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High-pressure structural study of the scheelite tungstates CaWO4 and SrWO4
D. Errandonea,1* J. Pellicer-Porres,1 F. J. Manjón,2 A. Segura,1 Ch. Ferrer-Roca,1
R. S. Kumar,3 O. Tschauner,3 P. Rodríguez-Hernández,4 J. López-Solano,4 S. Radescu,4
A. Mujica,4 A. Muñoz,4 and G. Aquilanti5
1 Departamento de Física Aplicada-ICMUV, Universitat de València,
Edificio de Investigación, c/Dr. Moliner 50, 46100 Burjassot (Valencia), Spain
2 Departamento de Física Aplicada, Universitat Politècnica de València,
Cno. de Vera s/n, 46022 València, Spain
3 High Pressure Science and Engineering Center, Department of Physics,
University of Nevada, 4505 Maryland Parkway, Las Vegas, Nevada 89154-4002, USA
4 Departamento de Física Fundamental II, Universidad de La Laguna, La Laguna 38205, Tenerife, Spain
5 European Synchrotron Radiation Facility, BP 220, Grenoble, F-38043 France
Abstract: Angle-dispersive x-ray diffraction (ADXRD) and x-ray absorption near-edge
structure (XANES) measurements have been performed on CaWO4 and SrWO4 up to pressures
of approximately 20 GPa. Both materials display similar behavior in the range of pressures
investigated in our experiments. As in the previously reported case of CaWO4, under
hydrostatic conditions SrWO4 undergoes a pressure-induced scheelite-to-fergusonite transition
around 10 GPa. Our experimental results are compared to those found in the literature and are
further supported by ab initio total energy calculations, from which we also predict the
instability at larger pressures of the fergusonite phases against an orthorhombic structure with
space group Cmca. Finally, a linear relationship between the charge density in the AO8
polyhedra of ABO4 scheelite-related structures and their bulk modulus is discussed and used to
predict the bulk modulus of other materials, like hafnon.
PACS NUMBERS: 7.35.+k, 61.10.Ht, 61.10.Nz, 61.50.Ks, 62.50.+p, 64.70.Kb, 71.15.Mb, 71.15.Nc
* Corresponding author; electronic mail: daniel.errandonea@uv.es, Tel.: (34) 96 354 34 32, FAX: (34) 354 3146
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I. Introduction
Scheelite ABX4 compounds are important materials from both a theoretical and a
technological point of view. Scheelite fluorides (ABF4) like YLiF4 and GdLiF4 are used
in rare-earth solid state lasers [1], scheelite oxides (ABO4) like CaWO4 and PbWO4 are
used as solid state scintillators [2, 3], and there is much interest in the use of scheelite
compounds in optoelectronic devices [4 - 6]. Moreover, a family of superhard materials
has been found in ABO4 compounds with A and B atoms having valence +4 [7].
In the last years there has arisen renewed interest in ABX4 compounds and its
evolution under pressure. Many of these compounds crystallize in the scheelite structure
(space group: I41/a, No. 88, Z = 4) or in related structures like zircon (space group:
I41/amd, No. 141, Z = 4), pseudoscheelite (space group: Pnma, No. 62, Z = 4),
wolframite (space group: P2/c, No. 13, Z = 2), M-fergusonite (space group: I2/a, No.
15, Z = 4), hereafter called fergusonite, and M’-fergusonite (space group: P21/c, No. 14,
Z = 2). In particular, the ambient conditions scheelite structure of CaWO4 and SrWO4
has eight symmetry elements and a body-centered tetragonal primitive cell that includes
two formula units, see Fig. 1(a). Each W site is surrounded by four equivalent O sites in
tetrahedral symmetry about that site. Each Ca (Sr) cation shares corners with eight
adjacent WO4 tetrahedra.
Several experimental and theoretical works have been reported in the last decade
on the pressure behavior of scheelite oxides and fluorides [8 - 33]. Upon compression
most of these compounds undergo structural transitions to monoclinic structures.
However, several of these low-symmetry structures are difficult to characterize in high-
pressure x-ray diffraction experiments and it has been further suggested that their
formation could depend on the stress conditions in the pressure chamber. In particular, a
discussion regarding the high-pressure phase of CaWO4 was open in recent years [8, 9].
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The occurrence of pressure-driven phase transitions in CaWO4 and CaMoO4 was
first reported by Nicol and Durana [10], who postulated that the high-pressure phases
had the wolframite structure. Other monoclinic structures that were considered during
decades as candidate structures for the ABO4 compounds at high pressure were those of
α-MnMoO4-type (space group: C2/m, No. 12, Z = 8) [11], BaWO4(II)-type (space
group: P21/n, No. 14, Z = 8) [12], and HgWO4-type (space group: C2/c, No. 15, Z = 4)
[13]. Errandonea and coworkers [8] performed for the first time energy-dispersive x-ray
powder diffraction (EDXRD) experiments on CaWO4 up to pressures where the high-
pressure phase was observed. They observed the occurrence of the pressure-driven
phase transition at 10 GPa. These authors considered the four monoclinic structures
previously postulated for the high-pressure phase of CaWO4 to index their EDXRD
patterns. Based on the quality of the unit-cell fit, they concluded that the high-pressure
phase of CaWO4 was most likely of the wolframite-type [8] (see Fig. 1(b)). The same
was also concluded by Shieh et al. from a high-pressure x-ray diffraction study on
CdMoO4 [14]. However, most recently Grzechnik et al. [9] performed high-resolution
angle-dispersive x-ray powder diffraction (ADXRD) on CaWO4 and reported the high-
pressure structure to be fergusonite-like (see Fig. 1(c)). Later measurements on BaWO4
[13], BaMoO4 [33], and CaMoO4 [29] also reported a scheelite-to-fergusonite phase
transition, but in the case of SrWO4, a recent study combining x-ray diffraction and
absorption observed a phase transition at 11.7 GPa and characterized the high-pressure
phase as wolframite [32]. From the theoretical side, support to the scheelite-to-
fergusonite transition with increasing pressure in ABX4 scheelite compounds has been
given by the works of Sen et al. [15, 16], while support to the scheelite-to-wolframite
transition was reported in the work of Li et al. [17].
In this work we report new high-pressure ADXRD experiments up to nearly 18
4
GPa and x-ray absorption near-edge structure (XANES) measurements up to nearly 20
GPa on CaWO4 and SrWO4 along with ab initio total energy calculations in both
compounds. From our ADXRD data we find that under hydrostatic conditions both
compounds undergo a scheelite-to-fergusonite phase transition with increasing pressure,
which is supported by the high-pressure XANES measurements and the ab initio total
energy calculations.
II. Experimental Details
CaWO4 and SrWO4 crystals were grown with the Czochralski method starting
from raw powders having 5N purity [4]. Samples were prepared as finely ground
powders from the single crystals of CaWO4 and SrWO4. High-pressure ADXRD
measurements were carried out in 450 µm culet Merrill-Basset diamond-anvil cell
(DAC) for CaWO4 and in a 400 µm culet Mao-Bell DAC for SrWO4. In the first case,
powder samples were loaded together with a ruby chip into a 180 µm diameter hole
drilled on a 200 µm thick rhenium (Re) gasket pre-indented to 60 µm. In the second
case, the Re gaskets were pre-indented to 40 µm and the diameter of the gasket hole was
100 µm. Silicone oil was used as pressure-transmitting medium in both cases. For
XANES measurements under pressure, fine powder samples were loaded together with
a ruby chip into a 200 µm diameter hole drilled on a 200 µm thick Inconel gasket pre-
indented to 50 µm and inserted between the diamonds of a 400 µm culet membrane-
type DAC with silicone oil as pressure-transmitting medium. The pressure was
measured by the shift of the R1 photoluminescence line of ruby [34].
ADXRD experiments were performed at the 16-IDB beamline of the HPCAT
facility at the Advanced Photon Source (APS) using monochromatic radiation with λ =
0.3679 Å (a Si (311) double-crystal monochromator was used). The monochromatic x-
ray beam was focused down to 10 x 10 µm2 using multilayer bimorph mirrors in a
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Kickpatrick-Baez configuration [35]. Diffraction images were recorded with a Mar345
image plate detector, 230 mm away from the sample, and were integrated and corrected
for distortions using the FIT2D software [36]. The indexing, structure solution, and
refinements were performed using the GSAS [37] and the POWDERCELL [38]
program packages.
XANES experiments were conducted at the ID24 energy dispersive x-ray
absorption station of the European Synchrotron Radiation Facility (ESRF) [39, 40]. The
key component of the dispersive setup is a curved monochromator that selects an energy
span around the absorption edge and focuses the beam in the horizontal direction. All
the energies contained in the diffracted beam are detected simultaneously by means of a
position sensitive detector. In order to establish the energy-pixel correlation, the
spectrum of a reference standard is measured and compared with an equivalent
spectrum acquired with the classical setup, where the knowledge of the Bragg angle
allows for a determination of the energy. A more detailed description of the principles
of energy-dispersive x-ray-absorption data collection is given in Ref. [41].
All XANES experiments were performed at the W L
3-edge (10.207 keV). At
ID24, the combination of a profiled curved Si (111) monochromator [42] and a
vertically focusing mirror defined a focus spot of approximately 30 x 20 µm2. The
membrane DAC was situated at the focus position. The incident and transmitted beams
were alternatively measured. In our experiments, the incident intensity was measured
outside the pressure chamber. An essential experimental aspect of x-ray absorption
spectroscopy (XAS) experiments in a DAC is the presence of diffraction peaks
originating from diffraction from the diamond single crystals. The pressure cell is
oriented with respect to the polychromatic x-ray beam so as to remove these glitches
from the widest spectral range around the x-ray-absorption edge. This operation takes
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advantage of the real time visualization of the XAS spectra, characteristic of the energy-
dispersive setup. The presence of harmonics was avoided thanks to the grazing
incidence mirrors situated between the undulator source and the monochromator. The
reference standard for the energy calibration was metallic W.
III. Overview of the calculations
The structural stability of the phases of CaWO4 and SrWO4 was further
investigated theoretically by means of total energy calculations performed within the
framework of the density functional theory (DFT) with the Vienna Ab Initio Simulation
Package (VASP) [43]. A review of DFT-based total energy-methods as applied to the
theoretical study of phase stability can be found in Ref. [44]. The exchange and
correlation energy was evaluated within the generalized gradient approximation (GGA)
[45]. We used ultrasoft Vanderbilt-type pseudopotentials [46] and basis sets including
plane waves up to a kinetic-energy cutoff of 850 eV for CaWO4 and 495 eV for SrWO4.
The tetrahedron method combined with Blöchl corrections was used for the Brillouin-
zone integrations. The total energies were converged to below 1 meV per formula unit.
The structural relaxation of the phases at each volume was conducted through the
calculation of the forces on the atoms and the components of the stress tensor.
IV. Results and discussion
A. ADXRD measurements at high pressures
A. 1. Low-pressure phase
Fig. 2 shows our ADXRD data for CaWO4 and SrWO4 at several selected
pressures up to 18 GPa. The evolution with pressure of the volume, lattice parameters,
and axial ratios is plotted in Figs. 3 and 4 where we also compare our results with
previously reported data for CaWO4 [8, 9, 19, 47, 48] and SrWO4 [47, 49] (in this case
only for ambient pressure).
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The pressure-volume (P-V) curves shown in Fig. 3(a) were analyzed in the
standard way using a Birch-Murnaghan equation of states (EOS) [50],
7/35/3'2/3
00
33
()[1(4)(1)]
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PBxxBx
=−+−−
, (1)
with 0
/
xVV
=, where the parameters V0, B0, and B0’ are the zero-pressure volume, bulk
modulus, and pressure derivative of the bulk modulus, respectively. For scheelite
CaWO4 we find V0 = 312(1) Å3, B0 = 74(7) GPa, and B0’ = 5.6(9) [V0 = 347.4(9) Å3, B0
= 63(7) GPa, and B
0’ = 5.2(9) for scheelite SrWO4]. These parameters are in good
agreement with previous reported results [9, 19] and indicate that SrWO4 is more
compressible than CaWO4, which is a direct consequence of the different
compressibility of the c-axis in the two compounds, see below. It is worth to mention
that the evolution of the volume of CaWO4 with pressure reported in Ref. [8], and
plotted as solid squares in Fig. 3(a) for the sake of comparison, underestimates the
decrease of the volume above 7 GPa. This result gives support to the idea that a non-
hydrostatic pressure environment may affect the structural pressure behavior of
scheelite tungstates, as we will comment later on.
Fig. 3(b) shows that the compressibility of the c-axis of the scheelite structure is
larger for SrWO4 than for CaWO4, while the a-axis compresses in the same way in the
two compounds (see Fig. 3(c)). The larger compressibility of the c-axis in SrWO4
compared to that of CaWO4 can be related to the difference in size of the Ca+2 and Sr+2
cations, which implies a larger charge density in the Ca environment with respect to that
around Sr, as we will discuss later. The larger compressibility along the c-axis as
compared to that along the a-axis is evident in Fig. 4.
We have also investigated the evolution of cation-anion distances in both
compounds. According to the single-crystal high-pressure investigation carried out by
Hazen et al. [19] up to 4.1 GPa, the relative positions of the atoms in the CaWO4 unit
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cell do not vary under pressure within the experimental error. In our experiment we
have determined the internal parameters at the lowest pressure by means of a Rietveld
refinement and then maintained them constant at higher pressures (see Table I). Fig. 5
shows the evolution of the atomic distances between nearest neighbors with increasing
pressure. The interatomic distances in CaWO4 evolve in a similar way as previously
reported [19, 27], but the present results systematically differ by less than ~2% from
those reported in Ref. [27]. This difference was observed before by Hazen [19] between
experiments performed inside and outside a DAC and can be attributed to the limited
access to the reciprocal space of the used DAC [19] and to the presence of impurities in
the studied samples [51]. The good agreement between our results and previous ambient
pressure results [19, 52] suggests that the pressure evolution of the interatomic distances
reported here is more reliable than previous published data. The decrease of Ca-O and
Sr-O distances can be compared with the rigidity of the W-O bond distance in both
compounds. In Fig. 5 it can be seen that there are two Ca-O and Sr-O distances, the
largest distances being more compressible than the shorter ones.
Our results support the description of AWO4 tungstate scheelites in terms of hard
anion-like WO4 tetrahedra surrounded by charge compensating cations. When pressure
is applied the WO4 units remain essentially undistorted and the reduction of the unit-cell
size is mainly associated to the compression of the A cation polyhedral environment
[19]. Along the a-axis the WO4 units are directly aligned, whereas along the c-axis there
is an A cation between two WO4 tetrahedra. Therefore, the different arrangement of
hard WO4 tetrahedra along the c- and a-axis accounts for the different compressibility
of the two cell axes. The different pressure behavior of the two A-O distances (Fig. 5) is
associated to the different compressibility of the cell parameters. Effectively, the longest
A-O distance has the largest projection along the c-axis. It is important to point out that
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the asymmetric behavior of c- and a-axis is also revealed in their different thermal
expansion [53], as well as in the evolution of the c/a ratio along a cationic A series [47].
A.2. High-pressure phases
The ADXRD spectra of CaWO4 exhibit a change around 11.3 GPa, while in
SrWO4 the change occurs near 10.1 GPa (see Fig. 2). These changes are completely
reversible upon pressure release. Below those pressures the observed diffraction peaks
shift smoothly with compression and all the reflections observed in the diffraction
patterns can be indexed within the scheelite structure whereas above those pressures
some of the diffraction peaks split and additional diffraction peaks emerge. In particular,
the appearance of a new peak around 2θ ≈ 3.8º (depicted by an arrow in Fig. 2) is
clearly distinguishable. The observed splitting of peaks and the appearance of new
reflections suggests the occurrence of a second-order phase transition. The measured
ADXRD patterns of the high-pressure phase can be indexed on the basis of the
fergusonite structure but not on the basis of the wolframite structure, confirming
Grzechnik’s results for CaWO4 [9]. The new Bragg peaks observed at 2θ ≈ 3.8º in the
high-pressure phase of both compounds correspond to the (020) reflection of the
fergusonite structure of CaWO4 and SrWO4. Two further facts support the assignment
of the fergusonite structure to the high-pressure phase of both compounds and rule out
the wolframite structure: The first one is that two of the stronger Bragg peaks of the
wolframite structure, viz. the (011) and (110) expected at 2θ ≈ 5.7º, are absent in the
measured diffraction patterns. The second one is that the (100) reflection of the
wolframite structure is not present at 2θ ≈ 4.15º.
Fig. 2 also shows the Rietveld refinements to the experimental spectra of CaWO4
at 11.3 GPa and of SrWO4 at 10.1 GPa obtained assuming the fergusonite structure. In
order to perform the Rietveld refinement the starting Ca (Sr), W, and O positions were
10
taken from Ref. [9]. For both tungstates, we obtained good agreement with the
experimental diffraction patterns. The residuals are: RWP = 1.75%, RP = 1.1%, and R(F2)
= 1.5% for CaWO4 (197 reflections) and RWP = 2.07%, RP = 1.4%, and R(F2) = 1.9%
for SrWO4 (324 reflections). Similar refinement quality was obtained for scheelite
CaWO4 at 1.4 GPa and scheelite SrWO4 at 0.2 GPa. Table I summarizes the lattice
parameters and atomic positions of CaWO4 at 1.4 and 11.3 GPa, and of SrWO4 at 0.2
and 10.1 GPa. Our structural parameters for fergusonite CaWO4 agree with those
reported by Grzechnik et al. [9].
It is worthwhile to discuss here the differences between the present and
Grzechnik´s results [9] with previous structural studies on CaWO4 and SrWO4. As we
mentioned above, in a previous EDXRD study Errandonea et al. [8] characterized the
high-pressure phase of CaWO4 as wolframite-type. This conclusion was a result of a
LeBail analysis [54] considering four candidate structures, among which the fergusonite
structure was not included. The exclusion of this structure was not accidental but a
consequence of the fact that the (020) Bragg peak and other characteristic reflections of
the fergusonite structure were not present in the EDXRD patterns of the high-pressure
phase reported in Ref. [8]. Furthermore, in these patterns there are also two reflections
around 23 keV which were assigned to the (011) and (110) Bragg peaks of the
wolframite structure and which cannot be indexed with the fergusonite structure – that
is, the experimental situation was quite different from what we observe in the present
experiments. We think that in the previous EDXRD experiments the presence of large
non-hydrostatic stresses inside the DAC [8] may have favored a transition to the
wolframite structure instead of the fergusonite structure. In Grzechnik’s study, both
helium and a 4:1 methanol-ethanol mixture were used as pressure-transmitting medium
[9]. In the present study silicone oil was used as pressure transmitting medium. In
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contrast, in Ref. [8] no pressure-transmitting medium was used. Using a non-hydrostatic
pressure medium as NaCl, Nicol and Durana assigned the wolframite structure to the
high-pressure phase of CaWO4 [10]. The bulk modulus of CaWO4 is three times larger
than that of NaCl and therefore the absence of a pressure-transmitting medium could
create highly non-hydrostatic conditions at the onset of the transition [55]. It is well
known that phase transitions can be greatly affected by non-hydrostatic conditions [55]
and therefore the fact that the less hydrostatic media was used in Ref. [8] could then
have affected the characterization of the high-pressure phase of CaWO4. The
observation of a scheelite-to-wolframite transition in CdMoO4 in experiments
performed by Shieh et al. [14] using CdMoO4 without pressure-transmitting medium, as
well as the differences between the compressibility observed for the scheelite phase in
these experiments and the one observed when a 4:1 methanol-ethanol mixture was used
as pressure-transmitting medium [19], give additional support to this hypothesis.
Regarding SrWO4, Kuzmin et al. [32] concluded recently from their x-ray diffraction
and absorption measurements that the high-pressure phase of this compound is of the
wolframite-type. There are two principal facts that may explain the differences between
the results reported in Ref. [32] and the present results. The first one is that the lower
quality of the EDXRD patterns reported in Ref. [32] in comparison with the ADXRD
patterns reported here. The x-ray patterns reported in Ref. [32] do not allow the authors
to perform a structural refinement and the only they can conclude is that there is a phase
transition at 11.7 GPa, a pressure that is in fairly good agreement with our own results.
The second one is that the Extended X-ray Absorption Fine Structure (EXAFS)
measurements reported in Ref. [32] show that the local structure around the W atoms is
compatible with an octahedral coordination at 30 GPa. However, from the EXAFS
analysis alone, it is not possible to identify the structure of the high-pressure phase.
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Then, the possible existence of a post-fergusonite phase with the tungsten atoms in an
octahedral coordination will resolve apparent controversies between our results and
those reported by Kuzmin et al. [32]. Another fact to be taken into consideration is the
possible metastability of two different monoclinic structures, an scenario that is
supported by the polytypism observed in other tungstates (e.g. PbWO4) even at ambient
conditions [56].
Figs. 3(b) and 3(c) shows the lattice parameters of the fergusonite phases of
CaWO4 and SrWO4 as a function of pressure up to ~18 GPa. Above 15 GPa the quality
of the ADXRD patterns deteriorated, but it was still possible to obtain the lattice
parameters at different pressures using the LeBail extraction technique [54]. The
degradation of the x-ray diffraction patterns was observed previously in CaWO4 [9] and
in similar compounds [13, 57], and is independent of the pressure-transmitting medium
employed in the experiments. This observation may be related to precursor effects either
of a martensitic transition [58] or of the amorphization observed in alkaline-earth
tungstates [8] and other scheelite-structured compounds [31] at higher pressures. The β
angle was found to increase slightly from 90.09° at 11.3 GPa to 93° at 18.3 GPa in
CaWO4 and from 90.35° at 10.1 GPa to 92° at 17.5 GPa in SrWO4. The difference
between the b/a and b/c axial ratios of the fergusonite phases of CaWO4 and SrWO4
also increases upon compression, see Fig. 4. These two facts imply an increase of the
monoclinic distortion with pressure. A volume discontinuity is not apparent at the
transition pressure, consistent with a second-order phase transition. The Birch-
Murnaghan fit to both the scheelite and the fergusonite pressure-volume data gives EOS
parameters (V0, B0, and B0´) that differ by less than one standard deviation from those
obtained for the scheelite data only. Hence, the EOS reported above can be assumed as
a valid EOS for CaWO4 and SrWO4 up to 18 GPa, as illustrated in Fig. 3(a). A Birch-
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Murnaghan fit to only the high-pressure fergusonite data gives slightly larger values for
B0 and B0´ [e.g. for CaWO4 we obtained: V0 = 312(2) Å3, B0 = 78(9) GPa, and B0’ =
5.7(12) and for SrWO4: V0 = 347(2) Å3, B0 = 64(8) GPa, and B0’ = 5.4(11)]. A similar
conclusion can be drawn from our ab initio calculations, see Sec. IV.C.
In order to close the discussion on the ADXRD results we would like to comment
that in both compounds the phase transition implies a distortion of the WO4 tetrahedra
accompanied by a small shear distortion of alternate (100) cation planes in the [001]
direction. The scheelite-to-fergusonite transition occurs together with a slight decrease
of two W-O bonds and the increase of the other two W-O bonds inside the WO4
tetrahedra, however, as a consequence of this deformation, the volume of the WO4
tetrahedra is enlarged less than 10%. On the other hand, at the transition six of the A-O
bonds in the AO8 polyhedra are compressed and the remaining two are enormously
expanded, see Fig. 5. The consequence of these changes is a decrease of the volume of
the AO8 polyhedra. In this way, as a result of the phase transition the WO4 tetrahedra in
the fergusonite phase are only slightly distorted, while the AO8 polyhedra are quite
distorted (see Fig. 1).
B. XANES measurements at high pressures
B.1. Low-pressure phase
The XANES part of the absorption spectrum is very sensitive to modifications in
the neighborhood of the absorbing atom and thus it can be used as a tool to detect
structural changes. We have performed XANES experiments on CaWO4 and SrWO4
under compression with the aim of investigating changes in W coordination after the
phase transition. In the scheelite structure the W environment is formed by four O atoms
in tetrahedral configuration. If the high-pressure phase were fergusonite, the tetrahedron
would become distorted which results in two slightly different near-neighbor distances
14
but the main characteristics of the W environment would be maintained. In this situation
we would expect small changes in the XANES spectra. If however the high-pressure
phase would be of the wolframite-type the W coordination would change to six (2+4)
and one would expect significant changes in the XANES spectra.
In order to confirm these ideas and as a guide to interpret changes in the
experimental spectra, we have performed XANES simulations of the scheelite,
fergusonite and wolframite phases. The XANES simulations were carried out using the
real-space multiple-scattering code implemented in the FEFF8 package [59]. We
employed a self-consistent potential calculated using 120 atoms clusters (6.9 Å or 14
shells) and the Hedin-Lundqvist energy-dependent self-energy. Full multiple-scattering
XANES calculations were performed using 87-atom clusters (6.5 Å or 11 shells). No
pseudo Debye-Waller factor has been considered in our simulations. The structural data
used are given in Table I for the scheelite and fergusonite structures and in Table II for
the wolframite structure. The description of wolframite is based on that of CdWO4
[60]. For this structure, the lattice parameters have been scaled to give the same volume
per formula unit as in the fergusonite structure. In Fig. 6 we present the results for the
XANES spectra simulated in the three structures for CaWO4 and SrWO4. The spectra
corresponding to both compounds are similar, with five resonances. The most dramatic
change observed when passing from fourfold coordination to sixfold coordination
affects the resonance named B in Fig. 6. In the scheelite and fergusonite structures the B
resonance is clearly observable, but it disappears in the wolframite simulation. Other
noticeable changes concern the intensity and width of the white line (A resonance).
Fig. 7 shows the experimental XANES spectra at different pressures for CaWO4
and SrWO4. The spectra of both compounds at atmospheric pressure show the five
resonances predicted by our simulations for the scheelite structure. The position and
15
intensity of each feature agree qualitatively with those of the simulation, except for the
resonances D and E in CaWO4 whose relative intensities are inverted. In the theoretical
spectra the resonances are more pronounced as a consequence of not considering the
pseudo Debye-Waller factor.
B.2. High-pressure phases
The high pressure XANES spectra of CaWO4 show no significant changes up to
11.3 GPa, see Fig. 7(a). At this pressure the B resonance looses intensity and the ratio
of intensities between the D and E resonances also decreases. Meanwhile the intensity
and width of the white line remain unaffected. The changes described indicate a
transition to the fergusonite phase at 11.3(10) GPa, in agreement with ADXRD results.
It is interesting to note that XANES spectra continue to evolve up to the maximum
pressure attained of 20.2 GPa suggesting, as we observed in our ADXRD
measurements, that the structural distortions leading to the fergusonite structure become
more pronounced when applying pressure. The phase transition is reversible, as the
spectrum of the recovered phase is identical to the initial one except for a diminution in
the white line intensity which we interpret as due to a decrease in sample thickness.
As regards to SrWO4 the XANES spectra up to 12.4 GPa show only a small
reduction of the intensity of the B resonance, see Fig. 7(b). At 15.0 GPa an acceleration
in the decrease of the B resonance is accompanied by the progressive disappearance of
the C resonance and an increase of the D resonance, while the white line remains
unchanged. These changes continue up to the maximum pressure attained of 22.2 GPa.
At this pressure the B resonance is still visible in the spectrum. Once again, the
evolution of the spectra is reversible and suggests a transition towards the fergusonite
phase. However, the onset of the phase transition is not as clear as in CaWO4 and the
distortion of the W tetrahedral environment is not evident up to 13.7(17) GPa.
16
C. Ab initio calculations
We compare now the experimental body of data presented in the previous sections
with the results from our total-energy theoretical study of several structural phases of
CaWO4 and SrWO4. Along with the observed scheelite and fergusonite phases we have
also considered the wolframite structure previously proposed for the high-pressure
phase of CaWO4 [8] as well as other candidate structures on account of their
observation or postulation in previous high-pressure work for related compounds: M’-
fergusonite [16], LaTaO4 [61], BaWO4-II [12], and YLiF4-Sen (as we call the very-high-
pressure structure found in the molecular dynamics study reported by Sen et al. [16]).
Several of these phases are structurally related and can be represented within the
monoclinic space group P21/c (No. 14), which has thus also received our special
attention.
Fig. 8 shows the energy-volume curves for the different structures of CaWO4 and
SrWO4, from which the relative stability and coexistence pressures of the phases can be
extracted by the common-tangent construction [44]. At all the pressures investigated
and for both compounds the M’-fergusonite structure reduced upon full relaxation to
fergusonite – it is thus not shown in Fig. 8. This figure shows the scheelite phases as
being stable at zero and low pressure, with V0 = 318.3 Å3, B0 = 72 GPa, and B0’ = 4.3 for
CaWO4 and V
0 = 362.2 Å
3, B
0 = 62 GPa, and B
0’ = 4.9 for SrWO4. These values
compare well with the experimental results, with differences within the typical reported
systematic errors in DFT-GGA calculations. A similar degree of agreement exists for
the calculated values of the internal parameters of the scheelite phases [O(16f) at (0.244,
0.097, 0. 039) and c/a = 2.16 for CaWO4; O(16f) at (0.237, 0.111, 0.042) and c/a = 2.20
for SrWO4, cf. Table I].
17
As pressure increases, the scheelite structure becomes unstable against
fergusonite. The fergusonite structure, a distortion of scheelite, only emerges as a
structurally different and thermodynamically stable phase above a compression
threshold of about 10 - 11 GPa in both compounds; at the lower pressures investigated
the relaxation of the fergusonite structure resulted in the scheelite structure. This is
consistent with a continuous or quasi-continuous scheelite-to-fergusonite transition with
none or very little volume collapse. The calculated structural parameters of the
fergusonite phases are also in good agreement with the experimental results [y(Ca)=
0.624, y(W) = 0.132, O1(8f) at (0.912, 0.963, 0.242), O2(8f) at (0.492, 0.217, 0.822), b/a
= 2.104, c/a= 0.977, and β= 91.6 for CaWO4 at 11 GPa; y(Sr)= 0.624, y(W) = 0.128,
O1(8f) at (0.905, 0.961, 0.235), O2(8f) at (0.485, 0.213, 0.840), b/a = 2.145, c/a= 0.990,
and β= 90.3 for SrWO4 at 11 GPa, cf. Table I].
The BaWO4-II and YLiF4-Sen structures are very high in enthalpy and nowhere
close to stability in either compound. The LaTaO4-type structure is similarly high in
enthalpy in CaWO4 though in SrWO4 it is placed considerably lower and is in fact a
competitive candidate for stability in a post-fergusonite regime around 20 GPa. The
wolframite structure is not thermodynamically stable in any interval of pressures though
it is close in energy (20 - 40 meV) to fergusonite in CaWO4 in the relevant range around
10 - 20 GPa which might have a bearing on its observation in previous experimental
work in which non-hydrostatic conditions were used [8].
A difficulty found in the relaxation of the monoclinic phases belonging to space
group P21/c is the existence of a number of local minima. For a significant interval of
medium and high pressures these structurally different minima are located very close in
energy, sometimes separated by shallow barriers, which make the precise determination
of the absolute minimum within this set of low-symmetry crystal structures a rather
18
tedious and difficult task. Nevertheless we have carried out such minimization ensuring
great care in the relaxation procedure, which requires in particular repeating relaxation
starting from different initial conditions and checking for local stability. In the course of
this minimum-trapping quest we have arrived at a well defined minimum in the
compressed region for a structure which after refinement and further analysis turned out
to have increased orthorhombic symmetry, with space group Cmca (No. 64). This
totally unexpected structural phase [62] has lower enthalpy than any other of the phases
considered above ~29 GPa in CaWO4 and ~21 GPa in SrWO4 (in this case in close
competition with the LaTaO4-type structure –see Fig. 8(b)). It has Z = 8 with Ca atoms
in 8e positions at (0.25, 0.164, 0.25), W in 8f (0, 0.409, 0.226) and O at 8d (0.157, 0.5,
0), 8e (0.25, 0.348, 0.25), 8f (0, 0.288, 0.005), and 8f (0, 0.084, 0.094) for CaWO4 at 30
GPa [for SrWO4 at 23 GPa: Sr(8e) (0.25, 0.167, 0.25), W(8f) (0, 0.413, 0.223), O1(8d)
(0.149, 0.5, 0), O2(8e) (0.25, 0.359, 0.25), O3(8f) (0, 0.292, 0.034), and O4(8f) (0, 0.084,
0.077)]. In both materials b/a~1.65 - 1.68 and c/a~0.68. In this structure the Ca (Sr) and
W cations are surrounded by 10 and 6 O atoms, respectively. It is worth noting that this
new structure is strongly energetically favored over fergusonite in the high-pressure
regime and thus the figures of ~29 GPa in CaWO4 and ~21 GPa in SrWO4 constitute
neat upper bounds for the thermodynamical stability of the respective fergusonite
phases. Such high pressures are just above those reached in x-ray diffraction
experiments.
D. Bulk modulus in scheelite ABO4 compounds.
Hazen et al. found that the bulk modulus of certain binary oxides and silicates can
be directly correlated to the compressibility of the A cation coordination polyhedra [63].
In particular, they proposed that the bulk compressibility in these compounds is
proportional to the average volume of the cation polyhedron divided by the cation
19
formal charge; i.e., B0 is proportional to the cation charge density per unit volume inside
the cation polyhedron. They also found that A
2+B6+O4 scheelite tungstates and
molybdates under pressure compressed in an anisotropic way with the WO4 and MoO4
tetrahedra behaving as rigid units [19]. Furthermore, they ordered the compressibility of
scheelite compounds according to the A cation formal charge and, on this basis,
suggested that the compressibility of ABO4 scheelites could be given by the
compressibility of the softer AO8 polyhedron and that the A4+B4+O4 scheelites could be
a family of ultrahard materials.
These last conclusions have been confirmed in two recent works, where the bulk
moduli of scheelites have been plotted as a function of the bulk volume [7, 64]. A
further insight can be obtained with the present data by plotting the bulk modulus of
scheelite and scheelite-related compounds as a function of the A cation charge density
per unit volume in the AO8 polyhedra, given by the A cation formal charge divided by
the cubic average A-O distance (see Fig. 9). All data plotted in Fig. 9, summarized in
Table III, correspond to approximately 25% of the ABO4 compounds with the scheelite
and scheelite-related structures that can be found in the Inorganic Crystal Structure
Database. The bulk modulus of all the plotted compounds obeys a linear relationship
according to the equation:
03
610(110)
A
AO
Z
Bd
−
= , (2)
where B0 is the bulk modulus (in GPa), ZA is the A cation formal charge (being
41
A
Z
≥≥
), and dA-O is the average A-O distance (in Å) inside the AO8 polyhedron.
This simple rule serves as an effective and simple empirical criterion for predicting the
bulk modulus of any scheelite or scheelite-related ABO4 compound. The linear
relationship between B0 and the A cation charge density of the AO8 polyhedra is
consistent with the fact that AO8 polyhedra exhibiting a large A cation charge density
20
result in a larger electronic cloud inside the polyhedra than those AO8 polyhedra with a
low A cation charge density. In the AO8 polyhedra with a high ZA the electrons around
the cation are highly localized and the bond distances cannot be highly deformed under
pressure. On the contrary, in AO8 polyhedra with a low ZA the density electrons around
the cation are highly delocalized and the bond distances can be considerably deformed
under pressure. Then, since the compressibility of ABO4 compounds is mainly given by
the compression of the AO8 polyhedra, the above described facts explains why B0 is
proportional to ZA. In addition to that, they also explains why AO8 polyhedra with A
valence (+1, +2, and +3) are highly deformed as compared to BO4 polyhedra with B
valence (+7, +6, and +5) in ABO4 scheelites and scheelite-related structures, being the
compounds with A and B cation valence equal to +4 the hardest ABO4 materials. In
fact, the linear relationship stated above should not be applicable to A4+B4+O4 scheelites
if AO8 and BO4 tetrahedra have similar compressibilities. However, despite both A and
B cations having equal valence, B-O bonds in tetrahedral configuration are shorter and
stronger than A-O bonds and the bulk modulus is again dictated by the AO8 polyhedra.
Therefore, Eq. (2) can also be effectively applied to A
4+B4+O4 scheelites as clearly
shown.
It has been recently reported that both the scheelite and the zircon structure of
YVO4 have a quite similar bulk modulus [64]. This result is in agreement with our
expectations since in both structures the Y-O bond distances differ by less than 2%. A
similar behavior should be expected also for ZrSiO4, with similar Zr-O bond distances
in the scheelite and zircon structures (see Table III). However, a bulk modulus of 300
GPa has been recently reported for the scheelite phase of ZrSiO4 [7]. This bulk modulus
exceeds by more than 30% the bulk moduli of the zircon structure of ZrSiO4. Therefore,
according to the systematic here reported, a bulk modulus of 300 GPa for the scheelite
21
phase of ZrSiO4 is unrealistic and we think that the extremely low compressibility
recently reported for this material could be mistaken. Following Eq. (2), we can predict
for the scheelite phase of ZrSiO4 a bulk modulus of 220(40) GPa, which is one of the
largest bulk modulus of ABO4 compounds. Theoretical calculations using either the
local-density approximation (LDA) or the generalized-gradient approximation (GGA)
gave a bulk modulus of 230(25) GPa [81], value that agrees well with our estimation. A
bulk modulus of 300 GPa can be only expected for a compound with octahedral
coordinated silicon atoms, like γ-Si3N4, but not for compounds with tetrahedral
coordinated Si atoms [82], like scheelite ZrSiO4. We attributed the overestimation of B0
to: i) the non-hydrostatic conditions of the experiments performed by Scott et al. [7]
who used a 16:3:1 methanol-ethanol-water mixture as pressure-transmitting medium up
to 52.5 GPa, and ii) to the large presence of impurities in the natural zircon samples
used by Scott et al., as suggested by Van Westrenen et al. [51]. The first argument leads
to large pressure gradients and inaccurate estimation of the pressure inside the DAC
when a 60 µm x-ray beam is used because the pressure transmitting medium used is not
hydrostatic above 15 GPa. In fact, the Pt diffraction peaks used for determining the
pressure in Ref. [7] are quite broad. These facts may easily cause an overestimation of
the bulk modulus of the scheelite phase of ZrSiO4. The second argument has proved to
lead to different transition pressures and different pressure coefficients. New
experiments using a micro-focus x-ray beam and better hydrostatic conditions are
needed to check the pressure behavior of the scheelite phase of ZrSiO4.
To conclude, we would like to mention that attempting to predict the pressure
behavior of other scheelite-structures and zircon-structured ABO4 materials we used Eq.
(2) to make a back-of-the-envelope estimation of the bulk modulus of several
compounds, which have been selected by considering their actual technological interest.
22
Our predictions are summarized in Table IV. In the case of BaMoO4, our estimation of
B0 is in quite good agreement with the recent experimental results of Panchal et al. [33].
On top of that, according to our estimations, hafnon (HfSiO4) is expected to be one of
the least compressible ABO4 compounds, being therefore a material of interest for
potential applications as an interphase component in toughened oxide ceramic
composites [83]. Our predictions for NaReO4 can be compared with the bulk modulus
obtained from DFT calculations by Spitaler et al. [84]. These authors reported B0 = 18.3
GPa. This value is approximately half of the value estimated by us. However, a Birch-
Murnaghan fit to the results reported by Spitaler et al. gives a negative value for the
pressure derivative of B0, something unexpected for a scheelite ABO4 compound, which
suggests the EOS of NaReO4 may be miscalculated in Ref. [84]. This conclusion is also
supported by the fact that the value predicted by us for B
0 is very similar to that
experimentally observed in other perrhenates (see Table III), as expected.
V. Conclusions
We have measured ADXRD and XANES spectra in CaWO4 and SrWO4 under
pressure up to ~20 GPa. In both cases our results support the existence of a reversible
scheelite-to-fergusonite structural transition under hydrostatic conditions. From our
ADXRD data we locate the onset of the transition at 10.8(5) GPa in CaWO4 and at
9.9(2) GPa in SrWO4. The monoclinic distortion triggered at the phase transition
continue up to the maximum pressures attained in our experiment, with no evidence of
any further structural transformation. The small changes of the local environment
around the absorbing atom make XANES sensitive to the phase transition at slightly
higher pressures, around 11.3(10) GPa in CaWO4 and 13.7(17) GPa in SrWO4. In the
case of SrWO4 precursor effects of the transition appear at 10 GPa but the transition is
not completed up to 15 GPa. The sluggish character of the transition is confirmed not
23
only by the present ADXRD and XANES experiments, but also by the Raman
investigation carried out in Ref. [30], where the pressure dependence of some modes
related to the internal movement in the WO4 tetrahedra are found to be strongly
nonlinear up to 3 - 4 GPa above the transition pressure. Our ab initio theoretical study
of the energetic of the phases support the scheelite-to-fergusonite transition and yield
structural characteristics for the scheelite and fergusonite phases in very good
agreement with the experimental results. In addition, from our ab initio study we can
place an upper bound (not reached experimentally) to the stability of the fergusonite
high-pressure phases, at ~29 GPa in CaWO4 and ~21 GPa in SrWO4, which calls for
experimental structural studies in this higher pressure region. Finally, we have showed
that the ambient-pressure bulk modulus of ABO4 scheelite and scheelite-related
compounds can be easily estimated if the average A-O distance is known.
Acknowledgments
The authors thank P. Bohacek (Institute of Physics, Prague) for providing the
CaWO4 and SrWO4 crystals used in the experiments. This study was made possible
through financial support from the Spanish government MCYT under grants MAT2002-
04539-CO2-01 and -02, and MAT2004-05867-C03-03 and-01. The U.S. Department of
Energy, Office of Science, Office of Basic Energy Sciences supported the use of the
Advanced Photon Source (APS) under contract No. W-31-109-Eng-38. DOE-BES,
DOE-NNSA, NSF, DOD-TACOM, and the W.M. Keck Foundation supported the use
of the HPCAT facility. We would like to thank D. Häusermann and the rest of the staff
at the HPCAT of the APS for their contribution to the success of the ADXRD
experiments. The XANES experiments were done under proposal number HS-2412 at
the ESRF. D. Errandonea acknowledges the financial support from the MCYT of Spain
and the Universitat of València through the “Ramón y Cajal” program of grants. J.
24
López-Solano and A. Muñoz acknowledge the financial support from the Gobierno
Autónomo de Canarias (PI2003/174).
25
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Kroll and R. Boehler, Nature, 400, 340-342 (1999).
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[84] J. Spitaler, C. Ambrosch-Draxl, E. Nachbaur, F. Belaj, H. Gomm, and F. Netzer,
Phys. Rev. B 67, 115127 (2003).
31
Table I: Structural parameters of the scheelite and fergusonite structure of CaWO4 and
SrWO4. These parameters were obtained from the present Rietveld refinements (see
text).
a) Structural parameters of scheelite CaWO4 at 1.4 GPa:
I41/a, Z = 4, a = 5.205(5) Å, c = 11.275(7) Å
Site x y z
Ca 4b 0 0.25 0.625
W 4a 0 0.25 0.125
O 16f 0.2289(3) 0.0910(4) 0.0421(5)
b) Structural parameters of fergusonite CaWO4 at 11.3 GPa:
I2/a, Z = 4, a = 5.069(2) Å, b = 10.851(5) Å, c = 5.081(7) Å, β = 90.091(9)
Site x y z
Ca 4e 0.25 0.6100(8) 0
W 4e 0.25 0.1325(3) 0
O1 8f 0.9309(39) 0.9684(23) 0.2421(24)
O2 8f 0.4850(35) 0.2193(31) 0.8637(37)
c) Structural parameters of scheelite SrWO4 at 0.2 GPa:
I41/a, Z = 4, a = 5.391(8) Å, c = 11.893(7) Å
Site x y z
Sr 4b 0 0.25 0.625
W 4a 0 0.25 0.125
O 16f 0.2497(9) 0.0925(9) 0.0421(6)
Structural parameters of fergusonite SrWO4 at 10.1 GPa:
I2/a, Z = 4, a = 5.263(9) Å, b = 11.182(6) Å, c = 5.231(6) Å, β = 90.35(1)
Site x y z
Sr 4e 0.25 0.6027(9) 0
W 4e 0.25 0.1243(8) 0
O1 8f 0.9309(49) 0.9598(53) 0.2619(42)
O2 8f 0.4903(39) 0.2278(35) 0.8779(32)
Table II: Atomic positions used to perform the XANES simulations for the wolframite
structure (P2/c, Z = 2) [60].
Site x y z
A 2f 0.5 0.3027 0.75
W 2e 0 0.1785 0. 25
O1 4g 0.242 0.372 0.384
O2 4g 0.202 0.096 0.951
32
Table III: Summary of the data plotted in Fig. 9. The structure, A-O bond distance,
cation formal charge, and bulk modulus are given.
ABO4
compound Space
Group mean A-O bond
distance [Å]
cation
formal
charge
B0
[GPa] Reference
ZrSiO4 I41/a 2.243 4 301(13)
7
ZrSiO4 I41/amd 2.198 4 215(15)
51, 65, 66
LaNbO4 I41/a 2.505 3 111(3) 67
YVO4 I41/a 2.387 3 138(9) 64
TbVO4 I41/amd 2.369 3 149(5) 68
BiVO4 I41/a 2.350 3 150(5) 69
DyVO4 I41/amd 2.354 3 160(5) 70
YVO4 I41/amd 2.348 3 130(3) 64
ErVO4 I41/amd 2.341 3 136(9) 71
LuPO4 I41/amd 2.306 3 166(9) 72
BaSO4 Pnma 2.879 2 58(5) 73, 74
BaWO4 I41/a 2.678 2 57(4) 13, 75
PbWO4 I41/a 2.579 2 64(2) 19
PbMoO4 I41/a 2.576 2 64(2) 19
SrWO4 I41/a 2.557 2 63(7) This work
EuWO4 I41/a 2.557 2 71(6) 75
SrMoO4 I41/a 2.556 2 73(5) 76
NaY(WO4)2
I41/a 2.478 2 77(8) 77
CaMoO4 I41/a 2.458 2 82(7) 19, 29
CaWO4 I41/a 2.457 2 75(7) This work, 8, 9, 19, 74
SrSO4 Pnma 2.452 2 82(5) 16
CdMoO4 I41/a 2.419 2 104(2) 19
KReO4 I41/a 2.791 1 18(6) 78
TlReO4 Pnma 2.765 1 26(4) 79
AgReO4 I41/a 2.524 1 31(6) 80
33
Table IV: Predicted bulk modulus for different scheelite-type and zircon-type
compounds.
ABO4
compound Space
Group mean A-O bond
distance [Å]
cation
formal
charge
B0
[GPa]
HfSiO4 I41/amd 2.186 4 235(40)
YPO4 I41/amd 2.337 3 145(25)
YAsO4 I41/amd 2.383 3 135(25)
EuCrO4 I41/amd 2.410 2 87(15)
ZrGeO4 I41/a 2.203 4 230(40)
BaMoO4 I41/a 2.741 2 59(12)
NaReO4 I41/a 2.446 1 42(8)
KIO4 I41/a 2.816 1 27(5)
34
Figure captions
Fig. 1: The (a) scheelite, (b) wolframite, and (c) fergusonite structures of AWO4
compounds. Large circles represent the A (Ca, Sr) atoms, middle-size circles correspond
to the W atoms, and the small circles are the O atoms. The unit-cell, A-O bonds and W-
O bonds are also shown. As a consequence of the scheelite-to-fergusonite transition two
A-O and W-O bonds are enlarged (see text and Fig. 5); these bonds are showed as dark
lines in (c). The AO8 and WO4 polyhedra are also shown. By comparing (a) and (c) it
can be seen the polyhedra distortion caused by the scheelite-to-fergusonite transition.
Fig. 2: Room-temperature ADXRD data of (a) CaWO4 and (b) SrWO4 at different
pressures up to 18 GPa. In all diagrams the background was subtracted. To better
illustrate the appearance of the (020) Bragg reflection of the fergusonite structure
around 2θ ≈ 4º a section of the upper trace is enlarged. In the ADXRD pattern of
CaWO4 collected at 11.3 GPa and of SrWO4 at 10.1 GPa (which are representative of
the high-pressure fergusonite structure) we also show the refined profile (symbols) and
the difference between the measured data and the calculated profile (dotted line). The
bars indicate the calculated positions of the reflections.
Fig. 3: Evolution of the (a) volume and (b)-(c) lattice parameters of CaWO4 and SrWO4
with pressure. Empty squares correspond to our data for the scheelite phase and empty
circles and diamonds to those for the fergusonite phase. Solid squares [8], solid triangles
[9], solid circles [19], stars [47], and empty hexagons [48, 49] are other data for the
scheelite phase obtained from the literature. Empty triangles are the fergusonite data
reported in Ref. [9]. In (a) the solid lines represent the EOS of the scheelite phase
described in the text.
Fig. 4: Pressure dependence of the axial ratios of CaWO4 and SrWO4. For a description
of the symbols see Fig. 3.
35
Fig. 5: Pressure dependence of the interatomic bond distances in the scheelite phase of
(a) CaWO4 and (b) SrWO4. Empty squares represent the distances in the scheelite phase
here reported. Solid circles [19], solid squares [27], and solid diamonds [52] represent
the distances in the scheelite phase reported in the literature. Empty diamonds represent
the new bond distances in the fergusonite phase after the phase transition.
Fig. 6: Ab initio simulation of XANES spectra of CaWO4 and SrWO4 in the three
phases scheelite, fergusonite, and wolframite. The main difference between the
fergusonite and the wolframite phases affects the intensity of the B resonance and the
intensity and width of the white line (labeled A in the figure). There are also minor
intensity changes in the C, D, and E resonances.
Fig. 7: Experimental XANES spectra of (a) CaWO4 and (b) SrWO4 measured at
different pressures. The spectra collected on pressure release are marked with “d”. The
analysis of the spectra reveals a transition to the fergusonite phase in both compounds.
At the transition we observed intensity changes in the resonances. In CaWO4 B
decreases a 8% and the ratio between the intensities of D and E decrease a 7%.
Fig. 8: Energy-volume curves (both per formula unit) calculated for (a) CaWO4 and (b)
SrWO4. The structures shown are: scheelite (circles), fergusonite (triangles), wolframite
(crosses), LaTaO4 (diamonds), Cmca (squares), BaWO4-II (dots), and YLiF4-Sen
(stars). The insets show differences in energy with respect to the scheelite phase in the
marked areas.
Fig. 9: Values of the ambient-pressure bulk modulus of ABO4 scheelite and scheelite-
related compounds plotted against the value of the cation charge density of the AO8
polyhedra. A-O distances and ambient-pressure bulk moduli were taken from different
references [7-9, 13, 16, 19, 27, 51, 65 - 80] and are summarized in Table III. The white
circle represents the bulk modulus reported by Scott [7] for scheelite ZrSiO4. The solid
line corresponds to the relation given in Eq. (2) and the dashed lines indicate its lower
and higher deviations.
36
Figure 1. Errandonea et al.
37
Figure 2(a) Errandonea et al.
38
Figure 2(b) Errandonea et al.
39
Figure 3(a) Errandonea et al.
40
Figure 3(b) Errandonea et al.
41
Figure 3(c) Errandonea et al.
42
Figure 4 Errandonea et al.
43
Figure 5(a) Errandonea et al.
44
Figure 5(b) Errandonea et al.
45
Figure 6 Errandonea et al.
46
Figure 7(a) Errandonea et al.
47
Figure 7(b) Errandonea et al.
10.20 10.25 10.30
D
CE
AB
0d
P (GPa)
22.2
20.2
18.0
15.0
12.4
0
SrWO4
Absorption (arb. units)
Energy (keV)
48
Figure 8(a) Errandonea et al.
49
Figure 8(b) Errandonea et al.
50
Figure 9 Errandonea et al.
