Phys Chem Minerals (1999) 26: 446±459
Ó Springer-Verlag 1999
ORIGINAL PAPER
R. Miletich á M. Nowak á F. Seifert á R.J. Angel
G. BrandstaÈtter
High-pressure crystal chemistry of chromous orthosilicate, Cr2SiO4.
A single-crystal X-ray diffraction and electronic absorption
spectroscopy study
Received: 23 July 1998 / Revised, accepted: 12 December 1998
Abstract The high-pressure behaviour of chromous orthosilicate, Cr2SiO4, has been studied by means of single-crystal X-ray di€raction and electronic absorption
spectroscopy. X-ray di€raction data show that the
structure remains orthorhombic to the highest pressure
reached of 9.22 GPa. The compressibility of the unit-cell
is strongly anisotropic with the c axis approximately six
times more compressible than the a and b axes. A thirdorder Birch-Murnaghan equation of state ®tted to the
volume-pressure data yields V0 = 610.10(3) AÊ3, K =
94.7(4) GPa, K¢ = 8.32(14). Cr2SiO4 is therefore more
compressible than the isostructural Cd analogue, even
though its molar volume is smaller. This unusual behaviour can be attributed to the fact that the Cr atom is
too small for the six-coordinated site that it occupies,
and the site is therefore strongly distorted. Structure
re®nements indicate that under high pressures the Cr
atom remains strongly displaced from the central position of the octahedron. Polarized and unpolarized electronic absorption spectra include a strong absorption
band occuring at 18.300 cm)1 for E//c (which is parallel
to the shortest Cr-Cr vector in the structure) which has
an unusually large half width (5000 cm)1), indicative of
electronic interaction between metal centres. Deconvolution of unpolarized high-pressure spectra show that
R. Miletich1 (&) á M. Nowak2 á F. Seifert á R.J. Angel
Bayerisches Geoinstitut, UniversitaÈt Bayreuth,
D-95440 Bayreuth, Germany
G. BrandstaÈtter
Atominstitut der OÈsterreichischen UniversitaÈten,
A-1020 Wien, Austria
Correspondence address:
Laboratory for Crystallography, ETHZ ZuÈrich,
Sonneggstrasse 5, CH-8092 ZuÈrich, Switzerland
e-mail: [email protected]
Also at:
2
Institut fuÈr Mineralogie, UniversitaÈt Hannover,
D-30167 Hannover, Germany
1
the relative integrated intensity of this component increases linearly from 40% at 1 bar to 60% at 11.2 GPa.
Both the structural changes and the absorption spectra
at high pressures suggest that pairs of adjacent Cr atoms
in chromous orthosilicate form chromium dimers with a
weak metal-metal bond, which is consistent with the
diamagnetic response found at ambient pressure.
Key words Chromous silicate á High-pressure á Crystal
chemistry á Chromium dimer á Metal-metal bonding
Introduction
Both terrestrial olivines included in diamonds from
mantle-derived magmas and lunar minerals contain Cr2+
(e.g. Haggerty et al. 1970; Burns 1975; Schreiber and
Haskin 1976; Hervig et al. 1980; Sutton et al. 1993). Based
on experimental work on Cr2+ substitution in olivine and
pyroxene Li et al. (1995) pointed out that the tendency for
the oxidation state of chromium (+2, +3) to change with
temperatures relative to other redox reactions makes
Cr2+ substitution a potentially useful monitor of temperature which could be used to evaluate lunar and terrestrial igneous di€erentiation processes. The distribution
of divalent chromium therefore provides an important
geochemical constraint for models of the evolution of the
Earth's mantle and its relationship to the Moon.
Chromous substitution in both (Mg,Cr)2SiO4 olivine
and (Mg,Cr)SiO3 clinopyroxene solid solutions increases
as temperature increases (Li et al. 1995). However, neither olivine-type Cr2SiO4 nor CrSiO3 clinopyroxene endmembers have been synthesized, and Cr2+ substitution is
limited to a maximum of approximately 25 mol-% and
75 mol-% respectively in the olivine and pyroxene solid
solution series (Li et al. 1995). All attempts to synthesize
the end-members at temperatures below 1400 °C result in
a phase assembledge of Cr2O3+Cr metal+SiO2. At
higher temperatures a non-olivine type chromous orthosilicate Cr2SiO4 is produced, which has also been
previously synthesized by quenching melts from super-
447
liquidus conditions (Scheetz and White 1972; Gasparik
1981). The structure of this phase, originally determined
on the basis of X-ray powder di€raction data (Dollase
et al. 1994), has the structure-type of thenardite
(=Na2SO4-V, Zachariasen and Ziegler 1932; Mehrota
et al. 1978; Rasmussen et al. 1995), although both thermodynamic considerations based upon partial molar
volumes in (Mg,Cr)2SiO4 solid solutions (Li et al. 1995)
and cation size arguments (Muller and Roy 1974) suggest
that Cr2SiO4 should adopt the olivine structure-type.
In Cr2SiO4 the chromium atom is strongly displaced
from the centre of its octahedrally co-ordinated site, so
that the co-ordination approximates a planar arrangement of four oxygen ligands with two additional, very
weak bonds to one side of this distorted-planar Cr2+O4
group. Stabilization of such a square-planar geometry is
expected for Cr2+ cations because the 3d4 con®guration
normally leads to strong Jahn-Teller distortion in sixfold
co-ordination. The observed out-of-centre displacement
of the Cr (relative to a regular octahedron) simultaneously leads to a reduction of the Cr Cr distance
between the Cr positions of adjacent polyhedra to
2.75 AÊ, a distance which is intermediate between that
typical of quadruple Cr-Cr bonds (1.83 and 2.54 AÊ,
Cotton and Walton 1993) and of non-interactive
Cr Cr contacts in oxygen-based compounds (>3.1 AÊ).
Dollase et al. (1994) suggested that the Cr Cr distance
was indicative of electronic interaction between the Cr
atoms and that weak metal-metal bonding was present,
a proposal supported by ®rst-principles density-functional theory calculations (Stranger personal communication). More recently, polarized electronic absorption
measurements (Furche and Langer 1998) were interpreted in terms of both localized dd and dd* transitions
which would suggest that a dynamic exchange process
occurs between mono- and dinuclear species on a short
time scale. Here we report high-pressure X-ray di€raction and optical spectroscopic measurements which were
undertaken in order to determine the in¯uence of pressure on the stereochemistry and the electronic structure
of chromium atoms, as well as the nature of interaction
between the Cr pairs. The interpretation is strengthened
by the comparison of the structural data to the highpressure behaviour of Cd2SiO4 (Miletich et al. 1998)
which does not exhibit any such electronic coupling.
Experimental
Sample material
Crystals up to 250 lm in size were synthesized following the
method of Dollase et al. (1994). A stoichiometric mixture of
Cr2O3+SiO2+metallic chromium was loaded into a chromium
capsule and held at 3.5 GPa and 1550 °C for 1 h in a piston-cylinder apparatus using a conventional 1/2¢¢ talc-pyrex assembly.
Some crystals were found to be twinned on (201), but twin-free
crystals were selected on the basis of optical microscopy and singlecrystal X-ray di€raction. The single crystals used for these highpressure investigations are from the same sample batch used by
Furche and Langer (1998) and Miletich et al. (1997b).
Magnetic measurements at ambient pressures
The magnetic response of Cr2SiO4 was investigated at room pressure by SQUID magnetometry using quartz threads as sample
holder. Because of the small crystal size (8 ´ 105 lm3 maximum
volume), a set of 32 oriented Cr2SiO4 crystals, optically free of
inclusions, with a total weight of 0.29(1) mg was mounted on a
quartz plate in order to obtain a signi®cant signal. Measurements
were carried out at temperatures between 5 K and 293 K in magnetic ®elds l0H (with H parallel to the crystallographic axes) varied
from 0 to 1 T. For none of these measurements of Cr2SiO4 a signi®cant signal for the magnetic moment greater than 10)8 Am2 was
obtained thus indicating diamagnetic behaviour. Equivalent measurements made on a multi-crystal mount of 0.24(1) mg CaCrSi4O10 (Belsky et al. 1984; Miletich et al. 1997) were performed
in order to test the magnetometer set-up, and con®rmed the
paramagnetic response of CaCrSi4O10 (m = 1.4 ´ 10)6 Am2 at
l0H = 1 T and T = 5 K, linear dependence of the applied ®eld
l0H, and exponential decay of the magnetic moment with increasing temperature) expected for a mononuclear high-spin
square-planar Cr2+ complex.
High-pressure single-crystal di€raction
All of the high-pressure di€raction measurements were performed
with a BGI design diamond-anvil cell (Allan et al. 1996), using
diamond anvils with a 0.6 mm culet face diameter, a T301 steel
gasket, and a 4:1 methanol-ethanol mixture as pressure-transmitting medium. A 140 ´ 70 ´ 20 lm crystal was loaded with its
morphologically-predominant (010) face parallel to the culet faces,
together with a ruby for approximate pressure determination and a
quartz crystal to act as internal pressure standard (Angel et al.
1997).
Unit-cell parameters of both the Cr2SiO4 and the pressure calibrant crystal were determined using a Huber four-circle di€ractometer operated with non-monochromatized Mo X-ray radiation.
Details of the instrument and the peak-centring algorithms are
provided by Angel et al. (1997). The e€ect of crystal o€sets and
di€ractometer aberrations were eliminated by applying the di€racted-beam technique (King and Finger 1979). Unit-cell parameters determined by a least-squares ®t to the corrected setting
angles of re¯ections showed no deviations from orthorhombic
symmetry. The values of symmetry-constrained lattice parameters
obtained by a vector-least squares ®t (Ralph and Finger 1982)
determined from 41 to 44 accessible re¯ections in the 9.1±33.5°
range in 2h are reported in Table 1.
X-ray intensity data-sets were collected at 3.11, 5.30, 7.30, and
9.22 GPa in addition to the two data collections at ambient pressure
)4
(10 GPa), one in the DAC without any pressure medium and one
with the crystal mounted on a glass ®bre in air. All intensity-data
collection were carried out on a Nonius CAD4 four-circle di€ractometer using graphite-monochromatized MoKa radiation from an
X-ray tube operated at 50 kV and 50 mA. The measurements were
carried out with x-scans (scan range: 0.66°+0.35° tanh, scan time: 12
to 600 s) according to the ®xed-u technique (Finger and King 1978)
in order to maximize re¯ection accessibility and minimize attenuation of the X-ray beams by the pressure-cell components. All symmetry-allowed accessible re¯ections (‹h, ‹k, ‹l) were collected to
(sinh/k)max = 0.81 AÊ)1. Integrated intensities were obtained from
the scan data using a modi®ed Lehmann-Larsen algorithm (Grant
and Gabe 1978). Intensities were corrected for Lorentz and polarization e€ects, crystal absorption and, in case of the high-pressure
experiments, for the absorption e€ects of the diamond and beryllium
components of the pressure cell by a modi®ed version of ABSORB
(Burnham 1966). Averaged structure factors were obtained by averaging symmetry equivalent re¯ections in Laue symmetry mmm
following the criteria recommended by Blessing (1987).
The structure re®nements were carried out with RFINE90, a
development version of RFINE4 (Finger and Prince 1975) using
the coecients for scattering factors of neutral atoms and the coecients for dispersion corrections from the International Tables
448
Table 1 Variation of the unit-cell parameters of Cr2SiO4 with pressure
P (GPa)
0.0001a
0.0001b
1.561(6)
2.308(6)
3.106(5)
4.060(6)
5.303(6)
6.404(5)
7.300(6)
7.733(7)
9.220(11)
Quartz
Cr2SiO4
V(AÊ)
Nre¯
a(AÊ)
b(AÊ)
c(AÊ)
V(AÊ3)
Nre¯
n.d.
112.993(8)
108.825(11)
107.153(11)
105.539(10)
103.795(11)
101.772(12)
100.166(10)
98.967(12)
98.471(13)
96.660(21)
±
14
11
13
11
11
11
11
12
11
9
5.7005(3)
5.7007(2)
5.6908(2)
5.6863(3)
5.6804(3)
5.6736(2)
5.6650(2)
5.6573(2)
5.6512(4)
5.6480(3)
5.6374(4)
11.1651(3)
11.1653(5)
11.1402(5)
11.1299(6)
11.1174(7)
11.1033(6)
11.0863(6)
11.0717(6)
11.0598(9)
11.0551(8)
11.0375(11)
9.5847(3)
9.5850(2)
9.4754(2)
9.4295(3)
9.3842(3)
9.3339(2)
9.2742(2)
9.2262(2)
9.1910(4)
9.1735(3)
9.1192(4)
610.01(4)
610.09(4)
600.71(4)
596.77(5)
592.62(5)
588.00(4)
582.45(4)
577.89(4)
574.45(7)
572.79(6)
567.42(8)
44
44
43
41
44
43
42
43
41
41
41
Note: Pressures determined from unit-cell volumes of quartz internal di€raction standard by applying the EOS of Angel et al.
(1997).
Nre¯ = number of re¯ection used for the vector least-squares
re®nement of the unit-cell parameters
a
Crystal in air
b
Crystal in DAC without pressure transmitting medium
Table 2 Results of the ®ts for the pressure dependencies of the orthorhombic axes and the Birch-Murnaghan equation of state
a/a0 = 1.00005(4))1.14(19) ´ 10)3 GPa)1 ´ P)7.7(1.9) ´ 10)6 GPa)2 ´ P2
b/b0 = 1.00001(3))1.46(2) ´ 10)3 GPa)1 ´ P + 2.33(15) ´ 10)5 GPa)2 ´ P2
c/c0 = 0.99961(26))7.25(13) ´ 10)3 GPa)1 ´ P + 1.23(13) ´ 10)4 GPa)2 ´ P2
v2w = 1.34
a-axis: a0 = 5.7005(3) AÊ, K = 872(15) GPa, K¢ = )12(4),
b-axis: b0 = 11.1653(3) AÊ, K = 675(9) GPa, K¢ = 28(3),
v2w = 0.65
Ê
v2w = 0.78
c-axis: c0 = 9.5852(2) A, K = 124.5(3) GPa, K¢ = 15.02(9),
Third-order BM-EoS:
V0 = 610.10(3) AÊ3, K = 94.7(4) GPa, K¢ = 8.32(14), jPobs)Pcalcj £ 0.0168 GPa,
for Crystallography (Maslen et al. 1992; Creagh and McAuley
1992). The atomic coordinates given by Dollase et al. (1994) were
used as starting model. Final re®nements were carried out with
anisotropic displacement parameters for all atoms. The b22 parameters in the re®nements of the high-pressure structures were
constrained to the values which resulted from the re®nement to
data collected in air because re®nement resulted in insigni®cant
values with large uncertainties. This is a result of the crystallographic b-axis being parallel to the axis of the diamond-anvil cell,
which is thus the direction of lowest resolution. All re®nements
included a correction for secondary isotropic extinction (Lorentzian type I distribution: Becker and Coppens 1974). Details of the
data reduction and re®nements are given in Table 3, the resulting
structural parameters are listed in Table 4, resulting bond angles
and distances are summarized in Tables 5 and 6.
r2 = 0.99987
r2 = 0.99993
r2 = 0.99969
v2w = 0.66
Electronic absorption spectroscopy
Crystal plates perpendicular to the principal orthorhombic axes
were oriented by the oscillation method to better than 0.3° and
double-polished to 8 to 11 lm in thickness. All spectroscopic
measurements were made using a Bruker IFS 120 HR spectrometer
equipped with a Bruker Cassegranian microscope A590. A Xe-arc
lamp and an aluminum coated quartz beam-splitter were used. The
spot size of the beam was approximately 40 lm. 500 scans with
8 cm)1 resolution were accumulated in the spectral range from
10 000 to 25 000 cm)1. The high-pressure spectroscopic measurements were performed with a modi®ed Merill-Bassett type diamond-anvil cell (DAC) using type IIa diamonds with 0.5 and
0.6 mm diameter culets. The three sample crystals, crystallographic
(1 0 0), (0 1 0), and (0 0 1) sections, were loaded together with
Table 3 Details of the data reduction and results of the re®nements
P (GPa)
0.0001a
0.0001b
3.106(5)
5.303(6)
7.300(6)
9.220(11)
Total jFj
Averaged jFj (F>0rF)
jFjobs (F>4rF)
Nvar
l(MoKa) (cm)1)
tmin (%)
tmax (%)
Rint (F>4rF)
R
wRc
Gof
1250
335
285
18
71.82
63.8
83.7
1.8
1.9
2.5
0.88
573
120
95
15
71.82
23.4
30.0
2.5
2.1
2.5
0.82
564
125
94
15
73.93
23.3
29.9
3.8
3.3
4.3
0.77
538
86
68
15
75.22
23.5
30.1
2.6
2.0
2.0
0.75
547
90
67
15
76.49
23.3
30.1
3.5
2.7
3.0
0.69
484
83
64
15
77.21
23.3
30.1
3.0
2.3
2.4
0.87
a
Crystal in air (mounted on a glass ®bre)
Crystal in the DAC without any pressure transmitting medium
c
w = (r2i +p2 F2))2, 0.010 £ p £ 0.035
b
449
Table 4 Re®ned positional and displacement parameters of Cr2SiO4
P (GPa)
0.0001
0.0001
3.106(5)
5.303(6)
7.300(6)
9.220(11)
Cr z/c
û11
û22
û33
û12
Beq
Si û11
û22
û33
Beq
O x/a
y/b
z/c
û11
û22
û33
û12
û13
û23
Beq
0.48166(4)
572(10)
137(3)
372(5)
15(3)
0.93
505(19)
129(5)
240(8)
0.73
)0.04364(19)
0.04919(10)
0.22985(12)
630(24)
170(7)
320(11)
)36(12)
58(13)
25(5)
0.95
0.48148(9)
568(15)
137
400(8)
34(15)
0.96
507(32)
129
244(15)
0.73
)0.0434(4)
0.0484(5)
0.2304(3)
635(46)
170
330(21)
)15(40)
58(29)
)59(34)
0.96
0.48147(14)
643(33)
137
366(12)
22(28)
0.93
519(68)
129
278(25)
0.76
)0.0424(7)
0.0501(9)
0.2314(4)
513(80)
170
410(39)
)17(94)
39(51)
)8(46)
0.98
0.48120(10)
620(19)
137
351(7)
)13(38)
0.89
575(38)
129
234(15)
0.73
)0.0415(4)
0.0492(7)
0.2336(3)
706(57)
170
363(23)
)260(111)
54(32)
)5(46)
1.00
0.48137(14)
640(37)
137
341(11)
)100(58)
0.88
541(68)
129
233(22)
0.70
)0.0425(7)
0.0502(11)
0.2344(4)
697(98)
170
346(33)
)84(113)
53(46)
47(65)
0.96
0.48168(14)
606(28)
137
308(9)
)16(52)
0.82
635(65)
129
209(21)
0.71
)0.0417(6)
0.0494(10)
0.2356(4)
745(88)
170
318(29)
)313(147)
110(45)
)56(55)
0.94
Note: Cr at 16g (. .2): 1/8, 1/8, z û13 = û23 = 0
Si at 8a (222): 1/8, 1/8, 1/8
û12 = û13 = û23 = 0
O at 32h: x, y, z
Atomic positions correspond to setting 2 (origin at 1) of space group Fddd (no.70)
several small rubies and the 4:1 methanol-ethanol pressure medium
in a 210 lm diameter hole in a steel gasket pre-intended to 70 lm
thickness. Pressures were determined to a precision of approximately 0.01 GPa by employing the laser-induced ruby-¯uorescence
technique and using the pressure-wavelength shift calibration curve
given by Mao et al. (1986). In order to relax deviatoric stresses due
to non-hydrostaticity of the pressure medium above 10 GPa, the
pressure-cell was heated to about 60 °C for approximately one
hour in advance of recording the spectra and measuring the pressure at room temperature. Polarized and unpolarized spectra at
ambient pressure were measured on the sample crystals mounted
on one of the anvil diamonds. At high pressures only unpolarized
spectra were recorded because linear polarization is lost by straininduced birefringence of the anvil diamonds (Langer 1990). Measurements of two independent cell loadings of di€erent crystals
con®rm the reproducibility of the high-pressure measurements with
respect to the background contributions due to the pressure medium and diamond anvils. All spectra were corrected using background measurements after subtraction of a linear baseline, and
®nally deconvoluted into Gaussian and Lorentzian components
with the Bruker Opus 2.0 software. Maxima, shoulders, and in¯ection points of the spectral envelopes were used to de®ne the
number and starting positions of the component bands for the ®ts
of the spectra. Band notations were chosen according to those used
by Furche and Langer (1998). The polarized spectra were ®tted
without any constraints with regard to the band position, peak
heights, and half widths. Attempts to ®t the band components with
mixtures of symmetric Gaussian and Lorentzian pro®les with
variable Gauss/Lorentz ratios converged towards pure Gaussian
and Lorentzian components. The unpolarized high-pressure spectra were deconvoluted with half widths constrained to the values
which resulted from the deconvolution of the polarized spectra.
Results
Equation of state and axial compressibilities
A least-squares ®t of the volume-pressure data (Table 1)
following the procedure described by Angel et al. (1997)
yields for a third-order Birch-Murnaghan ®nite strain
equation of state (Birch 1947) V0 = 610.10(3) AÊ3,
K0,T = 94.7(4) GPa, and K¢ = 8.32(14). Normally, increasing density, or equivalently decreasing speci®c
volume, within an isostructural series of compounds
should lead to a corresponding increase in the bulk
modulus; it is often found the product K0 ´ V0 remains
constant in such a series (Shankland 1972). However,
both the bulk modulus and the room pressure molar
volume (45.93 cm3 mol)1) of Cr2SiO4 are smaller than
that of isostructural Cd2SiO4 (V0 = 52.38 cm3 mol)1,
K0,T = 119.2(5) GPa; Miletich et al. 1998). The higher
compressibility of Cr2SiO4 appears to be related to the
stereochemical di€erences between the coordination of
the Cr and Cd on the six-fold coordinated sites, which
can be considered to be too large for the relatively small
Cr2+ cation (Muller and Roy 1974; Dollase et al. 1994).
The variation with pressure of all three orthorhombic
axes is signi®cantly non-linear as indicated by polynomial ®ts in which the terms in P2 are more than 4 times
their estimated standard deviations (Table 2). Fits to
higher order polynomials yielded terms of the same order of their uncertainties. In addition, the compression
of the unit-cell is highly anisotropic (Fig. 1) with the
c axis being the most compressible, as in Cd2SiO4, although the degree of anisotropy is greater in Cr2SiO4.
However, unlike Cd2SiO4 in which the a-axis is softer
than the b-axis, the overall compressibilities to 9.2 GPa
of the a and b axes of Cr2SiO4 are very similar (Fig. 1).
In addition, the a-axis of Cr2SiO4 shows signi®cant
negative curvature with pressure (Table 2, Fig. 1). Thus,
contrary to normally observed behaviour, this direction
becomes softer with increasing pressure. Because this
remarkable feature is not observed for Cd2SiO4, it is
450
Table 5 Bond distances (AÊ), bond angles (°), polyhedral volumes (AÊ3), and polyhedral distortion parameters (quadratic elongation, Q.E.;
angular variance A.V.; Robinson et al. 1971), mean linear compressibility coecients bL (GPa)1), and polyhedral bulk moduli (GPa) in
Cr2SiO4
P (GPa)
Cr-Oa,b
Cr-Oc,d
Cr-Oe,f
VP
Q.E.
Oa-Cr-Ob
Oa-Cr-Oc
Oa-Cr-Od
Oa-Cr-Oe
Oa-Cr-Of
Oc-Cr-Od
Oc-Cr-Oe
Oc-Cr-Of
Oe-Cr-Of
AP.P3
Si-Oe,f,g,h
VP
Q.E.
Oe-Si-Of
Oe-Si-Og
Oe-Si-Oh
A.V.
Sif-O-Crl,4
Sif-O-Crc
Sif-O-Crf
Crl-O-Crc
Crl-O-Crf
Crc-O-Crf
R X-O[3]-X¢5
(´2)
(´2)
(´2)
(´2)
(´2)
(´2)
(´2)
(´2)
(´2)
(´4)
(´2)
(´2)
(´2)
Symmetry code:
1
0.00011
0.00012
3.106(6)
5.303(6)
7.300(6)
9.220(11)
X0®t
bL(´105), Kp
1.999(1)
2.103(1)
2.732(1)
11.74
1.2414
180.99(5)
79.54(4)
100.64(4)
76.86(4)
102.24(4)
159.79(5)
73.39(4)
126.57(4)
55.91(3)
20.2
1.628(1)
2.18
1.0103
103.76(6)
117.35(6)
107.61(5)
39.2
130.39(7)
115.44(6)
100.16(5)
100.46(5)
112.04(5)
92.09(4)
346.29(11)
1.992(5)
2.107(3)
2.729(3)
11.67
1.2444
180.2(2)
79.39(16)
100.72(16)
76.87(14)
102.59(14)
160.58(10)
73.14(10)
126.58(10)
56.23(12)
19.4
1.635(4)
2.21
1.0096
103.68(17)
116.93(3)
108.10(15)
36.6
130.5(3)
114.9(3)
100.05(17)
100.61(14)
112.48(16)
92.03(13)
346.0(4)
2.002(10)
2.094(5)
2.665(5)
11.34
1.2397
180.0(5)
79.9(3)
100.1(3)
77.3(3)
102.7(3)
160.84(16)
72.56(16)
126.34(15)
56.61(20)
19.2
1.611(6)
2.11
1.0115
103.4(3)
117.7(5)
107.6(3)
43.6
129.9(4)
115.5(5)
100.0(3)
100.1(3)
112.8(3)
92.9(3)
345.5(7)
1.988(8)
2.093(4)
2.621(4)
10.95
1.2449
178.7(2)
79.8(2)
100.0(2)
77.5(2)
103.6(2)
162.06(12)
71.53(11)
126.17(11)
57.63(15)
18.0
1.616(5)
2.13
1.0111
102.9(2)
117.3(4)
108.6(2)
42.4
129.6(3)
114.5(4)
99.8(3)
100.2(2)
114.0(2)
93.4(2)
344.3(6)
1.993(12)
2.077(6)
2.595(5)
10.76
1.2444
178.4(2)
79.8(4)
100.0(4)
77.7(3)
103.7(3)
162.58(16)
71.06(17)
126.12(16)
57.96(24)
17.5
1.610(7)
2.10
1.0130
102.7(3)
118.2(6)
108.0(3)
49.4
128.9(5)
114.9(6)
99.7(4)
100.2(3)
114.0(3)
94.0(2)
344.0(8)
1.982(11)
2.077(5)
2.572(5)
10.52
1.2496
177.9(2)
79.7(3)
100.0(3)
77.7(3)
104.2(3)
163.48(16)
70.40(16)
125.88(15)
58.50(22)
16.6
1.611(6)
2.11
1.0121
102.5(3)
117.6(5)
108.6(3)
46.3
129.0(4)
114.2(5)
99.5(4)
100.3(3)
114.7(3)
94.3(3)
343.5(7)
1.998(4)
2.105(3)
2.726(6)
11.71(3)
1.2415(17)
180.6(3)
79.6(1)
100.6(2)
76.9(1)
102.4(2)
160.1(2)
73.3(1)
126.57(3)
56.02(12)
19.9
1.628(4)
2.18(2)
1.010(4)
103.73(5)
117.2(3)
107.8(3)
38.5(1.6)
130.4(1)
115.3(3)
100.13(4)
100.4(2)
112.2(2)
92.08(5)
346.17(15)
63(35)
152(21)
651(36)
89.3(3.5)
)49(26)
169(23)
)37(25)
78(20)
)128(14)
)191(25)
)221(26)
427(25)
56(4)
)480(42)
1724(20)
143(46)
221(70)
)27(8)
133(9)
)62(37)
)68(42)
)280(90)
133(15)
82(40)
63(8)
30(20)
)237(30)
)271(10)
86(8)
a
b
c
d
e
f
)x, 1/4+y, 1/4+z;
3/4)x, y, 3/4)z;
g
x, 1/4)y, 1/4)z;
k
1/2)x, 1/2)y, )z;
1/4+x, )y, 1/4+z;
1/4)x, 1/4)y, z;
h
1/4)x, y, 1/4)z;
l
)x, 3/4+y, 3/4+z
i
1/2+z, 1/4)y, 3/4)z;
x, y, z;
)x, )y, )z;
Crystal in air
Crystal in DAC without pressure transmitting medium
3
AP.P. = aplanarity parameter = [Si (180)xi)2])2 x = O-Cr-Otrans
4
O-Sif = Si-Oe, O-Crl = Cr-Oa, O-Crc = Cr-Oc, O-Crf = Cr-Oe
5
X, X¢ = Sif, Crl, Crc
2
probably the result of the di€erences between the Cr and
Cd stereochemistry and the nature of the bonding of the
cations.
High-pressure structures and comparative
compression mechanisms
Compression of the thenardite-type AB2O4 structures
and their compressional anisotropy are basically controlled by cation repulsion through shared polyhedral
edges and, as a result of this, through the polyhedral
geometries. Accordingly, the high compressional anisotropy in Cr2SiO4 arises from the fact that the coordination of the Cr atom is a square-planar CrO4
con®guration which lies is parallel to (0 0 1). Thus the
high compression along the c direction and the similar
compressibilities of a and b can be attributed to the
compressional behaviour of the Cr-O bonds (Fig. 2).
The role of the polyhedral connectivity has been illustrated by the high-pressure behaviour of cadmium orthosilicate (Miletich et al. 1998). Edge-sharing is the
most characteristic feature of this structure type, in
which even the SiO4 tetrahedra share edges with neigh-
Table 6 Selected inter-cation distances (AÊ) and ®tted compression parameters K0 (GPa) and K¢ for the respective distances in Cr2SiO4.
Data were ®tted to an two-parameter equation equivalent to the Murnaghan equation, that for Cr Cri,k to a mean linear modulus
P (GPa)
Cr Crg
Cr Cri,k
Cr Sif
(´2)
0.0001a
0.0001b
3.106(6)
5.303(6)
7.300(6)
9.220(11)
K0 (GPa)
K¢
2.748(1)
3.153(0)
3.418(0)
2.751(1)
3.154(0)
3.417(1)
2.694(2)
3.140(0)
3.345(1)
2.667(1)
3.132(0)
3.303(1)
2.640(2)
3.124(0)
3.275(1)
2.614(2)
3.116(0)
3.253(1)
158(13)
784(9)
115(5)
6.6(3.7)
±
17.9(1.8)
451
Fig. 1 Variation of the unit-cell parameters a, b, and c of Cr2SiO4
with pressure. Lines through the data points represent the ®ts to the
data by second-order polynomial equations whose coecients are
given in Table 2. The symbol size is approximately 4 times the
maximum standard deviation
bouring CrO6 polyhedra. The strong uniaxial elongation
of the SiO4 tetrahedra along the diad parallel to the
c-axis is a result of the topological connectivity (see also
Fig. 2 in Miletich et al. 1998), which is also responsible
for the distortion of the MO6 polyhedron.
Fig. 2 Variation of the bond distances with pressure. Estimated
standard deviations of the bond lengths are indicated by error bars.
Lines through Cr-Oa'b and Cr-Oc'd represent ®ts of linear function
to the data points, and lines through Cr-Oe'f and Cr Crg to ®ts of
the equation d/d0 = (1 + K¢ á P/K0)()1/K¢), d = interatomic distance
Fig. 3 Variation of the M M distances (M = Cr, Si) in Cr2SiO4
compared to the pressure variation of the analoguous distances in
Cd2SiO4 (dashed line)
Because of the large di€erence between the position
occupied by the Cr and Cd atom, as indicated by the
parameter z/c, there are major di€erences in the compression of the corresponding M Mg and M Sif distances which parallel to the c-axis (Fig. 3). As expected,
the increase of the Cr Si distance relative to the analogous Cd Si distance, and therefore the weaker elec-
Fig. 4 Variation of the polyhedral volumes (Vp) the mean quadratic
elongation (Q.E.) and the angular variance (A.V.) of the CrO6 (circles)
and SiO4 (squares) polyhedra. Errors and lines according to Fig. 2
452
trostatic repulsion, is re¯ected in its compressibility
(K0 = 115 ‹ 5 GPa) being three times higher than that
of Cd Si (K0 = 382‹15 GPa). On the other hand the
Cr Crg distance, although being dramatically shorter
(2.75 AÊ) than the equivalent Cd Cdg distance (3.62 AÊ),
shows approximately the same compressibility
(158 ‹ 13 GPa) as that in Cd2SiO4 (141 ‹ 3 GPa).
This suggests that the nature of interaction between the
two close Cr atoms might not be a simple repulsive one.
Another remarkable di€erence between the two
structures occurs in the compression of the SiO4 polyhedron. Both the quadratic elongation, which is a
measure for the bond-length distortion relative to an
undistorted polyhedron of equal volume, and the bondangle variance increase with pressure in Cr2SiO4 in
contrast to Cd2SiO4 for which the polyhedral distortion
decreases (Fig. 4). The distortion itself corresponds to an
uniaxial elongation of the tetrahedron along its diad
parallel to the c-axis. In the case of Cd2SiO4 this elongation can be attributed to the strong repulsive interaction between the Cd and Si atom across the edge
shared between SiO4 and CdO6 polyhedra. As pressure
increases, the displacement of the Cd position away
from the Si atom reduces the repulsion relative to the
other interactions which allows the SiO4 polyhedron to
relax and to reduce the distortion. In Cr2SiO4 the SiO4
tetrahedron is strained because of its function as a
bridging unit between the two adjacent CrO4 units.
Repulsion between Si and the M cation, which is critical
for the behaviour of Cd2SiO4, does not play a major role
in Cr2SiO4 because of the lack of signi®cant repulsion at
the larger M Si distance.
High-pressure electronic absorption spectra
The polarized electronic absorption spectra obtained at
room pressure for E//a, E//b, and E//c are shown in
Fig. 5, which are similar to the polarized spectra measured by Furche and Langer (1998). The ®t parameters
of the deconvoluted band components (Table 7) were
found to be in good agreement with the results reported
by Furche and Langer (1998) for E//b and E//c. The ®t
for E//a shows some minor di€erences: the high-energy
slope of the sharp absorption feature whose maximum is
at 18 300 cm)1 indicates that a ®t of a single band to this
region requires a strongly asymmetrical band shape in
order to match the observed spectral envelope. As an
alternative, we achieved satisfactory ®ts by adding a
symmetric Lorentzian band component f* at about
18 200 cm)1. This causes a slight shift of the two major
components h1 and h2 from 12 920 to 13 670 and from
15 330 to 15 905 cm)1 respectively. The other major
features of the polarized spectra correspond to those
recently reported, which have been assigned to both ddtransitions of localized d-electrons of Cr2+ in a distorted
square-planar co-ordination and d-d* transitions assuming a [Cr2]4+ dimer stereochemistry. The narrower
bands f and g near 18 500 cm)1 are probably due to the
Fig. 5 Polarized electronic absorption spectra of Cr2SiO4 at 1 bar
and 295 K recorded from 8 lm and 11 lm thick (0 1 0) and (0 0 1)
crystal plates. Thin lines represent deconvoluted Gaussian and
Lorentzian band components whose parameters are given in
Table 7
nominally spin-forbidden transitions, which have been
exchange-enhanced via antiferromagnetic coupling with
neighbouring Cr atoms. A detailed discussion of the
band assignment and interpretation is given by Furche
and Langer (1998) who explained the co-existing dd and
dd* excitation by invoking a short-time scale dynamic
exchange process between a mononuclear high-spin d4
and binuclear metal-metal bonded species. The complexity of the spectra and some spectral features certainly cannot be explained exclusively by a model of
crystal-®eld transitions in mononuclear CrO4 complexes.
Fit models with only a single h band component, suggested by Furche and Langer (1998) as an alternative
interpretation yielded a less satisfactory correspondence
between observed and calculated envelopes.
The unpolarized high-pressure spectra as obtained
for the (0 1 0) crystal plate (Fig. 6) were iteratively deconvoluted using the Gaussian and Lorentzian band
parameters starting from the polarized spectra and using
the band positions and intensities resulting from the
spectrum of previous pressure as respective starting
values. Convergence of these multi-component ®ts to the
complex spectral envelope was achieved only for ®ts
with half widths constrained to the values obtained for
453
Table 7 Component band for the polarized spectra at room pressure and the unpolarized spectra for the (010) orientation at pressures up
to 11.2 GPa. Gaussian and Lorentzian band shapes are indicated by G and L; FWHM = full width at half maximum; m = wavenumber
Band
Polarized spectra
E//a
h2
h1
g
f
f*
c
E//b
k(?)
h2
h1
f
d
c
E//c
e
Shape
m (cm)1)
Absorbance
FWHM
(cm)1)
Integrated
absorbance (cm)1)
G
G
L
L
G
L
G
G
G
L
L
L
G
13672
15906
16756
18346
18974
21095
10970
13679
16057
18390
19750
21014
18568
0.692
0.843
0.205
0.404
0.150
0.077
0.027
0.193
0.404
0.440
0.169
0.040
0.529
3044
2732
742
636
1966
1504
1138
3045
2847
1167
1490
957
5167
2243
2450
239
403
313
182
33
625
1224
806
396
60
2905
h1
g
f*
e
f
c
16110
16036
16293
16366
16280
16431
16403
16752
16773
16807
16957
17024
17159
17330
17208
17247
18286
18293
18276
18254
±
±
±
±
18334
17920
18299
18209
18401
18399
18434
18555
18584
18501
18412
18384
18339
18397
18412
18503
21349
21358
21409
21544
21656
21780
21910
21996
1267
1157
1079
871
511
419
307
287
247
286
218
182
246
157
111
38
153
148
102
63
1979
2207
2119
2231
2109
2246
2330
2334
108
145
233
259
314
262
242
214
246
279
211
224
171
169
166
148
Unpolarized spectra
P (GPa)
h2
Band position m (cm)1)
13581
10)4
1.30(1)
13372
2.74(1)
13566
4.03(1)
13659
5.58(1)
13857
7.66(1)
13982
9.55(1)
14078
11.21(2)
14285
Integrated absorbance (cm)1)
1006
10)4
1.30(1)
1149
2.74(1)
1084
4.03(1)
1034
5.58(1)
911
7.66(1)
921
9.55(1)
870
11.21(2)
910
±
±
±
±
the polarized spectra at room pressure. The resulting ®t
parameters are summarized in Table 7. Apart from
band f, all deconvoluted bands are shifted linearly with
pressure towards higher energies (Fig. 7) with very
similar rates between 35 to 74 cm)1 GPa)1. It is remarkable that ®ts of the problematic region around
band f can be achieved with a single symmetrically
shaped Gaussian band for the spectra at pressures
³5.58 GPa. In general f* was found to lose importance
as pressure increases. Considering an intermediate position between the f and f* positions for a single-band
model, a similar pressure-induced shift can be obtained.
Intensities of the ®tted peak components, in particular of
those which are attributed to crystal-®eld transitions of
localized d-electrons, were found to decrease signi®cantly as pressure increases.
In contrast, the integral intensity of band e slightly
increases with pressure and appears to be almost constant within the estimated error of the ®t procedure
compared to the signi®cant pressure-induced changes of
the other band components (Fig. 8). As shown in Table 7 and Fig. 9, the intensity of the component band e,
which is strictly polarized //c, relative to all the component bands with polarization //a, steadily increases
from 40% at 1 bar to 60% at 11.2 GPa. According to
general trends reported for spectral features at high
pressures, the observed blue-shift (that is towards higher
energies) is typical for absorption bands originating
from crystal-®eld transitions (Langer et al. 1997; Burns
1993, and references therein). Pressure-induced redshifts and a decrease of the dd* excitation energy with
pressure were reported for the few studies of M2X8
transition-metal dimer complexes (Morris et al. 1986;
1990; Roginski et al. 1988; Caroll et al. 1985, 1986), but
a generally valid explanation for the high-pressure behaviour of these features has not yet been given (Cotton
and Walton 1993).
Apart from the polarization and the broad width of
band e, the relative increase in intensity with pressure
might also suggest that band e originates from a homonuclear intervalence charge transfer (IVCT) transition, most probably between Cr2+ and Cr3+. Pressure
dependencies for IVCT transitions have been reported to
show both blue and red shifts (Taran et al. 1996; Taran
454
Fig. 6 Unpolarized electronic absorption spectra of the (0 1 0)
crystal plate at hydrostatic pressures between 10)4 and 11.21 GPa.
Spectra are shifted for clarity by 0.2 absorbance units
Fig. 8 Unpolarized electronic absorption spectra at 10)4, 4.0, and
11.2 GPa and deconvoluted band areas. The ®gure shows the relative
increase of band e from 40% to 59% of the total absorption
Fig. 9 Variation of the relative intensity of band e with pressure
Fig. 7 Variation of the position of the individual component bands
resulting from the deconvolution procedure of the unpolarized spectra
given in Fig. 6
and Langer 1998; see also examples cited in Burns 1993).
An IVCT transition is considered unlikely because of
lack of a charge compensation mechanism for signi®cant
amounts of Cr3+, which would require substantial
substitution of additional Cr3+ on tetrahedral sites. Any
model involving oxygen vacancies has been ruled out for
455
3+
substitution of Cr
at the level of a few % required for
such an IVCT transition.
Discussion
Chromium±oxygen bonding in Cr2SiO4
As the six-fold coordinated site appears to be too large for
the small Cr atom in a thenardite-type silicate, its displacement from the central position could be considered
as an attempt to achieve shorter Cr-O bonds. The JahnTeller e€ect, which accounts for the stabilization of the
3d4 con®guration, certainly would support the stereochemical changes in order to approach the energetically
favoured square planar geometry. In this model the short
Cr Cr distance would be merely the result of the polyhedral o€-centre displacement and symmetry coupling
between adjacent polyhedra (Dollase et al. 1994). To test
this hypothesis we calculated the ideal position of the Cr
atom for which the sum of the individual bond-valences
approximates the ideal 2 valence units (Fig. 10), with
contributions from only Cr-O bonds and none from
possible Cr-Cr interactions. The calculations for the oxygen con®guration at room pressure indicate one miniFig. 10a, b Calculations for ideal Cr-O bonding in Cr2SiO4:
a Calculated bond-valence de®ciency as a function of the positional
parameter z/c for the Cr atom. The minima in the strongly asymmetric
double-well potentials (marked with arrows) represent the Cr positon
of optimal Cr-O bonding. Bond valences were calculated on the basis
of the parametrized relation given by Brese and O'Kee€e (1991), using
an empirical bond-valence parameter of R = 1.742 AÊ for Cr2+-O
bonds, which was derived from the structural data of square-planar
coordinated Cr2+ atoms (Miletich et al. 1997a). For the high-pressure
data, the R parameter was corrected following the mean Cr-O bond
compressibility according the equation R = 1.742 ´ (1)1.075 ´
10)3 ´ P). Calculations with varied parameters for R show that the
potential's minima and maxima are essentially independent of the
variation of R, which only a€ects the absolute values for m and d,
respectively; b variation of the observed and calculated Cr positions as
a function of pressure. The values for the calculated positions
correspond to the minima in Fig. 10a. The position of minimal bondlength distortionPwas calculated for minimum of the distortion
ÿ di †2 Š1=2 with d
ˆ R ÿ 0:37 ln m being the
parameter D ˆ ‰ i …d
mean bond distance according to the polyhedral mean bond strengths.
mum of the asymmetric double-well potential to occur at
z/c = 0.4822(4) (Fig. 10a), which corresponds almost
perfectly to the observed position of the chromium atom
at z/c = 0.48166(4) (Fig. 10b). Thus it might suggest that
the displacement is purely driven by the cation size mismatch for proper bonding. In the structure at high pressures the calculations reveal a shift of this minimum
towards the central position of the oxygen con®guration
with increasing pressure. Simultaneously the maximum of
the double-well potential decreases as the con®guration of
six oxygen atoms reduces its volume and becomes more
suitable for the Cr cation.
These calculations with ideal Cr-O bonding
conditions indicate that in the case of exclusive chromium-oxygen bonding without any metal-metal bond
interaction, the strong o€-center displacement of the
chromium atom should be reduced as pressure increases.
In this case the Cr atom can be expected to be pushed
towards the central position within the distorted polyhedron (Fig. 10b), a trend that would likely be enhanced
by repulsion between the close Cr atoms. However, the
positions obtained from the structure re®nements show
that the Cr atoms actually remain in place and are not
pushed towards the centre of the polyhedra. This suggests
that there exists a bonding interaction between the adjacent Cr atoms which acts against the stereochemical
driving forces and thus retains the Cr atoms in place.
Further evidence for the presence of direct bonding interaction between the Cr atoms is provided by the fact
that, compared to other typically four- to six-fold coordinated Cr2+ atoms, the bond-valence sum from Cr-O
bonds alone is too small (1.82±1.88 v.u., depending on the
precise value of the bond-valence parameter; R = 1.73 AÊ
from Brese and O'Kee€e 1991, or R = 1.742 AÊ; determined from structural data of pure square-planar
Cr2+O4 con®gurations by Miletich et al. 1997a).
The dimer stereochemistry at high pressures
Chromium dimer complexes are well known in organometallic compounds (for an overview see Cotton and
Walton 1993), but there are also a few occurrences in
456
inorganic carbonates (Ouahes et al. 1973; Adam 1997).
In all of these cases the O2CR con®guration (R = CH3,
C(CH3)3 for carboxylates; R = O for carbonates) serves
as anionic bridging unit. The small size and the triangular planar geometry of the O2CR bridging units are
responsible for the ``eclipsed'' rotational conformation
of the two opposing square-planar CrO4 groups in all of
these binuclear complexes (see ®gures in Cotton and
Walton 1993). Bridging units other than O2CR have not
been reported previously for chromium dimers, even
though tetrahedral units such as SO4 and PO4 groups act
as bridging units in dimer complexes of molybdenum
and other transition metals (Cotton et al. 1975; Bino
and Cotton 1979; Cotton and Walton 1993). The nature
of Cr-Cr bonds in binuclear [Cr2]4+ systems is a formal
quadruple bond in the sense that they entail one r, two
p, and one d bonding overlaps, plus corresponding r*,
p*, d* antibonding energy levels. Since the Cr-Cr distance varies an astonishing amount from 1.83 to 2.60 AÊ,
the strength of these multiple bonds must vary greatly as
well (Cotton and Walton 1993). Benard and Viellard
(1977) calculated the lowest-energy con®guration for a
fully quadruple-bonded Cr-Cr dimer to have a Cr-Cr
distance between 1.7 and 1.8 AÊ. The presence of axial
ligands causes elongation, to which the Cr-Cr distance is
extremely sensitive (Cotton et al. 1978; Cotton et al.
1980; Cotton and Wang 1984) compared to the variation
of Mo-Mo or Re-Re distances. As the delta-overlap is
strictly angle-sensitive, the internal rotation between the
two opposing metal centres was found to signi®cantly
in¯uence the metal-metal distance as in dimolybdenum
complexes. Minimum overlap can be expected for torsion angles v = p/4+np/2 (n = 0,1,2,¼), which corresponds to the ``fully staggered'' conformation, whereas
for v = np/2 maximum overlap is achieved according to
the ``eclipsed'' conformation of the MO4 groups.
In Cr2SiO4 the internal torsion measures 35.9°, well
towards the 45° at which the two CrO4 con®gurations
would be in a completely ``staggered'' conformation and
the d overlap would be at a minimum. This explains why
the Cr-Cr distance is so large compared to the range
reported for other chromium dimer complexes which are
almost exclusively dimers with an eclipsed conformation. The large rotation within the tetrasilicato-bridged
dimer of Cr2SiO4 can be attributed to the bridging ligands, the SiO4 tetrahedra, being larger than any of the
other planar CO2R units found in the carboxylatobridged dimer systems. Although the internal torsion
reduces the orbital overlap and, therefore, the strength
of the metal-metal bond, the simultaneous rotation of
the SiO4 tetrahedra, which is coupled with the internal
torsion, reduces the distance between the Cr atoms and
thus increases the bond strength.
The internal torsion angle, v, shows almost no change
with pressure for Cr2SiO4 whereas a signi®cant increase
occurs in Cd2SiO4 (Fig. 11) towards angles corresponding to a more staggered con®guration. Pressureinduced torsional deformation from an eclipsed to a
partially or totally staggered conformation was previ-
Fig. 11 Variation of the torsion angle v and the b/a ratio of Cd2SiO4
with pressure. Internal torsion according to the rotational conformation was calculated from the angle between the chains of CrO4 squares
(see Fig. 2 in Dollase et al. 1994), which can be derived from lattice
parameters a and b as follows: v = p/2 ) 2arctan(a/b)
ously proposed for M2X8 transition-metal dimer complexes (Morris et al. 1986, 1990; Roginski et al. 1988;
Caroll et al. 1985, 1986; Cotton and Walton 1993) on
the basis of decrease of intensity and a red-shift in the
electronic absorption spectra with increasing pressure,
although there was no direct structural evidence. Although the staggered conformation allows a better
packing of ligands, the increase of the v reduces orbital
overlap and, as a result of this, the strength of metalmetal bonding as indicated by the correlation between
the M-M distance and v (Campbell et al. 1985). The
torsion angle in Cr2SiO4 changes only very little as
pressure increases, which might explain the relative insensitivity of the intensity of band e to pressure, which
was assumed to correspond at least partially to a dd*
transition. As pointed out by Cotton and Walton (1993),
the general behaviour of dimer complexes under pressure and the in¯uence of the two most important e€ects,
the change in internal rotation and the reduction of the
M-M distance, are still not well understood because of
lack of data.
The detailed analysis of v as a function of pressure in
Cr2SiO4 shows that v actually decreases slightly at lower
pressures to a minimum at 5 GPa and then increases
again for higher pressures. This behaviour is also displayed by the b/a ratio, and corresponds to the unusual
behaviour of the a axis, for which we ®nd a higher
compressibility at higher pressures as indicated by the
negative value for K¢. Both the change in the internal
torsion and the compressional behaviour of the crystallographic a axis appear to be related to the bending
behaviour of the Oa-Cr-Ob linkage, which is the O-Cr-O
457
a
link that lies most nearly parallel to the a axis. The O Cr-Ob angle is greater than 180° at room pressure and
gets reduced to angles smaller than 180° for pressures
greater than 3±3.5 GPa (Fig. 12). As long as the OaCr-Ob angle is greater than 180°, its reduction counteracts compression parallel to the a axis, whereas the
further reduction to values smaller than 180° supports
the compression along the a axis and thus allows the a
axis to be more compressible at higher pressures. The
process is continuous with pressure as a result of the
linear oxygen displacement along the c direction.
As there is only one crystallographically distinct oxygen site in Cr2SiO4, the displacement of Oc and Od as
coupled by symmetry leads to a continuous straightening of the second O-Cr-O axis. Thus the strong aplanarity of the CrO4 con®guration gets signi®cantly
reduced as pressure increases. The decreasing aplanarity
might also explain why the relatively strong absorption
bands h1 and h2, which have been assigned to localized
dd transitions, get reduced as pressure increases. It is
remarkable that the geometry of the aplanarity changes
from a very ¯at bisphenoidal CrO4 con®guration to a
pyramidal one as a result of the angular changes. This
also enables the Oe and Of atoms, which show almost no
Cr-O bonding at ambient pressure, to become more involved in bonding and thus increase the number of coordinating oxygens atoms. The very high compressibility
of the Cr-Oe'f bonds, which is responsible for the major
compression along the c axis and the strong compressional anisotropy, demonstrates this continuous change
in bonding. Nevertheless, the Cr atom does not behave
Fig. 12 Variation of selected O-Cr-O bond angles with pressure.
Bond angles between the Oa, Ob and Oc, Od represent transcon®gured ligands and are therefore a measure of the aplanarity of the
CrO4 group. The angle Oe-Cr-Of is the bond angle between the
additional two oxygen atoms, which represent the shared edge
between the CrO6 and SiO4 polyhedra
as though it would form an octahedral co-ordination
geometry at high pressures by moving towards the ideal
centre along the c direction. In contrast, the insigni®cantly small changes in the z/c parameter of the Cr atom
support the square-planar con®guration as required for
the dimer stereochemistry.
Conclusions and outlook
High-pressure investigations of Cr2SiO4 single crystals
by means of X-ray di€raction and electronic absorption
spectroscopy can be interpreted in terms of presence of a
weak metal-metal bonding interaction and the formation of a silicate-bridged chromium dimer within the
structure. Evidence for Cr-Cr bonding is given by: (1)
the high compressibility of the short Cr-Cr distance,
which would not be expected were the interaction to be a
purely repulsive one; (2) the fact that the Cr atoms are
not pushed towards the central position of the octahedron although from considerations of Cr-O bonding
requirements and electrostatic repulsion between Cr atoms this would be expected; (3) the changes of subtle
stereochemical features with pressure, such as the increasing planarity of the fourfold square-planar oxygen
con®guration and (4) the predominance of the absorption bands which have been assigned to electronic
transitions due to orbital overlap. Furthermore the apparent diamagnetic response indicates the presence of
electron pairing that would be expected for orbital
overlap due to metal-metal bonding. The relatively large
internal torsion towards a partially staggered conformation can be attributed to the fact that the bridging
SiO4 units are relatively too large for the small Cr atoms.
The M-M distance can be increased by twisting from an
eclipsed towards staggered conformation, which in turn
reduces the degree of orbital overlap and destabilizes the
dimer to a certain extent. Both pressure and temperature
appear to be required in order to stabilize such a silicatebridged dichromium complex: temperature enhances the
probability for electronic transfer between the two Cr
atoms, and pressure reduces all interatomic distances
which in turn increases orbital overlap. This is supported
by the fact that the formation of Cr2SiO4 as a stable
subsolidus phase was reported for elevated pressures
(Dollase et al. 1994) whereas 1 bar experiments yielded
Cr2SiO4 only as metastable quench product from superliquidus conditions (Healy and Schottmiller 1964;
Scheetz and White 1972; Gasparik 1981). The liquidussolidus phase relation suggest that such a dimer cluster
might exist in the melt, which recently has been proposed for chromium in poorly-polymerized SiO2-poor
silicate melts (Colson and Colson 1997). On the basis of
the results reported here for a chromium, it is highly
probable that other transition metals may form such
dimer species. Multiple metal-metal bonding and dimerisation might stabilize transition-metal species in
silicate melt structures at high pressures and temperatures and thus possibly play an important role for geo-
458
chemical fractionation of these elements during the
evolution of the Earth.
Acknowledgements We thank K Langer, Berlin, for intensive and
fruitful discussions concerning the results of the optical spectroscopy. We would also like to thank R Stranger for sharing with us
the results of the DFT calculations for Cr2SiO4 prior to publication. Furthermore we would like to thank H Schulze for the careful
preparation of the polished crystal platelets for all high-pressure
measurements. FS acknowledges support by the Fonds der
Chemischen Industrie, Frankfurt.
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