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Negative pressures in CaWO4nanocrystals
F. J. Manjón,1,a兲D. Errandonea,2J. López-Solano,3P. Rodríguez-Hernández,3and
A. Muñoz3
1MALTA Consolider Team, Departamento de Física Aplicada-IDF, Universidad Politécnica de Valencia,
Cno. de Vera s/n, 46022 Valencia, Spain
2MALTA Consolider Team, Departamento de Física Aplicada-ICMUV, Fundación General
de la Universidad de Valencia, C/. Dr. Moliner 50, 46100 Burjassot, Valencia, Spain
3MALTA Consolider Team, Departamento de Física Fundamental II e Instituto de Materiales
y Nanotecnología, Universidad de La Laguna, La Laguna 38205, Tenerife, Spain
共Received 28 January 2009; accepted 11 March 2009; published online 8 May 2009兲
Tetragonal scheelite-type CaWO4nanocrystals recently prepared by a hydrothermal method show
an enhancement of its structural symmetry with the decrease in nanocrystal size. The analysis of the
volume dependence of the structural parameters in CaWO4nanocrystals with the help of ab initio
total-energy calculations shows that the enhancement of the symmetry in the scheelite-type
nanocrystals is a consequence of the negative pressure exerted on the nanocrystals; i.e., the
nanocrystals are under tension. Besides, the behavior of the structural parameters in CaWO4
nanocrystals for sizes below 10 nm suggests an onset of a scheelite-to-zircon phase transformation
in good agreement with the predictions from our ab initio calculations. CaWO4nanocrystals exhibit
a reconstructive-type mechanism for the scheelite-to-zircon phase transition that seems to follow the
tetragonal path that links both structures. This result is in contrast with the mechanism recently
proposed for this transition in bulk ZrSiO4where the transition goes through an intermediate
monoclinic phase. © 2009 American Institute of Physics.关DOI: 10.1063/1.3116727兴
I. INTRODUCTION
Alkaline-earth metal tungstates 共AWO4;A=Ca,Sr,Ba兲
crystallizing in the scheelite structure have an increasing
number of applications.1In the last years intense efforts have
been witnessed in preparation of scheelite nanoparticles by
different methods with the aim of improving the lumines-
cence properties of scheelites.2–9During this search, it has
been found that nanocrystals usually have different structural
properties than bulk crystals and that nanocrystals can be
synthesized under certain conditions in phases that are not
stable for the bulk material at ambient conditions. Recently,
CdWO4nanocrystals have been synthesized in a tetragonal
scheelite structure despite bulk CdWO4crystallizes in the
monoclinic wolframite structure.9On the other hand, an in-
teresting symmetry enhancement of scheelite-type CaWO4
nanocrystals synthesized by a hydrothermal method was ob-
served when the dimensions of the nanocrystals were re-
duced from 31.7 to 3.4 nm.5,6An increase in the unit-cell
volume and a decrease in the c/aratio in the tetragonal
scheelite structure was reported when decreasing the nano-
crystal size below 8 nm.5,6
High-pressure experiments are a powerful tool to inves-
tigate the main physical properties of scheelites,10–12 helping
to improve their applications, since they depend on the struc-
tures, lattice parameters, and band structures of the different
compounds, which can be tuned by varying the unit-cell vol-
ume at different pressures. In the present work, we analyze
the behavior of the structural properties of the scheelite-type
CaWO4nanocrystals recently reported in Refs. 5and 6and
show that its unit-cell volume dependence on the nanocrystal
size can be explained by the presence of negative pressures
in them with respect to the bulk material. In order to explain
the variations in the structural parameters with the nanocrys-
tal size, we have compared the data available in the literature
for bulk and nanocrystalline scheelite-type CaWO4and per-
formed total-energy ab initio calculations within the frame-
work of the density functional theory, which helped us in
interpreting the structural data. Details of the calculation are
given elsewhere.10,13
II. STRUCTURAL DATA: RELATION BETWEEN
VOLUME AND PRESSURE
Li et al. recently reported the dependence of the unit-cell
volume and c/aratio of scheelite-type CaWO4nanocrystals
as a function of nanocrystal size.5They found that the vol-
ume of the tetragonal unit cell increased with the decrease in
nanocrystal size. Figure 1shows the variation in the aand c
lattice parameters of scheelite-type CaWO4nanocrystals
with the nanocrystal size, as calculated from data of Ref. 5.It
can be observed that the alattice parameter increases mono-
tonically as the nanocrystal size is reduced, while the clat-
tice parameter shows a nonmonotonous dependence on the
nanocrystal size, decreasing sharply for nanocrystal sizes be-
low 8 nm.
The increase in the nanocrystal volume reported for
CaWO4nanocrystals with decreasing their size5can be un-
derstood if nanocrystals below a certain size feel a “nega-
tive” pressure. Since the unit-cell volume in bulk CaWO4
decreases with the increase in pressure above ambient pres-
sure 共1 bar=0.1 MPa兲,10,14,15 an increase in the unit-cell lat-
tice parameters and consequently in the volume can only be
a兲Author to whom correspondence should be addressed. Electronic mail:
fjmanjon@fis.upv.es. Tel.: ⫹34 963 877000. FAX: ⫹34 963 877149.
JOURNAL OF APPLIED PHYSICS 105, 094321 共2009兲
0021-8979/2009/105共9兲/094321/7/$25.00 © 2009 American Institute of Physics105, 094321-1
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explained by the presence of negative pressures. However,
the dependence of the aand clattice parameters of scheelite-
type CaWO4nanocrystals with decreasing nanocrystal size
requires a deeper study and is analyzed later. In order to
interpret the size dependence of the nanocrystal volume of
Ref. 5, we assume, in a first approximation, that the
scheelite-type CaWO4nanocrystals have the same volume
compressibility,
=−
ln V/
P, or equivalently the same
bulk modulus, B0=1/
than their corresponding single
crystals.16 Under this assumption, we can use the equation of
state 共EOS兲deduced for bulk CaWO4共Ref. 10兲to calculate
the negative pressures present in nanocrystals with different
nanocrystal sizes. Figure 2shows the fit of the volumes at
different pressures according to the EOS obtained for bulk
CaWO4. We found that the smallest nanocrystal 共3.4 nm兲
must suffer approximately a negative pressure of ⫺0.62 GPa
in order to undergo the observed volume expansion. Table I
summarizes the nanocrystal sizes, their aand clattice param-
eters, their unit-cell volume, and their estimated negative
pressures.
III. PRESSURE EFFECTS ON THE SETTING ANGLE
It is well known that each compound crystallizing in the
tetragonal scheelite structure has a characteristic setting
angle 共
兲, which is the minimum angle between the W–O
bond inside the WO4tetrahedra and the aaxis. In particular,
the experimental setting angle for bulk CaWO4is near 32° at
ambient pressure.14 A rather simple calculation allows the
setting angle to be obtained as a function of the xand y
parameters of the main O atom in the tetragonal unit cell as
reported by Hazen et al.,14
cos
=0.5 − 2y
冑4共x2+y2兲+共0.25 − 2y兲.共1兲
Hazen et al. performed single crystal x-ray diffraction
共XRD兲measurements in bulk CaWO4under pressure and
determined the atomic positions of the O atoms in the
scheelite structure with increasing pressure of up to 4 GPa.14
In Fig. 3we plotted the measured x,y, and zatomic positions
of the O atom 共symbols兲as a function of pressure as taken
from the work of Hazen et al.14 By fitting the data of Hazen
et al. to a straight line 共solid line兲, we can estimate the x,y,
and zparameters of the O atom that should be present in
CaWO4nanocrystals according to the negative pressures
present in them, as obtained from Fig. 2. It can be observed
that under pressure they undergo a more or less monoto-
nously behavior. We also plotted in Fig. 3as black dashed
lines the x,y, and zparameters obtained from our ab initio
calculations in scheelite-type bulk CaWO4in the studied
a(Å)
5.240
5.245
5.250
5.255
5.260
5.265
Nanocrystal size (nm)
0 5 10 15 20 25 30 3
5
c(Å)
11.34
11.35
11.36
11.37
11.38
(a)
(b)
FIG. 1. Dependence of the aand clattice parameters on the nanocrystal size
in CaWO4after Ref. 5.
Pressure
(
GPa
)
-101234
Volume (Å
3
)
292
296
300
304
308
312
316
320
FIG. 2. Pressure dependence of unit-cell volume assumed for bulk and
nanocrystalline scheelite-type CaWO4. The data for the nanocrystals have
been fitted to the EOS obtained for bulk 共V0=312 Å3,B0=72 GPa, B0.
⬘
=4.8兲in order to assign a negative pressure corresponding to each nanocrys-
tal volume. Nanocrystal data 共circles兲are from Ref. 5and bulk data
共squares兲are from Refs. 10,14, and 15.
TABLE I. Size, unit-cell volume, lattice parameters, and estimated negative
pressures in the CaWO4nanocrystals of Ref. 5.
Size
共nm兲
V
共Å3兲
a
共Å兲
c
共Å兲
P
共GPa兲
31.7 312.3 5.241 11.371 ⫺0.08
28 312.5 5.242 11.373 ⫺0.12
19 313.1 5.246 11.379 ⫺0.26
15.2 313.5 5.248 11.381 ⫺0.33
10.5 313.9 5.251 11.384 ⫺0.44
8.4 314.2 5.253 11.384 ⫺0.49
4.7 314.6 5.260 11.372 ⫺0.59
3.7 314.7 5.264 11.358 ⫺0.61
3.4 314.8 5.267 11.345 ⫺0.62
094321-2 Manjón et al. J. Appl. Phys. 105, 094321 共2009兲
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pressure range. The calculations show that, despite the dif-
ference in the absolute value, the experimental pressure de-
pendence of the O parameters is rather well reproduced.
Figure 4共a兲shows the pressure dependence of the setting
angle of scheelite CaWO4in the bulk crystal that we calcu-
lated using Eq. 共1兲together with the experimental xand y
parameters of the O atom in the unit cell of bulk CaWO4at
different pressures given by Hazen et al. In this figure, we
also plotted the ab initio calculated pressure dependence of
the setting angle for negative pressures 共dashed line兲.Itcan
be observed that both experiment and theory show that the
setting angle increases as a function of pressure; i.e., it de-
creases for negative pressures 关see extrapolation of the solid
line to negative pressures in Fig. 4共a兲兴. Note that the theoret-
ical setting angle is slightly larger than the experimental one
due to the larger values obtained for the xand yparameters
of the O atom at each pressure. The increase in symmetry of
the nanocrystals with reducing size reported by Li et al.5is
related to the decrease in the setting angle as the nanocrystal
size decreases due to the negative pressure felt by
nanocrystals.17
Hazen et al. showed that the W–O bond distance in
AWO4scheelites is rather uncompressible,14 and, as a con-
sequence, the decrease in the lattice parameter awith in-
creasing pressure is mainly correlated with an increase in the
setting angle. Figure 4共b兲shows the evolution of the setting
angle as a function of the lattice parameter ain bulk CaWO4
as obtained from the data of Hazen et al. 共symbols兲. A linear
relationship between the setting angle and the lattice param-
eter acan be deduced from Fig. 4共b兲in good agreement with
our theoretical calculations 共dashed lines兲. This result means
that the increase in the lattice parameter ain the CaWO4
nanocrystals shown in Fig. 2共a兲with decreasing nanocrystal
size is related to a decrease in the setting angle with decreas-
ing the nanocrystal size in good agreement with the negative
pressure present in the nanocrystals. However, the decrease
in the c/aratio in scheelite-type CaWO4nanocrystals with
size smaller than 10 nm cannot be understood on the light of
the negative pressure present in the nanocrystals because it
was found that the decrease of pressure, i.e., increase in vol-
ume, produces an increase in the c/aratio in the bulk
material.10,18 Therefore, one would expect an increase in the
c/aratio in scheelite-type CaWO4nanocrystals with reduc-
ing size due to their increase in the unit-cell volume with
respect to the bulk.
x(rel.units)
0.148
0.152
0.156
0.160
0
.
164
y (rel. units)
0.000
0.002
0.004
0.006
0.008
(a)
(b)
Pressure
(
GPa
)
-2024
z(relunits)
0.208
0.212
0.216
0.220
(c)
FIG. 3. Pressure dependence of the atomic parameters 共a兲x,共b兲y, and 共c兲z
共in relative units兲of the generatrix O atom in the unit cell of bulk scheelite-
type CaWO4, as taken from Ref. 14. The solid line represents the linear fit of
the experimental data. Dashed lines indicate the theoretical pressure depen-
dence according to ab initio calculations.
FIG. 4. Setting angle in bulk CaWO4as a function of pressure 共a兲, and as a
function of the lattice parameter 共b兲, according to data from Ref. 14. Solid
lines represent the linear fit of the experimental data. Dashed lines indicate
the theoretical dependence of the setting angle according to ab initio
calculations.
094321-3 Manjón et al. J. Appl. Phys. 105, 094321 共2009兲
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IV. HINTS OF A SIZE-INDUCED PHASE TRANSITION
In order to understand the disagreement of the pressure
dependence of the experimental c/aratio between bulk and
nanocrystalline scheelite-type CaWO4, we plotted in Fig. 5
the dependence of the aand clattice parameters as a func-
tion of the unit-cell volume in the scheelite CaWO4nano-
crystals as obtained from Ref. 5. For comparison, we also
plotted the theoretical dependence of the lattice parameters at
the same volumes in the bulk as obtained from our ab initio
calculations 共dashed lines兲. It can be observed that the lattice
parameters of the nanocrystals with sizes below 10 nm do
not behave as if they were subjected to negative pressures
with their corresponding unit-cell volumes. Instead, a sudden
increase 共decrease兲is observed for the lattice parameter a共c兲
for unit-cell volumes above 314 Å3. We think that the rapid
changes of the lattice parameters showed by the nanocrystals
with unit-cell volumes above 314 Å3, or equivalently for
size smaller than 8.4 nm, could be indicative of a structural
instability of the tetragonal scheelite structure. In the follow-
ing we will discuss that the changes in the lattice parameters
observed in nanocrystals with sizes below 8.4 nm are indica-
tive of the onset of a phase transition from the scheelite to
the zircon structure.
Previous ab initio total-energy calculations suggest that
the zircon structure is a stable phase for CaWO4at negative
pressures and that the negative pressure necessary to trans-
form scheelite-type CaWO4into the zircon structure is
around ⫺2 GPa.13 This pressure value is not far away from
the negative pressure estimated to be applied to the CaWO4
nanocrystals with sizes smaller than 8.4 nm 共see Table I兲.In
fact, in some materials the bulk modulus of the nanocrystals
can be somewhat larger than that of the bulk.19,20 If this was
the case for the CaWO4nanocrystals, the negative pressures
acting on the nanocrystals would be even higher than those
estimated here and therefore closer to those necessary for the
phase transition. In this case, our hypothesis would be even
more confirmed than here assumed. Therefore, we think that
the deviation of the lattice parameters from their expected
behavior, at their associated negative pressures, is indicative
of the instability of the scheelite structure and the onset of a
transition to the zircon structure. A similar change in lattice
symmetry with an increase in symmetry has been already
observed in CdWO4nanoparticles, which crystallize in the
tetragonal scheelite structure instead of the monoclinic wol-
framite structure of the bulk material.9
The zircon structure is characterized by a ratio c/a⬍1
and a setting angle
=0°. Ab initio calculations in CaWO4
yield lattice parameters around a=7.359 Å and c= 6.648 Å;
i.e., with c/a=0.9034 for zircon-type CaWO4at the mini-
mum of the total-energy curve as a function of unit-cell
volume.13 One could think that due to the group-subgroup
relationship between the zircon and scheelite structures the
phase transition between both phases should be of displacive
type. The displacive-type mechanism for the scheelite-to-
zircon transition could be related to the decrease in the set-
ting angle from 32° in the scheelite phase to 0° in the zircon
phase. This change in the setting angle would be simulta-
neous to the change in the lattice parameters aand cof the
scheelite structure from a=5.2429 Å and c= 11.3737 Å in
bulk scheelite CaWO4to the above given values for the zir-
con structure. This mechanism would transform the a,b, and
caxes of the scheelite structure into the a,b, and caxes of
the zircon structure. However, the decrease in the setting
angle from 32° to 0° involves a considerable distortion of the
Ca–O distances in the CaO8dodecahedra and in fact four
Ca–O bonds in the scheelite phase should be broken to form
four new Ca–O bonds in the zircon phase. Therefore, this
simple transformation mechanism through a simple tetrago-
nal distortion is not displacive but reconstructive. The behav-
ior of the parameters aand cin the scheelite phase shown in
Fig. 1below 8.3 nm are compatible with this type of recon-
structive mechanism via a tetragonal path. An extrapolation
with a logarithmic function of the data reported in Table Ifor
nanocrystals smaller than 10.5 nm yields that a=7.359 Å
and c=6.648 Å would be reached for a nanocrystal size of
about 1 nm, i.e., CaWO4nanocrystals smaller than 1 nm
could likely crystallize in the zircon structure.
Kusaba et al.21 already studied the shock-induced
zircon-to-scheelite phase transition in ZrSiO4and suggested
that the mechanism for the zircon-to-scheelite phase transi-
tion was not the one described in the precedent paragraph.
They suggested a reconstructive mechanism for the zircon-
to-scheelite phase transition in ZrSiO4on the basis of 共1兲the
fast transition observed between both phases in shock-wave
measurements 共microsecond time scale兲,共2兲the nonrevers-
ibility of the phase transition and the rapid reversibility of
the transition on increasing temperature, 共3兲the near 10%
decrease in density when going from the zircon to the
scheelite phase, 共4兲the large difference in the c/aratios of
a(
Å
)
5.16
5.20
5.24
5.28
Vol
(
Å3
)
295 300 305 310 315 320
c(Å)
11.1
11.2
11.3
11.4
11.5
(a)
(b)
FIG. 5. Lattice parameters 共a兲aand 共b兲cof scheelite-type CaWO4nano-
crystals as a function of the unit-cell volume. The dashed lines indicate the
theoretical dependence of the lattice parameters as a function of the unit cell
volume.
094321-4 Manjón et al. J. Appl. Phys. 105, 094321 共2009兲
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both structures, and 共5兲the residual strain present in the
quenched crystals. The complex mechanism of the recon-
structive zircon-to-scheelite phase transition that they sug-
gested involves a two-step process: 共1兲a shearing deforma-
tion of the zircon tetragonal unit cell with an opening of the

angle from 90° to 115° causing a density increase of 10%
and 共2兲a small rearrangement of atoms leading to a change
of the 关110兴direction of the zircon phase into the 关001兴di-
rection of the scheelite phase. The reconstructive zircon-to-
scheelite phase transition mechanism proposed by Kusaba et
al. can only be accomplished if a lattice with a triclinic sym-
metry is involved in the transition mechanism as discussed
by Marqués et al.22 The recent ab initio calculations of Mar-
qués et al. that modeled the zircon-to-scheelite phase transi-
tion in ZrSiO4using an intermediate triclinic 共P1
¯
兲structure
whose

tangle evolves from 90° at the zircon phase to 115°
in the scheelite phase give support to the reconstructive
mechanism of Kusaba et al.22 Furthermore, Flórez et al. re-
cently showed that the zircon-to-scheelite reconstructive
transition in ZrSiO4occurs indeed via an intermediate struc-
ture with monoclinic C2/csymmetry since the parameters of
the relaxed triclinic structure obtained can be reduced to the
C2/cmonoclinic lattice.23 They also discussed that during
the reconstructive phase transition along the monoclinic path
two Zr–O bonds per ZrO8molecule must be broken and two
new Zr–O bonds must be formed so this monoclinic mecha-
nism is energetically favored against the tetragonal mecha-
nism where four Zr–O bond must be broken to form four
new Zr–O bonds. A similar “bond-switching” mechanism of
the zircon-scheelite phase transition with two Zr–O bonds
broken and two new ones formed, but with two intermediate
structures 共one orthorhombic and one monoclinic with C2/c
symmetry兲has also been recently proposed giving support to
the reconstructive mechanism of the zircon-to-scheelite
phase transition in ZrSiO4in agreement with Kusaba et al.24
In order to investigate whether the evolution of the lat-
tice parameters aand cof the scheelite phase for nanocrystal
sizes below 8.3 nm is compatible with the scheelite-to-zircon
phase transition through the monoclinic path recently pro-
posed for bulk ZrSiO4, we plotted in Fig. 6the lattice param-
eters of the monoclinic intermediate cell obtained from the
lattice parameters of the scheelite cell. According to Ref. 23,
the lattice vectors of the monoclinic cell written in terms of
the scheelite unit cell are am=−as−bs,bm=cs, and cm=bs.
Therefore, the lattice parameters of the monoclinic structure
given in terms of the lattice parameters of the scheelite struc-
ture are am=冑2as,bm=cs, and cm=bs. Figure 6shows that
the behavior of the lattice parameters below 8.3 nm is in
good agreement with the expected behavior of the scheelite-
to-zircon transition through the intermediate monoclinic
C2/cstructure reported in Refs. 23 and 24. Therefore, we
can conclude that the behavior of the structural parameters a
and cof the scheelite-type nanocrystals with size smaller
than 8.4 nm agree with the expected behavior of the lattice
parameters during the scheelite-to-zircon phase transition ei-
ther by the tetragonal or by the monoclinic path. In summary,
the present structural data do not allow us to determine
which one is the right mechanism of the scheelite-to-zircon
phase transition in CaWO4nanocrystals.
The mechanism of the schelite-to-zircon phase transition
in CaWO4nanocrystals can be determined if the x,y, and z
parameters of the generatrix O of the scheelite phase were
known for nanocrystals below 8.4 nm as they are known for
bulk CaWO4共see Fig. 3兲. It is expected that the zparameter
varies rather smoothly during the transition along the tetrag-
onal path because the WO4just suffers a rotation around the
caxis of the scheelite. On the other hand, the zparameter
must suffer a considerable change along the monoclinic path
because the WO4tetrahedra have to be completely reoriented
during this phase transition due to the fact that in the mono-
clinic path the adirection of the scheelite phase transforms
into the cdirection of the zircon phase. Another possibility to
determine the mechanism of the transition in nanocrystals is
to measure their Raman scattering. These measurements
could evidence the mechanism by observation or absence of
Raman peaks due to the change in lattice symmetry. In the
case of the tetragonal path, the Raman spectrum of the
scheelite phase will not change at all until it gets the setting
angle equal to 0°. At this very moment one of the phonon
peaks of the spectrum will disappear since the Raman spec-
trum of the zircon phase has 12 Raman-active modes com-
pared to the 13 Raman-active modes of the scheelite phase.
a
m
(Å)
7.41
7.42
7.43
7.44
7.45
b
m
(Å)
11.34
11.35
11.36
11.37
11.38
11.39
Nanocr
y
stal size (nm)
0 5 10 15 20 25 30 3
5
c
m
(Å)
5.24
5.25
5.26
5.27
sm a2a =
sm cb =
sm
bc =
(a)
(b)
(c)
FIG. 6. Lattice parameters am,bm, and cmof the monoclinic cell of CaWO4
as a function of the nanocrystal size as obtained from the lattice parameters
as,bs, and csof the scheelite cell of CaWO4plotted in Fig. 1.
094321-5 Manjón et al. J. Appl. Phys. 105, 094321 共2009兲
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On the other hand, if the transition mechanism is through a
monoclinic C2/cstructure then one would observe five ad-
ditional Raman peaks compared to those of the scheelite
phase or six compared to the zircon phase, since HgWO4and
CaWO4above 10 GPa crystallize in the monoclinic C2/c
phase and exhibit 18 Raman-active modes.25,26 A similar rea-
soning applies for the infrared-active modes. In fact, Raman
and infrared measurements on the CaWO4nanocrystals have
been already performed.6They show that only the Raman
modes of the scheelite phase are observed even for the small-
est nanocrystal sizes. This result, together with the abrupt
increase 共decrease兲in the a共c兲lattice parameter of the
scheelite phase for negative pressures, could be the evidence
of the scheelite-to-zircon phase transition occurring via the
tetragonal path instead of through the intermediate mono-
clinic structure proposed for ZrSiO4.22–24 It must be noted
that the only net effect observed in the Raman spectrum of
CaWO4nanocrystals with 3.6 nm 共Ref. 6兲is a broadening of
the Raman bands and a small Raman shift to lower wave
numbers of most of the observed peaks.26 This small shift is
fully compatible with the negative pressure present in the
nanocrystals and does not evidence any monoclinic distor-
tion of the scheelite structure.
V. CONCLUSIONS
We have shown evidence that CaWO4nanocrystals with
sizes below 30 nm reported in Refs. 5and 6are subjected to
negative pressures that cause an instability of the scheelite
phase and lead to the onset of the scheelite-to-zircon phase
transition in CaWO4nanocrystals with sizes smaller than 8.4
nm. The scheelite-to-zircon phase transition in CaWO4nano-
crystals is of reconstructive character and seems to proceed
through a tetragonal distortion of the scheelite structure un-
like in bulk ZrSiO4where it is proposed to proceed through
a monoclinic path. The hypothesis for the tetragonal path for
the phase transition is supported by the absence of Raman
peaks corresponding to the monoclinic deformation of the
scheelite structure even in the nanocrystals with smallest
size. The reason for the different transition mechanism ob-
served in the nanocrystals with respect to that proposed in
the bulk could be related to the reduction in the energy bar-
rier of the transition through the tetragonal path due to 共i兲the
important participation of the surface energy in nanocrystals
and/or 共ii兲the presence of impurities attached to the nano-
crystals. In this respect, we want to stress that it is possible
that the increase in the surface/volume ratio in the nanocrys-
tals and/or the chemical substances attached to the nanocrys-
tals 共H2O and C6H8O7兲might reduce the energy barrier
共around 236 kJ/mol in bulk22兲necessary for the tetragonal
scheelite-to-zircon phase transition resulting in a different
pressure-induced phase transition mechanism in the nano-
crystals not previously found in the bulk.27
Further studies in scheelite-type nanocrystals are needed
to confirm the mechanism of the scheelite-to-zircon phase
transition in the CaWO4nanocrystals. In particular, neutron
diffraction experiments in nanocrystals could help in deter-
mining the x,y, and zparameters of the O in the scheelite
phase under negative pressures to give information on the
behavior of the setting angle and the real behavior of the
Ca–O distances in the nanocrystals. Besides, new XRD ex-
periments could report the appearance or absence of a small
peak of the monoclinic C2/cphase at angles near 2
=4°, the
disappearance of the strong peak corresponding to the 共112兲
and 共103兲Bragg reflections of scheelite CaWO4共Ref. 28兲at
2
=27° in Ref. 5, and the appearance of a strong peak cor-
responding to the 共200兲Bragg reflection of zircon CaWO4at
2
=25°, provided that XRD experiments are performed at
the same energy used in Ref. 5. Additionally, new Raman
measurements with higher resolution and covering the whole
range from 50 to 1000 cm−1 could help in verifying whether
the mechanism of the reconstructive phase transition goes
along the tetragonal or monoclinic path. Finally, we want to
note that a similar behavior is also expected in CaMoO4
nanocrystals of similar size to those of CaWO4nanocrystals
since the stability of the scheelite phase in both compounds
is very similar.
ACKNOWLEDGMENTS
F.J.M. acknowledges interesting discussions with J.M.
Recio and M. Flórez. This study was supported by the Span-
ish MCYT under Grant Nos. MAT2006-02279, MAT2007-
65990-C03-01, MAT2007-65990-C03-03, and CSD2007-
00045 and by the Generalitat Valenciana 共Project No.
GV2008/112兲. F.J.M. also acknowledges financial support
from “Vicerrectorado de Innovación y Desarrollo de la UPV”
through Project No. UPV2008-0020.
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