Article pubs.acs.org/IC
Study of Phase Transformation in BaTe2O6 by in Situ High-Pressure X‑ray Diffraction, Raman Spectroscopy, and First-Principles Calculations K. K. Mishra,*,† S. Nagabhusan Achary,‡ Sharat Chandra,† T. R. Ravindran,† K. K. Pandey,§ Avesh K. Tyagi,‡ and Surinder M. Sharma§ †
Material Science Group, Indira Gandhi Centre for Atomic Research, Kalpakkam 603102, India Chemistry Division, and §High Pressure and Synchrotron Radiation Physics Division, Bhabha Atomic Research Center, Mumbai 400 085, India
‡
S Supporting Information *
ABSTRACT: Structural and vibrational properties of orthorhombic BaTe2O6, a mixed valence tellurium compound, have been investigated by in situ synchrotron X-ray diffraction (XRD) studies up to 16 GPa and Raman spectroscopy up to 37 GPa using a diamond-anvil cell. The structure of orthorhombic BaTe2O6 has layers of [Te2O6]2−, formed by TeO6 octahedra and TeO5 square pyramids and Ba2+ ions stacked alternately along the ⟨010⟩ direction. A reversible pressure-induced structural transformation from the ambient orthorhombic (Cmcm) to a monoclinic (P21/m) structure is observed in both XRD and Raman spectroscopic investigations around 10 GPa. Ab initio calculations using density functional theory (DFT) corroborate this phase transition as well as the transition pressure. Both XRD and DFT calculations reveal that the highpressure monoclinic structure is closely related to the ambient pressure orthorhombic structure, and the transformation is accompanied by a slight rearrangement of the structural units. Pressure evolution of unit cell parameters of the ambient pressure phase reveals an anisotropic compressibility with maximum compression along the b-axis as compared to other crystallographic directions. The bulk modulus and its derivative are found to be B0 = 88(2) GPa and B′0 = 4.1(7) from high-pressure experiments, while those calculated by DFT are B0 = 123 GPa and B0′ = 4.74. Pressure evolution of Raman spectra indicates significant changes across the orthorhombic to monoclinic phase transformation at 9.1 GPa and no evidence of further structural changes up to 37 GPa. Raman mode frequencies, pressure coefficients, and Grüneisen parameters in the low- and high-pressure phases of BaTe2O6 have been obtained for both monoclinic and orthorhombic phases. Finally, the mechanism for the instability of the orthorhombic phase under pressure is proposed.
I. INTRODUCTION Complex oxides of tellurium are of widespread interest due to their technologically useful dielectric and optical properties. They also exhibit interesting structural features due to the different oxidation states of tellurium as well as coordination polyhedra and lone pair effects.1−6 Tellurium oxide (TeO2) and several tellurium-based oxides such as BaTe4O9, BaTe2O6, BaTeO3, CaTe2O5, etc., exhibit excellent microwave dielectric properties with high quality factor, and find application in radar and communication systems.1−5,7 Oxides of lower valence tellurium, in particular those with Te4+ ions, exhibit large nonlinear polarizability and thus are promising materials for optical switching devices and optical amplifiers.8−10 The oxidation states of the Te cation govern the coordination polyhedra around it and their linkages in the crystal structure. Besides, the coexistence of Te4+ and Te6+ in complex tellurates leads to varieties of structures such as ribbons, tunnel, layered, © XXXX American Chemical Society
etc., structures, and they have been observed in a number of compositions in the M−Te−O system, where M = divalent and trivalent cations.6,11 With alkaline earth metal ions, formation of several complex tellurates has been reported depending on the stoichiometry of M, Te, and O.6 A number of studies have revealed the existence of a common composition, MTe2O5, where M = Ca2+, Sr2+, and Ba2+. However, depending on the ionic radius of the M2+ ions, they form different structures even at ambient conditions.11 In these structures, the Te4+ ions form distorted tetrahedra or five-coordinated polyhedra, and the arrangement of these polyhedra governs their properties. Among the MTe2O5 compositions, CaTe2O5 exhibits a series of temperature-induced structural phase transformations.11 Recently, it has been recognized that the composition Received: September 22, 2015
A
DOI: 10.1021/acs.inorgchem.5b02174 Inorg. Chem. XXXX, XXX, XXX−XXX
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Inorganic Chemistry
to obtain the phase transition sequence as a function of pressure.
BaTe2O6 could be conveniently formed from BaTe2O5 by a partial oxidation of the Te4+ ions. A high temperature study of this material indicated a slow oxidation of Te4+ to Te6+ leading to the formation of BaTeO4, which melts incongruently at higher temperature.7 Formation of BaTe2O6 by an incongruent melting of BaTe2O5 in air is also reported.7 The structure of BaTe2O6 has been reported to be orthorhombic (Cmcm) with layers of corner shared TeO6 octahedra and TeO5 squarepyramids with composition [Te2O6]2− and Ba2+ ions.12 The unit cell of the orthorhombic lattice contains 4 formula units as shown in Figure 1. One barium (Ba1) and two tellurim cations
II. EXPERIMENTAL DETAILS BaTe2O6 (BTO) was synthesized by a solid-state reaction method in static air atmosphere following a two-step heating procedure. Highpurity starting materials (BaCO3 and TeO2) in stoichiometric proportion were mixed and ground together. This homogeneous mixture was initially calcined at 550 °C for 6 h in air. The product was rehomogenized, pressed into thin pellets (thickness ≈ 1 mm), and heated again at 650 °C for 12 h. The XRD pattern of the final product was recorded by using Cu Kα radiation in a rotating anode-based Xray diffractometer (Rakagu, Japan) and matched with the JCPDS standard (no. 04-011-6957). Phase purity of the sample was further confirmed by recording the powder XRD pattern using synchrotron radiation in transmission mode at beamline (BL) 11 of INDUS-2 synchrotron at the Raja Ramanna Centre for Advanced Technology (RRCAT), Indore, India.20 High-pressure XRD measurements were carried out using compact, symmetric diamond anvil cell (DAC). Powder sample of BTO was loaded into a 200-μm hole of a stainlesssteel gasket (preindented to a thickness of ∼70 μm) in the DAC. 4:1 methanol−ethanol mixture as pressure transmitting medium (PTM) and silver powder as pressure calibrant were also loaded along with the sample. The used PTM is only quasi-hydrostatic up to 10 GPa, and the experimental results at high pressure could be influenced by deviatoric stresses.21−23 Often the influence of such deviatoric stresses is noticed in the phase transition of samples, which may or may not be observed in pure hydrostatic condition. In situ angle dispersive XRD measurements were performed with wavelength λ = 0.6716 Å at BL11 at INDUS-2. Microfocusing with a compound refractive X-ray lens (CRL) and x−y translational stage was used to align the X-ray beam into a tight spot of 45 μm × 32 μm on the sample in the DAC. Pressure was obtained from the EOS of Ag.24,25 A mar345 image plate of 3450 × 3450 pixel size with a readout resolution of 100 μm was used as the detector. Synchrotron XRD measurements were performed up to ∼16 GPa. The 2D diffraction images were integrated by using FIT2D software26 and converted into two-dimensional patterns. The analyses of the diffraction patterns were carried out by using PowderCell27 and Fullprof-2000.28 Raman spectra of the sample in the DAC were collected using a 514.5 nm excitation line from an Arion laser. The spectra were measured using a micro-Raman spectrometer (Renishaw, UK, model InVia) equipped with an aircooled charge coupled device (CCD) detector. Using a 20× long working distance objective, the spot size on the sample was about 1 μm. Raman spectra were also recorded in the pressure-reducing cycle. Ruby R1 fluorescence method was used for pressure measurements.
Figure 1. Crystallographic unit cell of BaTe2O6 ambient pressure orthorhombic structure for Z = 4. The dotted line represents a unit cell, whereas the solid line (red) corresponds to its primitive cell.
(Te1 and Te2) occupy the 4c, 4a, and 4c wyckoff sites, respectively, while three oxygen anions (O1, O2, and O3) reside at 4c, 4c, and 16h sites, respectively. The structure of BaTe2O6 is thus formed by linking the Te1O6 octahedra and square pyramidal Te2O5 polyhedra, which form a layer perpendicular to the ⟨010⟩ direction of the unit cell. The Ba2+ ions are occupied between these layers. Such layered arrangement of Te2O6 layer and Ba2+ ions is expected to give rise to anisotropic compressibilities as experimentally revealed in this study. Because of structural anisotropy, materials with such layered structures are often known to exhibit anomalous elastic properties as a function of temperature and/or pressure.13−19 In an analogy with other layered compounds, it is expected that BaTe2O6 may also exhibit novel high-pressure phase transformations.13−19 However, there are no reports of structural properties of BaTe2O6 as well as similar alkaline earth tellurates under pressure. To investigate the pressure-induced effects in BaTe2O6, in situ high-pressure X-ray diffraction (XRD) and Raman spectroscopic measurements were carried out. It is observed that the orthorhombic structure of the title compound becomes unstable at high pressure and transforms into a new structure that remains stable up to the highest pressure reached in this study. The equations of state (EOS) for both ambient pressure orthorhombic and high-pressure phases were obtained. The Raman active optical phonons, their pressure coefficients, and Grüneisen parameters are obtained for both of the phases. The experimental results on structural transition and phase stabilities are also corroborated by ab initio density functional (DFT) calculations, while lattice dynamics calculations were used to obtain the vibrational properties as a function of pressure. Volume-dependent total energy and pressure evolution of the enthalpy at ambient temperature is followed
III. COMPUTATIONAL STUDIES First-principles calculations were carried out within the framework of density functional theory (DFT) using the Vienna ab initio simulation package (VASP).29−31 The exchange and correlation energies were described by the Perdew−Burke−Ernzerhof32 generalized gradient approximation for the projected augmented wave (PAW) pseudopotentials. A plane-wave basis set with an energy cutoff of 450 eV and a 3 × 2 × 2 Monkhorst−Pack grid of k-points were used to obtain accurate results after testing for total energy convergence. The ground-state atomistic configurations (lattice parameters and positions of all 18 atoms in the primitive cell of BTO) were obtained after volume and atomic position relaxations starting from different experimental volumes across the phase transition. In all of the optimized configurations, the interatomic forces were lower than 10−4 eV/Å. Volumedependent total energy calculations were carried out to estimate the structural stability and also the transition pressure. The EOSs were obtained from the calculated total energy versus volume (E−V) data. The transition pressure and the B
DOI: 10.1021/acs.inorgchem.5b02174 Inorg. Chem. XXXX, XXX, XXX−XXX
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Inorganic Chemistry relative stability of the phases were obtained from the evolution of equilibrium volume and enthalpy of the calculated structures with pressure. Lattice dynamical calculations were carried out to calculate the phonon dispersions at various pressures for all of the phases using the General Utility Lattice Program (GULP) code.33 A core−shell model with springs along with interatomic pair potentials of Buckingham type were used to describe the interatomic interactions in the calculation. The ions are described by the core and shell charges that are screened Coulombically from each other, and the core and shell are coupled by a spring. The Coulomb interaction between ions with charges qi and qj in the crystal has the dominant contribution that is described by ΦCoulomb = qiqj/4πε0rij, and its ij contribution to total energy is evaluated by the 3D Ewald summation method.33 The spring between the core and shell of = (1/2)k2r2i + (1/24)k4r4i , where atom i is represented by Φspring i k2 is in eV Å−2 and k4 is in eV Å−4 units. The Buckingham = potential between the atoms i and j is described as ΦBuckingham ij Aij e−rij/ρij − Cij/r6ij, where Aij, ρij, and Cij are in eV, Å, and eV Å6 units, respectively, and rij is the interatomic distance in Å. All of the parameters of the interatomic potential34 are listed in Table 1.
Table 2. Refined Structural Parameters of BaTe2O6 at Ambient Conditiona atom
Wyckoff
Ba
4c
Te1
4a
Te2
4c
O1
4c
O2
4c
O3
16h
xb
yb
zb
Biso (Å2)
0 0 0 0 0 0 0 0 0 0 0.7370(7) 0.7380
0.2813(1) 0.2815 0 0 0.5859(1)) 0.5857 0.9530(6) 0.9507 0.7266(6) 0.7305 0.6055(3) 0.6076
0.2500 0.2500 0 0 0.2500 0.2500 0.2500 0.2500 0.2500 0.2500 0.4563(5) 0.4564
0.68(3) 0.05(3)) 0.11(3) 0.6(2) 0.5(2) 0.2(1)
a
DFT calculated parameters are shown in the second row in each case and are italicized. Orthorhombic (space group Cmcm); Z = 4; a = 5.5710(1), b = 12.7971(1), c = 7.3276(1) Å, V = 522.50(1) Å3; Rp, 3.55; Rwp, 4.88; χ2, 2.51. bDFT calculated values: a = 5.5907, b = 12.7385, c = 7.3872 Å, and V = 526.11 Å3.
Table 1. Core−Shell Model with Springs for Te, O, and Ba Atoms and Buckingham Potential Parameters for Interaction among Different Ionic Speciesa Core−Shell Model atoms
core charge (e)
shell charge (e)
k2 (eV Å−2)
k4 (eV Å−4)
cutoff (Å)
O Ba Te1 Te2
1.122 0.169 5.975 6
−3.122 1.831 −1.975
61.777 34.050 35.736
0 0 90
2.0 2.0 2.0
Buckingham Potential
a
species
A (eV)
ρ (Å)
C (eV Å6)
cutoff (Å)
O shell−O shell Ba shell−O shell Te1 core−O shell Te2 core−O shell
82 970.688 4818.416 1595.267 2296.526
0.1610 0.3067 0.3460 0.3338
31.362 0 1 1
12.0 10.0 12.0 10.0
Figure 2. X-ray diffraction pattern of BaTe2O6 at ambient pressure (λ = 0.7221 Å). Experimental data (○) and calculated diffraction patterns (red solid lines) are shown together with the residuals (blue solid lines) of the refinement. The vertical ticks indicate the position of the calculated Bragg’s reflections.
Only the core interactions are defined for Te2.
in close agreement with the reported parameters.12 The residuals of the refinement are Rp = 3.55 and Rwp = 4.88. An analysis of the refined structural parameters indicated that Te1 has a nearly regular octahedral coordination, and the typical bond lengths are: Te1−O1 = 1.928(2) Å × 2 and Te1−O3 = 1.915(4) Å × 4, which are similar to those expected for Te6+− O2− bonds.35 Te2 are surrounded by five oxygen atoms with typical bond lengths of Te2−O2 = 1.800(8) Å × 1 and Te2− O3 = 2.120(4) Å × 4, reminiscent of the square pyramidal configuration of lone pair containing Te4+ ions.36 A. High-Pressure X-ray Diffraction. The pressure evolution of XRD patterns of BaTe2O6 is shown in Figure 3. All peaks of the ambient pressure phase could be clearly observed up to the maximum pressure of the present study, but the peaks shift to larger 2θ due to the decrease in unit cell volume upon compression. The lowest pressure XRD data recorded for BTO inside the DAC (0.6 GPa) were refined by using parameters obtained from the ex situ diffraction study. The residuals of refinements are: Rp = 2.41, Rwp = 4.03. The refined unit cell parameters at 0.6 GPa are: a = 5.565(1), b = 12.788(2), c = 7.320(1) Å, which are in close agreement with
IV. RESULTS AND DISCUSSION The phase and structural parameters of BaTe2O6 sample were determined by Rietveld refinement of the observed powder XRD data. The initial structural parameters for Rietveld refinement were taken from an earlier report12 (orthorhombic, Cmcm, number of formula units (Z) = 4). The background of the diffraction pattern was fitted by a linear interpolation of selected points to create a smoothly varying background profile, while the profile of the Bragg peaks was modeled by pseudoVoigt function. Initial refinements were carried out for scale factor, unit cell parameters, and profile half width parameters. Subsequently, the position coordinates and isotropic thermal parameters for all atoms were refined. All structural parameters could be successfully refined from the powder XRD data, and the refined position coordinates are summarized in Table 2. The Rietveld refinement plot of BaTe2O6 at ambient conditions is shown in Figure 2. The final refined unit cell parameters of BaTe2O6 are a = 5.5710(1), b = 12.7971(1), c = 7.3276(1) Å and V = 522.50(1) Å3 at ambient pressure, and these values are C
DOI: 10.1021/acs.inorgchem.5b02174 Inorg. Chem. XXXX, XXX, XXX−XXX
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Inorganic Chemistry
obtained by the structural transformation were used to refine the profile of the XRD patterns of the high-pressure phase. In this pattern, the backgrounds were also modeled by linear interpolation of selected points. The unit cell and profile parameters were refined along with one overall thermal parameter (Bov). The position coordinates of the monoclinic phase were not further refined due to limited resolution of the data. The goodness of the fits were concluded from the matching of the observed and the calculated profiles and the resulting residual plot. The excellent residuals after refinement (Rp = 1.49 and Rwp = 2.32) thus confirm the correctness of the assumed structure. The position coordinates of the various atoms in the monoclinic phase observed at 15.7 GPa are given in Table 3. The refined unit cell parameters of the monoclinic Table 3. Structural Parameters of High-Pressure Monoclinic Phase of BaTe2O6 at the Highest Pressure of 15.7 GPaa
Figure 3. X-ray diffraction patterns of BaTe2O6 at successively high pressures. The asterisks (*) identify the new Bragg’s peaks for the high-pressure phase at 13.8 GPa. Bragg’s peaks of Ag are labeled using arrows for the diffraction pattern at 0.6 GPa. The patterns are vertically shifted for the sake of clarity.
those observed at ambient conditions for the orthorhombic BaTe2O6. At higher pressures, in particular above 13.8 GPa, the diffraction peaks are broadened considerably. In addition, the patterns recorded above this pressure show additional weak reflection peaks around 2θ ≈ 12.1°, 14.0°, and 20.4°, indicating a transformation of the ambient pressure orthorhombic phase to a phase with a lower symmetry. This has also been confirmed by Raman spectroscopy and DFT calculations as described later in this Article. Furthermore, the evolution of peak positions of the XRD patterns is anomalous as expected for materials with anisotropic compressibility. On the other hand, all XRD patterns recorded up to 11.9 GPa could be refined successfully using the structural parameters of orthorhombic BaTe2O6. No unaccounted peaks or anomalous shifts are observed in these diffraction patterns. These XRD patterns were refined by considering the refined position coordinates of the ambient pressure data recorded outside the DAC. Similar to the ambient pressure data, the backgrounds of the XRD patterns were fitted by linear interpolation of selected points. To carry out the Rietveld refinement, the profile half width parameters, unit cell parameters, and only one thermal parameter (Bov) were considered. The refinements were carried out by model biased methods to obtain accurate unit cell parameters. XRD patterns recorded at pressures >11.9 GPa could also be refined using the orthorhombic unit cell, but the additional peaks and anomalous broadening could not be properly accounted. The intensity of these new diffraction peaks increases upon further increasing the pressure, and they become discernible as clear peaks at 15.7 GPa, the highest pressure of this study. This suggests a transformation of the ambient pressure phase to a closely related structure at higher pressure. To follow the structural transition, the unit cell parameters were determined from the observed XRD pattern at 15.7 GPa. All of the newly observed peaks could be satisfactorily accommodated in a primitive monoclinic lattice (space group P21/m) with unit cell parameters a = 5.406, b = 7.184, c = 6.558 Å and β = 115.25°. The ambient pressure orthorhombic and high-pressure monoclinic phases can be related by unit cell relations as: am ≈ ao, bm ≈ −co, cm ≈ −(1/2)ao + (1/2)bo. Further analyses of the high-pressure structure were carried out by following group−subgroup relations. The position coordinates of the various atoms in the monoclinic phase as
atom
Wyckoff
xb
yb
zb
Ba
2e
Te1
2a
Te2
2e
O1
2e
O2
2e
O3
4f
O4
4f
0.7185 0.7258 0.0000 0.0000 0.4139 0.4143 0.0482 0.9975 0.2726 0.2841 0.3436 0.3568 0.8696 0.8849
0.2500 0.2500 0.0000 0.0000 0.2500 0.2500 0.2500 0.2500 0.2500 0.2500 0.5440 0.5258 0.9560 0.9442
0.5630 0.5762 0.0000 0.0000 0.1722 0.1757 0.9036 0.9078 0.4548 0.4785 0.7868 0.7866 0.7868 0.7669
a
DFT calculated parameters are shown in the second row in each case and are italicized. Monoclinic (space group P121/m1); Z = 2; a = 5.4047(7), b = 7.1847(3), c = 6.5490(2) Å, β = 115.237(4)°, and V = 230.035(2) Å3; Rp, 1.49; Rwp, 2.32. bDFT calculated values: a = 5.5598, b = 7.4297, c = 6.6763 Å, β = 113.12°, and V = 253.63 Å3.
high-pressure phase at 15.7 GPa are: a = 5.4047(7), b = 7.1847(3), c = 6.5490(2) Å, β = 115.237(4)°, and V = 230.035(2) Å3 with Z = 2. Similarly, the diffraction profile observed at 13.8 GPa was also refined with the observed monoclinic structure. Typical refinement plots for the ambient and high-pressure phases are shown in Figure 4. The CIF files for orthorhombic and monoclinic phases are provided in the Supporting Information (SI-1). Analysis of structural parameters of the high-pressure monoclinic phase reveals an atomic arrangement that is similar to that of the orthorhombic phase. In both cases, Te atoms retain their typical octahedral and square pyramidal coordination. However, both polyhedra are distorted, and the anion positions are split in the transformation process. In both structures, the octahedra formed by Te6+ ions are linked by sharing two opposite corners forming a chain, and they are held together by sharing other corners of square pyramids formed by Te4+ ions. Structures of both phases can be compared from Figures 1 and 5. Both structures have Te2O6 layers held together by Ba2+ ions along the ⟨010⟩ direction in the orthorhombic phase and the ⟨001⟩ direction in the monoclinic phase. The apex oxygen atoms of TeO5 point toward the interlayer space in both structures, and thus the layers containing Ba2+ are in fact BaO layers. This arrangement of D
DOI: 10.1021/acs.inorgchem.5b02174 Inorg. Chem. XXXX, XXX, XXX−XXX
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Inorganic Chemistry
To have a better comparison of cell parameters of the orthorhombic and monoclinic phases, the equivalent orthorhombic lattice parameters for the monoclinic phase are obtained by the relationships: aortho = amono, bortho = 2cmono cos(β − 90), cortho = bmono. The pressure evolution of unit cell parameters for the ambient and high-pressure phases shows a monotonously decreasing trend with increasing pressure in both phases, and with increase in pressures (P > ambient) anisotropic compression is observed, the effect being more along the b-axis of the orthorhombic phase and the c-axis of the monoclinic phase (i.e., along the stacking direction). Normalized unit cell parameters for both phases, shown in Figure 6, clearly reveal the anisotropic compressibility. To study Figure 4. Rietveld fitted patterns for different phases of BaTe2O6: orthorhombic (9.7 GPa) and monoclinic (15.7 GPa). The asterisks (*) identify the new Bragg’s peaks for the high-pressure monoclinic phase at 15.7 GPa. Experimental data (○) and calculated diffraction patterns (red solid lines) are shown together with the residuals (blue solid lines) of the refinement. Silver peak positions used as pressure marker are marked with red vertical ticks (lower row), and the two phases of BaTe2O6 are marked with black vertical ticks (upper row).
Figure 6. Normalized lattice parameters of the low-pressure orthorhombic and the equivalent orthorhombic lattice parameters of the high-pressure monoclinic phase as a function of pressure. Polynomial fits of the pressure evolution of their normalized unit cell parameters are also shown. Vertical dashed line indicates the discontinuity in b-lattice parameter. Figure 5. High-pressure monoclinic crystal structure. The solid line corresponds to its primitive cell for Z = 2.
the variation of the normalized lattice parameters with pressure, they are fitted to a quadratic polynomial. While a/a0 and c/c0 yield good fits, the one for b/b0 data is poorer in the neighborhood of the phase transition pressure. This could be due to the influence of the phase transformation. Because the variations of a/a0 and c/c0 are small, the effect of transformation is not noticeable on these parameters. A weak discontinuity in the variation of the b/b0 is observed near the transition pressure. The compressibility tensor for the studied structures is given by a symmetric second rank tensor βij (i and j = 1, 2, 3) where the lattice symmetry determines the number of tensor components.37,38 Using the linear Lagrangian approximation,37,38 the tensor components β11, β22, β33 for the orthorhombic phase (0.7−10.3 GPa) are calculated to be 2.11(1) × 10−3, 5.57(1) × 10−3, and 1.43(1) × 10−3, respectively; for the monoclinic phase (13.8−15.7 GPa), β11, β22, β33, and (β13 = β31) turn out to be 1.2(4) × 10−3, 3.9(5) × 10−3, 1.7(4) × 10−3, and 0.4(3) × 10−3, respectively. The error in the values of components of the compressibility tensor for the monoclinic phase could be attributed to the limited data set. It is seen that the compressibility, in particular along the b-axis, reduces appreciably at the transition. As mentioned earlier, the orthorhombic BaTe2O6 has a stacked layer like arrangement along the b-axis that is the easy axis for compression. At higher pressure, the reduction of compressibility indicates steric hindrance due to interlayer repulsion as reflected in the
anions contains six oxygen atoms around the Ba2+ ions (two O2 at 2.872(2) Å and four O3 at 2.979(4) Å). In addition, Ba2+ ions have four more O3 atoms as the next nearest neighbors at 3.015(4) Å in the orthorhombic phase. The larger ionic radius of the Ba2+ ion and weak interaction along the stacking direction make it easy axis for compression. As discussed above from the structural studies, transformation from the orthorhombic to monoclinic phase does not cause any change in the coordination polyhedra of Te 4+ and Te 6+ , while the coordination of the Ba2+ ion is increased where a significantly distorted polyhedra around it can be understandable. The coordination around the Ba2+ ions remains the same as computed in the ambient orthorhombic structure within the distance limit of 3.015 Å. However, additional bonds from TeO5 and TeO6 become closer to Ba2+, tending to increase the coordination number of Ba ion. In particular, the bond lengths for Ba−O1, 3.547 (Å) × 2, and for Ba−O2, 3.666 (Å) × 2, of the orthorhombic phase are compressed to 3.348 Å × 1 and 3.397 Å × 1 for Ba−O1, while that for Ba−O2 turns out to be 3.594 (Å) × 2. Thus, an increase in the coordination of Ba2+ from 12 to 14 is noticed within the distance limit of 3.6 Å. Typical interatomic distances between Ba2+ and O2− in orthorhombic and monoclinic phases of BaTe2O6 are provided in a figure in the Supporting Information (SI-2). E
DOI: 10.1021/acs.inorgchem.5b02174 Inorg. Chem. XXXX, XXX, XXX−XXX
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Inorganic Chemistry
Comparison of the calculated position coordinates also showed a close agreement with those obtained from experimental data. Calculations on the monoclinic (P21/m) phase resulted in the relaxed unit cell parameters a = 5.5597, b = 7.4297, c = 6.6762 Å and β = 113.12°, V = 253.62 Å3. Initially, the highest pressure experimental structural parameters of monoclinic phase (Table 3) are used as an input in DFT, and the relaxed structural parameters at ∼13 GPa (beginning of HP monoclinic phase) are obtained. The calculated position coordinates of the monoclinic phase (Table 3) differ by a maximum of ∼3% from the experimentally observed ones. A comparison of the calculated primitive cell parameters of both phases points to a subtle structural change involved in the phase transition. The average Te−O bond length in the TeO6 octahedra of the monoclinic structure is 1.846 Å (Te1−O1 = 1.885 Å × 2, Te1− O3 = 1.840 Å × 2, and Te1−O4 = 1.813 Å × 2), shorter than that observed for the orthorhombic structure (1.928 Å). Similarly, the calculated bond lengths in the TeO5 square pyramids are also shorter in the monoclinic structure (monoclinic, Te2−O3 = 2.069 Å × 2, Te2−O4 = 2.064 Å × 2, Te2−O2 = 1.674 Å × 1; orthorhombic, Te2−O3 = 2.120 Å × 4 and Te2−O2 = 1.808 Å × 1). Thus, both polyhedra are compressible in orthorhombic BaTe2O6; in particular, the apical bond of TeO5 (Te2−O2) is more compressible as compared to others. The fitting of the DFT calculated total energy versus volume data (Figure 8) to the third-order Birch−Murnaghan
rearrangement of atoms. Further, the close similarity of the XRD patterns recorded at ambient and the highest pressure suggests that the phase transition occurs with only slight distortions in the polyhedral units. The effectiveness of these distortions in driving the phase transformation cannot be commented upon from the XRD data alone. Therefore, a complementary technique such as Raman is employed for more insight. Further, the high-pressure behavior of BaTe2O6 is followed from the pressure evolution of unit cell volume (Figure 7). An
Figure 7. Fit of the P−V data to third-order Birch−Murnaghan equation of state. Using V0 = 522.4 Å3 and B0′ = 4.1(7), the bulk modulus was found to be B0 = 88(2) GPa. The dotted line is the extrapolated line in monoclinic phase using the EOS parameters of the orthorhombic phase.
about 2% reduction in volume is noticed across the transition. This small volume collapse and the structural closeness of both the low-pressure orthorhombic and the high-pressure monoclinic phases (group−subgroup relation) suggest for the displacive nature of the phase transition. Because there is no appreciable volume collapse, and almost no hysteresis, it looks like a second-order phase transition. A similar kind of highpressure transition is also reported in another layered structure material Sr2ZnGe2O7.13 For the low-pressure orthorhombic phase, the pressure (P)−volume (V) data were fitted to the third-order Birch−Murnaghan equation of state:39 P = 1.5B0(x2 − 1)x5[1 + 0.75(B′0 − 4)(x2 − 1)], where x = (V/V0)−1/3, B0 is the bulk modulus, and B0′ is the pressure derivative of bulk modulus by using EOSfit7c package.40 The fitting was carried out by considering the standard error of the unit cell volumes. Goodness of fit is assessed from the residuals Rv = 1.84%, Rw = 2.20%, and χ2 = 0.026. The maximum observed ΔP is 0.346 GPa. The fitting yields B0 = 88(2) GPa and B0′ = 4.1(7). Bulk modulus for the monoclinic phase could not be obtained due to an insufficient number of data points in this phase, but this could be obtained from computations as described later in this Article. B. Ab Initio Studies of the Phase Transformation. To obtain more insight into the nature of the high-pressure phase and phase transformation, ab initio DFT calculations using VASP were performed on orthorhombic and monoclinic BaTe2O6. The calculated ground-state structural parameters for the ambient orthorhombic phase are tabulated in Table 2. The calculated unit cell parameters for the orthorhombic (Cmcm) phase are: a = 5.5907, b = 12.7385, c = 7.3872 Å and V = 526.11 Å3, which are close to those observed experimentally.
Figure 8. Calculated total energy versus unit cell volume curves for orthorhombic (red) and monoclinic (black) phases.
EOS gives the bulk modulus and its variation with pressure for the two phases as: orthorhombic (primitive cell), B0 = 123.16 GPa, B0′ = 4.74, V0 = 272.13 Å3; monoclinic, B0 = 129.29 GPa, B′0 = 4.28, V0 = 264.05 Å3. The calculated bulk modulus of the orthorhombic phase differs by ∼28% from the experimental value (88 GPa). There can be several reasons for this observed discrepancy. It can often arise due to the lack of nonlocal electron correlations41 and point to the limitations of the LDA/ GGA approximation. The difference between these bulk modulus values could be related to the mismatch between the experimental and calculated equilibrium volumes. The difference could also be due to the fact that while the DFT calculations are carried out on ideal systems (at 0 K), the experimental structures are far from ideal: point defects such as vacancies, interstitials, and finite temperature can affect the bulk modulus of the structure significantly.42−44 Such overestimation F
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Inorganic Chemistry of the calculated B0 with respect to experimental values is reported in several systems.41 The V/V0 in the orthorhombic phase when extrapolated into the monoclinic phase follows nearly the same trend except at the highest pressure of ∼16 GPa (Figure 7). At this pressure, the experimental V/V0 is higher, indicating the possibility of increased bulk modulus in the monoclinic phase that is in accordance with our calculations. As the orthorhombic primitive cell volume decreases to ∼250 Å3, the monoclinic structure becomes more stable as compared to the orthorhombic phase, which corroborates our experimentally observed orthorhombic to monoclinic phase transition. Further understanding of the instability and phase transition is obtained from the variation of enthalpy with pressure. At ambient conditions, the enthalpies of the primitive orthorhombic and monoclinic unit cells are −103.60 and −103.17 eV, respectively, which suggests that the orthorhombic structure is more stable as compared to the monoclinic structure. Evolution of enthalpies of both structures with volume reveals that while at ambient conditions the orthorhombic phase is more stable, it becomes unstable below a certain volume. Variation of the difference in enthalpy of high-pressure monoclinic and low-pressure orthorhombic phase with pressure (Figure 9) indicates the transition pressure to be ∼10 GPa, close to that observed in the XRD and Raman studies (described below).
Raman active modes (7Ag + 7B1g + 3B2g + 7B3g) and 23 infrared active modes (8B1u + 8B2u + 7B3u) are expected in BaTe2O6. Figure 10 shows the Raman spectra obtained at
Figure 10. Representative Raman spectra of BaTe2O6 at different pressures. The spectra denoted by (r) correspond to pressure release. Blue tick marks locate the Raman bands of the low-pressure phase at 0.9 and 9.1 GPa, whereas red tick marks do it for the high-pressure phase at 9.1 and 18 GPa. New Raman bands appearing at 9.1 GPa are labeled using asterisks. For the sake of clarity, the spectra are vertically shifted.
several different pressures between the ambient and 37.3 GPa. The Raman spectrum recorded inside DAC at 0.9 GPa is similar to the ambient one. At ambient conditions, 14 distinct Raman bands out of the expected 24 could be obtained in our measurements. The observation of a lower than expected number of Raman bands could be due to accidental degeneracy of phonon frequencies or insufficient intensities arising from the small scattering cross section of several modes.46 The Raman bands below 400 cm−1 correspond to the external and lattice modes, while those at higher wavenumbers arise due to the internal vibrations of the TeO6 octahedra and TeO5 pyramid units.47,48 The Raman band at 708 cm−1 is attributed to the antisymmetric stretching vibration of the Te−O bond of the TeO6 octahedra, whereas that at 789 cm−1 arises from the symmetric stretching vibration of the TeO6 octahedra.47,48 As discussed earlier, the average Te−O bond length in TeO5 pyramid (1.846 Å) is shorter than that in TeO6 octahedra (1.928 Å); therefore, the Raman bands at the highest wavenumbers (822 and 866 cm−1) are attributed to the symmetric stretching and antisymmetric stretching vibration49 of Te−O bonds in the TeO5 pyramid, respectively. The bands at 423 and 513 cm−1 arise from the bending vibration of tellurium ion.47,48 Low frequency Raman bands correspond to the lattice modes. The lowest frequency lattice mode at 58 cm−1 and several of the internal vibrations exhibit themselves as the strongest bands in the ambient orthorhombic phase. As the pressure is increased, the Raman spectra exhibit significant changes (Figure 10). The unique Raman bands of the orthorhombic phase at 886, 423, 288, and 70 cm−1 reduce intensity with pressure. While the intensity of the bands reduces upon compression, the bands at 288 and 423 cm−1 do not disappear but they split into 315, 323 cm−1 and 446, 460 cm−1, respectively, around 9 GPa (Figure 10). The band at 70 cm−1 is a weak shoulder that merges into the more intense band nearby. Only the band at 886 cm−1 gradually reduces in
Figure 9. Variation of the difference in enthalpy of high-pressure monoclinic and low-pressure orthorhombic phase with pressure. The enthalpy of the orthorhombic phase is shown as a horizontal reference line.
C. High-Pressure Raman Spectroscopy. To examine the changes that occur in the Raman spectrum of BaTe2O6 at high pressure, we have also measured its Raman spectra in situ in a DAC up to 37.3 GPa. As mentioned earlier, the ambient orthorhombic crystallographic unit cell (Cmcm) contains four formula units (Z = 4), and this translates to 2 formula units in the primitive cell. Therefore, one expects a total of 54 degrees of freedom that are distributed as optical and acoustic modes at the Brillouin zone center. We have obtained the irreducible representation for each of the atoms from the factor group analysis using the Halford−Hornig site-group method.45 The total irreducible representation for optical phonons is Γopt = 7Ag+ 7B1g + 3B2g + 7B3g + 4Au + 8B1u + 8B2u + 7B3u, and that for acoustic phonons is ΓAcoustic = B1u + B2u + B3u. Au modes are optically silent (neither Raman nor IR active). Twenty-four G
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Inorganic Chemistry intensity before dropping to zero above 9 GPa. Note that the intensity of a Raman band is proportional to the square of the derivative of the polarizability (χ) with respect to the normal coordinate (q), (∂χ/∂q)2. Although a plot of square root of I versus P of the vanishing modes would be of some help to identify the occurrence of a phase transition,50 such an analysis in the present case did not yield correct results. Furthermore, new Raman bands at 460, 446, 323, 315, 285 cm−1 appear at 9.1 GPa (Figure 10), possibly corresponding to the onset of the new monoclinic phase, and the intensities of these new bands increase systematically with increasing pressure. As mentioned, the bands at 446, 460, 315, and 323 cm−1 originate from the splitting of the 423 and 288 cm−1 bands of orthorhombic phase. This can be attributed to the lowering of symmetry across the orthorhombic−monoclinic transition observed from the XRD and corroborating the phase transition in BTO. To gain further insight into the vibrational properties of BaTe2O6, the pressure evolution of Raman modes of both orthorhombic and monoclinic phases was analyzed (Figure 11a). Simultaneous presence of a few bands of the orthorhombic phase at 124, 142, and 155 cm−1 and the new bands characteristic of the monoclinic phase over a small range of pressure (∼9−13 GPa) suggests the coexistence of the orthorhombic and high-pressure monoclinic phases. However, this coexistence could not be observed in the XRD studies, which could be due to the limited number of experimental data points in XRD or the fact that X-rays probe the average behavior while the Raman scattering probes the local behavior.51,52 The pressure dependences of change in the mode frequencies with respect to the ambient pressure values for orthorhombic phase are shown in Figure 11b (Δω ≈ pressure; where Δω is the difference between the mode frequency at higher pressure and the corresponding mode frequency at ambient pressure). It can be noticed that the high frequency modes that are attributed to the stretching of TeOn (n = 5 or 6) polyhedra have larger pressure dependencies. The pressure coefficients of Raman bands are obtained from the slope of mode frequencies (ωi) versus pressure curve. All modes of BaTe2O6 follow the normal hardening behavior under compression. Mode Grüneisen parameters are calculated from the expression,14 γi = (B0/ωi)(dωi/dP). The experimental value of the bulk modulus B0 = 88 GPa is used for these calculations. Table 4 lists the pressure coefficients and their Grüneisen parameters of all modes of the orthorhombic phase. Although the slopes of several internal modes are large, their Grüneisen parameter values are small because this parameter is a normalized value of the pressure dependence of mode frequencies: for example, the slope of the 822 cm−1 stretching mode is larger than that of the 58 cm−1 lattice mode; however, the Grüneisen parameter of this lattice mode is 4 times larger than that of the stretching mode. In principle, the Grüneisen parameter being a dimensionless quantity can only be compared14 for different modes. Therefore, small values of Grüneisen parameter for different internal modes indicate that the TeO5 square pyramidal and TeO6 octahedral units are less sensitive to pressure. On the other hand, large Grüneisen parameters for the low frequency lattice modes suggest that these vibrations are more sensitive to pressure, and can be easily compressed and deformed with pressure. This can be attributed to the weaker and more compressible nature of Ba2+−O2− bonds as compared to the Te−O bonds. The Ba2+ sublattice is the first to become unstable at high pressure. This results in slight displacement of the Ba2+ ion positions
Figure 11. (a) Raman mode frequencies of BaTe2O6 as a function of pressure. Small-sized symbols correspond to the modes in the ambient orthorhombic phase, while the larger symbols represent the highpressure monoclinic phase. Open circles indicate the mode behavior in the decompression cycle. Vertical dashed lines show the coexistence region between 9 and 13 GPa. Lines through the data are linear leastsquares fit. (b) Pressure dependencies of the shift in Raman modes (cm−1) with respect to the ambient pressure values in the orthorhombic phase (Δω ≈ pressure).
consequent to which the Te and O ions have to also move due to the large size of the Ba2+ ion. Consequently, the TeOn polyhedral units are distorted to maintain the polyhedral network and the integrity of the structure. Similar observations have been reported earlier in complex oxide Sr2ZnGe2O7.13 Similar analysis of the Raman spectra of the high-pressure monoclinic phase (space group P21/m) of BaTe2O6 has been carried out. This phase has 2 formula units (Z = 2) in the crystallographic unit cell, and from group theoretical analysis we find the irreducible representations of the zone center vibrational modes for the monoclinic phase: Γopt = 12Au + 15Bu + 14Ag + 10Bg, out of which 24 are Raman active (14Ag + 10Bg) and 27 infrared active (12Au + 15Bu). Therefore, the number of Raman active modes is the same as those obtained for the ambient phase; however, the change in the structure is reflected in the different sets of Raman bands. At 9.1 GPa, the transition pressure, a total of 15 distinct Raman bands are identified (Table 5). On further compression, several lattice modes and internal modes are broadened and their intensities are reduced considerably; these lattice modes could not be H
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Inorganic Chemistry Table 4. Theoretical and Experimental Optical Mode Frequencies (cm−1) for the Orthorhombic Phase
Table 5. Theoretical and Experimental Optical Mode Frequencies ω (cm−1), for the High-Pressure Monoclinic Phase
orthorhombic (Cmcm) calculation ω 62 (IR) 72 (R) 73 (R) 74 (R) 81 (R) 84 (IR) 97 (IR) 103 (IR) 109 (R) 125 (R) 145 (R) 149 (R) 155 (S) 169 (IR) 172 (R) 185 (IR) 229 (R) 252 (IR) 253 (IR) 267 (R) 269 (IR) 322 (IR) 325 (IR) 328 (R) 330 (R) 336 (R) 340 (S) 357 (IR) 398 (IR) 405 (R) 412 (S) 417 (IR) 431 (R) 440 (R) 459 (R) 514 (IR) 524 (IR) 602 (R) 609 (IR) 701 (R) 707 (R) 716 (R) 805 (R) 811 (IR) 832 (S) 833 (R) 851 (IR) 879 (IR) 884 (R) 948 (R) 949 (IR)
dω/dP 1.821 1.424 1.992 2.599 2.227 2.477 1.616 2.147 2.291 1.677 1.708 1.429 1.691 0.239 0.891 0.112 2.684 1.101 1.560 0.049 −0.0364 0.958 0.883 1.045 1.368 1.081 0.920 0.953 2.775 2.463 1.822 2.349 2.479 1.573 2.959 2.123 1.455 1.558 1.238 2.481 2.440 2.750 2.029 1.967 0.825 2.026 1.338 1.011 2.101 1.627 1.694
monoclinic (P21/m)
experimental γi 2.585 1.740 2.401 3.091 2.419 2.595 1.466 1.834 1.849 1.181 1.036 0.843 0.960 0.124 0.456 0.053 1.031 0.384 0.542 0.016 −0.012 0.262 0.239 0.280 0.365 0.283 0.238 0.235 0.614 0.535 0.389 0.496 0.506 0.315 0.567 0.363 0.244 0.228 0.179 0.311 0.304 0.338 0.222 0.213 0.087 0.214 0.138 0.101 0.209 0.151 0.157
ω 58 70 80
dω/dP 2.099 1.927 2.774
3.185 2.422 3.051
124 142
2.138 1.994
1.517 1.236
155
1.615
0.917
288
3.221
0.984
330
2.768
0.738
423 442 513
2.447
0.509
3.058
0.524
708
4.050
0.503
789
3.994
0.445
822
7.229
0.774
886
3.767
calculation
γi
0.374
followed up to 37 GPa, the highest pressure in this study. For this phase, the pressure dependencies of the modes are shown in Figure 11a, and their pressure coefficients and Grüneisen parameters are tabulated in Table 5. The Grüneisen parameters of the phonon modes for this phase are calculated by using a
experimental
ω
dω/dP
γi
80 (IR) 86 (R) 91 (R) 94 (R) 104 (R) 108 (IR) 114 (IR) 127 (IR) 142 (R) 161 (R) 162 (IR) 164 (R) 170 (IR) 171 (IR) 173 (R) 187 (IR) 256 (R) 260 (IR) 264 (IR) 268 (IR) 269 (R) 290 (IR) 332 (IR) 334 (R) 338 (R) 345 (R) 350 (IR) 367 (IR) 431 (IR) 433 (R) 439 (IR) 444 (IR) 455 (R) 456 (R) 489 (R) 508 (IR) 535 (IR) 538 (R) 637 (IR) 726 (R) 731 (R) 744 (R) 825 (IR) 829 (IR) 830 (IR) 841 (R) 869 (IR) 887 (IR) 889 (R) 964 (IR) 975 (R)
1.239 1.061 1.827 1.897 2.411 2.084 2.196 3.437 2.063 0.523 0.887 1.083 0.993 1.332 1.684 1.667 0.403 1.286 0.893 0.879 2.648 1.294 0.683 1.096 1.225 1.796 1.389 0.905 2.052 2.258 1.855 1.595 0.978 1.696 1.961 1.362 0.882 0.766 0.602 1.73 1.598 1.218 1.593 1.274 1.483 0.522 0.701 0.590 0.384 1.416 1.456
1.425 1.135 1.847 1.857 2.133 1.775 1.772 2.490 1.336 0.299 0.504 0.607 0.537 0.717 0.895 0.820 0.145 0.455 0.311 0.302 0.906 0.411 0.189 0.302 0.333 0.479 0.365 0.227 0.438 0.479 0.389 0.330 0.198 0.342 0.369 0.247 0.152 0.131 0.087 0.219 0.201 0.151 0.178 0.141 0.164 0.057 0.074 0.061 0.040 0.135 0.137
ω
dω/dP
γi
79 98
1.072 1.645
1.248 1.544
107
1.986
1.707
154
1.810
1.081
172
1.735
0.928
285
1.682
0.543
315 323 357
1.777 2.658 2.253
0.519 0.757 0.581
443
3.013
0.626
446 460 542
2.239 1.995 1.992
0.462 0.399 0.338
745
2.738
0.338
827
3.114
0.346
888
4.331
0.448
more realistic value of B0 (rather than the computed B0 of 129 GPa) that can be obtained by suitably scaling up the experimental B0 value of orthorhombic phase (88 GPa) by the ratio of their calculated values: that is, (129/123) × 88 = 92 I
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Inorganic Chemistry
phase, the theoretical mode Grüneisen parameters are obtained. The bulk modulus estimated from the lattice dynamics calculations is similar to the experimentally obtained value for the orthorhombic phase. This value depends on the interatomic potentials used to describe the inter atomic−atomic interactions for the lattice dynamics calculations and is not calculated ab initio. Hence, the experimental bulk modulus for orthorhombic and the scaled value for the monoclinic phases, as discussed in the previous section, are used to estimate the theoretical mode Grüneisen parameters. A comparison of the calculated mode frequencies, pressure coefficients, and their Grüneisen parameters with experimental values is done in Tables 4 and 5. Most of the phonon mode frequencies are found to agree within ∼2% with the experimentally observed Raman values. Furthermore, the calculated pressure coefficients and Grüneisen parameters of both of the phases are reasonably matched. Calculation predicts that the infrared active external mode ∼269 cm−1 (Table 4) softens, whereas other modes exhibit normal hardening with pressure in the orthorhombic phase. The existence of such a soft mode suggests instability of the low-pressure orthorhombic phase against a possible structural phase transition,15 and further supports our observed phase transition. This mode is not Raman active, and could not be detected in our Raman experiment. The computed phonon dispersion curves, total, and partial phonon density of states at equilibrium volume (ambient pressure) are shown in Figure 12a and b. The labels
GPa. Upon such scaling, a comparison of Grüneisen parameters of both phases can be meaningfully done. From these slopes of mode frequencies versus pressure, it is noticed that all modes of the high-pressure monoclinic phase continue to harden, as observed for the ambient orthorhombic phase. Furthermore, as compared to the ambient phase, the Grüneisen parameters of several modes in the monoclinic phase are observed to be small. This suggests that the high-pressure phase is less compressible (larger B0) and is in accordance with our finding on larger bulk modulus predicted from DFT studies. As anticipated, for both phases, it can be seen that the Grüneisen parameters (Tables 4 and 5) for the high-frequency internal modes are almost 2−3 orders of magnitudes smaller than those of the lattice modes, thus confirming the stronger bonding within the TeO6 and TeO5 units. Broadening of internal modes of tellurium polyhedra is expected because the bond lengths and bond angles of the polyatomic units have a distribution about a mean value in contrast to those remaining constant as in regular polyhedra.53,54 Because polyhedral distortion increases with pressure, especially in the high-pressure monoclinic phase, the broadening related to its vibrational modes is quite appreciable. Furthermore, several low frequency lattice modes are found to disappear possibly due to lack of translational symmetry/longrange order.15,55 Thus, these changes in Raman features in the high-pressure monoclinic phase suggest possible development of positional disorder. Growth of static positional disorder beyond a critical value results in loss of long-range order and often leads to amorphization.56 Therefore, it is likely that the title compound can amorphize at higher pressures. In fact, several oxide systems containing polyhedral units such as CaWO4,57 Ag2MoO4,53 etc., have been observed to show similar features under pressure. Furthermore, beyond the hydrostatic pressure limit, positional disorder can be due to deviatoric stresses that cause significant distortions to the structure.57 After reaching the highest pressure of 37 GPa in the present study, the pressure was reduced gradually, and Raman spectra were recorded at a few pressures (Figure 10). The pressure dependence of the mode frequencies (shown in Figure 11a as ○) is similar to the trend in the increasing pressure run, confirming the reversibility of phase transition. This reversibility and the presence of broad but distinct Raman bands at 37 GPa imply that BTO does not amorphize up to this pressure. On the other hand, persistence of broad Raman bands even after complete release of pressure implies that it still retains vestiges of pressure-induced positional disorder. D. Lattice Dynamical Studies of Phonons at High Pressure. Phonon spectra of the orthorhombic and monoclinic phases of BaTe2O6 were computed in the whole Brillouin zone for pressures up to 20 GPa employing lattice dynamics using GULP. Relaxed structural parameters at 0 GPa of the orthorhombic and monoclinic phases were used for these calculations. A total of 21 sets of spectra in each phase were calculated at different pressures in the range 0−20 GPa in steps of 1 GPa for both the orthorhombic and the monoclinic phases. The mode frequencies of the calculated phonon spectra for the orthorhombic phase were collected up to 10 GPa, the structural transition pressure obtained from DFT, while the mode frequencies of the monoclinic phase were calculated from 11 to 21 GPa to study the behavior of phonon modes with pressure. Pressure variation of mode frequencies is found to be similar to the experimental results, and the phase transition from orthorhombic to monoclinic phase has been found at ∼10 GPa. Using the slope of pressure variation of the modes in each
Figure 12. Phonon dispersion curves, total, and atom-decomposed phonon density of states of BaTe2O6 obtained for (a) orthorhombic and (b) monoclinic phase. J
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Inorganic Chemistry on the x-axis represent the high symmetry directions in the Brillouin zones of the respective space groups. The k-vector path is so chosen that it follows the same directions in both of the Brillouin zones, but the labels are according to the respective space groups. The k-vector path in both phonon dispersion plots is (0,0,1/2) → (0,0,0) → (0,1/2,0) → (−1/ 2,1/2,0) → (−1/2,0,0) → (−1/2,0,1/2) → (−1/2,1/2,1/2) → (0,1/2,1/2). This way it is easy to compare both phonon dispersion plots to study the transformation from the orthorhombic to the monoclinic phase. As can be noticed, in both phases no imaginary phonon frequencies are seen, suggesting that both the low- and the high-pressure phases are dynamically stable at ambient pressure. A mixing of the acoustic and optic modes at energies less than 100 cm−1 can be seen in Figure 12a and b in the phonon dispersions corresponding to both structures. There is considerably more mixing in the orthorhombic than in the monoclinic phase. The phonon modes in the orthorhombic structure can be inferred to have softer harmonic spring constants as they show larger dispersion as compared to those in the monoclinic phase, which has relatively narrow dispersion. This behavior results in the smaller compressibility observed for the monoclinic structure. The phonon DOS shown alongside the dispersion curves is similar for both structures. It can be seen from Figure 12 that contribution from the Ba ion to the phonon DOS is significant only in the low energy range (
