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First-principles study of the high-pressure phase transition in ZnAl2O4and ZnGa2O4:From
cubic spinel to orthorhombic post-spinel structures
Sinhué López*and A. H. Romero†
CINVESTAV-Queretaro, Libramiento Norponiente No 2000, Real de Juriquilla, 76230 Queretaro, México
P. Rodríguez-Hernández‡and A. Muñoz§
Departamento de Física Fundamental II, MALTA Consolider Team, Instituto de Materiales y Nanotecnología, Universidad de La Laguna,
La Laguna, 38205 Tenerife, Spain
共Received 14 January 2009; revised manuscript received 26 March 2009; published 3 June 2009兲
In this work we present a first-principles density functional study of the electronic, vibrational, and structural
properties of ZnGa2O4and ZnAl2O4spinel structures. Here we focus our study in the evolution of the
structural properties under hydrostatic pressure. Our results show that ZnGa2O4under pressure has a first-order
phase transition to the marokite 共CaMn2O4兲structure, which is in good agreement with recent angle-dispersive
x-ray diffraction experiments. We also report a similar study for the ZnAl2O4spinel; we found that this
compound under pressure has a first-order phase transition to the orthorhombic CaFe2O4-type structure. Our
results in both compounds support, under nonhydrostatic condition, the possibility of a second-order phase
transition from the cubic spinel to the tetragonal spinel as reported experimentally in ZnGa2O4.
DOI: 10.1103/PhysRevB.79.214103 PACS number共s兲: 61.50.Ks, 61.50.Ah, 62.50.⫺p, 63.20.dk
I. INTRODUCTION
Oxide spinel compounds AB2O4are ceramics that have
many interesting electric, mechanic, magnetic, and optical
properties. These compounds have been characterized by
means of theory and experiments to get a better understand-
ing of its properties. Among all those interesting properties,
the structural dependence under pressure has called a lot of
attention, mainly due to their occurrence in many geological
settings of the Earth’s crust and mantle. Many AB2O4spinels
crystallize in the cubic spinel structure 共Fd3
¯
m兲exemplified
by MgAl2O4. Reid and Ringwood1suggested that a possible
postspinel phase in MgAl2O4would be similar to
CaFe2O4-type, CaTi2O4-type, or CaMn2O4-type structures,
with the space groups 共SGs兲Pnma,Cmcm, and Pbcm, re-
spectively. Very recently Ono et al.2showed, by first-
principles calculations, that cubic spinel MgAl2O4undergoes
a phase transition to orthorhombic CaFe2O4- and
CaTi2O4-type structures when compressed at high pressure.
However, the structure and properties of post-spinel phases
are presently still under debate.
Unlike MgB2O4compounds, there are only few experi-
mental high-pressure studies about the structural character-
ization of cubic spinels ZnB2O4, ZnAl2O4,3ZnFe2O4,4and
ZnGa2O4.5All these spinels have been recently characterized
by angle-dispersive x-ray powder diffraction under high
pressures. In the case of ZnFe2O4they found that there is an
evident phase transition from spinel to CaTi2O4-or
CaMn2O4-type structure between 26 and 36.6 GPa, where
the cubic spinel phase is practically negligible.4Unlike
ZnFe2O4, Levy et al.3found that there is no phase transition
of ZnAl2O4up to a pressure of 43 GPa. On the other hand,
ZnGa2O4was characterized very recently by Errandonea et
al.5by following the structural changes up to 56 GPa and
showing clear evidence of two structural phase transitions. In
their work, the ZnGa2O4has a first second-order phase tran-
sition from the cubic spinel to a tetragonal spinel with
I41/amd symmetry above 31 GPa. The tetragonal spinel is
the structure of ZnMn2O4and that of MgMn2O4at ambient
pressure. Finally, a second structural phase transition was
reported in ZnGa2O4around 55 GPa from the tetragonal spi-
nel to the orthorhombic Pbcm structure. This last structure
corresponds to marokite 共CaMn2O4兲at ambient pressure.
From the theoretical side, the cubic spinels ZnAl2O4and
ZnGa2O4, have been characterized by ab initio calculations.
The majority of reports is concentrated on the structural,
electronic, elastic,6,7,11 and vibrational properties of the
ZnAl2O4共Ref. 9兲at equilibrium volume. The behavior of the
structural parameters and elastic constant under pressure has
been reported in Refs. 7and 11. But to our knowledge, there
is not any theoretical report concerning the study of possible
phase transition induced by pressure as the ones showed by
other spinel compounds.2,5
In this paper, we report first-principles calculations of the
structural, electronic, and vibrational properties of the cubic
spinels ZnAl2O4and ZnGa2O4compounds at zero pressure.
Besides, we report the variation in the structural parameters
under pressure and compare directly with recent experimen-
tal measurements. Finally, we study the possible pressure-
induced structural phase transitions for both compounds.
The paper is organized as follows: computational details
are described in Sec. II. The characterization results of
ZnAl2O4and ZnGa2O4compounds at zero pressure and un-
der pressure are presented in Secs. III A and III B, respec-
tively. Finally, we present the conclusions of this work in
Sec. IV.
II. COMPUTATIONAL DETAILS
Total energy calculations were done within the framework
of the density functional theory 共DFT兲and the projector-
augmented wave 共PAW兲共Refs. 12 and 13兲method using the
Vienna ab initio simulation package 共VASP兲.14–17 The ex-
change and correlation energy was described within the local
PHYSICAL REVIEW B 79, 214103 共2009兲
1098-0121/2009/79共21兲/214103共7兲©2009 The American Physical Society214103-1
density approximation 共LDA兲.18 We use a 500 eV plane-
wave energy cutoff to guarantee a pressure convergence to
less than 2 kBar. Monkhorst-Pack scheme was employed for
the Brillouin-zone integrations19 with a mesh 4⫻4⫻4, 6
⫻3⫻3, 8⫻4⫻4, and 8⫻4⫻4, which corresponds to a set
of 10, 12, 16, and 16 special kpoints in the irreducible
Brillouin-zone, for structures: cubic spinel 共Fd3
¯
m兲, tetrago-
nal spinel 共I41/amd兲, and the orthorhombic structures with
space groups Pbcm and Pnma, respectively. In the relaxed
equilibrium configuration, the forces are less than
0.9 meV/Å per atom in each of the cartesian directions. The
highly converged results on forces are required for the dy-
namical matrix calculations using the direct force-constant
approach 共or supercell method兲.20 The construction of the
dynamical matrix at the ⌫point is particularly simple and
involves separate force calculations, where the displacement
from the atomic equilibrium configuration, within the unit
cell, are considered. Symmetry aids by reducing the number
of such independent distortions to six independent displace-
ments within the cubic spinel phase. Dynamical matrices
where estimated by considering positive and negative dis-
placements 共u⬇⫾0.03 Å兲. We have also checked that these
displacements are within the harmonic approximation. Di-
agonalization of the dynamical matrix provides both the fre-
quencies of the normal modes and their polarization vectors.
It allows us to identify the irreducible representation and the
character of the phonon modes at the zone center.
III. RESULTS AND DISCUSSION
A. Cubic spinels ZnGa2O4and ZnAl2O4
Zinc gallate 共ZnGa2O4兲and gahnite 共ZnAl2O4兲crystallize
at ambient pressure in a diamond-type cubic spinel structure
with space-group Fd3
¯
m共227兲共see Fig. 1兲. The Acations are
tetrahedrally coordinate, and the Bcations are in BO6octa-
hedra. The Zn atoms are located at the Wyckoff positions, 8a
共1/8,1/8,1/8兲tetrahedral sites, while Ga 共or Al兲atoms are
located on the 16d共1/2,1/2,1/2兲octahedral sites and the oxy-
gen atoms at 32e共u,u,u兲. The spinel crystal structure is
characterized only by the lattice parameter aand the internal
parameter u.
The equilibrium lattice parameters have been calculated
by minimizing the crystal total energy obtained for different
volumes and fitted with the Murnaghan’s equation of state
共EOS兲.21 The calculated equilibrium lattice constants are
8.289 and 8.020 Å in good agreement with the experimental
values of 8.341 Å5and 8.0911 Å3for ZnGa2O4and
ZnAl2O4, respectively. We also performed a similar study
using the generalized gradient approximation 共GGA兲in the
Perdew-Burke-Ernzerhof 共PBE兲共Refs. 22 and 23兲exchange-
correlation functional, and we have obtained similar results,
with an overestimation of the lattice constant of 1.63%.
Therefore, all reported results in this paper are obtained
within the LDA approximation. The values of the oxygen
internal-parameter uare found to be u=0.2608 and 0.2638,
also in good agreement with the experimental values 0.25995
and 0.26543for ZnGa2O4and ZnAl2O4, respectively. In
Table Iwe report our obtained structural parameters, bulk
modulus B0, bulk-modulus pressure derivative B0
⬘, and bond
distances for both compounds. Our calculated B0are in good
agreement with experimental results and our values for B0
⬘
are bigger than the experimental results, probably due to the
experimental nonhydrostatic conditions.
Figures 2共a兲and 2共b兲display our calculated band struc-
ture along the high-symmetry directions of the ZnAl2O4and
ZnGa2O4compounds. These cubic spinel oxides are wide-
FIG. 1. 共Color online兲Unit cell of the AB2O4structures 共a兲
cubic spinel, 共b兲marokite-type, and 共c兲CaFe2O4-type structure. The
atom color palette for A共Zn兲,B共Ga or Al兲, and O are yellow, blue,
and red, respectively.
TABLE I. Ground-state parameters of the spinel structures
ZnGa2O4and ZnAl2O4. Where ais the lattice parameter, uis the
oxygen parameter, dZn-O is the distance between Zn and O, dX−O is
the distance between X共Al or Ga兲atom and O,B0is bulk modulus,
and B0
⬘is the bulk-modulus pressure derivative.
ZnGa2O4ZnAl2O4
Present Exp.aOthers Present Exp.bOthers
a
共Å兲8.289 8.341 8.2506c8.020 8.0911 7.998f
8.4063d8.0505d
7.977e8.086g
u0.2608 0.2599 0.2611c0.2638 0.2654 0.389f
0.2614d0.2651d
0.2673e0.3886g
dZn-O
共Å兲1.950 1.949 1.943c1.929 1.9662 1.93f
1.966e
dX−O
共Å兲1.987 2.004 1.975c1.901 1.9064 1.89f
1.866e
B0
共GPa兲218.93 233 217c219.65 201.7 218f
156d183d
207.52e
B0
⬘4.35 8.3 3.77e4.02 7.62
aReference 5.
bReference 3.
cReference 6.
dReference 7.
eReference 8.
fReference 9.
gReference 10.
LÓPEZ et al. PHYSICAL REVIEW B 79, 214103 共2009兲
214103-2
band-gap semiconductors. According to Sampath and
Cordaro24 the optical-band gap derived from reflectance
measurements are between 3.8–3.9 and 4.1–4.3 eV for
ZnAl2O4and ZnGa2O4, respectively.
Previous tight-binding calculations25 obtain a direct band
gap of 4.11 eV for ZnAl2O4and 2.79 eV for ZnGa2O4.In
this work, Sampath et al.25 suggested that the band gap in
Ref. 24 for ZnAl2O4is probably incorrect. Other linear-
augmented plane-waves studies from Pisani et al.6for
ZnGa2O4report a band gap at the ⌫point of 2.7 eV, with no
indication about if it is direct or indirect. In our calculations
the ZnAl2O4has a direct band gap, ⌫-⌫, of 4.24 eV while
ZnGa2O4has an indirect band gap, K-⌫, of 2.78 eV, in good
agreement with previous theoretical results.6,11,25 In
ZnGa2O4, the presence of the occupied Ga 3dstate is the
origin of the indirect gap, due to the symmetry-forbidden
Ga 3d-O 2pcoupling at the ⌫point. Of course, it is well-
known that LDA systematically underestimates the band gap,
but the symmetry and the pressure evolution of the band gap
are usually well described.
Cubic spinels ZnAl2O4and ZnGa2O4belong to the space-
group 227 and have 2 f.u. per primitive cell. The phonon
modes at the ⌫point are classified as follows:26
⌫=A1g共R兲+Eg共R兲+T1g+3T2g共R兲+2A2u+2Eu+4T1u共IR兲
+2T2u,
where Rand IR corresponds to Raman and infrared-active
modes, respectively. Our calculated phonon frequencies at
zero pressure are listed in Table II.
The experimental Raman and IR active modes obtained
by Manjon27 and Gorkom et al.28 for ZnGa2O4, Chopelas
and Hofmeister,26 and the theoretical data from Fang et al.9
for ZnAl2O4are listed in Table III. In general, there is fair
agreement for ZnAl2O4between available experimental, pre-
vious theoretical data and our results, with a slight deviation
of 0.5%–2.4% in the Raman-active modes. In the case of
ZnGa2O4, to our knowledge, there is no previous first-
principles study of Raman frequencies, even though we can
report good agreement with available experimental data, ex-
cept for the Egmode from Ref. 28. In particular, we obtain a
frequency of Eg=395 cm−1 which happens to be in good
agreement with other experimental values reported for other
spinel compounds such as ZnAl2O4and MgAl2O4.26
The role of the cations in the phonon frequencies of
MgAl2O4, ZnAl2O4, and ZnGa2O4can be understood from
the cation masses. Mainly because the A2+ 共Mg2+ and Zn2+兲
cations have a similar ionic radius and local bonding envi-
-8
-6
-4
-2
0
2
4
6
8
Energy
(
eV
)
-8
-6
-4
-2
0
2
4
6
8
Energy
(
eV
)
ΓXW L ΓK
X
ΓXW L ΓK
X
a)
b)
FIG. 2. Calculated band structure of 共a兲ZnGa2O4and 共b兲
ZnAl2O4spinel structures at equilibrium volume.
TABLE II. Calculated vibrational-modes 共cm−1兲for ZnGa2O4
and ZnAl2O4at zero pressure in the ⌫point.
Species ZnGa2O4ZnAl2O4
T2u135 250
T1u共IR兲175 222
T2g共R兲186 194
Eu229 402
T1u共IR兲342 496
T1g366 371
Eg共R兲395 427
A2u419 672
T1u共IR兲429 548
T2u450 484
T2g共R兲488 513
Eu563 600
T1u共IR兲580 666
T2g共R兲618 655
A2u702 769
A1g共R兲717 775
FIRST-PRINCIPLES STUDY OF THE HIGH-PRESSURE…PHYSICAL REVIEW B 79, 214103 共2009兲
214103-3
ronment, the same occurs for the cation B3+ 共Al3+ and Ga3+兲.
The differences on the phonon frequencies are larger by con-
sidering different cations B3+ than cations A2+.Asanex-
ample, we compare the Raman-active modes 共T2g,Eg,T2g,
T2g, and A1g兲of MgAl2O4共312, 407, 492, 666, and
767 cm−1兲, ZnAl2O4共196, 417, 509, 658, and 768 cm−1兲,26
and ZnGa2O4共186, 395, 462, 606, and 706 cm−1 from our
results and Ref. 27兲共see Table III兲. It is clear that the abso-
lute frequency difference, between the theoretical and the
experimental data, is bigger when the B3+ cation is changed,
mainly for the second and third T2gand A1gactive modes.
B. High-pressure phases
In order to show the behavior of the structural parameters
under pressure for ZnAl2O4and ZnGa2O4, the equilibrium
geometries of these cubic spinel compounds were studied up
to a pressure of around 50 GPa, in steps of ⬇2.5 GPa. Op-
timization of internal coordinates at each pressure was per-
formed. The variations in the lattice-parameter aand oxygen
parameter u, with respect to the pressure, are shown in Fig.
3. The behavior of ais almost the same for both compounds,
while the variation in uis more important for ZnGa2O4. This
difference can be explained by looking at the dependence on
the structural changes with respect to the masses differences
of the B3+ cation for both compounds. It is shown in Table I
that at zero pressure the distances dZn-O and dX−O共X
=Al,Ga兲have a larger difference in ZnGa2O4than in
ZnAl2O4. Figure 4shows that dZn-O decreases faster with
pressure than dX−O, and also evidences that dZn-O is larger
than dX−O in ZnAl2O4while the converse is true for
ZnGa2O4. We conclude, in general, that as the pressure in-
creases, the absolute distance dZn-O and dX−O, in ZnAl2O4,
gets closer to each other, while the opposite behavior is pre-
sented in ZnGa2O4.
According to Ono et al.,29 the spinel MgAl2O4decom-
poses into an assemblage of periclase 共MgO兲and corundum
共Al2O3兲at pressures above 15 GPa. This behavior has not
been observed in experiments on ZnAl2O4or ZnGa2O4.In
order to test this possibility, we probe the configurations
periclase+corundum as in Ref. 2共for MgAl2O4兲for both
spinels, and we have found that this possibility is not ener-
getically competitive.
The first phase transition obtained by Errandonea et al.5in
ZnGa2O4appears at 31.2 GPa from cubic spinel to a tetrag-
onal spinel structure without changes in volume and c/a
=1.398, clearly different from the ideal value c/a=冑2. The
lattice parameters for the different phases from Ref. 5and
our theoretical results are listed in Table IV. The second
first-order phase transition was obtained at 55.4 GPa,5where
they have suggested that a better agreement between the ob-
served and calculated patterns is achieved by considering a
CaMn2O4-type structure 共marokite兲, with an estimated vol-
ume collapse of around 7% at the transition pressure.
Following the path explained in Ref. 5we find that the
tetragonal spinel structure has almost the same energy than
the cubic spinel structure with c/a=1.4142, almost equal to
the ideal value c/a=冑2. It means that under hydrostatic con-
ditions the tetragonal structure reduces to the cubic spinel
TABLE III. Comparison between calculated and experimental
Raman and IR-active modes 共cm−1兲of ZnGa2O4and ZnAl2O4.
Modes ZnGa2O4Exp.aExp.bZnAl2O4Exp.cTheoryd
Raman
T2g186 194 196 197
Eg395 638 427 417 442
T2g488 462 467 513 509 520
T2g618 606 611 655 658 665
A1g717 706 714 775 758 785
IR
T1u175 175 222 220共231兲226共240兲
342 328 496 440共533兲507共528兲
429 420 548 543共608兲562共648兲
580 570 666 641共787兲675共832兲
aReference 27.
bReference 28.
cReference 26.
dReference 9.
0 1020304050
P
(
GPa
)
0.256
0.258
0.260
0.262
0.264
0.266
u
0 1020304050
P (GPa)
7.6
7.7
7.8
7.9
8.0
8.1
8.2
8
.
3
a(Å
³)
b)
a)
FIG. 3. 共Color online兲Pressure dependence of the 共a兲lattice-
parameter aand 共b兲oxygen-parameter uof the spinels ZnAl2O4and
ZnGa2O4compounds up to 50 GPa. In both figures, the labels for
ZnGa2O4are as follows: black-filled circles for theoretical and
black open circles for experimental data; and for ZnAl2O4: red-
filled squares for theoretical and red open squares for experimental
data. The experimental data are taken from Refs. 3and 5.
LÓPEZ et al. PHYSICAL REVIEW B 79, 214103 共2009兲
214103-4
phase. In order to test the effect of nonhydrostatic conditions,
we performed similar calculations at 32 GPa by imposing the
c/avalues reported in experiments from Ref. 5. Our results
show that at this pressure the tetragonal phase, under nonhy-
drostatic conditions, is competitive in energy with the hydro-
static one. It means that probably the nonhydrostatic condi-
tions can play an important role in the experiments
performed by Errandonea et al.5This result would corre-
spond to the observed first phase-transition that corresponds
to a second-order type without volume changes as reported
in experiments.5
In the second step the marokite 共SG: Pbcm兲,
CaFe2O4-type 共SG: Pnma兲, and CaTi2O4-type 共SG: Cmcm兲
structures were used to search a possible candidate to the
second phase transition from the tetragonal to orthorhombic
structure suggested by experiments. The Fig. 5shows the
calculated energy-volume curves of ZnAl2O4and ZnGa2O4
compounds for the Fd3
¯
m-, I41/amd-, Pnma-, and
Pbcm-analyzed structures. The insets show the variation in
enthalpy with pressure of spinel in black solid line, blue
dashed line for marokite in 共a兲, and green dashed line for
Pnma in 共b兲. Also, this figure shows the theoretical transition
pressure, PT, at the structural phase transition.
Our results for ZnGa2O4show that the CaFe2O4-type
structure is not competitive for any pressure, while the ma-
rokite and the CaTi2O4-type structures have almost the same
energy, and from the energetic point of view both are good
candidates to explain the second transition.
We conclude, by comparing with experimental results, the
marokite structure gives the best agreement with the ob-
served diffraction data. Besides, the structural parameters
that we obtain for the marokite structure are in good agree-
ment with experimental measurements, as seen in Table IV.
Lattice parameters of marokite structure from Table IV cor-
responds to the volume at the phase transition. Figure 6sum-
0 1020304050
P (GPa)
1.80
1.83
1.86
1.89
1.92
1.95
1.98
2.01
bond distances (Å)
FIG. 4. 共Color online兲Pressure dependence of the bond-
distances dZn-O,dGa-O, and dAl-O, of the spinel structures up to 50
GPa. The labels are as follows, for dZn-O in ZnGa2O4: black-filled
circles for theoretical and black open circles for experimental data
共Ref. 5兲; and black-filled triangles up for theory and black open
triangles for experimental data for dGa-O. For theoretical values of
ZnAl2O4the labels are: red-filled squares for dZn-O and red triangles
down for dAl-O.
TABLE IV. Lattice parameters from all the structures studied.
The parameters of SGs Fd3
¯
mand I41/amd are from equilibrium
volume, while parameters of Pnma,Pbcm, and Cmcm structures
are at the volumes of transition pressure.
SG
a
共Å兲
b
共Å兲
c
共Å兲c/au
ZnAl2O4Fd3
¯
m8.020 0.2638
I41/amd 5.671 8.021 1.414
Pnma 2.661 9.548 8.236
ZnGa2O4Fd3
¯
m8.289 0.2608
I41/amd 5.861 8.290 1.414
Pbcm 2.760 9.245 9.156
Exp. 共Ref. 5兲Fd3
¯
m8.341 0.2599
I41/amd 5.743 8.032 1.398
Pbcm 2.93 9.13 8.93
20 25 30 35 40 45 50
P (GPa)
-70
-65
-60
-55
H (eV)
110 115 120 125 130 135 140
V(Å
³)
-91
-90
-89
-88
-87
-86
E (eV)
30 35 40 45 50
P (GPa)
-85
-80
-75
-70
-65
H (eV)
100 105 110 115 120 125 13
0
V
(
ų
)
-105
-104
-103
-102
-101
-100
E (eV)
b)
a)
PT= 38.5 GPa
V1= 112.96 ų
V2= 104.62 ų
V2= 116.8 ų
V1= 126.63 ų
PT= 33.4 GPa
FIG. 5. 共Color online兲Calculated energy-volume curves of 共a兲
ZnGa2O4and 共b兲ZnAl2O4. The labels are black-filled circles for
cubic spinel 共Fd3
¯
m兲, red open circles for tetragonal spinel
共I41/amd兲, green-filled squares for orthorhombic Pnma, and blue
triangles up for orthorhombic Pbcm. Where V1and V2are the vol-
umes at the transition pressure. The inset shows the enthalpy vs
pressure curves in which the black solid lines are for spinel struc-
ture, blue dashed line in 共a兲for Pbcm and green dashed line in 共b兲
for Pnma; The volume and energy are given per two unit formula.
FIRST-PRINCIPLES STUDY OF THE HIGH-PRESSURE…PHYSICAL REVIEW B 79, 214103 共2009兲
214103-5
marizes our findings and shows the path of the phase transi-
tion in a pressure-volume plot from spinel to orthorhombic
marokite-type structure in ZnGa2O4. According to Fig. 6,
ZnGa2O4has a volume collapse of 7.76%, in good agree-
ment with results from Ref. 5. Our theoretical transition pres-
sure is lower than the experimental one, but as it is known,
the equal enthalpy construction usually gives lower pressure
transitions that the experimental ones.30 Also, the big differ-
ence between the experimental and theoretical transition
pressure can be explained from the possible existence of ki-
netic barriers that are not included in the calculations. Also,
the experimental nonhydrostatic conditions can play a role in
the value of the observed transition pressure. It is well-
known that the transition pressures reported by x-ray diffrac-
tion experiments are higher than transition pressures reported
by Raman experiments under pressure.30 We believe that fu-
ture Raman experiments will obtain a lower transition pres-
sure in better agreement with our calculations.
The cubic spinel-ZnAl2O4structure was characterized ex-
perimentally by Levy et al.3up to a pressure of 43 GPa with
no observation of a phase transition. We have performed a
similar study for the ZnAl2O4spinel. Our results demonstrate
a similar behavior as with ZnGa2O4, in particular with re-
spect to the potential phase transition between the cubic to
the tetragonal spinel. For such purpose, we have performed
calculations under nonhydrostatic conditions at 36 GPa by
imposing a c/avalue similar to the case of ZnGa2O4, and we
found that the tetragonal spinel structure is competitive in
energy with the hydrostatic one, as reported in Table IV and
Fig. 5. It may suggest that probably under nonhydrostatic
conditions this second-order phase transition could be ob-
served. We also have performed total-energy calculations for
different candidate structures for a possible first-order phase
transition. In particular, we tried with structures Pbcm,
Pnma, and Cmcm. Our results show that in this case, a first-
order phase transition occurs at 38.5 GPa in ZnAl2O4from
cubic spinel to a Pnma structure, while the marokite-type
structure is not competitive. Again, like in ZnGa2O4, prob-
ably due to the kinetic barriers, the experimental transition
pressure would be higher and this transition was not ob-
served by Levy et al.;3we expect that high-pressure experi-
ments over 50 GPa will observe these transitions.
The cubic-spinel ZnAl2O4, under pressure, has a first
phase transition to the CaFe2O4-type structure. This high-
pressure phase also appears in MgAl2O4. From the experi-
mental study5and our results, ZnGa2O4under pressure goes
to the marokite structure. This different behavior can be un-
derstood due to the replacement of the cation B共Al or Ga兲,in
fact it is well-known the role of the delectron in many semi-
conductor compounds under pressure.30,31
In regards to the cation coordination, we observe an in-
crease from 4 to 8 in Zn coordination in ZnAl2O4and
ZnGa2O4, at high-pressure phases. Both orthorhombic struc-
tures are made up of BO6共B=AlorGa兲- distorted octahedra
and ZnO8zinc-centered distorted polyhedra 共see Fig. 1兲.
IV. CONCLUSIONS
In summary, we have performed first-principles calcula-
tions to study structural, electronic, and vibrational proper-
ties for cubic spinels ZnAl2O4and ZnGa2O4at zero pressure.
The results are in good agreement with previous reported
calculations and with the available experimental data. With
respect to vibrational characterization, we report the zone-
center phonon frequencies at zero pressure of both cubic
spinels.
We found that ZnGa2O4and ZnAl2O4spinel compounds
can have a second-order phase transition from cubic to te-
tragonal spinel I41/amd under nonhydrostatic conditions.
When increasing pressure the ZnGa2O4has a first-order
phase transition to a marokite Pbcm structure at 33.44 GPa.
In the case of ZnAl2O4we predict a first-order phase transi-
tion to a Pnma structure at 38.5 GPa. In both cases the high-
pressure phases are orthorhombic and contain BO6共B=Al or
Ga兲-distorted octahedra and ZnO8zinc-centered distorted
polyhedra. We hope that this work will stimulate future high-
pressure Raman and x-ray experiments in these compounds.
ACKNOWLEDGMENTS
A.H.R. has been supported by CONACYT Mexico under
Projects J-59853-F and J-83247-F. P.R.-H and A.M. ac-
knowledge the financial support of the MICINN of Spain
under Grants No. MAT2007-65990-C03-03 and No.
CSD2007-00045, and the computer resources provided by
MareNostrum, Spain and Kan Balam Supercomputer,
UNAM, México.
0 1020304050
P (GPa)
100
110
120
130
140
V(Å
³
)
Pbcm
Fd3m Pnma
∆V = -7.76 %
∆V = -7.41 %
I41/amd (exp.)
FIG. 6. 共Color online兲Path of the phase transition from cubic
spinel to orthorhombic structures, for ZnAl2O4: green-blue-filled
squares for theory, and green open squares for experimental data
共Ref. 3兲; ZnGa2O4: black-red-filled circles for theory, and black
open circles 共Fd3
¯
m兲, orange-filled triangle up 共I41/amd兲for experi-
mental data 共Ref. 5兲. The volume collapse at the transition pressure
are 7.41% and 7.76% in ZnAl2O4and ZnGa2O4, respectively.
LÓPEZ et al. PHYSICAL REVIEW B 79, 214103 共2009兲
214103-6
*lsinhue@qro.cinvestav.mx
†aromero@qro.cinvestav.mx
‡placida@marengo.dfis.ull.es
§amunoz@marengo.dfis.ull.es
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