ORIGINAL PAPER
High-pressure properties of diaspore, AlO(OH)
A. Friedrich Æ D. J. Wilson Æ E. Haussu¨hl Æ
B. Winkler Æ W. Morgenroth Æ K. Refson Æ
V. Milman
Received: 19 July 2006 / Accepted: 26 November 2006

Springer-Verlag 2006
Abstract The structural compression mechanism and
compressibility of diaspore, AlO(OH), were investi-
gated by in situ single-crystal synchrotron X-ray
diffraction at pressures up to 7 GPa using the diamond-
anvil cell technique. Complementary density functional
theory based model calculations at pressures up to
40 GPa revealed additional information on the pres-
sure-dependence of the hydrogen-bond geometry and
the vibrational properties of diaspore. A fit of a second-
order Birch–Murnaghan equation of state to the p–V
data resulted in the bulk modulus B0 = 150(3) GPa and
B0 = 150.9(4) GPa for the experimental and theoretical
data, respectively, while a fit of a third-order Birch–
Murnaghan equation of state resulted in B0 =
143.7(9) GPa with its pressure derivative B¢ = 4.4(6) for
the theoretical data. The compression is anisotropic,
with the a-axis being most compressible. The compres-
sion of the crystal structure proceeds mainly by bond
shortening, and particularly by compression of the
hydrogen bond, which crosses the channels of the crystal
structure in the (001) plane, in a direction nearly parallel
to the a-axis, and hence is responsible for the pro-
nounced compression of this axis. While the hydrogen
bond strength increases with pressure, a symmetrisation
is not reached in the investigated pressure range up to
40 GPa and does not seem likely to occur in diaspore
even at higher pressures. The stretching frequencies of
the O–H bond decrease approximately linearly
with increasing pressure, and therefore also with
increasing O–H bond length and decreasing hydrogen
bond length.
Keywords Diaspore
High pressure

Crystal structure
Synchrotron radiation

Density functional theory calculations
Introduction
The stability of minerals with structurally incorporated
water (or hydroxyl groups) at high pressures and
temperatures is of great relevance to the interpretation
of processes occurring in the Earth’s crust and upper
Electronic Supplementary Material The online version of this
article (http://dx.doi.org/10.1007/s00269-006-0135-5) contains
supplementary material, which is available to authorized users.
A. Friedrich (&)
D. J. Wilson
E. Haussu¨hl

B. Winkler
Institut fu¨r Geowissenschaften, Abt. Kristallographie,
Johann Wolfgang Goethe-Universita¨t Frankfurt,
Senckenberganlage 30, 60054 Frankfurt am Main, Germany
e-mail: friedrich@kristall.uni-frankfurt.de
W. Morgenroth
Insitut fu¨r Anorganische Chemie,
Georg August Universita¨t, Tammannstraße 4,
37077 Go¨ttingen, Germany
W. Morgenroth
Department of Chemistry, Aarhus University,
Langelandsgade 140, 8000 Aarhus C, Denmark
W. Morgenroth
c/o DESY/HASYLAB, Notkestrasse 85,
22603 Hamburg, Germany
K. Refson
Rutherford Appleton Laboratory,
Chilton, Didcot, Oxfordshire OX11 0QX, UK
V. Milman
Accelrys Inc., 334 Cambridge Science Park,
Cambridge CB4 0WN, UK
123
Phys Chem Minerals
DOI 10.1007/s00269-006-0135-5

mantle. Dehydration can trigger melting, and can be
further related to volcanism and even earthquakes, as
water has a large influence on the physical and chem-
ical properties of Earth materials (Meade and Jeanloz
1991; Thompson 1992; Lundgren and Giardini 1994;
Stalder and Ulmer 2001). In nominally anhydrous
minerals, such as olivine, trace amounts of water in the
form of OH defects can significantly affect rheological
properties (Hirth and Kohlstedt 1996). Often, OH
defects can only be identified by infrared spectroscopy
(Aines and Rossman 1984). In such measurements, the
stretching frequency of the O–H bond is correlated to
the characteristics of the hydrogen bond. Correlations
can be drawn not only with the d(O–H) bond length,
but also with the d(O


O) and d(H


O) inter-atomic
distances of the hydrogen bond. Such empirical cor-
relations have previously been described (Nakamoto
et al. 1955; Novak 1974; Mikenda 1986; Lutz et al. 1990;
Libowitzky 1999). In general, the O–H stretching fre-
quency decreases with decreasing d(O


O) distance, as
the O–H bond is weakened when the H


O hydrogen
bond strength increases and the O–H


O hydrogen
bond becomes more symmetric.
A central question is the potential of high pressure
to induce or strengthen hydrogen bonds, and the
resultant change of the physical properties of these
materials. While numerous studies have dealt with the
pressure dependence of weak hydrogen bonding in
brucite-related minerals (e.g., Kruger et al. 1989;
Sherman 1991; Parise et al. 1994; Catti et al. 1995;
Duffy et al. 1995a; Duffy et al. 1995b; Kunz et al. 1996;
Leinenweber et al. 1997; Parise et al. 1998a; Parise
et al. 1998b; Raugei et al. 1999; Garg et al. 2004), very
few investigations have focused on the behaviour of
short or intermediate hydrogen bonds at high pressure.
Initial theoretical studies were performed on diaspore,
a-AlO(OH) (Winkler et al. 2001), and experimental
studies up to 24 GPa on isostructural goethite,
FeO(OH) (Williams and Guenther 1996; Nagai et al.
2003) in this interesting class of hydrogen bonded
compounds. Diaspore is an ideal model system for
high-pressure studies, as it combines relatively high
symmetry (orthorhombic) and a relatively small unit
cell (unit-cell volume = 117.96(8) A˚3, Busing and Levy
1958) with simple chemistry and a non-linear hydrogen
bond of intermediate strength (O–H stretching fre-
quency m is about 3,000 cm–1, Ryskin 1974).
The crystal structure of diaspore (space group
Pbnm, Z = 4) is built from ‘‘double rutile strings’’
(Ewing 1935) of edge-sharing AlO3(OH)3 octahedra
(Fig. 1). These double strings are arranged parallel to
the c-axis and are connected via common oxygen cor-
ners. The OH groups form hydrogen bonds in the (001)
plane across the channels formed by the coordination
octahedra, with the O


O and O–H vectors tilted away
from the a-axis by about 31 and 20, respectively. All
the oxygen atoms are arranged in a slightly distorted
hexagonal close packing, with the aluminum atoms
occupying some of the octahedral sites.
Earlier high-pressure investigations concentrated on
the determination of the bulk modulus and the p–T
stability field of diaspore. There have been large
discrepancies in the bulk moduli B0 reported from
experimental data, with values ranging from 134 to
230 GPa (B0 = 170 GPa, Ruoff and Vanderborgh 1991,
1993; B0 = 230 GPa, Xu et al. 1994; B0 = 167.5 GPa,
Mao et al. 1994; B0 = 134 GPa, Grevel et al. 2000). The
elastic constants of diaspore were measured at room
temperature by Haussu¨hl (1993) and from these data the
bulk modulus can be calculated to be B0 = 147 GPa and
extrapolated to 0 K using the thermoelastic constants
also determined by Haussu¨hl (1993) (B0 = 152 GPa at
0 K as described in Winkler et al. 2001). Recently,
Winkler et al. (2001) reported a bulk modulus of B0 =
148 GPa (at 0 K) from calculations based on density
functional theory.
While diaspore is stable up to at least 15 GPa and
1,123 K (Schmidt 1995), a high-pressure phase of
diaspore, d-AlO(OH) (space group P21nm), was syn-
thesized and found to be stable at pressures from 17
to at least 25 GPa at around 1,273–1,473 K (Suzuki
et al. 2000; Ohtani et al. 2001; Sano et al. 2004). This
phase was reported to be the least compressible hy-
drous phase currently known, with B0 = 252(3) GPa
(Vanpeteghem et al. 2002). It was suggested by first
principles calculations that, in the athermal limit, the
a-to-d phase transition occurs around 18 GPa (Li
et al. 2006).
Fig. 1 Projection of the crystal structure of diaspore along the c-
axis at 0 GPa (left). ‘‘Double rutile strings’’ of AlO3(OH)3
octahedra are connected via common corners. The hydrogen
bonds are formed across the channels. The assignment of the
different Al–O distances is illustrated in two enlarged octahedra
(right)
Phys Chem Minerals
123

An asymmetric-to-symmetric hydrogen bond phase
transition is predicted to occur in the d phase below
50 GPa at the pressure conditions of the lower mantle
(Tsuchiya et al. 2002; Li et al. 2006). In the symmetric
hydrogen bond phase the H-atom is located on a cen-
tral position between two oxygen atoms.
In the present study, the crystal structure of diaspore
was investigated at various pressures by in situ single-
crystal synchrotron X-ray diffraction. While it is
experimentally very challenging to determine the
hydrogen position unambiguously by this method,
information on the strength of the hydrogen bond can
be inferred from the interatomic O


O distances. For
example, systematics on the relationships between
O


O and O


H distances have been drawn from
organic compounds by Steiner and Saenger (1994).
Additionally, we have performed quantum mechanical
calculations, which can provide accurate structural data
(including hydrogen positions) for a wide range of
pressures. These calculations employed density func-
tional theory, which has previously been shown to
provide accurate structures and properties for a wide
range of materials (e.g. Milman et al. 2000), and has
been applied to diaspore previously (Winkler et al.
2001). Recently there has been some debate as to
whether the O-H vibration can be modelled within the
harmonic approximation (Pascale et al. 2004; Tosoni
et al. 2005). Based on the analysis of the anharmonicity
of O–H bonds in a variety of crystalline environments
(Szalay et al. 2002; Shinoda et al. 2000), we believe that
a full treatment of anharmonicity (e.g., by ab initio
molecular dynamics) would be desirable. Szalay’s
analysis showed that for a range of O–H stretching
frequencies differing by about 500 cm–1, the anhar-
monicity shift changed by less than 100 cm–1 (Szalay
et al. 2002). Furthermore, for portlandite, the effect of
pressure on the anharmonic coefficient was measured
to be a few percent at low pressures (about 12% at
8 GPa) (Shinoda et al. 2000). Hence, a systematic
offset with respect to experiment can be expected in
our calculations. However, a rigorous treatment would
be extremely computationally demanding and would
most likely not change the observed variations, and
therefore we have not attempted this here.
Experimental
A small single crystal of diaspore (150 · 100 · 40 lm3)
was obtained from a large gem-quality natural single
crystal of unknown origin. The sample was pressurised
using an ETH-type diamond-anvil cell (Miletich et al.
2000). A hole of 220 lm in diameter, serving as pres-
sure chamber, was drilled through a steel gasket (pre-
indented to a thickness of 90 lm) using a spark-eroding
drilling machine. A mixture of methanol and ethanol
(4:1) served as a pressure-transmitting medium.
In situ high-pressure single-crystal synchrotron X-ray
diffraction was performed at the bending-magnet beam
line D3 at HASYLAB. Unit-cell parameters and inten-
sity data were collected on a HUBER four-circle dif-
fractometer using a NaJ point detector and a wavelength
of 0.4 A˚, provided by a Si(111) double-crystal mono-
chromator. Experimental details and crystal data are
summarised in Table 1. Pressures were determined from
the unit-cell volumes of quartz, applying the equation
of state reported by Angel et al. (1997). We did not
measure the unit-cell volume at ambient conditions at
HASYLAB and, hence, applied the reference volume
from Angel et al. (1997). Therefore, a slight systematic
deviation from the real pressures cannot be excluded.
However, the pressures agree within two standard
deviations with the pressures measured by the ruby-flu-
orescence method (Mao et al. 1978). Pressure–volume
data were fitted by a Birch–Murnaghan equation of state
(BM-EOS) using the program EOS-FIT (Angel 2001)
and a fully weighted least-squares procedure.
The intensity measurements were carried out with
x-scans according to the fixed-/ technique (Finger and
King 1978), in order to select the beam path of least
attenuation through the pressure cell. All accessible
reflections within half an Ewald sphere and at / = 0
were collected in x-scan-mode up to 2h  30 (sin h/
k  0.623 A˚–1). For each pressure, the appropriate
scan parameters were selected (Table 1).
Intensity data were obtained from the scan data by
the Lehmann–Larsen algorithm implemented in the
beamline-specific software REDUCE (Eichhorn 1987),
and corrected for Lorentz and polarisation effects as
well as intensity drifts of the primary beam (AVSORT;
Eichhorn 1978). The absorption of the X-ray beam by
the sample, the diamonds and the beryllium plates of
the pressure cell was corrected using the program
ABSORB, Version 6.0 (Angel 2004). Structure refine-
ments were carried out with SHELXL97-2 (Sheldrick
1997). The starting parameters for the refinements
were taken from structural data published by Busing
and Levy (1958). The final refinements of the high-
pressure data sets were carried out with isotropic
displacement parameters for all atoms. While the high-
pressure cell environment normally leads to a decrease
in the data quality, our high-pressure data nevertheless
allowed us to observe the hydrogen site as a weak
maximum above the background in the difference
electron density (e.g., 0.43 e–A˚–3 at 2 GPa and 0.60
e–A˚–3 at 7 GPa, Table 1). The inclusion of the hydro-
Phys Chem Minerals
123

gen atom in the refinement significantly improved the
structural model (e.g., R1 = 0.0430 and wR2 = 0.0938
at 2 GPa; R1 = 0.0425 and wR2 = 0.1114 at 7 GPa; Ta-
ble 1) against a model without hydrogen (e.g., R1 =
0.0486 and wR2 = 0.1332 at 2 GPa, and R1 = 0.0509 and
wR2 = 0.1402 at 7 GPa). Due to the low scattering
power of a single electron (of hydrogen) and the
accompanied numerical instability of the fit, a geomet-
rical restraint (i.e. the O–H and H


O distances were
restrained to 0.90(9) A˚ and 1.60(9)–1.55(9) A˚, respec-
tively) had to be imposed in the refinement. The
resulting high uncertainty of the hydrogen position,
however, prevents us from drawing conclusions on the
pressure-dependent behaviour of the hydrogen bond
from the experimental data.
Computational details
The quantum mechanical calculations performed here
were based on density functional theory, DFT. While
DFT itself is exact, practical calculations employing the
Kohn Sham formalism require an approximation for
the treatment of the exchange and correlation effects.
The most widely used schemes are the generalized
gradient approximation, GGA, or the local density
approximation, LDA. For systems containing hydrogen
bonds, GGA calculations are generally in better
agreement with experiment than those obtained with
the LDA. All calculations reported here were per-
formed with the GGA functional of Perdew, Burke and
Ernzerhof (PBE) (Perdew et al. 1996), as implemented
in the academic and commercial versions of the CA-
STEP program (Segall et al. 2002, Clark et al. 2005).
In one set of calculations, ultrasoft pseudo-poten-
tials (Vanderbilt 1990) were used which had 3, 6 and 1
valence electrons, along with core radii of 2.0a0, 1.3a0
and 0.8a0, for the Al, O, and H atoms, respectively.
When used with a plane wave basis set truncated at a
kinetic energy of 380 eV, errors in the total energy of
the unit cell of less than 0.02 eV were observed. For a
second set of calculations we employed optimised
Table 1 Crystal data, details of the data collection and agreement factors for diaspore, AlO(OH) at various pressures p
p (GPa) 2.0(1) 3.41(3) 4.89(6) 5.71(3) 7.1(2)
Crystal data
a (A˚) 4.374(5) 4.354(1) 4.335(4) 4.328(1) 4.315(4)
b (A˚) 9.39(2) 9.369(4) 9.34(1) 9.336(5) 9.32(2)
c (A˚) 2.833(4) 2.8281(6) 2.820(2) 2.818(1) 2.812(3)
V (A˚3) 116.3(3) 115.36(6) 114.2(2) 113.86(9) 113.0(3)
Z (formula units) 4 4 4 4 4
Molecular weight (g mol–1) 59.99 59.99 59.99 59.99 59.99
F(000) (e–) 120 120 120 120 120
Density (g cm–3) 3.425 3.454 3.490 3.499 3.525
Linear abs. coeff. (mm–1) 0.15 0.15 0.15 0.15 0.15
Data collection
Instrument, beamline Four-circle diffractometer, D3, HASYLAB
Monitor Polarimeter
E (keV); k (A˚) 30.9954; 0.4
sin h/kmax (A˚
–1) 0.5936 0.5879 0.6213 0.6217 0.6232
Scan mode x scan (continuous)
Steps 101 91 101 101 101
Dx (deg); time per step (s) 0.002; 0.4–0.8
Standards 2 2 3, 3 4 1 every 60 min
h –5; 5 –4; 4 –5; 5 –5; 5 –5; 5
k –5; 5 –4; 6 –5; 6 –5; 6 –5; 6
l –3; 3 –2; 3 –3; 3 –3; 3 –3; 3
Rint(F
2) 0.11(6) 0.16(7) 0.17(8) 0.19(9) 0.10(6)
Observed reflections 455 231 557 560 494
Unique reflections 68 42 79 78 78
Reflections with I > 4r(I) 68 42 80 80 79
Parameters 14 11 14 14 14
R1 [I > 4r(I)] 0.0430 0.0540 0.0533 0.0499 0.0425
wR2 0.0938 0.1261 0.1351 0.1371 0.1114
GoF 1.198 1.200 1.202 1.172 1.189
D qmax 0.34 0.32 0.53 0.58 0.48
D qmin –0.42 –0.46 –0.71 –0.79 –0.48
For comparison, the cell parameters at ambient pressure are a = 4.401(1) A˚, b = 9.421(4) A˚ and c = 2.845(1) A˚ (Busing and Levy
1958). Space group: Pbnm (No. 62)
Phys Chem Minerals
123

norm-conserving pseudo-potentials (Lin et al. 1993,
Lee 1995). An oxygen pseudo-potential with a small
core radius of 1.4a0 was used to model the short
covalent bonds, which required a considerably in-
creased cut-off energy of 1,000 eV. In addition to these
cut-off energies, one further parameter determines the
quality of the calculations, namely the density of points
with which the Brillouin zone (BZ) is sampled. We
used a standard Monkhorst–Pack grid of 8 · 4 · 10 k-
points in the first BZ (Monkhorst and Pack 1976),
which gave very well converged results (|F| < 5 meV/A˚
and |r| < 20 MPa). In all calculations performed here,
the space group symmetry was constrained to Pbnm.
The present calculations were limited to the athermal
limit, in which temperature effects and zero-point
motions are neglected.
Initially, the frequencies of the gamma-point pho-
nons were calculated using the finite-displacements
technique and ultrasoft pseudo-potentials for a range
of applied pressures up to 40 GPa. For each pressure,
all symmetry-inequivalent atoms were displaced, in
turn, by 0.01a0. These calculations were relatively
inexpensive, but were limited to the simple case of
gamma-point frequencies without any consideration of
LO/TO splitting effects. In order to investigate the
phonon properties in greater detail, a second set of
calculations were performed using the recently-imple-
mented linear response module in CASTEP (Refson
et al. 2006), which can calculate phonon frequencies
and their infrared intensities at any reciprocal space
vector, including the effects of LO/TO splitting at the
gamma point. As linear response is not yet imple-
mented with ultrasoft pseudo-potentials we used the
norm-conserving pseudo-potentials described above,
which made these calculations computationally much
more demanding. As calculations of phonon frequen-
cies often require tighter convergence criteria, we
investigated the effects of increasing both the basis set
cut-off energy, and the k-point density. The calculated
frequencies were within a few wave numbers of the
values calculated using the parameters reported above,
and hence the results presented can be considered
converged with respect to both k-point sampling and
basis set.
Results and discussion
Theoretical and experimental unit cell volumes from
their equations of state are listed in Table 2. As with
other GGA-DFT calculations, the lattice parameters
are systematically (slightly) overestimated leading to a
better than expected agreement between our athermal
DFT results and our room-temperature experimental
results. The agreement between the relative pressure-
dependencies of the experimental and calculated unit-
cell parameters is excellent (see the following section).
Experimentally determined atom positions and iso-
tropic displacement factors are given in Table 3, while
inter-atomic distances and polyhedral volumes are lis-
ted in Table 4. The hydrogen bond geometries, inter-
and intra-polyhedral angles are deposited as electronic
supplementary material and can be obtained from the
authors upon request. A comparison of experimental
and theoretical interatomic distances (Fig. 2) shows
that the GGA-DFT calculations also give a very sat-
isfactory description of the structural details. There is a
small systematic offset between the absolute values of
the theoretical and experimental interatomic distances
(see below), but again, the relative pressure depen-
dencies are in excellent agreement. In the following
sections, our results relating to the compressibility,
crystal-structural compression and vibrational proper-
ties are reported.
Table 2 Results from fits of
Birch–Murnaghan equations
of state to the experimental
(exp.) and calculated (DFT)
data
B0 (GPa) B¢ v2
V0 (A˚
3)
Exp. (second order) 117.96(7) 150(3) 4 (Fixed) 0.59
DFT (second order) 121.06(7) 150.4(9) 4 (Fixed) 0.03
DFT (third order) 121.20(3) 143.7(9) 4.44(6) 0.002
a0 (A˚)
Exp. (second order) 4.401(1) 103(2) 4 (Fixed) 0.57
DFT (third order) 4.4332(5) 107.8(7) 4.14(5) 0.003
b0 (A˚)
Exp. (second order) 9.421(4) 191(14) 6 (Fixed) 0.14
DFT (third order) 9.5108(9) 166(2) 6.1(1) 0.005
c0 (A˚)
Exp. (second order) 2.8448(9) 188(9) 3.44 (Fixed) 0.23
DFT (third order) 2.8749(1) 174.2(5) 3.44(2) 0.001
Phys Chem Minerals
123

Compressibility
Results of fits of second-order and third-order Birch–
Murnaghan equations of state to the pressure–volume
data and the pressure dependencies of the individual
cell axes are summarised in Table 2. As only a few
experimental data points with large uncertainties have
been fitted, the pressure derivative of the bulk modulus
had to be fixed during the fitting procedure. While fits
of second-order to the experimental and theoretical
p–V data result in B0 = 150(3) GPa and B0 = 150.9(4)
GPa (at T = 0 K), respectively, the theoretical p–V
behaviour shows a significant deviation from B¢ = 4 at
pressures above 7 GPa, which justifies a third-order fit,
resulting in B0 = 143.7(9) GPa and B¢ = 4.4(6) (Fig. 3;
Table 2). Furthermore, our results are in very good
agreement with the bulk moduli calculated from the
precise elastic constants measured at room tempera-
ture (B0 = 147 GPa, Haussu¨hl 1993) and from the
elastic constants extrapolated to 0 K, as derived from
experimentally determined thermoelastic constants
(Haussu¨hl 1993), as described by Winkler et al. (2001)
(B0 = 152 GPa at 0 K), and with the bulk modulus
calculated from DFT in an earlier study by Winkler
et al. (2001) with B0 = 148 GPa (at 0 K). The extreme
value of B0 = 230 GPa reported from powder X-ray
diffraction at pressures up to 27 GPa might be attrib-
uted to strain artifacts that arose from stress onto the
sample, as no pressure medium was used (Xu et al.
1994). A bulk modulus of B0 = 170 GPa (Ruoff and
Vanderborgh 1991, 1993) was reported from ultrasonic
measurements. Bulk moduli of B0 = 167.5 and
134 GPa were reported from energy-dispersive powder
X-ray diffraction data up to 25.5 and 7 GPa, respec-
tively (Mao et al. 1994; Grevel et al. 2000). From our
data, and their good agreement with the elastic
behaviour reported by Haussu¨hl (1993), we conclude
that diaspore is much more compressible than its high-
pressure phase d-AlO(OH), which is considered to be
the least compressible hydrous phase currently known,
with B0 = 252(3) GPa (Vanpeteghem et al. 2002), and
that diaspore is significantly less compressible than
isostructural goethite, FeO(OH) (B0 = 111(2) GPa;
Nagai et al. 2005). This is expected from conventional
crystal chemical arguments, as the value of V0B0 is
empirically assumed to be approximately constant
Table 3 Atom positions and isotropic displacement parameters (A˚2) for diaspore, AlO(OH) from the experiment; z = 0.25 for all
atoms. The hydrogen position and Uisowere fixed in the refinement at 3.41(3) GPa
p (GPa) 2.0(1) 3.41(3) 4.89(6) 5.71(3) 7.1(2)
Al, x 0.0452(4) 0.0448(9) 0.0451(4) 0.0452(4) 0.0447(3)
Al, y 0.8558(4) 0.8568(6) 0.8563(3) 0.8568(4) 0.8572(3)
Al, Uiso 0.002(1) 0.009(2) 0.004(1) 0.003(1) 0.003(1)
O1, x 0.7104(9) 0.709(2) 0.7080(8) 0.7080(8) 0.7069(7)
O1, y 0.1994(9) 0.200(2) 0.198(1) 0.198(1) 0.1975(8)
O1, Uiso 0.002(1) 0.009(3) 0.004(1) 0.003(1) 0.004(1)
O2, x 0.199(1) 0.200(2) 0.2010(8) 0.2008(8) 0.2005(8)
O2, y 0.0536(9) 0.055(2) 0.053(1) 0.054(1) 0.0535(8)
O2, Uiso 0.003(1) 0.008(3) 0.004(1) 0.004(1) 0.004(1)
H, x 0.40(2) 0.39 0.39(2) 0.38(2) 0.35(2)
H, y 0.10(1) 0.10 0.10(2) 0.11(2) 0.12(1)
H, Uiso 0.03(3) 0.03 0.05(3) 0.09(5) 0.03(2)
Table 4 Selected inter-atomic distances (A˚) and polyhedral volume V (A˚3) from experimental and theoretical data of diaspore
p (GPa) 0a 0.0001b 2.0(1) 3.41(3) 4.89(6) 5.71(3) 7.1(2) 40a
Al–O1¢ 2x 1.876 1.851(2) 1.849(4) 1.852(7) 1.843(4) 1.841(4) 1.840(4) 1.806
Al–O1 1.888 1.858(4) 1.845(9) 1.84(1) 1.838(9) 1.842(9) 1.842(7) 1.797
Al–O2¢ 2x 1.987 1.975(3) 1.967(6) 1.956(9) 1.960(5) 1.954(5) 1.947(5) 1.880
Al–O2 1.998 1.980(3) 1.976(9) 1.97(2) 1.958(10) 1.957(10) 1.949(8) 1.869
OQEc 1.020 1.020(4) 1.019(6) 1.02(1) 1.018(7) 1.018(7) 1.018(6) 1.009
V 9.392 9.10(1) 9.02(3) 8.99(5) 8.92(3) 8.89(3) 8.83(2) 8.189
O1


O2 2.624 2.650(3) 2.623(8) 2.60(2) 2.583(9) 2.577(9) 2.565(7) 2.382
a Theoretical data as obtained from density functional theory based model calculations
b Ambient pressure; data were taken from Busing and Levy (1958)
c The octahedral quadratic elongation (OQE) values were calculated using the VOLCAL program (Finger 1971), following the
method of Robinson et al. (1971)
Phys Chem Minerals
123

compression the two longer distances compress slightly
more than the Al–O1 distances at lower pressures,
the discrepancy in the bond distances decreases less
at higher pressures, such that an equalisation of the
hydrogenated and the non-hydrogenated Al–O dis-
tances is not expected from our data (Fig. 5). This is in
contrast to the assumption by Nagai et al. (2003), who
proposed a convergence of the respective Fe–O1 and
Fe–O2 distances in goethite at about 40 GPa from
linear extrapolation of structural data from up to
9 GPa. The intra-octahedral angles of the AlO3(OH)3
octahedron show only slight deviations with increasing
pressure (up to 4) except for the strongly bent O1–Al–
O2 octahedral-axis angle (161.97 at 0 GPa), which
straightens by about 8 towards 170.11 at 40 GPa. This
octahedral axis is nearly parallel to the b axis, with only
a small component along the a-axis. Hence, the ob-
served straightening of the O1–Al–O2 angle in the
direction of the b-axis is correlated to the lower com-
pressibility of the b-axis, with respect to the c-axis, at
increasing pressure. In general, the slight distortion of
the AlO3(OH)3 octahedron from a regular octahedron
decreases with pressure as expressed in the quadratic
octahedral elongation (Table 4). The fit of a third-order
Birch–Murnaghan equation of state to the pressure-
dependence of the octahedral volume results in the
octahedral bulk modulus B0(AlO6) = 213.1(9) GPa
and its pressure derivative B¢ = 4.59(5) at V0 =
9.390(1) A˚3. This value is much higher than the overall
bulk modulus of B0 = 143.7(9) GPa (Table 2), but is
typical for AlO6 octahedra, which in many structures
show bulk moduli within 10% of 235 GPa (Hazen et al.
2000). For comparison, the bulk modulus of the AlO6
octahedron is significantly higher than that of an
average MgO6 octahedron (150 GPa ± 10%, Hazen
et al. 2000), while SiO6 octahedra are much more rigid,
and exhibit higher bulk moduli (e.g. 380 GPa in
perovskite-type MgSiO3, Kudoh et al. 1987).
Pressure-induced polyhedral tilting is strongly re-
stricted within this structure type (<4 up to 40 GPa),
where all atoms are located on special positions in the
z-direction and where all of the inter-octahedral an-
gles, except for the Al–O1–Al¢ angle, link edge-sharing
octahedra within the double-rutile strings. The Al–O1–
Al¢ angle connects these strings via shared corners
approximately along the a-axis (Fig. 1). The change of
this angle with increasing pressure is extremely small,
at less than 0.4 over the range of pressures studied
here.
The main structural compression is neither obtained
by octahedral compression nor by polyhedral tilting,
but by the compression of the hydrogen-containing
channels. This is accompanied by the compression and
strengthening of the hydrogen bond, which bridges the
channels within the (001) plane, being mainly oriented
along the a-axis (Fig. 1). Hence, the strong compres-
sion of the O1


O2 donor-acceptor distance with
increasing pressure (Fig. 5) is related to the high
compressibility of the a-axis, as has been previously
discussed for goethite (Nagai et al. 2003) (Fig. 4, Ta-
ble 2). The strengthening of the hydrogen bond with
pressure is further confirmed by the slight increase of
the O2–H hydrogen-bond distance and the more pro-
nounced decrease of the H


O1 proton-acceptor dis-
tance (Fig. 6a), while the strongly bent hydrogen-bond
angle O2–H


O1 (162.71 at 0 GPa) hardly increases
(<0.6), as was also found in earlier calculations by
Winkler et al. (2001). However, complete symmetri-
sation, i.e. an equalisation of the O2–H and H


O1
distances, is not reached in the investigated pressure
range up to 40 GPa (Fig. 6) and 50 GPa (Winkler et al.
2001), respectively. As discussed above, this is corre-
lated to the remaining discrepancy between Al–O1 and
/
Å
A
l
-
O
1.76
1.80
1.84
1.88
1.92
1.96
2.00
0 10 20 30 40
Pressure / GPa
2.37
2.41
2.45
2.49
2.53
2.57
2.61
2.65
O
2
.
.
.
O
1
/
Å
Fig. 5 Pressure-dependencies of the O1


O2 donor–acceptor
distance of the hydrogen bond (top) and the Al–O bond
distances (bottom) from experiment (symbols with error bars)
and theory. Symbols (bottom): Al–O1¢ (filled diamonds), Al–O1
(open squares), Al–O2¢ (filled triangles), Al–O2 (open circles).
Linear fits to the experimental data are shown as guide to the
eyes
Phys Chem Minerals
123

Interestingly, a comparison between our results and
the commonly used correlation diagrams such as those
by Novak (1974) and Libowitzky (1999) (Fig. 9) re-
veals marked deviations. While these deviations could
simply be attributed to the very non-linear O–H


O
angle in diaspore, especially at elevated pressures,
Libowitzky’s correlation diagram includes a number of
examples of non-linear hydrogen bonds. This suggests
that the analytical expression used to correlate vibra-
tional frequencies to structural parameters may break
down in the low-frequency/short bond-length limit. We
are currently performing further calculations on the d-
phase and related compounds to investigate this mat-
ter, the results of which will be reported in a sub-
sequent publication.
Conclusions
We have studied the structural compression mecha-
nism and compressibility of diaspore, AlO(OH) using a
combination of in situ single-crystal synchrotron X-ray
diffraction and density functional theory based calcu-
lations. We found that this combination was ideal for
investigation of materials such as diaspore, as the DFT
calculations can provide accurate information on the
Fig. 7 Illustrations of the
four O–H stretching modes of
diaspore, derived via
diagonalisation of the
calculated dynamical matrix.
Throughout this work, these
are referred to as modes A–D
(left to right). Pink (light
grey), red (dark grey) and
white spheres correspond to
aluminium, oxygen and
hydrogen ions, respectively
Table 5 The gamma-point O–H vibrational frequencies for a range of pressures, calculated using both the finite displacements meth-
odology with ultrasoft pseudo-potentials (FD), and the linear response methodology with norm-conserving pseudopotentials (LR)
Pressure
(GPa)
Method LO/TO
splitting?
d(O–H) (A˚) d(O


H)
(A˚)
Mode A
(cm–1)
Mode B
(cm–1)
Mode C
(cm–1)
Mode D
(cm–1)
0 FD · 1.018 1.635 2934 2959 2961 2966
LR · 1.002 1.628 2907 2924 2929 2933
LR
1.002 1.628 2907 2924–2968 2929 2933–3108
2 FD · 1.021 1.606 2883 2902 2908 2912
LR · 1.006 1.598 2845 2862 2870 2874
LR
1.006 1.598 2845 2862–2912 2870 2874–3066
5 FD · 1.025 1.567 2790 2812 2822 2826
LR · 1.011 1.559 2762 2779 2790 2793
LR
1.011 1.559 2762 2779–2836 2790 2793–3009
10 FD · 1.031 1.516 2676 2696 2712 2714
LR · 1.018 1.506 2636 2652 2671 2671
LR
1.018 1.506 2636 2652–2722 2671 2671–2925
25 LR · 1.038 1.392 2320 2340 2374 2367
LR
1.038 1.392 2320 2340–2445 2374 2367–2724
40 FD · 1.060 1.348 2250 2281 2318 2311
LR · 1.055 1.320 2120 2154 2191 2179
LR
1.055 1.320 2120 2154–2280 2191 2179–2612
The four stretching modes are illustrated in Fig. 7. When LO/TO splitting effects are included in the linear response calculations, the
frequencies of the IR-active modes depend upon the direction of approach to the zone centre, and therefore they are quoted as
frequency ranges, rather than distinct values
Phys Chem Minerals
123

corundum: an in situ X-ray diffraction study comparing
different pressure media. J Geophys Res–Sol Ea 105:27877–
27887
Haussu¨hl S (1993) Thermoelastic properties of beryl, topaz,
diaspore, sanidine and periclase. Z Kristallogr 204:67–76
Hazen RM, Downs RT, Prewitt CT (2000) Principles of
comparative crystal chemistry. In: Hazen RM, Downs RT
(eds) High-temperature and high-pressure crystal chemistry.
Mineral Soc Am Rev Mineral Geochem 41:1–33
Hirth G, Kohlstedt DL (1996) Water in the oceanic upper mantle:
implications for rheology, melt extraction and the evolution
of the lithosphere. Earth Planet Sci Lett 144:93–108
Kruger MB, Williams Q, Jeanloz R (1989) Vibrational spectra
of Mg(OH)2 and Ca(OH)2 under pressure. J Chem Phys
91:5910–5915
Kudoh Y, Ito E, Takeda H (1987) Effect of pressure on the
crystal structure of perovskite-type MgSiO3. Phys Chem
Minerals 14:350–354
Kunz M, Leinenweber K, Parise JB, Wu T-C, Bassett WA,
Brister K, Weidner DJ, Vaughan MT, Wang Y (1996) The
baddeleyite-type high pressure phase of Ca(OH)2. High
Press Res 14:311–319
Lee MH (1995) Advanced pseudopotentials for large scale
electronic structure calculations. Ph.D. Thesis, University
of Cambridge; Psi-k Newsletter 67 http://psi-k.dl.ac.uk/
newsletters/News_67/Highlight_67.pdf
Leinenweber K, Partin DE, Schuelke U, O’Keeffe M, Von
Dreele RB (1997) The structure of high pressure Ca(OD)2
II from powder neutron diffraction: relationship to the ZrO2
and EuI2 structures. J Solid State Chem 132:267–273
Li S, Ahuja R, Johansson B (2006) The elastic and optical
properties of the high-pressure hydrous phase d-AlOOH.
Solid State Commun 137:101–106
Libowitzky E (1999) Correlation of O–H stretching frequencies
and O–H


O hydrogen bond lengths in minerals. Monatsh
Chem 130:1047–1059
Lin JS, Qteish A, Payne MC, Heine V (1993) Optimised and
transferable non-local separable ab initio pseudopotentials.
Phys Rev B 47:4174–4180
Lundgren P, Giardini D (1994) Isolated deep earthquakes and
the fate of subduction in the mantle. J Geophys Res
99:15833–15842
Lutz HD, Henning J, Engelen B (1990) Lattice vibration spectra
Part LVIII. OD(OH) frequency versus H-bond distance
correlation diagrams a case study for isomorphic
M(SO3)2
3H2O (M = Mg, Mn, Fe, Co, Ni, Zn). J Mol Struct
240:275–283
Mao H, Bell P, Shaner J, Steinberg D (1978) Specific volume
measurement of Cu, Mo, Pd, and Ag and calibration of the
ruby R1 fluorescence pressure gauge from 0.06 to 1 Mbar.
J Appl Phys 49:3276–3283
Mao H-k, Shu J, Hu J, Hemley RJ (1994) High-pressure X-ray
diffraction study of diaspore. Solid State Commun 90:497–500
Meade C, Jeanloz R (1991) Deep-focus earthquakes and
recycling of water into the earths mantle. Science 252:68–72
Mikenda W (1986) Stretching frequencies versus bond distance
correlation of O-D(H)


Y (Y = N, O, S, Se, Cl, Br, I)
hydrogen bonds in solid hydrates. J Mol Struct 326:123–130
Miletich R, Allan DR, Kuhs WF (2000) High-pressure single-
crystal techniques. In: Hazen RM, Downs RT (eds) High-
temperature and high-pressure crystal chemistry. Mineral
Soc Am Rev Mineral Geochem 41:445–520
Milman V, Winkler B, White JA, Pickard CJ, Payne MC,
Akhmatskaya EV, Nobes RH (2000) Electronic structure,
properties, and phase stability of inorganic crystals: a
pseudopotential plane-wave study. Int J Quantum Chem
77:895–910
Monkhorst HJ, Pack JD (1976) Special points for Brillouin-zone
integrations. Phys Rev B 13:5188–5192
Nagai T, Kagi H, Yamanaka T (2003) Variation of hydrogen
bonded O


O distances in goethite at high pressure. Am
Mineral 88:1423–1427
Nakamoto K, Margoshes M, Rundle RE (1955) Stretching
frequencies as a function of distances in hydrogen bonds.
J Amer Chem Soc 77:6480–6486
Novak A (1974) Hydrogen bonding in solids. Correlation of
spectroscopic and crystallographic data. Struct Bond 18:177–
216
Ohtani E, Litasov K, Suzuki A, Kondo T (2001) Stability field of
new hydrous phase, delta-AlOOH, with implications for
water transport into the deep mantle. Geophys Res Lett
29:3991–3993
Parise JB, Leinenweber K, Weidner DJ, Tan K, Von Dreele RB
(1994) Pressure-induced H bonding: Neutron diffraction
study of brucite, Mg(OD)2, to 9.3 GPa. Am Mineral 79:193–
196
Parise JB, Cox H, Kagi H, Li R, Marshall WG, Loveday JS,
Klotz S (1998a) Hydrogen bonding in M(OD)2 compounds
under pressure. Rev High Press Sci Technol 7:211–216
Parise JB, Theroux B, Li R, Loveday JS, Marshall WG, Klotz S
(1998b) Pressure dependence of hydrogen bonding in metal
deuteroxides: a neutron powder diffraction study of
Mn(OD)2 and b-Co(OD)2. Phys Chem Miner 25:130–137
Pascale F, Tosoni S, Zicovich-Wilson C, Ugliengo P, Orlando R,
Dovesi R (2004) Vibrational spectrum of brucite, Mg(OH)2:
a periodic ab initio quantum mechanical calculation includ-
ing OH anharmonicity. Chem Phys Lett 396:308–315
Perdew JP, Burke K, Ernzerhof M (1996) Generalized gradient
approximation made simple. Phys Rev Lett 77:3865–3868
Raugei S, Silvestrelli PL, Parrinello M (1999) Pressure-induced
frustration and disorder in Mg(OH)2 and Ca(OH)2. Phys
Rev Lett 83:2222–2225
Refson K, Tulip PR, Clark SJ (2006) Variational density-
functional perturbation theory for dielectrics and lattice
dynamics. Phys Rev B 73:155114
Robinson K, Gibbs GV, Ribbe PH (1971) Quadratic elongation–
quantitative measure of distortion in coordination poly-
hedra. Science 172:567–570
Ruoff AL, Vanderborgh CA (1991) Hydrogen reduction at high
pressure: Implication for claims of metallic hydrogen. Phys
Rev Lett 66:754–757
Ruoff AL, Vanderborgh CA (1993) Hydrogen reduction at high
pressure: Implication for claims of metallic hydrogen. Phys
Rev Lett 71:4279
Ryskin YI (1974) The vibrations of protons in minerals:
hydroxyl, water and ammonium. In: Farmer VD (ed) The
infrared spectra of minerals. Mineralogical Society, London,
pp 137–182
Sano A, Ohtani E, Kubo T, Funakoshi K-i (2004) In situ
observation of decomposition of hydrous aluminum silicate
AlSiO3OH and aluminum oxide hydroxide d-AlOOH at
high pressure and temperature. J Phys Chem Solids 65:1547–
1554
Schmidt MW (1995) Lawsonite: upper pressure stability and
formation of higher density hydrous phases. Am Mineral
80:1286–1292
Segall MD, Lindan PJD, Probert MJ, Pickard CJ, Hasnip PJ,
Clark SJ, Payne MC (2002) First-principles simulation:
ideas, illustrations and the CASTEP code. J Phys Condens
Matter 14:2717–2744
Phys Chem Minerals
123

Sheldrick GM (1997) SHELXL97-2. Program for refinement of
crystal structures. University of Go¨ttingen, Go¨ttingen,
Germany
Sherman DM (1991) Hartree-Fock band structure, equation of
state, and pressure-induced hydrogen bonding in brucite,
Mg(OH)2. Am Mineral 76:1769–1772
Shinoda K, Nagai T, Aikawa N (2000) Pressure-dependent
anharmonic coefficient of OH in portlandite by NIR-IR
spectroscopy with DAC. J Miner Petrol Sci 95:65–70
Stalder R, Ulmer P (2001) Phase relations of a serpentine
composition between 5 and 14 GPa: significance of clinohu-
mite and phase E as water carriers into the transition zone.
Contrib Mineral Petrol 140:670–679
Steiner Th, Saenger W (1994) Lengthening of the covalent O–H
bond in O–H


O hydrogen bonds re-examined from low-
temperature neutron diffraction data of organic compounds.
Acta Crystallogr B50:348–357
Suzuki A, Ohtani E, Kamada T (2000) A new hydrous phase
d-AlOOH synthesized at 21 GPa and 1000C. Phys Chem
Miner 27:689–693
Szalay V, Kova´cs L, Wo¨hlecke M, Libowitzky E (2002) Stretch-
ing potential and equilibrium length of the OH bond in
solids. Chem Phys Lett 354:56–61
Thompson AB (1992) Water in the earth’s upper mantle. Nature
358:295–302
Tosoni S, Pascale F, Ugliengo P, Orlando R, Saunders VR,
Dovesi R (2005) Quantum mechanical calculation of the
OH vibrational frequency in crystalline solids. Mol Phys
103:2549–2558
Tsuchiya J, Tsuchiya T, Tsuneyuki S, Yamanaka T (2002) First
principles calculation of a high-pressure hydrous phase,
delta-AlOOH. Geophys Res Lett 29:1909
Vanderbilt D (1990) Soft self-consistent pseudopotentials in a
generalised eigenvalue formalism. Phys Rev B 41:7892–7895
Vanpeteghem CB, Ohtani E, Kondo T (2002) Equation of state
of the hydrous phase delta-AlOOH at room temperature up
to 22.5 GPa. Geophys Res Lett 29:1119
Williams G, Guenther L (1996) Pressure-induced changes in the
bonding and orientation of hydrogen in FeOOH-goethite.
Solid State Commun 100:105–109
Winkler B, Langer K, Johannsen PG (1989) The influence of
pressure on the OH valence vibration of zoisite—An infrared
spectroscopic study. Phys Chem Miner 16(7):668–671
Winkler B, Hytha M, Pickard C, Milman V, Warren M, Segall M
(2001) Theoretical investigation of bonding in diaspore. Eur
J Mineral 13:343–349
Xu J-a, Hu J, Ming L-c, Huang E, Xie H (1994) The compression
of diaspore, AlO(OH) at room temperature. Geophys Res
Lett 21:161–164
Phys Chem Minerals
123