Article Cite This: Inorg. Chem. XXXX, XXX, XXX−XXX
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High-Pressure Single-Crystal X‑ray Diffraction of Lead Chromate: Structural Determination and Reinterpretation of Electronic and Vibrational Properties Javier Gonzalez-Platas,† Alfonso Muñoz,‡ Placida Rodríguez-Hernández,‡ and Daniel Errandonea*,§
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†
Departmento de Física, Instituto Universitario de Estudios Avanzados en Física Atómica, Molecular y Fotónica (IUDEA) and MALTA Consolider Team, Universidad de La Laguna, Avda. Astrofísico Fco. Sánchez s/n, E-38206 La Laguna, Tenerife, Spain ‡ Departamento Física, Malta Consolider Team and Instituto de Materiales y Nanotecnología, Universidad de La Laguna, 38206 La Laguna, Tenerife, Spain § Departamento de Física Aplicada-ICMUV, Universidad de Valencia, MALTA Consolider Team, Edificio de Investigación, C. Dr. Moliner 50, 46100 Burjassot, Spain S Supporting Information *
ABSTRACT: We have investigated the high-pressure behavior of PbCrO4. In particular, we have probed the existence of structural transitions under high pressure (at 4.5 GPa) by single-crystal X-ray diffraction and density functional theory calculations. The structural sequence of PbCrO4 is different than previously determined. Specifically, we have established that PbCrO4, under pressure, displays a monoclinic−tetragonal phase transition, with no intermediate phases between the low-pressure monoclinic monazite structure (space group P21/n) and the high-pressure tetragonal structure. The crystal structure of the high-pressure polymorph is, for the first time, undoubtedly determined to a tetragonal scheelite-type structure (space group I41/a) with unit-cell parameters a = 5.1102(3) Å and c = 12.213(3) Å. These findings have been used for a reinterpretation of previously published Raman and optical-absorption results. Information of calculated infrared-active phonons will be also provided. In addition, the pressure dependence of the unit-cell parameters, atomic positions, bond distances, and polyhedral coordination are discussed. The softest and stiffest direction of compression for monazite-type PbCrO4 are also reported. Finally, the theoretical pressure dependence of infrared-active modes is given, for the first time, for both polymorphs.
1. INTRODUCTION A decade-long effort has been dedicated by several research groups around the world to study the high-pressure (HP) behavior of chromates with formula ACrO4. The interest in their HP conduct is many-fold, going from Earth to material sciences.1,2 Several articles have been published reporting structural phase transitions and discussing the influence of compression on the electronic, magnetic, and vibrational properties of these compounds.3−18 In particular, barite-type BaCrO4 has been studied by means of ab initio calculations, Raman spectroscopy, and powder X-ray diffraction up to 50 GPa.3−5 A phase transition has been reported near 27 GPa, and the crystal structure of the HP phase determined.4 Interestingly, the existence of two soft-mode phonons has been found in the HP polymorph indicating that it is unstable at pressures higher than those achieved in the experiments.4 In the case of YCrO4 and lanthanide chromates,6−11 a nonreversible phase transition from the ambient-pressure (AP) zircon-type structure to the HP scheelite-type structure occurs at pressures as low as 5 GPa.6 The transition involves a large © XXXX American Chemical Society
volume collapse, and a complete reorganization of the crystalline structure, which trigger drastic changes in both the magnetic and electronic properties.6−11 A similar phase transition has been found in CaCrO4 but at a pressure close to 10 GPa.12,13 In contrast with the above-mentioned compounds, in which only one phase transition is known, monazite-type chromates (i.e., SrCrO4 and PbCrO4) show a remarkable complex structural sequence under HP.14−18 In SrCrO4, successive phase transitions occur at 9, 14, 35, and 48 GPa.14,15 They cause changes not only in the crystal structure but also in the vibrational and transport properties. The transition at 9 GPa is from the monazite-type to a scheelite-type structure and involves a band gap collapse.14,15 On the other hand, in PbCrO4 the HP structural is apparently different. In particular, an intermediate phase has been found to exist between the monazite- and scheelite-type polymorphs.16,17 This intermediReceived: January 30, 2019
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DOI: 10.1021/acs.inorgchem.9b00291 Inorg. Chem. XXXX, XXX, XXX−XXX
Article
Inorganic Chemistry
Figure 1. Images of a section of the reciprocal space in the (hk0) plane of monazite PbCrO4 (left) and scheelite PbCrO4 (right) at 0.6 and 4.5 GPa, respectively. The drastic changes of the patterns indicate the occurrence of the phase transition. In both figures, the origin of the reciprocal space is at the center. b* and a* makes a 77.6° (90°) angle in monazite (scheelite). c* is the same for both (perpendicular to the shown plane). Single-crystal XRD experiments were performed using a BraggMini diamond-anvil cell (DAC) from Almax-EasyLab, with an opening angle of 90° and anvil culets of 500 μm in diameter. To use as a pressure chamber, we employed a stainless gasket preindented to a thickness of 75 μm with a 200-μm-diameter hole in the center. Two independent experiments were performed giving reproducible results. In one experiment (run 1), a methanol− ethanol−water mixture (16:3:1) was used as a pressure-transmitting medium; in the other experiment (run 2), methanol−ethanol (4:1) was employed. Both media remain nearly quasi-hydrostatic in the range of pressure used for the experiments.24,25 The sample was loaded in the center of the gasket hole, and its thickness guarantees that there was no sample bridging between diamonds in the complete pressure range covered by the experiments. Pressure was determined with an error of 0.04 GPa by means of the ruby fluorescence method.26 There was no detectable broadening of the ruby lines up to the highest pressure covered by the experiment, which suggests that nonhydrostatic effects were negligible. HP-XRD experiments up to 6.28(4) GPa were performed using a Rigaku SuperNOVA diffractometer equipped with an Eos chargecoupled device (CCD) detector and a Mo radiation microsource (λ = 0.71073 Å). The CrysAlisPro27 software was used to collect, index, scale, and apply a Gaussian absorption correction based on the method of Burnham used in the ABSORB program28 in order to take the sample and DAC considerations into account. The structure of the compound was determined by a dual-space algorithm, using the SHELXT program,29 and refinement was performed using the SHELXL program30 against F2 by a full-matrix least-squares refinement. Because of limitations of the opening angle of our DAC, it is only possible to collect ∼60% of the total reflections present in a full dataset under ambient conditions for the monoclinic low-pressure phase. The number of reflections increases up to 70%− 78% for tetragonal high-pressure phase. Structure refinements were performed anisotropically displacement parameters except for oxygen atoms in the last two HP experiments due to a gradual deterioration in the quality of data. No restraints were used during this process. One Raman experiment was performed for the scheelite-type polymorph at 5.3 GPa in order to confirm the presence of this polymorph and for reinterpretation of previously published results.18 The experiment was executed with a DAC setup similar to the one used in the XRD experiments. A methanol−ethanol−water mixture (16:3:1) served as the pressure medium, and the pressure was determined using the ruby scale.26 The Raman measurement was made in the backscattering geometry, using a Horiba Yvon Jobin LabRam spectrometer and a 632 nm laser with a power of c) differs from the standard setting (with a < c), which has been used by us to analyze the singlecrystal XRD experiments, given the transformation matrix i 0 0 1y between them: jjj 0 −1 0 zzz. k 1 0 0{ The agreement between our results and those published by Effenberg and Pertlik41 is excellent (see Table 1 for comparison). On the other hand, results from previous powder XRD experiments22 are ∼0.5% smaller than results from present and previous single-crystal XRD measurements. When comparing with calculations, we found that PBEsol functionals lead to an underestimation of unit-cell parameters (∼0.5%), the use of PBE functionals result in a 1.5% overestimation of unit-cell parameters, and use of the AM05 functionals results in an overestimation of b > c. From ambient pressure to 4.4 GPa, their lengths change by 3.1%, 2.4%, and 1.6%, respectively. In addition, the β-angle is reduced under compression. The results of the linear pressure
Figure 6. (Top) Pressure dependence of the unit-cell parameters. Solid circles represent the monazite phase (run 1); solid squares represent the monazite phase (run 2); empty circles and squares are results from refs 16 and 18; solid triangles represent scheelite phase (run 1); solid diamonds represent the scheelite phase (run 2). The lines are the results from DFT calculations. For the scheelite phase, c/ 2 was plotted to facilitate the comparison. (Bottom) Volume versus pressure. Symbols correspond to experiments. Different symbols are from different experiments and are as described for the top panel. The black solid lines are DFT calculations (AM05 functionals). The red dashed lines are the EOS determined from present experiments. The inset shows the pressure dependence of the β-angle in the monazite phase.
coefficients (dx/dP) for the different unit-cell parameters are given in Table 4. DFT calculations (AM05 functionals) slightly overestimate the values of the unit-cell parameters (as discussed in the previous section) but give a qualitative similar Table 4. Linear Pressure Coefficients for Different Unit-Cell Parameters (dx/dP) and Compressibilities (λi) along the Main Compression Axes (evi)
F
parameter
value
da/dP (Å GPa−1) db/dP (Å GPa−1) dc/dP (Å GPa−1) dβ/dP (° GPa−1) λ1 (× 10−3 GPa−1) ev1 (λ1) λ2 (× 10−3 GPa−1) ev2 (λ2) λ3 (× 10−3 GPa−1) ev3 (λ3)
−0.0494(7) −0.0399(7) −0.0251(5) −0.1671(5) 7.28(29) (−0.9902, 0, 0.1398) 5.75(35) (0, 1, 0) 2.15(1.15) (−0.3089, 0, −0.9511) DOI: 10.1021/acs.inorgchem.9b00291 Inorg. Chem. XXXX, XXX, XXX−XXX
Article
Inorganic Chemistry Table 5. EOS Parameters for the Two Polymorphs of PbCrO4a Monazite 3
V0 (Å ) B0 (GPa) B0′
Scheelite
XRD
AM05
PBE
PBEsol22
XRD18
XRD
AM05
PBE
351.32(14) 55(1) 3.2(8)
357.1(4) 48(1) 3.3(9)
372.8(1) 43(1) 3(1)
348 51.9 4.9
351(1) 56(1) 4 (fixed)
340 (fixed) 58(6) 6(3)
337(1) 61(1) 6(1)
349.3(8) 63(3) 5.5(5)
a
Results from refs 16 and 22 are included for comparison.
compressibility is mainly driven by the influence of pressure in PbO8 or equivalent units (CrO4) playing a negligible role. To conclude this part, we would like to deepen the discussion on the anisotropic compression of monazite PbCrO4. Since the structure is monoclinic, the compressibility tensor has nondiagonal components, and therefore, the directions of maximum and minimum compressibility do not have to be any of the unit-cell axis. Indeed, since β changes with pressure, the change of the crystal with pressure cannot be described only by the change of a, b, and c with pressure. In our case, by the diagonalization of the compressibility tensor using PASCaL59 we determined the main axes of compression. The results are summarized in Table 4. In the Supporting Information we include the compressibility indicatrix (Figure S1). We have found that the softest direction is (−0.9902, 0, 0.1398) and that the stiffest direction, which has a compressibility 3.4 times smaller than the softest direction, is (−0.3089, 0, −0.9511). The unique b-axis has an intermediate compressibility. This behavior resembles that of monazite BiPO4 and LaVO4.60,61 We have also found that if the pressure behavior of b-axis is described by a third-order BM EOS, the pressure derivative of the bulk modulus has a negative value [we got b0 = 7.4321(1) Å, Bb = 181(6) GPa, and B′b = −5(3)]. Normally, this situation is associated with a large shear during compression, which can be related to elastic softening. There are examples with similar behavior and, generally, it drives a phase transition that occurs, in this case, for PbCrO4 passing from the monoclinic crystalline system to the tetragonal crystalline system at 4.5 GPa. 4.3. Raman and Infrared Spectra. It is well-known that, at the zone center, the monazite structure has 36 Raman-active (Γ = 18Bg + 18Ag), 33 infrared (IR)-active (Γ = 16Bu + 17Au), and three acoustic (Γ = 2Bu + 1Au) phonons.62 For monazite PbCrO4, because of frequency degeneracy and/or low intensities, 30 of the 36 Raman modes have been measured.18 Based on DFT calculations, a mode assignment has been proposed.22 Here, we will present an improvement of this assignment by considering not only the measured and calculated frequencies (ω) but also the pressure coefficient (dω/dP). The results obtained from the present DFT calculations are summarized in Table 6, together with previous experimental results.18 In the table, we also give the new proposed mode assignment. Table 6 shows that the agreement between calculations and experiments for most modes and pressure coefficients is good. This is illustrated by the last column, where we present the value of Rω (Rω = (ωexp − ωtheory)/ωexp), which represents the relative difference between measured (ωexp) and calculated (ωtheory) frequencies.63 The Raman modes with frequencies below 200 cm−1 can be assigned to vibrations in which the CrO4 units vibrate as rigid units (external vibrations). For most of them, the differences between experiments and theory are
