + B3312e.2 + 2B~2hka* b* cos 7* +
2B13hla* c* cos fl* + 2B23klb* c* cosa *)].
Equipoint
position x y z B~ B~2 (B)
T 8(a)* ~ ~ ~ 349 (14) 0 0.34 (2)
M 16(d) ½ ½ ½ 461 (14) 45 (5) 0.46 (2)
O 32(e) 0.2549 (1) 0.2549 (1) 0.2549 (1) 541 (24) -3 (17) 0.49 (3)

* Origin at centre (3m).

Table 2. Residual peaks on F o - F c maps f o r (Coppens & Hamilton, 1970), is 1.32 (10) x 10 -4, for
refinement with anisotropic thermal parameters refinement with anisotropic thermal parameters.
Very weak residual peaks are present in F o - F c
Relative maps for the refined magnetite structure (Table 2, Fig.
electron
Equipoint density 1). The most prominent residual electron density, that
position x y z (%)* in the 8(b) equipoint position, was tentatively assigned
to a second tetrahedrally coordinated position for iron,
8(b) ~ ~ ~ 1.0
96(g) 0.06 0.06 0.125 0.7 T(2). Further refinement with anisotropic thermal
96(h) 0 0.205 0.795 0.6 parameters and an assumed T(2) occupancy pro-
32(e) 0.22 0.22 0.22 0.7 portional to the residual electron density (Table 2)
reduced the weighted and conventional residual indices
* Relative electron density is percentage of peak Fo electron
density at position of T site. to 0.032 and 0.023 respectively.

Discussion. The present results for the oxygen position-

x 12 grid using a linear absorption coefficient of 14.65 al parameters (u) and interatomic distances and bond
mm -1. The crystal was oriented with [220] parallel to
angles in magnetite at room temperature (Table 3) are
the ~0 axis. The calculated transmission factors varied
similar to the earlier data of Hamilton (1958), with
from 0.245 for 020 to 0.348 for 0,12,10. The original improved precision. Comparison of the observed u
data list of 2565 reflexions was reduced to 147 parameter and metal-oxygen bond distances with
reflexions non-equivalent in Fd3m. Standard deviations values calculated from effective ionic radii (Shannon &
were calculated from the agreement between equivalent Prewitt, 1969, 1970) favours both the inverse-spinel
reflexions. Zero intensity was assigned if more than configuration (Verwey & de Boer, 1936; Hamilton,
25% of a set of equivalent reflexions had peak 1958) and a single Fe 3+ nucleus for M-site Fe atoms
intensities less than background plus one standard (Table 4).
deviation.
The magnetite crystal structure was refined in space
Table 3. Some interatomic distances and bond angle
group F d 3 m using program L I N E X 7 7 (SUNY at
in magnetite
Buffalo). Initial structural parameters were from Hamil-
ton (1958). Scattering curves for the neutral atomic T-O 1.8883 (17)/k O-O" 2.9689 (3)/k
species, and real and imaginary components of the M-O 2.0584 (9) O-O'" 2.8519 (27)
anomalous-dispersion corrections were taken, respec- M-M'* 2.9678 (3)
O-O' 3.0836(27) O-M-O"' 87.70 (6) °
tively, from Tables 2.2B and 2.3.1 of International
Tables f o r X-ray Crystallography (1974). The refine- *M' at It + x,t + y, ,~1, O' at Ix, l - y , l - z l , O" at [½-x,
ment with anisotropic thermal parameters and iso- ] +y,t + zl, O'" at Ix,]t-y,k-z].
tropic extinction converged on values for the weighted
and conventional residual indices of 0.033 and 0.024, Table 4. Observed and calculated bond distances and
respectively. Equivalent data for refinement with u parameters
isotropic thermal parameters are 0.039 and 0.027,
respectively. Final positional and thermal parameters Bond distances (A)
are given in Table 1.* The isotropic extinction Tetrahedral: Fe2+-O 2.03
parameter for type I extinction, Lorentzian distribution Fe3+-O 1.89 1.888 (2)
Octahedral: (Fe2+,Fe3+)-O 2.113
* A list of structure factors has been deposited with the British Fe3+-O 2.045 2.0584 (9)
Library Lending Division as Supplementary Publication No. SUP
35901 (2 pp.). Copies may be obtained through The Executive Parameter u
Secretary, International Union of Crystallography, 5 Abbey Normal structure 0.2618
Square, Chester CH 1 2HU, England. Inverse structure 0.2527 0.2549 (1)
920 MAGNETITE

The isotropic temperature factors (Table 1) are consistent with, respectively, occupied 1'2 orbitals on T
generally similar to the respective B parameters in atoms, occupied t2g orbitals on M atoms (as surmised
well-refined room-temperature structures of end- by Fleet, 1975), and even a singly occupied sp 3 orbital
member-composition oxide spinels and related phases lobe on O atoms.
(e.g. Morimoto, Tokonami, Watanabe & Koto, 1974; The presently proposed crystal structure may have
Yagi, Marumo & Akimato, 1974), and are signifi- profound ramifications for interpretation of the solid-
cantly lower than the respective data for a natural state properties of magnetite and related ferrites. The
titanomagnetite (Stout & Bayliss, 1975). However, anomalously high electrical conductivity of magnetite
many well-refined structures of related phases with may be more appropriately described by a semi-
mixed metal-site occupancies yield relatively low B conductor band model than by fast electron hopping.
parameters, and this correlation is probably not Investigation of other magnetite specimens, particularly
significant. For example, the mean B parameters of the those exhibiting diffuse scattering, is continuing.
T, M and O positions in a natural olivine (Mg0.gs-
Fe~.0~SiO4) are 0.41 (2), 0.48 (2) and 0.58 (5), respec- Dr P. Coppens kindly provided copies of computer
tively (Finger, 1970). programs D A T A P 7 7 and L I N E X 7 7 . This study was
The bulk electron density distribution in the vicinity supported by a Natural Sciences and Engineering
of the O atom is not noticeably bimodal or anisotropic. Research Council of Canada operating grant.
This observation favours a common nucleus for most,
if not all, M site atoms in the magnetite structure.
The weak but significant residual electron density at
References
equipoint position 8(b) must logically be associated
with one of the following possibilities: (i) incoherent BAUMINGER, R., COHEN, S. G., MARINOV, A., OFER, S. &
twinning, (ii) coherent twinning, (iii) interstitial Fe SEGAL, E. (1961). Phys. Rev. 122, 1447-1450.
atoms in the T(2) position. Additional reflexions BRAGG,W. H. (1915). Philos. Mag. 30, 305-315.
consistent with incoherent twinning have not been CLAASEN, A. A. (1926). Proc. Phys. Soc. London, 38,
observed in spite of extensive precession and Weissen- 482-487.
berg work on this magnetite. Furthermore, continuous COPPENS, P. & HAMILTON,W. C. (1970). Acta Cryst. A26,
71-83.
diffraction streaks consistent with coherent twinning EVANS,B. J. (1975). Am. Inst. Phys. Conf. Proc. 24, 73-78.
have not been observed. However, magnetite crystals FINGER, L. W. (1970). Carnegie Inst. Wash. Yearb. 69,
from another locality did exhibit markedly anisotropic 302-305.
diffuse scattering in the vicinity of certain Bragg FLEET, M. E. (1975). Acta Cryst. B31, 1095-1097.
reflexions. These diffraction streaks are non- HAMILTON,W. C. (1958). Phys. Rev. 110, 1050-1057.
systematically distributed in reciprocal space: streaks International Tables for X-ray Crystallography (1974). Vol.
on neighbouring Bragg reflexions are not parallel to IV. Birmingham: Kynoch Press.
common or symmetry-related reciprocal-lattice direc- ITO, A., ONO, K. & ISHIKAWA,Y. (1963). J. Phys. Soc. Jpn,
tions. Hence, this diffuse scattering may be attributed 18, 1465-1473.
LOTGERING, F. K. & VAN DIEPEN, A. M. (1977). J. Phys.
to point defects. Subsequently, long-exposure pre-
Chem. Solids, 38, 565-572.
cession films of magnetite crystals of the present MORIMOTO,N., TOKONAM1,M., WATANABE,M. & KOTO, K.
investigation showed similar diffuse scattering but of (1974). Am. Mineral. 59, 475-485.
weaker intensity. Thus, it is provisionally concluded ROTH, W. L. (1960). A cta Cryst. 13, 140-149.
that at room temperature natural magnetite has a SAMUELSEN,E. J. (1974). J. Phys. C, 7, L115-L117.
defect structure, with interstitial Fe 3+ atoms in the T(2) SHANNON,R. D. & PREWITT,C. T. (1969). Acta Cryst. B25,
position and corresponding vacancies in, most prob- 925-946.
ably, the octahedral position. This interstitial-vacancy SHANNON,R. D. & PREWITT,C. T. (1970). Acta Cryst. B26,
couple is similar to that reported for the defect structure 1046-1048.
of ferrous oxide (Roth, 1960). SHULL, C. G., WOLLAN, E. O. & KOEHLER, W. C. (1951).
Phys. Rev. 84, 912-921.
The weak residual electron density at equipoint
STOUT, M. Z. & BAYLISS, P. (1975). Can. Mineral. 13,
positions 96(g), 96(h) and 32(e) is consistent with the 86-88.
local displacements of neighbouring T, O and M atoms, VERWEV, E. J. W. & DE BOER, J. H. (1936). Recl. Tray.
respectively, required for equilibrium T ( 2 ) - O and Chim. Pays-Bas, 55, 531-540.
T(2)--M bond distances (Fig. 1). However, the spatial YAGI, T., MARUMO,F. & AKIMOTO,S. (1974). Am. Mineral.
distribution of this residual electron density is also 59, 486-490.