Theoretical and Experimental Study of the Crystal Structures, Lattice Vibrations, and Band Structures of Monazite-Type PbCrO4, PbSeO4, SrCrO4, and SrSeO4

Article abstract of DOI:10.1021/acs.inorgchem.5b01135

The crystal structures, lattice vibrations, and electronic band structures of PbCrO₄, PbSeO₄, SrCrO₄, and SrSeO₄ were studied by ab initio calculations, Raman spectroscopy, X-ray diffraction, and optical-absorpt

Full text of DOI:10.1021/acs.inorgchem.5b01135

Article
pubs.acs.org/IC
Theoretical and Experimental Study of the Crystal Structures, Lattice
Vibrations, and Band Structures of Monazite-Type PbCrO , PbSeO ,
4
4
SrCrO , and SrSeO
4
4
,
†
‡
‡
§
̃
́
Daniel Errandonea,* Alfonso Munoz, Placida Rodríguez-Hernandez, John E. Proctor,
⊥
∥
Fernando Sapina, and Marco Bettinelli
̃
†
‡
§
́
Departamento de Física Aplicada, ICMUV, MALTA Consolider Team, Edificio de Investigacion, Universidad de Valencia,
C. Dr. Moliner 50, 46100 Burjassot, Spain
Departamento Física, Malta Consolider Team, and Instituto de Materiales y Nanotecnología, Universidad de La Laguna,
8206 La Laguna, Tenerife, Spain
Joule Physics Laboratory, University of Salford, Manchester M5 4WT, U.K.
3
⊥
́ ́ ́
Institut de Ciencia dels Materials (ICMUV), Universitat de Valencia, C/Catedratico Jose Beltran 2, 46890 Paterna, Spain
Luminescent Materials Laboratory, Department of Biotechnology, University of Verona and INSTM, UdR Verona,
Strada Le Gracie 15, 37134 Verona, Italy
∥
ABSTRACT: The crystal structures, lattice vibrations, and
electronic band structures of PbCrO , PbSeO , SrCrO , and
4
4
4
SrSeO4 were studied by ab initio calculations, Raman
spectroscopy, X-ray diffraction, and optical-absorption meas-
urements. Calculations properly describe the crystal structures
of the four compounds, which are isomorphic to the monazite
structure and were confirmed by X-ray diffraction. Information
is also obtained on the Raman- and IR-active phonons, with all
of the vibrational modes assigned. In addition, the band
structures and electronic densities of states of the four
compounds were determined. All are indirect-gap semi-
conductors. In particular, chromates are found to have band
gaps smaller than 2.5 eV and selenates higher than 4.3 eV. In the chromates (selenates), the upper part of the valence band is
dominated by O 2p states and the lower part of the conduction band is composed primarily of electronic states associated with
the Cr 3d and O 2p (Se 4s and O 2p) states. Calculations also show that the band gap of PbCrO (PbSeO ) is smaller than the
4
4
band gap of SrCrO (SrSeO ). This phenomenon is caused by Pb states, which, to some extent, also contribute to the top of the
4
4
valence band and the bottom of the conduction band. The agreement between experiments and calculations is quite good;
however, the band gaps are underestimated by calculations, with the exception of the bang gap of SrCrO , for which theory and
4
calculations agree. Calculations also provide predictions of the bulk modulus of the studied compounds.
1
. INTRODUCTION
kinds of oxides, allowing both a better understanding of the
experimental results and making accurate predictions. On the
basis of this and the facts described above, we consider it timely
to perform a theoretical study of PbCrO , PbSeO , SrCrO , and
Recently, there has been a large amount of interest in the study
of monazite-type structured oxides. These compounds have
importance in areas such as earth, planetary, and materials
4
4
4
1
−12
SrSeO . X-ray diffraction (XRD), Raman spectroscopy, and
4
sciences.
Because of their relevance, most of the studies
optical-absorption experiments were also carried out. The
combinations of calculations and experiments have allowed us
to systematically study the structural, lattice-dynamics, and
electronics properties of the four above-mentioned compounds,
making considerable progress in their understanding. The
have been focused on monazite-type structured phosphates.
Among other oxides, only LaVO , PbCrO , and CaSeO have
been thoroughly studied.
SrCrO , PbSeO , and SrSeO , their crystal structures have been
experimentally determined, but few of their Raman-active modes
have been measured. In the case of SrCrO , attempts have been
made to determine the electronic band gap, but values ranging
from 2.4 to 2.9 eV can be found in the literature.
4
4
4
1
,2,6,7,12
For other compounds, like
4
4
4
knowledge of the studied properties for the chromates is
4
16−18
important for their technological applications.
The
13−15
inclusion of selenates in the study was done with the aim of
better understanding the physical properties of the whole family
Ab initio calculation has shown to be an accurate method to
study the physical and chemical properties of CaSeO and
compounds related to the monazites. Usually, these quantum-
4
1
Received: May 19, 2015
mechanical calculations provide an accurate description of these
©
XXXX American Chemical Society
A
DOI: 10.1021/acs.inorgchem.5b01135
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Inorganic Chemistry
Article
of monazite-type oxides. The reported results will be compared
with the literature.
not affect our experiments. The scattered light was analyzed with a
single spectrograph (Shamrock 303i) equipped with an edge filter and
an air-cooled multichannel charge-coupled-device detector (iDus 420).
The paper is organized as follows: In the next section, we
give a detailed description of the experimental techniques. The
computational details are presented in section 3. The crystal
structures of the four compounds are described together with
the vibrational and electronic properties in section 4. Finally,
we summarize the results of this work in section 5.
−1
The spectral resolution was better than 2 cm . For PbCrO , Raman
4
experiments were carried out by our group in the backscattering
geometry using a Horiba Yvon Jobin LabRam spectrometer and were
17
previously published. The results of those experiments have been
included here for comparison with ab initio calculations and with the
experiments performed in the other three compounds. For PbCrO , a
4
6
32 nm laser was used in the Raman experiments because of the high
2
. EXPERIMENTAL METHODS
absorption of PbCrO at 532 nm.
4
In the optical-absorption studies, we used for PbCrO and SrCrO
SrCrO in powder form was prepared by precipitation by adding
4
4
4
2
0-μm-thick parallel face crystals, which were cleaved from the larger
5
0 mL of a 1 M Sr(NO ) solution to 50 mL of a 1 M K CrO solu-
3 2 2 4
single crystals that we described above. For PbSeO and SrSeO ,
2
were obtained by compressing a powder sample to 1 GPa using a
large-volume press equipped with Bridgman anvils. Optical-
tion. Single crystals were grown using a ternary flux system composed
4
4
1
9
0-μm-thick polycrystalline platelets were employed. The platelets
of NaCl, KCl, and CsCl, as described by Schenker et al. The weight
composition of the mixture was NaCl (24.8%), KCl (26.4%), CsCl
2
4
(
41.3%), and SrCrO (7.5%). The starting reagents were mixed, placed
4
absorption measurements in the ultraviolet−visible−near-infrared
in a platinum crucible with a tight-fitting lid, and kept for 12 h at
20 °C in a horizontal furnace under an air atmosphere. The melt
was slowly cooled first to 530 °C with a temperature gradient of
(UV−vis−NIR) have been carried out by making use of both
6
deuterium and halogen lamps integrated in the DH-2000 light-source
from Ocean Optics. Light was collimated and focused on the samples
by a confocal system consisting of a pair of Cassegrain reflecting
objectives (15×). Transmittance of the samples was measured using
the sample in/sample out method and detected with an Ocean Optics
−
1.5 °C/h, then to 450 °C at −2 °C/h, and finally to room tem-
perature at −50 °C/h. The crystals were separated by careful
dissolution of the flux in deionized water. Yellow single crystals of
3
about 1 × 1 × 1 mm were obtained.
2
5−27
USB2000 UV−vis−NIR spectrometer.
the absorption-coefficient spectrum and the energy of the fundamental
band gap (Eg).
From it, we determined
The PbCrO crystals used for the experiments reported here were
4
obtained from natural crocoite minerals provided by Excalibur Mineral
Company. Electron microprobe analysis found that the only impurity
present at a detectable level was iron (0.06%). Crystals were
translucent with a red-orange color, and their dimensions were
3
. OVERVIEW OF THE CALCULATIONS
3
about 10 × 1 × 1 mm .
Powder SrSeO and PbSeO were prepared by precipitation from
The ab initio simulations were performed with the Vienna
4
4
28
aqueous solutions of strontium chloride and sodium selenate, and lead
acetate and sodium selenate, adapting the synthesis described by
Pistorius and Pistorius. The strontium chloride solution was
prepared by the addition of a 2 M HCl solution (13.6 mL) to a
strontium carbonate suspension in water (2.00 g of SrCO in 11.4 mL
of H O). The lead acetate solution was prepared by dissolving the
Ab-initio Simulation Package (VASP) program in the frame-
29
work of density functional theory (DFT). The atomic species
were described with projected-augmented-wave pseudopoten-
2
0
30
tials. The exchange-correlation energy was taken in the
generalized gradient approximation with the PBEsol prescrip-
tion. Because of the presence of oxygen, a cutoff energy of
5
3
2
31
reagent in water (5.14 g of in 25 mL of H O). The sodium selenate
2
20 eV was used in order to obtain accurate results when
solutions were prepared by the addition of water (7.9 mL) and a 2 M
sodium hydroxide solution (13.6 mL) to a commercial 40 wt %
solution of selenic acid (4.91 g). The selenate solution was then added
dropwise to the strontium and lead solutions, and precipitation occurs.
In both cases, the pH of the resulting suspensions was adjusted to be
calculating the valence electronic wave functions expanded in
32
a plane-wave basis set. A dense Monkhorst−Pack special
k-points grid was used for the Brillouin zone (BZ) integrations
in all of our simulations. The k-points sampling and cutoff
energy employed ensure a high convergence, better than 1 meV
per formula unit, in the total energy. The optimized lattice
external and internal parameters at different selected volumes
were obtained for each compound by fully relaxing all of the
internal atom positions and external lattice constants until the
forces on the atoms were lower than 0.006 eV/Å and the stress
tensor was diagonal, with differences smaller than 0.1 GPa
(hydrostatic conditions). Our calculations provided a set of
accurate energy (E), volume (V), and pressure (P) data for
each compound, from which we obtained the crystal structure
at ambient conditions and the P−V equation of state (EOS) for
the studied compounds. The band structure and electronic
density of states (DOS) are also calculated.
The direct method (direct force-constant approach) was
employed to study the lattice vibrations. The lattice-dynamic
simulations of phonon modes were performed at the zone
center (Γ point) of the BZ. The construction of the dynamical
matrix at the Γ point required performing highly accurate
calculations of the forces on the atoms when fixed small
displacements from the equilibrium configuration of the atoms
are considered. The number of needed independent displace-
ments was reduced by using the crystal symmetry. Diagonaliza-
tion of this matrix provided the frequencies of the modes, their
symmetry, and their polarization vectors as well as the
7
−8. The suspensions were then heated at 80 °C for 2 h. The solids
were separated by filtration, washed with cold water, and dried in air.
It was confirmed by powder XRD using Cu Kα radiation that the
PbCrO , SrCrO , and SrSeO samples are single-phased and present
4
4
4
the monazite-type structure (space group P2 /n). Their unit-cell
parameters are in very good accordance with those determined by
Effenberg and Pertlik from single-crystal XRD experiments. On the
other hand, the XRD pattern of PbSeO corresponds to a mixture of a
majority phase, which can be assigned to the monazite-type
structure, and a minority phase, which can be assigned to the
β-PbSeO orthorhombic barite-type structure (space group Pnma).
The description of the orthorhombic structure and its relationship
with the monazite structure have been described in the literature.
There is a group−subgroup relationship between barite and monazite,
and the main difference between them is given by the orientation of
the CrO tetrahedra. A more detailed description of the barite-type
phases of PbSeO and PbCrO is beyond the scope of this work and
1
2
1
4
21
2
2
4
2
3
33
23
4
4
4
23
can be found in the work by Knight. In spite of the phase coexistence
of the synthesized PbSeO4 powder, after dividing it into small
fractions, we have been able to find portions of it in which XRD only
detected the monazite-type phase. These samples were used for the
experiments described here.
Raman experiments were performed for SrCrO , PbSeO , and
4
4
SrSeO in the backscattering geometry using a 532 nm laser with a
4
power of less than 20 mW to avoid sample heating. Laser power
reduction to 5 mW does not produce changes other than an intensity
reduction in the Raman spectra, confirming that sample heating did
B
DOI: 10.1021/acs.inorgchem.5b01135
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Inorganic Chemistry
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Figure 1. (a) Energy−volume curves calculated for PbCrO , SrCrO ,
4
4
PbSeO , and SrSeO . In order to facilitate comparison, the energy
4
4
curve of SeSeO was shifted down by −43 eV, the energy curve of
4
PbSeO was shifted down by −23 eV, and the energy curve of PbCrO
4
4
was shifted down by −10 eV. (b) Unit-cell volume versus pressure for
the four studied compounds.
irreducible representations and the character of the phonon
modes at the Γ point. Temperature effects and zero-point
energy have been included with the vibrational free energy
3
4−37
calculated within the quasi-harmonic approximation.
Finally, the supercell method was used to obtain the phonon
dispersion, phonon density of states (PDOS), and projected
DOS.
4
. RESULTS
We will start describing the results of the XRD experiments.
The structures of these compounds were accurately determined
21
3
decades ago by Effenberg and Pertlik, and we have
confirmed that our samples have the monazite-type structure
and determined the unit-cell parameters. These parameters are
C
DOI: 10.1021/acs.inorgchem.5b01135
Inorg. Chem. XXXX, XXX, XXX−XXX

Inorganic Chemistry
Article
given in Table 1. They agree within 0.5% with those reported in
the literature.
them. We also fitted the energy−volume curves with a Birch−
2
1
38
Murnaghan third-order EOS to determine the bulk modulus
We will now compare our structural calculations with the
experimental results. We have made total energy calculations to
determine the crystal structures of PbCrO , PbSeO , SrCrO ,
and its pressure derivative, two important parameters that
characterized the behavior of the materials under compression.
These parameters are given in Table 3. For PbCrO , the
4
4
4
4
and SrSeO . The equilibrium unit-cell parameters were
4
calculated by minimizing the crystal total energy obtained for
different volumes. The atomic positions at the equilibrium
volume were also calculated. Figure 1a shows the energy−
volume curves for the four compounds. For the equilibrium
volume, the calculated vibrational free energies in the quasi-
harmonic approximation, at 300 K and including the zero-point
energy, are 60.7, 78.5, 115.9, and 135.4 meV/pfu (per formula
unit) for PbSeO , PbCrO , SrSeO , and SrCrO , respectively.
Table 3. Unit-Cell Volume (V ), Bulk Modulus (B ), and Its
0
0
Pressure Derivative (B′ ) Determined Using a Third-Order
0
Birch−Murnaghan EOS To Fit the DFT Results of Figure 1
3
V (Å )
B0 (GPa)
B ′
0
0
PbCrO4
PbSeO4
SrCrO4
SrSeO4
348
360
341
348
51.89
56.75
58.70
57.83
4.92
4.56
4.58
5.08
4
4
4
4
The calculated unit-cell parameters are given in Table 1. The
agreement with the experimental data is excellent. In Table 2,
theoretical bulk modulus (51.89 GPa) is comparable with the
experimental value (56 ± 1 GPa), which was determined with
2
Table 2. Calculated Atomic Positions for Monazite-Type
a
PbCrO , PbSeO , SrCrO , and SrSeO
a second-order Birch−Murnaghan EOS. In our case, if the
second-order EOS is used in the fitting of the energy−volume
curves, the bulk modulus is 53.84 GPa. For the other three
compounds, there are no previous results to compare them
with. According to our calculations, PbCrO (PbSeO ) is more
4
4
4
4
PbCrO4
Pb
Cr
O1
0.2194 [0.22130]
0.2012 [0.20107]
0.2509 [0.2538]
0.1244 [0.1245]
0.0321 [0.0295]
0.3882 [0.3859]
0.1426 [0.14545]
0.1654 [0.16364]
0.0085 [0.0042]
0.3464 [0.3425]
0.0982 [0.0999]
0.2137 [0.2141]
PbSeO4
0.4000 [0.39692]
0.8824 [0.88184]
0.0607 [0.0574]
−0.0146 [−0.0110]
0.6852 [0.6858]
0.7847 [0.7819]
4
4
compressible than SrCrO (SrSeO ), which is consistent with
4
4
O2
39,40
the behavior observed when PbMoO4 (PbWO4)
compared with SrMoO (SrWO ).
is
O3
41,42
4
4
O4
We will now discuss the vibrational properties of the studied
materials. From factor group analysis, it can be established
that the monazite structure presents 36 Raman-active phonons
Pb
Se
0.2157 [0.21598]
0.1948 [0.19595]
0.2365 [0.2397]
0.1163 [0.1196]
0.0255 [0.0252]
0.3826 [0.3806]
0.1479 [0.14932]
0.1644 [0.16362]
0.0029 [0.0057]
0.3440 [0.3396]
0.1090 [0.1102]
0.2081 [0.2083]
SrCrO4
0.4053 [0.40191]
0.8823 [0.88195]
0.0526 [0.0490]
−0.0139 [−0.0142]
0.6796 [0.6851]
0.7871 [0.7881]
(
Γ = 18B + 18A ), 33 IR-active phonons (Γ = 16B + 17A ),
g
g
u
u
O1
O2
O3
O4
and three acoustic phonons (Γ = 2B + 1A ) at the zone center.
The Raman- and IR-active modes have been reported earlier for
u
u
Sr
0.2269 [0.22813]
0.1974 [0.19769]
0.2583 [0.2584]
0.1188 [0.1201]
0.0231 [0.0256]
0.3798 [0.3776]
0.1574 [0.15869]
0.1651 [0.16487]
0.0033 [0.0055]
0.3393 [0.3373]
0.1002 [0.1012]
0.2214 [0.2179]
SrSeO4
0.3980 [0.39806]
0.8860 [0.88691]
0.0597 [0.0562]
0.0018 [0.0024]
0.6917 [0.6981]
0.7848 [0.7881]
Cr
O1
O2
O3
O4
Sr
0.2199 [0.22082]
0.1931 [0.19364]
0.2467 [0.2484]
0.1125 [0.1154]
0.0178 [0.0192]
0.3774 [0.3752]
0.1561 [0.15773]
0.1647 [0.16510]
0.0029 [0.0052]
0.3392 [0.3375]
0.1049 [0.1094]
0.2154 [0.2167]
0.4005 [0.39876]
0.8857 [0.88588]
0.0592 [0.0552]
0.0000 [−0.0004]
0.6868 [0.6935]
0.7859 [0.7872]
Se
O1
O2
O3
O4
a
21
All atoms are at 4e Wyckoff positions. The experimental positions
are also included in square brackets for comparison.
we present the calculated atomic positions and compare them
21
with those obtained from single-crystal XRD. The agreement
between the calculations and experimental results is again
excellent. Both facts indicate that DFT calculations accurately
describe the crystal structures of the four studied compounds,
suggesting that DFT could be a powerful tool to calculate
other physical properties of PbCrO , PbSeO , SrCrO , and
4
4
4
SrSeO . In particular, from the energy−volume curves shown in
4
Figure 1a, we obtained the pressure dependence of the unit-cell
volume. The results we obtained are shown in Figure 1b. It can
be seen that the four compounds have similar compressibilities,
Figure 2. Raman spectra of the four studied compounds. The low-
frequency region is magnified (5×) to better show the modes of this
region, which are the least intense modes.
with PbCrO being the most compressible compound among
4
D
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Inorganic Chemistry
Article
−1
Table 4. Experimental (expt) and Calculated (theory) Raman Modes of All Monazite Compounds (cm ) Including Mode
Assignment
PbSeO4
theory
SrSeO4
theory
SrCrO4
theory
PbCrO4
theory
mode
expt
46
mode
expt
60
mode
expt
mode
expt
Ag
Bg
Ag
Bg
Ag
Bg
Ag
Bg
Ag
Ag
Bg
Bg
Bg
Ag
Bg
Ag
Bg
Ag
46.70
47.40
Bg
Ag
Ag
Bg
Ag
Bg
Bg
Ag
Bg
Ag
Ag
Bg
Ag
Bg
Bg
Ag
Bg
Ag
60.04
69.25
Bg
Ag
Ag
Ag
Bg
Bg
Ag
Bg
Bg
Ag
Ag
Bg
Ag
Bg
Bg
Bg
Ag
Ag
58.37
64.81
Ag
Bg
Ag
Bg
Ag
Bg
Bg
Ag
Ag
Ag
Bg
Bg
Ag
Bg
Bg
Ag
Bg
Ag
43.83
44.60
42
45
48.93
76.39
76.62
79
89
49.83
58.41
59
84.59
84
91.66
52.40
57
62
61.31
93.40
92.16
94
54.77
66.25
66
79
104.47
109.28
112.34
117.62
126.42
127.52
144.30
148.74
167.08
168.75
188.40
197.14
204.84
104
109
106.61
109.68
114.38
119.42
122.69
130.29
155.04
158.74
174.72
184.36
192.13
192.40
197.40
108
61.98
73
79.09
81.80
81
81.59
114
85.13
83
94.80
117
126
99.87
95
99.34
100
127
138
104.41
110.41
121.75
137.56
145.27
146.77
158.08
184.43
185.00
99
107.34
108.51
125.69
129.96
135.20
155.11
182.56
191.53
110
116
136
149
111
125
144
148
167
161
177
181
187
196
211
134
156
171
188
180
195
178
185
Bg
Ag
Ag
Bg
Ag
Ag
Bg
Bg
Ag
Bg
285.40
297.17
327.90
353.24
356.05
371.69
379.50
389.44
399.64
408.35
Bg
Ag
Ag
Ag
Bg
Ag
Bg
Bg
Ag
Bg
295.44
308.91
347.31
365.22
376.69
391.74
391.74
411.72
434.30
440.20
311
328
341
365
377
397
427
448
463
467
Bg
Ag
Bg
Ag
Ag
Bg
Ag
Bg
Bg
Ag
333.60
344.17
349.04
359.88
367.12
389.44
391.84
399.24
423.16
429.10
333
342
350
364
367
376
398
403
424
432
Bg
Ag
Bg
Ag
Ag
Bg
Ag
Bg
Bg
Ag
321.76
335.13
346.51
346.67
353.71
369.96
367.00
375.39
393.97
394.21
327
338
347
359
378
402
407
440
451
479
315
328
358
387
405
413
425
430
437
Ag
Ag
Bg
Ag
Bg
Bg
Ag
Bg
774.34
791.28
791.85
808.23
808.29
809.79
821.44
826.41
Ag
Bg
Ag
Ag
Bg
Ag
Bg
Bg
814.50
821.04
830.14
838.45
845.89
858.76
866.27
870.40
Bg
Ag
Ag
Ag
Bg
Ag
Bg
Bg
901.39
904.16
910.20
933.91
938.72
941.05
959.73
975.61
859
868
Ag
Ag
Bg
Ag
Bg
Ag
Bg
Bg
866.83
877.64
879.78
886.35
894.32
906.46
914.63
922.74
801
825
821
827
832
837
846
860
863
854
871
884
889
900
908
916
894
918
932
951
970
840
856
879
4
3,44
PbCrO , PbSeO , SrCrO , and SrSeO .
However, less than
detected for PbCrO and SrCrO and 28 modes for PbSeO
4 4 4
4
4
4
4
half of the expected Raman and IR modes have been mea-
and SrSeO . A Lorentzian multipeak fitting analysis was used to
identify partially overlapping peaks. The wavenumbers
4
4
3,44
45
sured.
In contrast, for the case of PbCrO , our recent
4
1
7
Raman measurements, performed using state-of-the-art
techniques, found 30 Raman-active modes. Here we report
new Raman experiments for PbSeO , SrCrO , and SrSeO .
determined for the observed Raman modes are summarized
43,44
in Table 4. In those cases, a comparison with the literature
is possible and the agreement is quite good. Table 4 also gives
the theoretically calculated wavenumbers. Calculations also
allowed us to make a mode assignment, which is given in the
table. It can be seen that the agreement between theory and
experiments is excellent in the low-frequency region (below
4
4
4
These results, together with those we previously reported for
4
3,44
PbCrO , will be compared here with previous studies
and
4
our ab initio calculations. Figure 2 shows the Raman spectra of
the four compounds. All of the studied compounds do not have
−1
−1
Raman-active modes from 500 to 800 cm . The Raman modes
in the low-wavenumber region are weaker than the modes in
the high-wavenumber region. For these reasons, we introduced
in the plot a break in the horizontal axis and magnified 5 times
the Raman spectra in the low-wavenumber region to facilitate
identification of the Raman modes on it. The first conclusion
we obtained from the figure is that the four compounds have a
similar overall mode distribution. Ticks in the figure show the
identified Raman modes. A total of 30 modes have been
205 cm ). For the rest of the Raman modes, theory and
experiments agree within 10%. This small discrepancy between
the DFT calculations and experiments has previously been
9
,46
observed in related compounds.
In particular, in the high-
−
1
frequency region (above 750 cm ), the wavenumbers are
underestimated by calculations in selenates and overestimated
in chromates; see Table 4.
The crystal structure of monazite has been broadly discussed
47
in the literature. In our case, it can be viewed as being
E
DOI: 10.1021/acs.inorgchem.5b01135
Inorg. Chem. XXXX, XXX, XXX−XXX

Inorganic Chemistry
Article
3
2,33
−1
Table 5. Experimental (expt)
Assignment
and Calculated (theory) IR Modes of All Monazite Compounds (in cm ) Including Mode
PbSeO4
SrSeO4
theory
SrCrO4
theory
PbCrO4
theory
mode
theory
expt
mode
expt
mode
expt
mode
expt
Au
Bu
Au
Bu
Au
Au
Bu
Bu
Au
Bu
Au
Bu
Au
Au
Bu
50.80
56.37
Au
Bu
Au
Bu
Au
Bu
Au
Au
Bu
Bu
Au
Au
Bu
Au
Bu
75.89
78.29
Au
Bu
Au
Au
Bu
Bu
Au
Au
Bu
Bu
Au
Bu
Au
Au
Bu
74.48
82.19
Au
Au
Bu
Au
Bu
Bu
Au
Au
Bu
Bu
Au
Au
Bu
Au
Bu
48.53
55.77
58.81
98.63
100.84
102.97
114.75
129.86
131.69
140.50
146.30
152.71
159.98
185.39
188.63
200.64
210.78
55.84
74.85
107.81
111.01
119.18
129.49
143.07
148.70
149.90
172.39
176.82
180.02
194.33
208.44
75.52
81.36
77.89
87.13
90.33
93.23
99.90
103.07
106.47
108.44
133.09
145.33
154.87
170.98
178.62
114.91
117.21
121.18
132.66
154.11
157.18
167.98
177.46
Au
Bu
Au
Bu
Au
Bu
Au
Bu
Bu
Au
276.59
279.93
332.06
343.90
359.72
363.75
380.23
382.63
396.84
407.11
Bu
Au
Au
Bu
Au
Bu
Au
Bu
Bu
Au
288.83
290.27
343.40
365.22
376.83
380.43
399.84
400.38
421.26
443.87
Bu
Au
Au
Bu
Au
Au
Bu
Bu
Bu
Au
324.89
331.90
339.13
367.92
375.89
379.16
383.30
397.54
423.86
441.91
Bu
Au
Au
Bu
Au
Au
Bu
Bu
Bu
Au
314.22
318.92
335.37
344.37
351.38
362.42
371.22
379.33
390.37
415.45
350
366
372
394
415
427
381
396
414
425
447
410
431
397
Bu
Au
Bu
Au
Au
Bu
Bu
Au
769.53
773.87
785.18
790.18
807.89
807.89
831.31
835.98
Bu
Au
Bu
Au
Bu
Au
Bu
Au
806.02
806.06
829.31
829.37
841.92
846.35
871.90
877.61
Bu
Au
Au
Bu
Bu
Au
Bu
Au
888.11
892.32
914.57
916.93
934.55
946.45
960.03
969.44
845
855
875
887
912
927
Bu
Au
Bu
Au
Bu
Au
Bu
Au
860.13
871.00
876.04
878.74
885.25
893.75
924.81
929.18
833
858
844
867
884
904
919
820
827
857
905
−
1
composed of [001] chains formed of alternating polyhedral
SrO (PbO ) and SeO (CrO ) tetrahedral units. Therefore, to
between 300 and 475 cm ), and the modes in the bottom of
the table are the internal stretching modes (wavenumbers
9
9
4
4
−
1
a good approximation, the monazite structure can be
considered as composed of two alternating sublattices
separately containing the Sr (Pb) and SeO (CrO ) ions. As
between 750 and 1000 cm ). As expected, the last modes are
the most intense modes in our experiments; see Figure 2. In
particular, the most intense mode is the symmetric stretching
4
4
4
3,44,48
a consequence, the vibrational spectra of monazites have been
Ag mode,
usually named as ν (A ). In our experiments,
the most intense modes are located at 840 cm in PbCrO ,
846 cm in PbSeO , 868−894 cm in SrCrO , and 871 cm
in SrSeO , suggesting that these are the symmetric stretching
1 g
−1
interpreted in terms of internal modes associated with the SeO
4
4
48
−1
−1
−1
(
(
CrO ) tetrahedron, in which the center of mass of the SeO4
4
4
4
CrO ) units does not move, or external modes, when they
4
4
involve movements of both the Sr (Pb) and SeO (CrO ) ions.
A modes of the four compounds. Previously, Scheuermann
4
4
g
4
3,44
The external modes can be divided into translational- and
rotational-like modes, and the internal modes can be classified
as bending and stretching modes. In general, the external
et al.
tentatively made the same mode assignment in
PbCrO4 and PbSeO . On the other hand, these authors
4
−1
proposed the mode at 860−868 cm in SrCrO and 854−
870 cm in SrSeO as the symmetric stretching A mode. In
4
48
−1
modes occur at low wavenumber. In addition, the internal
stretching modes are the most intense modes and occur at the
highest frequencies.
4
g
SrSeO , the second mode agrees with our suggestion for this. In
4
−1
SrCrO , the mode at 868 cm proposed by Scheuermann et al.
4
According to our calculations, we tentatively assigned the
external and internal modes of the four studied compounds.
They are separated by extra rows of space in Table 4. The
modes on the top of the table are the external modes (wave-
numbers between 0 and 210 cm ). The modes in the center
of the table are the internal bending modes (wavenumbers
agrees with one of our candidates for the ν (A ) mode. Note
1
g
that the frequency of this mode is slightly different in monazite-
−
1
−1
type PbCrO (840 cm ), SrCrO (868 cm ), and LaCrO
4
4
4
−
1
49
(830 cm ), which implies that the mode frequency is slightly
sensitive to a change of the nine-coordinated cation (Sr, Cr,
and La). However, the frequency difference from one
−1
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Inorganic Chemistry
Article
Figure 3. PDOSs of (a) PbCrO , (b) SrCrO , (c) PbSeO , and (d) SrSeO .
4
4
4
4
−1
−1
−1
compound to the other is around 3%, while the frequency
(868 cm ) > PbCrO (840 cm ) > LaCrO (830 cm ) and
4
4
difference between the external modes of SrCrO and PbCrO4
the Cr−O average bond distance increases following the
sequence SrCrO (1.626 Å) > PbCrO (1.663 Å) > LaCrO
1.703 Å).
There are in the literature many empirical rules relating the
4
range from 6% to 50%. These facts justify the use of the
internal/external mode model as a first approximation to
describe lattice vibrations in monazites.
It is also interesting to note here than in other chromates,
where Cr is in tetrahedral coordination, that the symmetric
4
4
4
(
55
Raman stretching frequencies to the bond length. One of
55
these is Badger’s rule, which has been found not to adequately
correlate bond distances to stretching frequencies in
stretching A mode is also always the most intense Raman-
g
56
chromates. A more accurate relationship for chromates was
active mode, having frequencies similar to those observed in
56
−
1
50
developed by Weckhuysen and Wachs. They proposed the
following expression for the bond length−stretching frequency
correlation:
monazite-type chromates, e.g., BaCrO (862 cm ), YCrO
4
4
−1
51
−1 52
−1 53
(
863 cm ), Ag CrO (847 cm ), CaCrO (880 cm ),
and NdCrO (844 cm ). This fact is not a mere coincidence
2 4 4
−
1
49
4
but a consequence of the fact that the mode frequency is
basically determined by the Cr−O bond strength, which should
be similar in all chromates discussed here because in all of them
Cr is identically coordinated and the Cr−O distances are
v1 = 13055 exp(−1.6419R)
where ν is in cm− and the Cr−O bond distance, R, in Å.
1
1
−1
Using this expression, we obtained ν = 851 (886) cm for
1
5
4
similar. This is consistent with the fact that the frequency of
PbCrO (SrCrO ). These values differ by less than 2% from the
4
4
the ν (A ) mode decreases following the sequence SrCrO
wavenumbers that we determined experimentally, which
1
g
4
G
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Inorganic Chemistry
Article
support the assignation that we made for the symmetric
stretching mode.
To conclude the discussion on Raman modes, we would
remark that, among the stretching modes, there should be 4 Ag
and 4 B modes, which is in agreement with our mode
g
assignment (see Table 4). In addition, among the bending
modes, there should be 6 A and 6 B modes, which have been
g
g
properly identified in Table 4. Finally, we assigned 9 A and
g
9
Bg external modes for each compound as expected.
From our DFT calculations, we have also determined the
IR-active frequencies for the four studied compounds. To the
best of our knowledge, the only previous study of IR modes
4
3,44
was made by Scheuermann et al.
more than 40 years ago.
In their works, between 4 and 10 modes were reported for the
different compounds. They are summarized in Table 5. In the
table, we also report the calculated frequencies for the 33
IR-active modes, together with their mode assignment. Again,
the modes can be divided into external (13 modes), internal
bending (10 modes), and internal stretching (8 modes). The
three types of modes are separated by dotted lines in the table,
going from external modes in the top (low-wavenumber
region), to internal bending in the center (central-wavenumber
region), and internal stretching in the bottom (high-wavenumber
region). The IR mode distribution in frequencies is qualitatively
similar to the Raman mode distribution. The information
obtained from our calculations and summarized in Table 5 will
allow mode assignment in future experiments. As can be seen in
the table, the agreement between the calculated and measured
IR modes is as good as that for the Raman modes. Therefore,
our calculations can be a good guide in future IR measure-
ments. Note that previous studies did not report any of the
external IR modes.
Figure 4. (Top) Measured absorption spectra (solid lines) and fits
(
dotted lines). (Bottom) Tauc plots used to determine E . The dashed
g
lines show extrapolation of the linear region to the abscissa.
To conclude the discussion of lattice vibrations, we would
comment that, in addition to phonon frequencies at the Γ
point, we have also calculated the PDOSs for the four
compounds, which are given in Figure 3. As can be seen, in
the harmonic approximation, there are no imaginary phonon
branches near the Γ point; therefore, the monazite phase is
dynamically stable. In general, the PDOSs of the four
compounds present three zones separated by two phonon
Table 6. Experimental and Theoretical Values of the Band
Gaps (E ) at Ambient Pressure
g
experiment
compound Eg (eV) Eu (eV)
theory
Eg (eV)
PbCrO4
SrCrO4
PbSeO4
SrSeO4
2.25(5)
2.45(5)
4.30(5)
4.75(5)
0.066(6)
0.083(8)
0.090(9)
0.094(9)
A−Y → Y: 1.6183 Y → Y: 1.7153
Y → Z−Γ: 2.6762 Y → Γ: 2.6860
−1
gaps: one around ≈200−300 cm and another larger one
Y → C: 3.1798
C → C: 3.2832
−1
between ≈400 and ≈800 cm . According to the PDOS, it is
Y → Γ: 3.6182
Γ → Γ: 3.6292
observed that in the low-frequency zone the PDOS is
a
The Urbach energy (E ) determined from the fits to the experi-
u
composed of vibrations of PbO (SrO ) polyhedra and a
9
9
mental results is also included. For the calculations, we have listed the
k points for the top of the valence band and bottom of the conduction
band.
lower contribution by CrO (SeO ) tetrahedra. The inter-
4
4
mediate-frequency zone is mainly due to vibrations from the
tetrahedron with a very small contribution from the PbO9
(
SrO ) polyhedra, while the high-frequency zone is only due to
9
vibrations from CrO (SeO ). In this sense, the vibrational
previously observed in related ternary oxides and seems to be
4
4
1
7,26,27
spectra of the four studied compounds can be interpreted in
terms of modes from the CrO (SeO ) tetrahedra, which can be
related to the presence of defects.
Its nature has been the
57
4
4
subject of considerable debate and is beyond the scope of this
work. This tail overlaps partially with the fundamental
absorption, which makes it hard to conclude whether the
smallest band gap is direct or indirect. In previous works, on the
basis of the large values measured for the absorption coefficient
considered as independent units in the monazite structure.
Thus, our calculations confirm that the phonon modes in the
studied monazites can be classified either as internal (the CrO4
or SeO4 center of mass does not move) or as external
(
movements of CrO or SeO tetrahedra as rigid units).
We will now describe the results of the optical-absorption
of PbCrO , it was assumed that this material was a direct-band-
4
4
4
6
,17
gap material, determining that E was 2.3 eV.
However, the
g
studies. The absorption coefficient (α) of the four studied
compounds at ambient conditions is shown in Figure 4 (top).
The absorption spectrum shows a steep absorption, which
corresponds to the fundamental absorption plus a low-energy
absorption band that overlaps partially with the fundamental
absorption. The low-energy absorption band has been
gradual increase of α (with respect to the photon energy) that
we observed in the four studied compounds suggests an
indirect nature for the fundamental band gap. Therefore, to
determine more accurately the nature of the fundamental band
58
gap, we analyzed the experimental results using a Tauc plot.
We found that for high energies (αhν)1 is proportional to the
/2
H
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Inorganic Chemistry
Article
Figure 5. Band structures of (a) PbCrO , (b) SrCrO , (c) PbSeO , and (d) SrSeO .
4
4
4
4
photon energy (hν), as can be seen in Figure 4 (bottom),
which supports the hypothesis that the four materials are
indirect-band-gap semiconductors. This conclusion is in good
agreement with our band-structure calculations. From the Tauc
plots shown in Figure 4, we estimated Eg for the four
compounds by extrapolating the linear region of (αhν)1 to the
abscissa (blue dashed lines). The obtained values are
summarized in Table 6. The value determined here for
PbCrO [E = 2.25(5) eV] is slightly smaller but consistent
absorption and emission are neglected, the absorption spec-
trum is given by
⎧
⎪
g
(hv−E )/Eu
A e
,
g
hv ≤ E + 2Eu
1
α(hv) = ⎨
/2
2
⎪A (hv − E ) , hv ≥ E + 2E
⎩
2
g
g
u
where the parameters A and A are correlated by imposing that
1
2
4
g
α(hν) should be continuously differentiable. This condition
with the value that we determined previously (E = 2.3 eV). The
g
also determines the E + 2E critical energy, below which
g
u
band gap determined for SrCrO [E = 2.45(5) eV] is consistent
4
g
the Urbach exponential absorption is assumed, where E is the
1
4
u
with the value determined by Yin et al. [E = 2.44(5) eV], sug-
gesting that other studies overestimate the value of Eg.
g
Urbach energy. Assuming the E values determined from the
g
1
3−15
Tauc plots (see Table 6) and using an iterative procedure,
we have fitted the absorption spectra shown in Figure 4 (top).
The fits (red dotted lines) reproduce well the experimental
results (black solid lines), indicating that assuming an indirect
band gap plus an Urbach tail is a reasonable hypothesis to
describe the absorption spectra of the four studied compounds.
In contrast with the chromates, which absorb visible light, we
found that the selenates only absorb UV light and have band
gaps more than 2 eV larger than those in their chromate
counterpart. In addition, in Table 6, it can be seen that the Pb
compounds have a smaller E than the Sr compounds, which is
g
consistent with the observations when PbWO (PbMoO ) is
4
4
From the fits, we have determined E , which is also related to
u
5
9
compared with SrWO (SrMoO ). The reasons for this
4
4
the steepness of the absorption tail. The values obtained are
summarized in Table 6. They are comparable with the values
behavior will be discussed when the results of the electronic
structure calculations are described. Before going into this
discussion, we would mention that the measured absorption
spectra can be well fitted assuming that the low-energy part
of the absorption edges exhibits an exponential dependence
1
7,26
obtained in related ternary oxides.
We will now discuss the results of the electronic structure
calculations. The calculated band structures and DOSs of the
four studied compounds are shown in Figures 5 and 6, res-
pectively. The band structures are qualitatively similar in all
cases. According to calculations, PbCrO , PbSeO , SrCrO , and
6
0
on the photon energy following Urbach’s law and that the
high-energy part can be described by an allowed indirect
transition. Under this assumption and when the phonon
4
4
4
SrSeO4 are indirect-band-gap materials. This fact is in
I
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Inorganic Chemistry
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Figure 6. Total and partial DOSs of (a) PbCrO , (b) SrCrO , (c) PbSeO , and (d) SrSeO .
4
4
4
4
agreement with the conclusion extracted from the Tauc plot
analysis. The calculated band-gap values are summarized in
Table 6. These values underestimated the experimental values
band separated by 0.01 eV, at the Y and Γ points of the BZ.
In this material, the minimum of the conduction band is at the
Γ point of the BZ. Consequently, SrSeO has an indirect band
4
by around 1 eV (0.6 eV) in the selenates (PbCrO ). In the case
gap and a direct band gap, which are nearly degenerated.
We will discuss now the nature and relative magnitude of the
band gaps of the different studied compounds. In order to do
this, we will use the calculated DOSs given in Figure 6. It can be
seen that, in the four compounds, the upper part of the valence
band is dominated by O 2p states. On the contrary, the lower
part of the conduction band is composed primarily of electronic
states associated with the Cr 3d (Se 4s) and O 2p states.
Therefore, as a first approximation, it can be considered that
the band-gap energy of the chromates and selenates is mainly
4
of SrCrO , theory slightly overestimates the band-gap energy
4
(
see Table 6). These discrepancies are typical of DFT
2
6,27
calculations.
In spite of that, the calculated ordering of
the band gaps is given by PbCrO < SrCrO < PbSeO <
4
4
4
SrSeO , which is in agreement with the experiments.
4
Let us describe now in detail the band structures of the
different compounds (Figure 5). One important feature of the
band structures is that, with the exception of PbCrO , the
4
dispersion of the valence bands is relatively small, with
comparable dispersions along different directions. In PbCrO4,
the maximum of the valence band is between the Y and A
points of the BZ and the minimum of the conduction band at
the Y point. Calculations also established that the Y−Y direct
band gap is 0.1 eV higher than the indirect band gap. In
2
−
determined by the molecular electronic structure of the CrO
4
and SeO42 ions in which the hexavalent atom is in a
−
tetrahedral environment. The classical field splitting in the
SeO42 ion is much larger than that in CrO4 ion, which
strongly supports our previous statement. Additional support to
our conclusion comes from the fact that different related
ternary oxides containing Pb (and having related crystal
structures) have band gaps ordered following the sequence
PbCrO < PbMoO < PbWO < PbSeO . That is, the band gap
−
2−
SrCrO , the maximum of the valence band is the Y point of the
4
BZ. On the other hand, the conduction band has two minima
very close in energy, one at the Γ point of the BZ and the other
between the Z and Γ points. Consequently, SrCrO has two
4
4
4
4
4
2
−
2−
indirect band gaps that are separated by only 0.01 eV, as shown
increases as the field splitting increases: CrO < MoO4
<
4
WO42 < SeO4 . Another important fact that can be seen in
Figure 6 is that the Sr states are completely empty near the
Fermi level. Thus, they do not have any influence on the band-
gap energy. On the contrary, in PbCrO and PbSeO , there is a
−
2−
in Table 6. In PbSeO , there are two maxima in the valence
4
band at the Y and C points of the BZ, separated by 0.1 eV.
Additionally, the minimum of the conduction band is also at
the C point of the BZ. Consequently, PbSeO has an indirect
4
4
4
band gap of 3.17 eV and a direct band gap of 3.28 eV. In the
contribution of Pb 6s electrons to the top of the valence band
and of Pb 6p states to the bottom of the conduction band.
fourth compound, SrSeO , there are two maxima in the valence
4
J
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Inorganic Chemistry
Article
As a consequence, the band gap is smaller in the Pb compounds
than in the Sr compounds, as we found in the experiments.
Notice that the same conclusion can be extracted from the
comparison of the band gaps of PbWO (PbMoO ) and
(10) Achary, S. N.; Errandonea, D.; Mun
Hernandez, P.; Manjon, F. J.; Krishna, P. S. R.; Patwe, S. J.; Grover,
̃
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014, 70, 533−538.
SrWO (SrMoO ).
4
4
(
̃
5. CONCLUDING REMARKS
2
We performed an experimental and theoretical study of
PbCrO , SrCrO , PbSeO , and SrSeO that has allowed us to
(
13) Stoltzfus. M. W. Structure−property relationships in solid state
4
4
4
4
materials: A computational approach emphasizing chemical bonding.
analyze the structural, electronic, and vibrational properties of
the four compounds. We found that calculations accurately
reproduce the crystal structure of the four materials. They also
are useful to deepen the understanding of the electronic and
vibrational properties. In particular, calculations have helped us
with the assignment of phonon modes and allowed us to
predict where future experiments might find the as-yet-
unobserved IR-active modes. Finally, the study of the electronic
structure has demonstrated that the studied chromates and
selenates behave as indirect-band-gap materials, with the
chromates having a band gap in the visible and the selenates
a band gap in the UV. Using theoretical calculations, we have
been able to propose an explanation to this fact and also
understand why the Pb compounds have a smaller band gap
than the Sr counterparts.
Ph.D. Thesis, The Ohio State University, Columbus, OH, 2007.
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