Polymorphs of CaSeO4 under Pressure - American Chemical Society

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Polymorphs of CaSeO4 under Pressure: A First-Principles Study of Structural, Electronic, and Vibrational Properties Sinhué López-Moreno,*,† Daniel Errandonea,‡ Plácida Rodríguez-Hernández,§ and Alfonso Muñoz§ †

Centro de Investigación en Corrosión, Universidad Autónoma de Campeche, Av. Héroe de Nacozari 480, Campeche, Campeche 24029, México ‡ MALTA Consolider Team, Departamento de Física Aplicada-ICMUV, Universitad de Valencia, Edificio de Investigación, c/Dr. Moliner 50, Burjassot, 46100 Valencia, Spain § MALTA Consolider Team, Departamento de Física, Instituto de Materiales y Nanotecnología, Universidad de La Laguna, La Laguna 38205, Tenerife, Spain ABSTRACT: In this paper we report a theoretical study of the CaSeO4 compound at ambient pressure and under pressure. Here we made a structural analysis of its three known polymorphsorthorhombic (Cmca), monoclinic monazite, and tetragonal scheelitewhere direct comparison with experimental measurements is done. Besides, the electronic and vibrational structures are reported for the first time for those structures. In addition, the behavior of CaSeO4 as a function of pressure is studied, where phase transitions are investigated by considering a quasiharmonic approximation at 300 K. After a total energy study of 14 possible high-pressure phases of CaSeO4, the following sequence of pressure-driven structural transitions has been found: orthorhombic (Cmca) → tetragonal scheelite → monoclinic AgMnO4-type structure. It was observed that monazite is less stable as temperature increases, while the opposite occurs for the AgMnO4-type structure, this being a novel polymorph. This high-pressure structure is a distortion of the monazite structure and resembles the distorted barite-type structure (P21/n) of CaSO4. The equation of state and the pressure evolution of the structural, electronic, and vibrational properties are also reported. pressure17 and as a high pressure phase of monazite, which remains stable at ambient conditions once the pressure is released.12 On the other hand, according to a recent ambient pressure study of Pristacz et al., CaSeO4 has been synthesized in the monazite and scheelite, but also in an orthorhombic structure.18 It was reported that this orthorhombic structure does not match with the previously reported orthorhombic structure with space group (S.G.) (P212121).17 Instead of it, the new phase has S.G. Cmca. According to ref 18 this structure represents an intermediate atomic arrangement between that of zircon and anhydrite (S.G. Amma, No. 63). These observations and the stereochemical relation among these structures and AgClO4 are well described in the literature.19 Moreover, according to refs 1 and 18, orthorhombic structures with S.G. Cmca have been reported in ABO4 compounds only as highpressure phases of molibdates, tungstates, and vanadates. Regarding other alkaline-earth selenates ASeO4, it was reported that these compounds crystallize in scheelite, monazite, orthorhombic, and barite type structures.14,20 On the other hand, the possible occurrence of phase transitions in related compounds such as CaSO4,15 TiSiO4,21 and APO4 [A = In, Ti]13 has been successfully explored by means of firstprinciples calculations. For CaSO4 the following sequence of

1. INTRODUCTION In the last two decades there has been a large interest in studying ABO4 compounds due to their importance in areas such as earth, planetary, and materials sciences.1 In particular, high-pressure investigations have been growing in order to get a better understanding of the main physical properties of these compounds under hydrostatic or quasi-hydrostatic compression. 2 Much effort has been dedicated to study ABO 4 compounds with structures such as zircon,3 scheelite,4 wolframite,5,6 monazite,7 and barite,8 to name a few. Their structural phase transition sequences driven by pressure were well described within the trends observed in the Bastide’s diagram.1,9,10 However, much less endeavor was dedicated to study the high pressure behavior of orthorhombic type compounds that crystallize in the space groups Cmca and Cmcm,11 such as selenates12 and phosphates,13 respectively. Regarding selenates, only a few compounds are known: ASeO4 [A = Be, Mg, Ca, Sr, Ba, and Ra].14 In contrast with related compounds with a different chalcogen atom, such as CaSO4, for which there are several studies,15 to the best of our knowledge, selenates have been very little studied under compression. Previous experimental studies reported that the dehydrated calcium selenate (CaSeO4) crystallizes in the monoclinic monazite12,16 and tetragonal scheelite12,17 structure types. While the monazite is always synthesized at ambient pressure, the scheelite was obtained by two methods: at ambient © XXXX American Chemical Society

Received: November 10, 2014

A

DOI: 10.1021/ic502690f Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry structural transitions was found: Cmcm → monazite → barite → Pnma → scheelite. For TiSiO4 the sequence Cmcm → zircon → scheelite was observed. Whereas for APO4 compounds the transition path follows Cmcm → zircon → scheelite → wolframite. This suggests that similar calculations can be a good tool to explore the occurrence of phase transition under compression in CaSeO4. While Pristacz et al.18 make a precise description of the crystal structure from the three known polymorphs of CaSeO4, the electronic, mechanical, and vibrational properties of all of them are still unknown. In another way, although Crichton et al.12 study the pressure behavior of CaSeO4 up to 42 GPa, the evolution of some parameters of the structure under pressure, such as lattice parameters and interatomic bond-distances, remains unknown. Therefore, a theoretical high-pressure study of CaSeO4 could be important in order to explore the behavior of the physical properties of this compound at ambient conditions and high pressures. In order to improve the understanding of CaSeO4 and its pressure behavior, in this paper we made a first-principles study of this compound. We investigate the structural, electronic, and vibrational properties of the known ambient pressure polymorphs of CaSeO4. The crystal structure is well described and compared with the available experimental data. The effect of pressure on the electronic and vibrational properties is discussed. Besides, by using the quasiharmonic approximation, we investigate the structural phase transitions sequence as a function of pressure at room temperature. Finally, we explore the stability of the main phases at high-temperatures and highpressure in order to make a good description of the stability of monazite structure, which is the most known polymorph of CaSeO4 compound. The paper is organized as follows: In the next section, we give a detailed description of the computational procedure. The description of the most important polymorphs of CaSeO4 at ambient pressure is presented in Section 3.1, while their structural behavior under temperature and pressure is presented in Section 3.2. The study of the electronic and vibrational properties of CaSeO4 is shown in Sections 3.3 and 3.4, respectively. Finally, we discuss and summarize the main results of this work in Section 4.

type) phases, respectively. Then we follow the pressure evolution of the Gibbs free energy at 300 K to calculate the phase transition. We have also calculated the possible phase transitions at higher temperatures to elucidate the stability of the monazite phase as a function of pressure and temperature against the other low pressure structures.

3. RESULTS AND DISCUSSION 3.1. Ambient pressure crystal structures. As was mentioned above, CaSeO4 occurs at ambient pressure in the monazite, scheelite, and Cmca phases. Figures 1 and 2 show the

Figure 1. Structures of CaSeO4: here the Ca atoms are shown as large blue spheres, Se atoms as medium-size cyan spheres, and O atoms as small yellow spheres.

2. COMPUTATIONAL DETAILS

structure of these phases and the coordination polyhedra of Ca and Se, respectively, whereas Figure 3a shows the energy− volume curves for these three polymorphs of CaSeO4. Our study indicates that Cmca structure has the lowest energy at ambient pressure, followed by scheelite and monazite phases. We will deal with the stability of these phases at different pressures and temperatures in Section 3.2. The equilibrium lattice parameters were calculated by minimizing the crystal total energy obtained for different volumes. These lattice parameters were used to fit a third-order Birch−Murnaghan equation of state (EOS).34 The results for the lattice parameters a, b, and c, the beta angle (β), at ambient pressure, equilibrium volume V0, bulk modulus B0, and bulk modulus pressure derivative B0′ are summarized in Table 1. In the next section we will show that a novel monoclinic polymorph (AgMnO4-type) becomes stable under compression. We also performed the calculations with local-density approximation (LDA)35 and with the GGA Perdew−Burke− Ernzerhof (PBE)36 exchange correlations, and we found that LDA underestimates the equilibrium volume by ≈5% with

Calculations of the total energy were performed within the framework of the density functional theory (DFT) and the projector-augmented wave (PAW)22,23 method as implemented in the Vienna ab initio simulation package (VASP).24−27 We use a plane-wave energy cutoff of 520 eV to ensure a high precision in all our calculations. For the exchange correlation energy, we have used the generalized gradient approximation (GGA) in the AM0528−30 prescription. The Monkhorst−Pack scheme was employed to discretize the Brillouin-zone (BZ) integrations31 with meshes 3 × 1 × 3, 4 × 4 × 2, and 3 × 3 × 2, which correspond to sets of 4, 4, and 6 special k-points in the irreducible BZ for orthorhombic Cmca, tetragonal scheelite, and monoclinic monazite and AgMnO4-type, respectively. In the relaxed equilibrium configuration, the forces are less than 2 meV/Å per atom in each of the Cartesian directions. The high degree of convergence for the calculated forces is required for the calculations of the dynamical matrix using the direct force constant approach (or supercell method).32 To see the temperature effect on the phase transition, we have used the quasiharmonic approximation.33 We get the free energy from the phonon density of states obtained by calculating the phonon dispersion relation in the whole BZ, at several pressures. To do this we have used supercells 2 × 1 × 2 and 2 × 2 × 2 times the conventional unit cell for Cmca and scheelite (monazite and AgMnO4B


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Inorganic Chemistry

The orthorhombic structure Cmca S.G. (No. 64) has four and eight f.u. in the primitive and unit cells, respectively. In this structure the Ca and Se atoms are 8- and 4-fold-coordinated. According to our results, in the CaO8 polyhedra, the Ca−O bond distances range from 2.384 to 2.695 Å, while in the SeO4 tetrahedra all the distances are almost equal with a mean value of 1.661 Å. These results are summarized in Table 2. In this structure Ca, Se, and two O atoms are located in the 8f (0, y, z) Wyckoff position, while the remaining O atom is in the 16g (x, y, z) one. In this structure, chains of alternating CaO8 and SeO4 polyhedra with shared edges run parallel to the respective [001] directions. The CaO8 polyhedra share edges to form rows along the [100] direction, where the arrangement of the CaO8 polyhedra leads to a slight tilt of the SeO4 tetrahedra.18 The monazite phase has a monoclinic structure, S.G. P21/n (No. 14). This structure has been the focus of intense studies due to its occurrence in many ABO4 compounds.7 The unit cell contains four formula units (f.u.), Z = 4; see Figure 1c. In this structure all atoms occupy the 4e (x, y, z) Wyckoff position. In Table 3 the Wyckoff positions of this and other relevant structures are listed. Unlike other ABO47 compounds, where the A cation of monazite has a coordination of 9, in CaSeO4 the Ca(Se) are 8(4)-fold-coordinated to O atoms (see Figure 2), and the CaO8 polyhedra and SeO4 tetrahedra share corners and edges among each other, as shown in Figure 1. The ninth nearest O atom to Ca is located at 3.131 Å, while the values of Ca−O bond distances are in a range from 2.394 to 2.578 Å, with the mean Ca−O bond distance being ⟨Ca−O⟩ = 2.508 Å. The interatomic bond distances Ca−O for the CaO 8 dodecahedra and Se−O for the SeO8 tetrahedra, and the angles O−Se−O for the SeO4 tetrahedra are listed in Table 3. As can be seen in Tables 2 and 3, our results are in very good agreement with the experimental data of ref 18. Scheelite is the name of the mineral CaWO4, which is used to describe the family of all the minerals isostructural to CaWO4. For example, among these compounds are the orthomolybdates and orthotungstates. The scheelite structure is tetragonal with S.G.: I41/a (No. 88). In this structure the primitive unit cell has two f.u., while the unit cell has 4 f.u. In the scheelite structure the Ca and Se atoms occupy S4 sites, whereas the O atoms are in the C1 sites. The Ca atoms are coordinated to eight O atoms forming bisdisphenoids. In this structure there are only two different bond distances of 2.442 and 2.507 Å. The Se atoms

Figure 2. Details of CaOx and SeOx coordination polyhedra for the most representative polymorphs of CaSeO4. The atoms are labeled according to the Wyckoff positions listed in Tables 2 and 3.

respect to experimental values of ref 18, whereas PBE overestimates it by ≈5%. According to the results of Table 1, this value is overestimated by less than 2% with the functional AM05.28−30 Hence, the difference in the lattice parameters with this exchange-correlation functional is reduced to less than 1% with respect to experimental data.

Figure 3. Calculated total energy-volume curves for (a) low pressure polymorphs of CaSeO4, and (b) considered structures for the high pressure range. The inset in (b) shows the most representative phases at high pressures. C


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Inorganic Chemistry Table 1. Lattice Parameters of CaSeO4 at Ambient Pressure (54 GPa for AgMnO4-type structure)a Cmca a (Å) b (Å) c (Å) β (deg) Z V0 (Å3) B0 (GPa) B0′

monazite

scheelite

DFT

Exp.18

DFT

Exp.18

Exp.12

7.262 14.547 6.399

7.192(1) 14.404(2) 6.398(1)

6.872 7.144 6.740 104.36

6.860(1) 7.086(1) 6.692(1) 104.21(1) 4 315.3(1)

6.865 7.077 6.699 104.29

8 662.8(2)

676.0 59.18 5.13

320.5 61.28 4.80

DFT

315.28 69.1(7)

Exp.18

5.073

5.054(1)

11.694

11.678(2)

301.0 77.57 4.93

AgMnO4-type Exp.12

4 298.3(1)

5.04801(11) 11.6644(5)

297.21(3) 84.2(5) 5.00(5)

DFT 6.059 6.327 5.478 90.92 4 210.0

Where a, b, and c are the lattice parameters, V0 the volume at ambient pressure, β the angle of monoclinic structures, Z the number of formula units, B the bulk modulus, and B0′ the pressure derivative of the bulk modulus.

a

Table 2. Interatomic Bond Distances, Ca−O and Se−O, and Angles, O−Se−O, of CaSeO4 (at ambient pressure for Cmca, monazite, and scheelite, and at 54 GPa for AgMnO4-type)a Ca−O dist. (Å)

a

Se−O dist. (Å)

DFT

Exp.18

Ca−O3 (×2) Ca−O2 (×1) Ca−O1 (×1) Ca−O2 (×1) Ca−O3 (×2) Ca−O1 (×1) ⟨Ca−O⟩

2.384 2.436 2.439 2.459 2.493 2.695 2.473

2.367(1) 2.433(1) 2.428(1) 2.453(1) 2.514(1) 2.683(1) 2.470

Se−O1 (×1) Se−O2 (×1) Se−O3 (×2) ⟨Se−O⟩

Ca−O3 (×1) Ca−O4 (×1) Ca−O2 (×1) Ca−O3 (×1) Ca−O4 (×1) Ca−O1 (×1) Ca−O2 (×1) Ca−O1 (×1) ⟨Ca−O⟩

2.394 2.458 2.477 2.513 2.540 2.541 2.562 2.578 2.508

2.411(1) 2.455(1) 2.489(1) 2.584(1) 2.557(1) 2.491(1) 2.580(1) 2.555(1) 2.515

Se−O4 (×1) Se−O1 (×1) Se−O3 (×1) Se−O2 (×1) ⟨Se−O⟩

Monazite P21/n 1.658 1.661 1.664 1.668 1.663

Ca−O (×4) Ca−O (×4) ⟨Ca−O⟩

2.442 2.507 2.474

2.453(1) 2.503(1) 2.478

Se−O (×4) ⟨Se−O⟩

Scheelite I41/a 1.665 1.665

Ca−O4 (×1) Ca−O3 (×1) Ca−O2 (×1) Ca−O1 (×1) Ca−O1 (×1) Ca−O3 (×1) Ca−O1 (×1) Ca−O4 (×1) Ca−O3 (×1) Ca−O4 (×1) ⟨Ca−O⟩

2.134 2.204 2.231 2.243 2.264 2.292 2.311 2.355 2.418 2.455 2.291

Se−O1 (×1) Se−O4 (×1) Se−O3 (×1) Se−O2 (×1) Se−O2 (×1) ⟨Se−O⟩

AgMnO4-type P21/n 1.618 1.648 1.662 1.751 1.850 1.706

O−Se−O angles (deg)

Exp.18

DFT

Exp.18

O3−Se−O3 (×1) O1−Se−O2 (×1) O1−Se−O3 (×2) O2−Se−O3 (×2) ⟨O−Se−O⟩

102.36 103.86 112.15 113.31 109.52

103.19(7) 104.32(7) 111.73(4) 113.06(4) 109.51

1.632(1) 1.637(1) 1.638(1) 1.646(1) 1.638

O3−Se−O4 (×1) O1−Se−O2 (×1) O2−Se−O3 (×1) O1−Se−O4 (×1) O2−Se−O4 (×1) O1−Se−O3 (×1) ⟨O−Se−O⟩

100.93 105.51 107.19 114.07 114.43 114.76 109.48

102.23(6) 105.20(7) 107.22(6) 113.36(7) 114.50(7) 114.46(6) 109.49

1.643(1) 1.643

O−Se−O (×4) O−Se−O (×2) ⟨O−Se−O⟩

106.81 114.93 109.52

107.00(2) 114.53(2) 109.51

O2−Se−O3 O2−Se−O3 O2−Se−O3 O2−Se−O4 O1−Se−O2 O1−Se−O2 O3−Se−O4 O1−Se−O4 O1−Se−O3 O2−Se−O2

79.67 84.85 84.88 87.71 99.34 101.58 113.59 120.75 125.60 158.96

DFT

Orthorhombic Cmca 1.661 1.635(1) 1.661 1.638(1) 1.661 1.636(1) 1.661 1.636

(×1) (×1) (×1) (×1) (×1) (×1) (×1) (×1) (×1) (×1)

The oxygen atoms are labeled according to their Wyckoff positions; we also include their average values.

AgMnO4-type structures and the lattice parameters of the most important polymorphs of CaSeO4 are shown in Figure 4a and b, respectively. In the low range of pressure, up to 6 GPa, we can describe the pressure dependence of lattice parameters by means of linear equations. The axial compressibilities are given by κx = −∂(ln x)/∂P, where x can be any lattice parameter. The values obtained for Cmca (monazite, scheelite) are κa = 4.7 (4.2,

are coordinated by four O atoms with a bond distance of 1.665 Å; see Table 2. According to Table 3 the Ca atoms are located in the 4b (0, 1/4, 5/8) Wyckoff position, while Se atoms are on the 4a (0, 1/4, 1/8), and the oxygen atoms at 16f (x, y, z). In Section 3.2 we will show that a novel monoclinic polymorph (AgMnO4) becomes stable under compression. The pressure evolution of the β angle for the monazite and D


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Inorganic Chemistry Table 3. Wyckoff Positions (WP) for the Polymorphs of CaSeO4 Presented in Table 1a Atom

a

WP

Ca

8f

Se

8f

O1

8f

O2

8f

O3

16g

Ca

4e

Se

4e

O1

4e

O2

4e

O3

4e

O4

4e

Ca Se O

4a 4b 16f

Ca Se O1 O2 O3 O4

4e 4e 4e 4e 4e 4e

x

y

Orthorhombic Cmca 0 0.37537 [0.37523(2)] 0 0.12366 [0.123228(10)] 0 0.21905 [0.21804(8)] 0 0.03991 [0.03912(8)] 0.17823 0.11908 [0.17826(12)] [0.11928(5)] Monazite P21/n 0.279709 0.146933 [0.27892(5)] [0.15117(5)] 0.305748 0.161436 [0.30519(2)] [0.16205(2)] 0.257824 0.829183 [0.2540(2)] [0.00082(18)] 0.395678 0.345890 [0.39112(18)] [0.34361(17)] 0.478562 0.997707 [0.48010(18)] [0.10180(19)] 0.112412 0.208897 [0.11561(18)] [0.21040(19)] Scheelite I41/a 0 0.25 0 0.25 0.13390 0.00777 [0.12915(15)] [0.00902(13)] AgMnO4-type P21/n 0.52563 0.015270 0.38296 0.622410 0.14706 0.858240 0.19108 0.798810 0.85704 0.875300 0.29856 0.892350

z 0.37998 [0.38050(5)] 0.38481 [0.38410(2)] 0.24230 [0.24350(2)] 0.20836 [0.21179(19)] 0.54271 [0.54271(15)] 0.086929 [0.09456(5)] 0.614507 [0.61495(2)] 0.430526 [0.43436(18)] 0.514120 [0.5090(2)] 0.824280 [0.81895(18) 0.712290 [0.71334(18)]

Figure 4. Pressure dependence of (a) β angle and (b) lattice parameters of CaSe4. The experimental data was taken from ref 12.

0.125 0.625 0.20159 [0.20106(6)] 0.75278 0.68648 0.49618 0.99556 0.77768 0.74388

The experimental values are in brackets18.

2.8) × 10−3 GPa−1, κb = 5.6 (5.0) × 10−3 GPa−1, and κc = 3.6 (4.8, 4.9) × 10−3 GPa−1. Similar values for κb and κc of Cmca where observed in the orthorhombic Cmcm phase of InVO4.37 The lattice parameters a and b from Cmca and monazite are almost two times more compressible than in scheelite, while c is more compressible in scheelite followed by monazite and Cmca. In general, the scheelite phase is less compressible than the other phases, which is reflected in the bulk modulus, as can be seen in Table 1, whereas at higher pressures (≈55 GPa) the compressibilities of scheelite (AgMnO4-type) are κa = 1.1 (1.0) × 10−3 GPa−1, κb = 1.1 (0.9) × 10−3 GPa−1, and κc = 1.4 (1.2) × 10−3 GPa−1. It is evident that at higher pressures the scheelite will be more compressible than the AgMnO4-type structure since the phase transition scheelite → AgMnO4-type involves a change in the cation coordination from 8 to 10 (4 to 5) in Ca (Se), which makes the AgMnO4-type phase less compressible. The pressure dependences of the interatomic bond distances Ca−O (Se−O) are show in Figure 5a and b (c and d), where the left panels show these values for the low pressure regime up to ≈5.5 GPa. According to Figure 5 the Ca−O bond distances are more compressible than the Se−O. Figure 5a and c shows that as pressure increases the change in Se−O distances is very small in comparison with the changes in the Ca−O distances. Also, Figure 5a and b helps to demonstrate the distortion

Figure 5. Pressure dependence of interatomic bond distances Ca−O and Se−O. The low pressure range is ilustrated in (a) and (c) for Cmca, monazite, and scheelite phases, while the high pressure range is in (b) and (d) for scheelite and AgMnO4-type structures.

presented in the Ca−O polyhedra of monazite, Cmca, and AgMnO4-type phases in comparison with scheelite. On the other hand, in the SeO4 octhahedra the Se−O bond distances are very similar for the three low pressure polymorphs, while in the SeO5 polyhedra of the AgMnO4-type structure there are differences of up to 0.23 Å in the Se−O distances. To measure the grade of the distortion in the coordination polyhedra, we used the distortion parameter Δd, defined as37 E


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Inorganic Chemistry Δd =

⎛1⎞ ⎜ ⎟ ⎝n⎠

Comparing these results with the bulk modulus reported for scheelite (B0 = 163.4 GPa) and monazite (B0 = 146.0 GPa) of CaSO4,21 a very large difference is found for these structures. In general these two phases of CaSeO4 are more compressible than those from another ABO4 compounds with the same structure.1 On the other hand, the orthorhombic Cmca (B0 = 59.18 GPa) phase of CaSeO4 and the Cmcm (B0 = 63.9 GPa) phase of CaSO4 have very similar values of bulk modulus. However, they are up to 20% smaller than the bulk modulus of other ABO4 compounds with orthorhombic Cmcm type structure, such as APO4 compounds.13 3.2. Phase transitions. As commented previously, there is not much information about the high pressure behavior of CaSeO4. To the best of our knowledge, there are only two high pressure studies of CaSeO4,12,20 which report only some structural parameters of monazite and scheelite phases. In order to go deeper in the understanding of CaSeO4 under pressure to identify possible high pressure phases, besides the Cmca, monazite, and scheelite, we studied several candidate structures at high pressure. By taking into account the Bastide’s diagram and previous studies of ABX4 compounds, we have considered the following structures: barite (S.G.: Pbnm, No. 62, Z = 4), AgMnO4-type (S.G.: P21/n, No. 14, Z = 4), which has been found as high pressure phases of CaSO4,20 β-SnWO438 (S.G.: P213, No. 198, Z = 4), wolframite6,39,40 (S.G.: P2/c, No. 13, Z = 2), and fergusonite41 (S.G.: I2/a, No. 15, Z = 4). Due to the occurrence of CaSeO4 in monazite, we also tried other possible phases with monoclinic structure, such as raspite (S.G.: P21/a, No. 14, Z = 4), and BaWO4-II-type structure (S.G.:P21/n, No. 14, Z = 8), which has been considered as a high-pressure hightemperature postscheelite phase of AWO4 compounds.1 The orthorhombic P212121 (No. 19, Z = 4) observed as a postmonazite phase of PbCrO442 was also considered. Also, the tetragonal structures of KAlF4-type (S.G.: P4/mbm, No. 127, Z = 2) and a superstructure of wolframite (S.G.:P4/nbm, No. 125, Z = 2) were taken into account, as well as the orthorhombic BaMnF4-type (S.G.:A21/am, No. 36, Z = 4) and SrUO4-type (S.G.: Pbcm, No. 57, Z = 4) structures have also been considered as postscheelite phases.13 Finally, we included in our study the decomposition of CaSeO4 under pressure to form CaO43 + SeO3.44 However, we found that the subproducts are not energetically competitive against the polymorphs considered in this work. Figure 3b shows the energy−volume curves of all the mentioned structures. From these curves, the relative stability and coexistence pressures of the phases can be extracted by the common-tangent construction.45 According to this figure the Cmca is the lowest energy structure of all studied polymorphs. From Figure 3b, it is clear that most of the studied crystal structures are not competitive against the Cmca, scheelite, AgMnO4-type, and SrUO4-type structures. Figure 7a shows the pressure evolution of the enthalpy difference, ΔH, for all the structures studied at 0 K. According to the calculations, Cmca is the most stable phase at 0 K. As pressure increases, there is a first transition to the scheelite structure at a very low pressure (1.6 GPa) and then a second phase transition to the SrUO4type structure at 35.7 GPa. Figure 7a shows the ΔH vs P diagram referred to the enthalpy of the scheelite phase. This is in agreement with the experimental results of ref 12. On the other hand, one point to take into consideration in the pressure induced phase transitions at 0 K is the inclusion of the zeropoint energy (ZPE) corrections in the ΔH vsP diagram. In particular, it was demonstrated that ZPE corrections have

⎡ di − d ⎤2 ∑ ⎢⎣ ⎥ d ⎦ i=1 N

where d is the average Ca−O (Se−O) bond distance, di are the individual Ca−O (Se−O) bond distances, and n is the coordination number of the different polyhedra. The pressure evolution of the distortion parameter for CaOx and SeOy polyhedra appears in Figure 6a and b, respectively. As expected,

Figure 6. Pressure behavior of distortion parameter Δd for (a) CaOx and (b) SeOy polyhedra.

the scheelite has less distortion in its octahedron, where the Cmca and AgMnO4-type structures have a distortion almost an order of magnitude higher than the scheelite. In the case of SeOy polyhedra, Δd = 0 for scheelite for all the range of pressure; Δd of Cmca grows with pressure while that for monazite remains almost constant in the range of studied pressure. On the other hand, the distortion in the AgMnO4type structure is much bigger than in monazite and Cmca phases. However, this distortion in the AgMnO4-type structure is reduced as pressure increases. It is noteworthy that monazite and orthorhombic Cmca phases have been synthesized at about 210−220 °C, while scheelite at 70 °C.18 This topic will be treated in detail in Section 3.2. Also, according to our calculations (experiments),18 we found that scheelite has the highest density ρ among the three polymorphs followed by monazite and Cmca structures with the values 4.04 (ρexp = 4.08), 3.79 (ρexp = 3.86), and 3.60 (ρexp = 3.67) g/cm3, respectively. The highest density of scheelite could be explained in terms of the packingefficiency criteria proposed by Bastide.1 Since the ⟨Se−O⟩ bond distances are almost equal for the three polymorphs, as can be seen in Table 2, it follows that the closest packing is due to the CaO8 polyhedra. The bulk modulus of CaSeO4, is experimentally reported only for monazite and scheelite structures. For these structures there is a difference in our calculated bulk modulus of ≈10% with respect to the experimental results; see Table 1. F


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Figure 8. Pressure dependence of the volume for the studied polymorphs of CaSeO4. The experimental data was taken from refs 12 and 18.

phase is not considered in the calculations, the first-order phase transition will be monazite → scheelite at 1.32 GPa with ΔV = 6% (see Figure 8), which is close to the experimental value of ref 12. The pressure evolution of volume for monazite is also in good agreement with the experimental data of ref 12, as can be seen in Figure 8. In order to study in more detail the monazite phase, we have analyzed its behavior with pressure and temperature (up to 700 K). Our results show that as temperature and/or pressure increases, the monazite becomes even less stable than Cmca and scheelite structures. It was observed that at temperature above 350 K the scheelite is still more stable than monazite. The PTG phase diagram shows also that the range of pressure stability of Cmca phase grows with temperature. According to Figure 7b the scheelite phase is stable in a very large range of pressure. Figure 8 shows that our P vs V data are in very good agreement with the experimental results,12 which found that scheelite is stable up to 42.2 GPa. According to Figure 7b, the scheelite should undergo a phase transition to the SrUO4-type structure at 35.4 GPa. However, the phonon spectrum of this phase has many phonon branches with imaginary frequency in several high symmetry points, including the zone center (Γ point) of the BZ. This behavior could suggest that a SrUO4-type phase can be stable at high-pressure and high-temperature, as happens with other scheelite-type compounds, such as BaWO4, where the BaWO4−II phase is stable only at high-temperature and high-pressure.1 This is a clear example that calculations of phonon spectrum are very important in order to describe correctly the stability of high pressure phases. Therefore, our results suggest that CaSeO4 cannot be stable in the SrUO4-type structure at room conditions, which is supported by the experimental results12 that only observe the scheelite phase in this range of high pressure. A similar phenomenon also has been observed in InPO4 and TiPO4.13 Of course, the occurrence of CaSeO4 in this polymorph will have to be verified by future high-pressure, high-temperature experiments. Excluding the SrUO4-type structure, upon further compression, there is a first-order phase transition from scheelite to a monoclinic AgMnO4-type structure at 53.34 GPa; this transition is accompanied by a volume reduction of 4.9%. This monoclinic structure is a distortion of monazite structure. However, as can be seen in the structural data of Tables 1−3, the new phase has significant differences with monazite. The same AgMnO4-type structure was reported for CaSO4 in ref 20.

Figure 7. (a) Enthalpy (at 0 K) and (b) Gibbs free energy (at 300 K) curves as a function of pressure for the most representative polymorphs of CaSeO4.

important effects in compounds such as BiFeO346 and solid rare-gases.47 The procedure to obtain the energy contribution from the quasiharmonic approximation33 and apply these corrections is well documented in refs 45−47. In our study we also have considered the ZPE corrections, and we found the same trend observed in Figure 7a but with a very small difference in the phase transition of ≈0.2 GPa. Hence, we conclude that ZPE correction does not have important effects in the phase transitions presented in CaSeO4 when T → 0 K. Since the above ab initio study was done at 0 K, the temperature effects, in the stability of the structures, were taken into account, as was previously done in other ABO 4 compounds.13,48 We have used the quasiharmonic approximation by means of the calculations of the phonon structure in the whole Brillouin zone. In this way, we calculate the phase transitions at 300 K. However, since most of the structures are not energetically competitive against the previously mentioned phases, we only make the calculations of the phonon spectrum for the Cmca, monazite, scheelite, raspite, SrUO4-type, and AgMnO4-type structures. Hence, in what follows we will discuss the phase transitions with respect to the results obtained at 300 K. At ambient pressure and 300 K, the Cmca remains as the most stable phase, although the monazite structure, reported experimentally, is close in energy at low pressure, as seen in Figure 7b. As pressure increases up to 2.03 GPa, there is a firstorder phase transition from Cmca phase to scheelite phase. This transition involves a volume reduction ΔV = 10.3%; see Figure 8. However, according to X-ray powder diffraction experiments,12 monazite undergoes a first-order phase transition to the scheelite phase at 4.57 GPa with ΔV = 4.5%. If the Cmca G


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Figure 9. Band structure and density of states (DOS in arb. units) of CaSeO4 for (a) Cmca, (b) monazite, (c) scheelite, and AgMnO4-type structures.

Regarding sulfates and selenates, only the optical properties of a few of them have been studied.51,52 This is understandable in the case of selenates, since, as we mentioned previously, only a few structural studies have been reported for these semiconductors. Hence, we will compare our results only with those from other ABO4 isostructural compounds. The calculated crystal structures at ambient pressure from Section 3.1 have been used to obtain the band structure and the density of states (DOS) of each phase. The band structures of the Cmca, monazite, scheelite, and AgMnO4-type structures are plotted in Figure 9 along the high symmetry directions within the Brillouin zones of Figure 10. The primitive (unit) cells of the Cmca and scheelite (monazite and AgMnO 4-type) structures have been used to get the band structure. The DOS was calculated with a dense k-points mesh. According to our calculations, in the Cmca structure the valence-band maxima is located in the Y point, while the conduction-band minima is located at the Γ point. Hence, the CaSeO4 in the Cmca phase has an indirect band gap of Eg = 3.59 eV and a direct gap of 3.84 eV. The valence-band at the Y and Γ points is populated by O 2px and O 2py states, whereas the conduction band at the Γ point is filled with O 2pz, O 2s, and Se 4s states. The monazite phase is the only one among the other polymorphs that behaves like a direct band material with Eg = 3.56 eV. As in the monazite phase of NdVO4,49 the dispersion of the valence band is smaller in comparison with the other phases. However, the monazite of NdVO4 has an

The lattice parameters, Wyckoff positions, and interatomic bond distances for the new AgMnO4-type high pressure phase of CaSeO4 are listed in Tables 1−3. It is important to mention that in the AgMnO4-type structure the Se and Ca atoms are 5and 10-fold-coordinated to O atoms, where the mean Ca−O bond distance is ⟨Ca−O⟩ = 2.291 Å, significantly smaller than the values for the other phases at ambient pressure. Note that in the ΔH vs P diagram of Figure 7a the raspite and AgMnO4type structures have almost the same energy; however, at 300 K the AgMnO4-type is clearly lower in energy than raspite (see Figure 7 b). At 0 K the AgMnO4-type phase is stable up to 65 GPa, which is the highest pressure reached in this study. The PTG phase diagram shows that as temperature increases the scheelite → AgMnO4-type transition occurs at higher pressure; for example, at 700 K this transition takes place at 54.7 GPa. 3.3. Electronic properties. Firs-principles calculations have demonstrated to be an efficient tool to study, in a systematic way and in conjunction with experiments, the electronic structure and the pressure behavior of some ABO4 compounds.1,6,49,50 It was found that these compounds are wide-gap semiconductors with band gap energies in a range from 2 to 5 eV, in good agreement with experiments.1,6,49,50 Although the gap energy values are underestimated by calculations in comparison with experiments, in general, the sign of the pressure coefficients and the order of magnitude are in agreement. H


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3.4. Vibrational properties. To the best of our knowledge, there is not a previous study of Raman or infrared spectroscopy of CaSeO4. In contrast, there are some reports about the Raman and infrared spectra of CaSeO4·nH2O.55,56 On the other hand, there are some reports of vibrational properties under pressure for similar compounds to CaSeO4, such as CaSO457 and PbSO4,58 which identified the phase transitions driven by pressure with the help of Raman spectroscopy. Here, the frequencies of the Raman and IR active modes for the Cmca, monazite, scheelite, and AgMnO4-type structures have been calculated as well as their pressure dependences. Our results could be considered as a guide for future experimental or theoretical studies of selenates under pressure. The phonon spectrum and phonon density of states (PDOS) for the ambient pressure polymorphs and the AgMnO4-type structure at 54 GPa are given in Figure 11. We have used the primitive unit cell of the polymorphs and the same path of special k-points used in the electronic structure calculations of the previous section. As can be seen, the monazite phase presents, in the harmonic approximation, an imaginary phonon branch near the Γ point, which suggests that the monazite phase is not dynamically stable. This behavior was also observed at elevated pressures. It is noteworthy that the phonon spectra for the three polymorphs have been calculated in all the studied ranges of pressure. In general, the PDOS of the three ambient pressure phases present three zones separated by two phonon gaps: one around ≈300 cm−1 and other larger one between ≈490 and ≈810 cm−1. According to the PDOS, it is observed that in the first zone the PDOS is composed of vibrations of CaO8 dodecahedra and a lower contribution by SeO4 tetrahedra. The second zone is mainly due to vibrations from the tetrahedron with a very small contribution from the dodecahedron, while the third zone is only due to vibrations from SeO4. In this sense, the vibrational spectra of ABO4 compounds can be interpreted in terms of modes from the SeO4 tetrahedra, which can be considered as independent units in the structures. Thus, the phonon modes can be classified either as internal (the SeO4 center of mass does not move) or as external (movements of SeO4 tetrahedra as rigid units). The translational modes (T) and the rotational modes (R) are considered to be external modes of the SeO4 tetrahedra. The internal modes of the SeO4 tetrahedra are ν1 (symmetric stretching), ν2 (symmetric bending), ν3 (asymmetric stretching), and ν4 (asymmetric bending).13 The T modes are usually the lowest in frequency, the νx modes are the highest in frequency, and the frequencies of the R modes are between those of the T and νx modes. According to the group theory, the orthorhombic Cmca low pressure phase has the following Raman and infrared active phonon modes at zone center Γ = 11Ag + 7B1g + 7B2g + 11B3g and Γ = 10B1u + 10B2u + 6B3u, respectively. The calculated Raman and infrared frequencies at the Γ point for this and the other phases at ambient pressure appear in Tables 5 and 6, respectively, where the frequencies are listed according to the classification of the previous paragraph. Also, the pressure coefficients, dω/dP, and Grüneisen parameters, γ = −∂(ln ω)/ ∂(ln V), are also listed in the tables. This phase presents several Raman and infrared phonon frequencies with negative pressure coefficients, specifically, four Raman modes, 2B1g and 2B2g, and 3 infrared modes, 1B2u and 2B3u. This negative shift can be related with the instability of this phase under pressure to promote the phase transition to the scheelite phase. The negative pressure coefficients range from −0.23 to −2.12 cm−1/

Figure 10. Brillouin zones for (a) orthorhombic Cmca, (b) monoclinic monazite and AgMnO4-type, and (c) tetragonal scheelite. The figure shows the high symmetry points used in the band structure and phonon spectrum.

indirect band gap Eg = 3.3 eV at ≈6 GPa.49 For scheelite, the valence band maxima is located at Δ (a point between Γ and X) and the conduction-band minima at Γ. In contrast, other ABO4 scheelites49 are direct band gap materials. In the case of the AgMnO4-type phase the band gap is from the Y to Γ point with a value of 2.92 eV. This value is quite different from the value of the other phases at room pressure; see Table 4. Table 4. Calculated Gap Energy, Eg, and Its Pressure Dependence, for CaSeO4 Phase

Pressure (GPa)

Cmca monazite scheelite AgMnO4-type

ambient ambient ambient 54

Eg (eV) 3.5923 3.5564 3.4751 2.9272

(Y − Γ) (Γ − Γ) (Δ − Γ) (Y − Γ)

dEg/dP (meV/GPa) 29.3 31.4 34.5 5.6

The valence-band maxima of monazite, scheelite, and AgMnO4-type phases are mainly filled by O 2px and O 2py states with a minor contribution of O 2pz states, while the conduction-band minima are populated by 4s from Se and 2s with a small contribution from 2px, 2py, and 2pz states from O. Note that in other ABO4 compounds, the valence-band maxima are occupied by O 2p states, as happens in CaSeO4. However, in most ABO4 compounds, where B is a transition metal, the valence-band minima are filled with d states, as in wolframates1,6,53 and vanadates.49 We also calculated the effect of pressure on the gap energy for the studied phases. The variation of the band gap with pressure, dEg/dP, for all phases is positive, and the values are listed in Table 5. The order of dEg/dP is similar to that observed in other ABO4 compounds,1,6,21,49,53 with the exception that in CaSeO4 these values are positive for the low and high pressure phases. We have to mention that, as pressure increases, in the scheelite phase the valence-band maxima is moving from Δ to the Γ point, and that the energy difference among these points is very small; so that at ≈23.5 GPa the scheelite CaSeO4 has a direct band gap. Another point to have in mind is that as the gap of the scheelite phase is Eg = 4.57 at 54 GPa, we can predict a large-gap collapse at the scheelite → AgMnO4-type transition, PT = 54 GPa, of ΔEg ≈ 1.6 eV. This collapse in the gap is associated with the reduction in the volume at a phase transition. We would like to remark that the band gap values here reported for the different polymorphs of CaSeO4 are within the energy range that can be covered by high-pressure experiments,6,49,54 and therefore, they can be tested easily by future experiments. I


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Table 5. Calculated Raman Frequencies, ω (cm−1), Pressure Coefficients, dω/dP (cm−1/GPa), and Grünesien Parameters, γ, for CaSeO4 at Ambient Pressure (at 54 GPa for AgMnO4-type) in the Γ Point Cmca B1g B3g B3g B2g Ag Ag B2g B2g B1g Ag B3g B1g B3g Ag B2g B1g Ag B3g B1g B2g B1g Ag B3g B3g Ag B2g B3g Ag B1g B3g Ag B3g B2g Ag Ag B3g

monazite

ω

dω/dP

γ

57.18 89.63 97.41 99.27 113.32 117.69 121.06 144.44 144.51 145.41 152.58 165.79 167.79 204.68 214.36 227.34 227.67 240.04 253.49 293.22 342.79 361.83 392.26 396.46 399.76 401.66 457.87 458.81 826.01 835.79 839.76 850.06 854.33 858.24 865.87 880.02

−1.04 2.29 0.24 −2.12 2.80 2.23 −0.69 0.98 2.53 5.33 7.37 2.96 7.66 10.97 10.12 7.13 5.54 5.56 0.47 0.99 −0.88 2.47 1.41 2.94 1.17 1.63 3.31 2.65 6.98 6.91 5.08 3.74 6.71 6.87 5.42 7.49

−1.21 1.61 0.17 −1.41 1.55 1.20 −0.37 0.44 1.11 2.27 2.95 1.13 2.80 3.26 2.90 1.96 1.53 1.46 0.11 0.22 −0.17 0.44 0.23 0.48 0.19 0.26 0.46 0.37 0.54 0.53 0.39 0.28 0.50 0.51 0.40 0.54

Bg Ag Ag Bg Bg Ag Bg Ag Bg Ag Ag Bg Bg Ag Ag Bg Bg Ag Bg Ag Ag Ag Bg Ag Bg Bg Ag Bg Bg Ag Ag Ag Bg Ag Bg Bg

scheelite

ω

dω/dP

γ

75.56 86.10 100.91 109.08 117.49 118.65 130.10 130.50 132.70 152.31 157.65 168.29 176.00 180.83 187.74 197.28 218.53 226.53 301.89 321.34 347.09 366.44 375.04 395.93 402.23 425.92 448.20 456.37 824.48 827.15 827.85 836.15 853.93 865.94 871.11 879.35

−3.24 1.06 2.12 1.25 2.72 1.77 0.95 2.67 3.27 3.99 5.22 7.30 6.25 3.27 8.50 7.91 7.03 5.51 2.14 1.37 3.12 1.77 3.81 2.54 1.59 2.81 1.99 2.29 4.63 4.49 5.40 5.70 4.53 4.67 5.39 5.10

−3.18 0.84 1.40 0.78 1.53 1.00 0.50 1.36 1.63 1.72 2.15 2.79 2.30 1.21 2.89 2.58 2.10 1.61 0.48 0.29 0.61 0.33 0.69 0.43 0.27 0.45 0.30 0.34 0.38 0.37 0.44 0.46 0.36 0.37 0.42 0.39

T(Bg) T(Eg) T(Eg) R(Ag) T(Bg) R(Eg) ν2(Ag) ν2(Bg) ν4(Eg) ν4(Bg) ν3(Eg) ν1(Ag) ν3(Bg)

GPa, while the positive values are from 0.24 to 10.97 cm−1/ GPa. The increase of frequency in these and the high-frequency modes could be related with the distortion in the SeO4 tetrahedra as pressure increases; see this distortion in Figure 5b. The pressure evolution of the Raman and infrared phonon modes is illustrated in Figure 12. The frequencies in the low range of pressure are plotted in Figure 12a, b, c, e, f, and g to compare the frequencies of the ambient polymorphs, while Figure 12d and h shows the pressure dependence in the highpressure range for scheelite and AgMnO4-type structures. The monazite phase presents 36 Raman (Γ = 18Bg + 18Ag) and 33 infrared (Γ = 16Bu + 17Au) active phonon modes at the zone center. This phase has only one Bg Raman active mode that softens with pressure. Figure 12 shows how the frequency values of the monazite phase are almost in the same range as the Cmca phase. The scheelite structure has 13 Raman (Γ = 3Ag + 5Bg + 5Eg) and 8 infrared (Γ = 4Au + 4Eu) activate modes at the zone center. In this phase, one Au infrared mode has a negative shift upon compression, as seen in Figure 12g and h. We have calculated the phonon spectrum and PDOS for all the range of pressure stability, and we found that scheelite is

AgMnO4-type

ω

dω/dP

γ

140.44 141.04 180.53 197.95 198.61 253.79 331.78 362.87 417.54 435.46 816.34 819.41 838.22

0.74 1.13 3.04 2.50 5.44 4.17 2.45 2.21 3.05 2.81 3.94 3.32 3.42

0.66 0.97 1.85 1.45 2.72 1.82 0.89 0.74 0.88 0.79 0.60 0.51 0.51

Ag Bg Bg Ag Ag Ag Bg Ag Ag Bg Ag Ag Bg Bg Bg Ag Bg Ag Bg Ag Ag Bg Bg Bg Ag Bg Bg Ag Bg Ag Ag Bg Ag Bg Ag Bg

ω

dω/dP

γ

142.21 141.91 183.27 194.28 226.50 251.45 270.00 275.97 300.32 316.47 326.78 356.70 358.23 367.14 379.45 399.63 407.03 426.65 444.46 448.33 486.83 511.95 528.76 547.27 575.69 615.72 649.25 693.58 793.82 837.32 891.83 906.61 934.76 951.14 967.98 988.27

0.84 0.79 0.66 0.63 1.18 0.43 0.76 0.86 1.68 1.55 1.73 1.79 0.96 2.11 1.87 1.72 1.49 1.99 2.21 1.93 2.81 2.08 1.88 2.17 2.32 2.47 2.14 2.46 1.75 2.51 1.90 1.69 1.93 2.14 2.07 2.08

1.83 1.72 1.11 1.01 1.61 0.52 0.87 0.96 1.72 1.51 1.63 1.55 0.83 1.77 1.52 1.33 1.13 1.43 1.53 1.32 1.77 1.25 1.09 1.21 1.24 1.23 1.01 1.09 0.67 0.92 0.65 0.57 0.63 0.69 0.66 0.64

dynamically stable in the whole BZ. In this phase all Raman modes shift to higher frequencies upon compression. Note that the slopes of two Au infrared phonon modes change their sign at ≈23 GPa, which coincide with the change from indirect to direct band gap in the scheelite phase. It is also noticeable that almost all phonon modes from the scheelite phase show a nonlinear behavior with two main regions with different pressure coefficients: one from ambient pressure to ≈10 GPa and a second from ≈10 to 50 GPa. The values of dω/dP from Tables 4 and 6 correspond to the first zone. Note that highfrequency phonons (internal modes, νx) present an almost linear behavior under pressure, which is related with the zero distortion of the SeO4 octahedra observed in Figure 5b. Regarding the AgMnO4-type structure, it has the same phonon representations as the monazite structure at the Γ point. In this phase the lower phonon branches are more dispersive than in the other phases. Also, in its phonon spectrum the phonon branches fill the first gap at ≈300 cm−1 and almost fill the upper phonon gap observed in the other polymorphs. We found that all the Raman and almost all the J


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Figure 11. Phonon spectrum and phonon density of states (PDOS in arb. units) of CaSeO4 for (a) Cmca, (b) monazite, (c) scheelite, and AgMnO4type structures.

Figure 12. Pressure dependence of the Raman and infrared phonon frequencies in the low [(a), (b), (c), (e), (f), and (g)] and high [(d) and (h)] pressure regimes of CaSeO4.

infrared modes harden upon compression. Here only one Bu infrared mode has a negative pressure dependence. K


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Table 6. Calculated Infrared Frequencies, ω (cm−1), Pressure Coefficients, dω/dP (cm−1/GPa), and Grünesien Parameters, γ, for CaSeO4 at Ambient Pressure (at 54 GPa for AgMnO4-type) in the Γ Point Cmca B2u B1u B3u B1u B2u B3u B2u B1u B1u B3u B2u B3u B3u B2u B1u B2u B1u B1u B2u B3u B2u B1u B2u B1u B1u B2u

monazite

ω

dω/dP

γ

113.35 114.68 121.66 140.30 164.19 180.20 181.17 185.90 233.81 234.74 254.72 271.70 338.68 354.63 356.43 390.99 408.17 437.49 462.24 827.98 833.82 835.79 840.56 842.12 872.21 892.76

0.82 3.64 −0.44 8.74 3.96 3.97 12.0 7.09 5.21 8.03 6.57 0.40 −1.12 −0.23 0.33 2.78 2.95 2.64 2.59 6.93 5.88 3.99 5.37 7.64 5.86 6.30

0.47 1.99 −0.24 3.75 1.52 1.39 4.00 2.36 1.40 2.13 1.62 0.10 −0.22 −0.04 0.06 0.46 0.46 0.39 0.36 0.53 0.45 0.31 0.41 0.58 0.43 0.45

Bu Au Au Au Bu Bu Au Bu Au Bu Au Bu Au Au Bu Bu Au Au Bu Au Bu Au Bu Bu Au Au Bu Au Bu Bu Au Bu Au

scheelite

ω

dω/dP

γ

79.23 93.40 107.91 118.75 136.13 150.48 152.35 167.56 173.60 175.23 181.73 195.48 197.35 212.42 223.13 289.35 294.22 340.69 365.67 380.58 386.65 410.04 412.31 433.49 461.38 813.44 814.87 828.18 831.08 837.52 841.39 873.81 881.55

1.75 1.25 3.72 2.42 0.93 0.93 5.13 7.30 4.05 6.92 6.24 6.95 6.57 6.56 4.63 1.79 1.32 0.21 2.72 2.75 2.93 2.91 2.63 1.64 2.53 4.97 5.19 3.97 4.13 5.05 5.64 5.08 5.20

1.46 0.91 2.24 1.35 0.47 0.43 2.19 2.80 1.55 2.55 2.23 2.31 2.16 2.02 1.38 0.42 0.30 0.04 0.51 0.49 0.51 0.48 0.43 0.26 0.37 0.42 0.43 0.33 0.34 0.41 0.45 0.40 0.40

T(Eu) T(Au) R(Eu) ν4(Au) ν4(Eu) ν2(Au) ν3(Au) ν3(Eu)

4. CONCLUSIONS

AgMnO4-type

ω

dω/dP

γ

146.88 163.42 219.10 310.06 386.55 432.85 800.33 821.68

0.48 4.36 4.75 −0.21 1.75 3.86 3.80 3.50

0.43 2.66 2.28 −0.10 0.56 1.06 0.59 0.53

Au Au Bu Au Au Au Bu Bu Au Bu Bu Au Au Bu Au Bu Au Au Bu Bu Bu Bu Au Au Bu Bu Au Au Bu Au Bu Bu Au

ω

dω/dP

γ

176.46 192.58 198.55 232.11 258.69 276.57 283.74 306.36 317.97 317.27 349.86 351.36 374.78 418.91 434.49 441.59 455.04 492.10 489.30 502.91 551.31 603.81 636.17 660.82 684.51 771.91 831.12 874.55 904.84 931.76 944.07 978.89 985.80

0.81 0.21 −0.30 0.87 0.72 1.18 1.03 0.83 1.35 0.76 1.89 1.89 2.26 2.19 2.66 2.60 1.97 2.49 1.47 2.11 2.22 1.57 2.66 1.97 2.72 2.22 2.58 1.69 1.91 1.82 2.14 2.12 1.98

1.19 0.32 −0.45 1.28 1.07 1.73 1.51 1.22 1.98 1.11 2.78 2.77 3.32 3.22 3.90 3.82 2.88 3.65 2.15 3.09 3.26 2.31 3.90 2.89 3.99 3.26 3.78 2.48 2.81 2.67 3.13 3.11 2.91

structure. Furthermore, we present a discussion of lattice dynamics and electronic structure under pressure. We expect this study to encourage theoretical and experimental researchers to investigate the structural, electronic, and vibrational properties of ASeO4 compounds at room conditions and under pressure.

We performed first-principles calculations on CaSeO4 at ambient pressure to study the very recently reported polymorphs of this compound. For them we have analyzed the structural, electronic, and vibrational properties, and determined that Cmca is the lower energy structure at ambient pressure. It was also determined that the phonon spectrum of monazite presents a branch with imaginary phonon frequency. This fact is further associated with the instability of this phase as pressure and temperature increases. The study of electronic structure demonstrates that the ambient pressure and the HP polymorphs are wide-gap semiconductors with band gap energy values around 3.5 eV. Among them only the CaSeO4 in the monazite phase behaves like a direct band gap material. We also study the high pressure behavior of CaSeO4 up to 65 GPa, for which we have determined the phase transition sequence at 300 K: Cmca → scheelite → AgMnO4-type. The AgMnO4-type resembles the high pressure phase of CaSO4. Our results suggest that monazite can be a metastable phase at ambient pressure; this could be the reason for the imaginary phonon branch near the Γ point. It was also observed that monazite becomes more unstable as pressure and temperature increases, while the opposite occurs for the AgMnO4-type

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interests.

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ACKNOWLEDGMENTS The authors acknowledge the MICINN of Spain under Grant Nos. MAT2010-21270-C04-01/03 and CSD2007-00045, and the financial support from the Spanish MCYT through Grants MAT2010-21270-C04-01 and MAT2013-46649-C4-1/3-P. This work is also supported by Generalitat Valenciana (GVA/ACOMP/2014/243). The support from CONACyT México under the program of CATEDRAS for young researchers is also acknowledged. We acknowledge the computer time provided by the RES (Red Española de Supercomputación) and the MALTA cluster. L


Article

Inorganic Chemistry

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