Structural Stability and Anharmonicity of Pr2Ti2O7: Raman

Nov 7, 2016 - Swayam Kesari†, Nilesh P. Salke†, Sadeque Jahedkhan Patwe‡, Srungarpu Nagabhusan Achary‡, Anil K. Sinha§, Pulya Umamaheswara ...
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Structural Stability and Anharmonicity of Pr2Ti2O7: Raman Spectroscopic and XRD Studies Swayam Kesari,† Nilesh P. Salke,† Sadeque Jahedkhan Patwe,‡ Srungarpu Nagabhusan Achary,‡ Anil K. Sinha,§ Pulya Umamaheswara Sastry,† Avesh Kumar Tyagi,‡ and Rekha Rao*,† †

Solid State Physics Division and ‡Chemistry Division, Bhabha Atomic Research Centre, Trombay, Mumbai 400085, India § Indus Synchrotron Utilization Division, Raja Ramanna Centre for Advanced Technology, Indore 452013, India S Supporting Information *

ABSTRACT: Herein we report results of pressure- and temperaturedependent Raman scattering studies on Pr2Ti2O7. Pressure-dependent studies performed up to 23 GPa suggest a reversible phase transition above 15 GPa with subtle changes. Temperature-dependent investigations performed in the range of 77−1073 K showed anomalous temperature dependence of some of the Raman modes. Temperature-dependent X-ray diffraction data indicated no structural transition but nonlinear expansion of unit-cell parameters with increasing temperature. With increasing temperature, the structure dilates anisotropically, and volume of coordination polyhedra around all the atoms expands. Also with increasing temperature the distortions in coordination polyhedra around all the atoms decrease, and appreciable decrease is observed in Pr(1)O10 and Pr(3)O9 units. The pressure evolution of Raman-mode frequencies was analyzed for both ambient as well as high-pressure phases, and mode Grüneisen parameters for ambient pressure phase were obtained. The temperature evolution of Raman-mode frequencies was analyzed to obtain the explicit and implicit anharmonic components, and it was found that some of the modes attributable to TiO6 octahedra and PrOn polyhedra have dominating explicit anharmonic component. Comparison of the structural data with the temperature dependence of Raman modes suggests that the anomalous behavior in Raman modes is due to phonon−phonon interaction.

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INTRODUCTION The ternary oxides of the family A2B2O7 in which A is a trivalent rare-earth cation and B is a tetravalent cation like Ti, Zr, Hf, and Sn are widely studied due to their interesting crystal chemistry as well as due to various properties such as catalytic, electrical, magnetic, ionic conductivity, etc.1−4 Compounds of this family are also useful in many technological applications such as nuclear waste immobilization,1 electrochemical systems,2 fuel cell, catalytic converter, etc. Depending on the ratio of radii of A and B cations, the A2B2O7 family of compounds stabilize in various types of crystal structures at ambient conditions, namely, fluorite (rA/rB < 1.48), cubic pyrochlore (1.48 < rA/rB < 1.78), and monoclinic perovskite type (rA/rB > 1.78) structures.3 Among these, if B is Ti (i.e., rare-earth titanates) with A = La, Nd, Ce, and Pr, then they crystallize in monoclinic perovskite-type structure, while for the rest of the rare-earth elements, such titanates form cubic pyrochlore type of structure.4 Monoclinic perovskites have been of interest due to their high Curie temperature, ferroelectric and piezoelectric properties, high dielectric constant, and nonlinear optical and photocatalyic properties.3,4 Cubic pyrochlore structure of A2Ti2O7 compounds form three-dimensional geometrically frustrated magnetic compounds.5−10 Most of these compounds show complex magnetic structures and have been extensively studied at various nonambient temperatures and pressures. Temperature-dependent Raman spectroscopic investigations of Dy2Ti2O7 and © XXXX American Chemical Society

Lu2Ti2O7 indicated anomalous temperature dependence of phonon frequencies due to phonon−phonon anharmonic interactions, whereas coupling between spin, crystal field, and phonons have been reported in Tb2Ti2O7.6,7 High-pressure investigations of pyrochlores of this family have revealed interesting results. For example, X-ray diffraction (XRD) studies on pyrochlore Tb2Ti2O7 at high pressures and low temperatures reported the ambient pyrochlore phase to be stable up to 24 GPa and 6.5 K.11 Another high-pressure Raman and XRD study performed on Tb2Ti2O7 reported deformation of coordination in pyrochlore lattice near 9 GPa.9 This was followed by one more high-pressure XRD study on Tb2Ti2O7 that reported structural transition to monoclinic phase at 39 GPa.12 High-pressure Raman and XRD investigation of Sm2Ti2O7 shows anionic disorder around 40 GPa,8 but recent high-pressure single-crystal study and density functional theory calculations did not support this finding of Sm2Ti2O7.13 Similarly Raman and XRD studies on Yb2Ti2O7 have revealed a reversible structural transition to monoclinic phase at 28.6 GPa.10 XRD studies at high pressures on Ho2Ti2O7 and Y2Ti2O7 have indicated structural transition to monoclinic phase at 37 and 42 GPa, respectively.12 High-pressure investigations on cubic pyrochlores of Ln2Zr2O7 (Ln = Ce, Nd, Gd) family reported transition to lower symmetric Received: August 2, 2016

A

DOI: 10.1021/acs.inorgchem.6b01873 Inorg. Chem. XXXX, XXX, XXX−XXX

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Pressure was measured using ruby fluorescence method. Beyond 15 GPa, Raman modes are broadened due to deviatoric stress. Error in determination of Raman mode frequency above 15 GPa is within ±1 cm−1.This is estimated from pressure dependence of mode frequencies of three different experimental runs. The Raman spectra were fitted to Lorentzian line shapes using Origin program to determine the Ramanmode frequency, full width at half-maximum (FWHM), and integrated intensity. In the spectral analysis, we adopted the standard strategy to use the minimum number of peaks that yield a good fit and peak centers. We followed the goodness-of-fits, the uncertainties in position, integrated intensities, and FWHM to arrive at the best fit. This procedure is followed consistently for all temperatures and pressures. The FWHM values presented are obtained by deconvoluting the Raman spectroscopic data with instrument function. Temperature-dependent XRD studies were performed in two instrumental facilities, specifically, temperature above ambient temperature by using a rotating anode (Cu target) based X-ray diffractometer and temperature below ambient temperature by using ADXRD beamline (BL-12) of Indus-2 (2.5 GeV, 200 mA) Synchrotron source at Raja Ramanna Centre for Advanced Technology (RRCAT), Indore, India.25 For high temperature (298−1473 K), the powder sample was filled in a groove of a platinum sample holder and placed inside a heater with opening for X-ray beams. The room-temperature XRD patterns were recorded in the 2θ range of 10−100° with steps of 0.02° and time 2 s. The low-temperature measurements were performed in transmission mode by placing small amounts of sample between kapton foils. The sample holder was cooled using a liquid helium cryostat, and the temperature was controlled by Lakeshore temperature controller. The sample was cooled to 20 K and held for an hour to equilibrate the temperature, and the diffraction data were collected in transmission mode while heating the sample. At each temperature the sample is equilibrated for ∼30 min before recording the data. The diffraction data were collected on an image plate (mar 345) detector using monochromatic X-ray of wavelength 0.6614 Å. The wavelength and the sample-to-detector distance were accurately calibrated by obtaining XRD pattern of LaB6 NIST standard in the same setup. The diffraction images were integrated by using FIT2D program.26 Both the low-temperature and high-temperature XRD data were analyzed by Rietveld method using Fullprof-2K software package.27

monoclinic structure.14 Recent molecular dynamics simulations on A2B2O7 pyrochlores have revealed the influence of ionic radii of A and B atoms on bulk modulus, specific heat, and thermal expansion coefficient in a large number of pyrochlores.15 There are various other compounds of A2B2O7 family such as In2Ge2O7,16 Bi2Ti2O7,17 Bi2Sn2O7,17 Eu2Sn2O7,18 Cd2Re2O7,19 etc., which have also been explored under pressure. On the one hand, monoclinic In2Ge2O7 shows pressure-induced transition to another monoclinic phase above 6.6 GPa, which is accompanied by a large reduction in volume and increase in cation coordination number of both the cations. On the other hand, cubic In2Ge2O7 is relatively stable under pressure.16 Similarly while Bi2Ti2O7 was found to transform from cubic pyrochlore phase to disordered fluorite type structures beyond 33 GPa,17 Bi2Sn2O7, which has monoclinic structure at ambient conditions, exhibits a series of structural transitions at relatively lower pressures. Interestingly, Bi2Sn2O7 showed the same series of structural transitions both as a function of pressure as well as temperature.17 Monoclinic perovskites A2Ti2O7 (A = La, Nd, Ce and Pr) compounds are relatively less explored compared to the cubic pyrochlores. Among the monoclinic rare-earth titanates, Pr2Ti2O7 and Ce2Ti2O7 are likely to have exceptional behavior due to the possible variable valence states of the rare-earth ions. A comparative low-temperature Raman spectroscopic study of Pr2Sn2O7 and Pr2Ti2O7 revealed phonon-crystal field coupling only in Pr2Sn2O7.20 XRD and Raman spectroscopic studies at high pressures on La2Ti2O7 indicated a reversible structural transition above 16.7 GPa to a new monoclinic structure due to tilting of TiO6 octahedra.21 To understand the structural stability of Pr2Ti2O7 under pressure we performed highpressure Raman spectroscopic experiments up to 23 GPa. Recent temperature-dependent XRD, Raman spectroscopy, and differential thermal analysis studies revealed no structural transitions up to temperatures of 1473 K.22 However, some of the Raman modes in Pr2Ti2O7 showed anomalous behavior in the temperature range of 300−1073 K. Here, we performed pressure- and temperature-dependent studies on Pr2Ti2O7 and complimented the previously reported Raman data and interpreted the results in terms of anharmonicity using the pressure and temperature dependence of Raman modes. XRD measurements on Pr2Ti2O7 at low temperatures in the range of 20−300 K were performed to find out if the anomalous behavior is associated with any change in the crystal structure.

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RESULTS AND DISCUSSION a. Ambient Structure and Raman Spectra. The crystal structure of Pr2Ti2O7 at ambient conditions is monoclinic (space group P21) and contains four formula units in the unit cell. The typical structure of Pr2Ti2O7 is shown in Figure 1. It consists of layers of corner-shared TiO6 octahedra and Pr3+ ions. The empty spaces between the TiO6 octahedra are occupied by Pr3+ ions. All the TiO6 octahedra are distorted and

EXPERIMENTAL DETAILS

Polycrystalline sample of Pr2Ti2O7 was prepared by solid-state reaction using Pr6O11 and TiO2 as starting reactants using a procedure similar to that given in ref 22. Bandgap of Pr2Ti2O7 measured experimentally is 3.1 eV.22 Raman spectra of polycrystalline sample were excited using 532 nm (2.3 eV) to avoid laser absorption. Backscattered light was analyzed using a home-built 0.9 m single monochromator, coupled with an edge filter and detected by a cooled CCD. Entrance slit was kept at 50 μm, which gives a spectral band-pass of 3 cm−1. Raman spectra could be reproduced with an accuracy of ±0.2 cm−1. Temperature-dependent Raman spectroscopy measurements in the range from 77 to 293 K were performed using Linkam THMS 600 temperature stage with temperature stability better than ±0.5 K over the sample. Raman spectroscopic measurements on Pr2Ti2O7 at high pressures up to 23 GPa were performed using a diamond anvil cell (Diacell B-05). To maintain hydrostatic environment inside sample chamber, 16:3:1 methanol−ethanol−water mixture was used as pressure-transmitting medium, which remains hydrostatic up to 10.5 GPa.23,24 The experiment was also repeated with 4:1 methanol− ethanol mixture, which freezes at 10.5 GPa, as well as with silicone oil.

Figure 1. Crystal structure of Pr2Ti2O7 at ambient conditions. B

DOI: 10.1021/acs.inorgchem.6b01873 Inorg. Chem. XXXX, XXX, XXX−XXX

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various pressures up to 23 GPa. All the observed Raman-mode frequencies of Pr2Ti2O7 harden with increase in pressure. Under pressure new modes emerge gradually around 88, 108, 123, 166, 363, and 520 cm−1 at different pressures. The emergence of new modes could be due to lifting of the degeneracy under pressure. With further increase in pressure many of the weak modes merge with stronger modes. Around 15 GPa, while the Pr−O modes below 200 cm−1 remained intact, those between 200 and 400 cm−1 broaden, and there is a redistribution of intensity. Beyond 15 GPa, we could follow only modes around 80, 88, 565, 785, and 814 cm−1 because of overlapping and broadening of rest of the modes. Around 15 GPa, there is a discontinuous change in Ti−O stretching mode frequencies. This nonlinear behavior was noted in our earlier study also.29 Under pressure, intensity exchange is observed between Raman mode at 88 cm−1 and the new mode at 91 cm−1, which corresponds to Pr−O vibrations as shown in Figure 4a. Similar intensity exchange is also observed for Ti−O

connected by sharing the corners. Ti−O bond lengths range from 1.83 to 2.25 Å, while the Pr3+ ions are 10, 9, or 8 coordinated with the oxygen atoms. The Pr3+ ions inside the perovskite layers show larger distortion and dispersion in bond lengths compared to those between these layers. As the unit cell of Pr2Ti2O7 structure has four formula units, 132 normal modes of vibration are expected. Factor group analysis gives irreducible representations for normal mode of vibration as Γ = 66A + 66B, of which A + 2B are acoustic modes. Raman spectra of Pr2Ti2O7 at ambient conditions are shown in Figure 2, which matches with those reported.20,28 Of

Figure 2. Raman spectra of Pr2Ti2O7 at ambient conditions showing Lorentzian fitting of the data.

129 expected Raman-active modes, only 32 distinct peaks are observed in the Raman spectra at ambient conditions. The smaller number of modes observed in the Raman spectra at ambient conditions could be due to weak intensity or accidental degeneracy of some modes. The modes appearing in the range of 50−490 cm−1 are attributed to the Pr−O vibrations. In particular, the mode at 105 cm−1 is an external mode due to Pr3+ translation. Modes in the range of 490−575 cm−1 are assigned to the internal vibrations of the distorted TiO6 octahedron. The Raman-mode frequencies associated with the Ti−O stretching vibrations are observed above 600 cm−1.28 b. Raman Spectroscopic Measurements as a Function of Pressure. Figure 3 shows the Raman spectra of Pr2Ti2O7 at

Figure 4. Raman spectra of Pr2Ti2O7 at various pressures showing intensity exchange.

stretching modes at 785 and 814 cm−1 around 15 GPa as can be noticed in Figure 4b. The intensity exchange could be due to phonon−phonon coupling, but the pressure dependence of mode frequencies suggests that there is a clear discontinuity at 15 GPa. Figure 5a,b shows the pressure dependence of the Raman-mode frequencies. The features observed across 15 GPa point toward a phase transition in Pr2Ti2O7 with subtle

Figure 5. Pressure dependence of Raman modes of Pr2Ti2O7. Solid lines are the linear fit to data.

Figure 3. Raman spectra of Pr2Ti2O7 at various pressures. C

DOI: 10.1021/acs.inorgchem.6b01873 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry Table I. Pressure and Temperature Dependence of Raman Modes phase I

phase II anharmonicity (1 × 10−5)

ωi (cm−1) 59 72 80 b 84 a 88 91 105 a 108 115 a 123 136 a 166 158 172 179 b 187 193 200 217 231 249 261 269 284 312 b 320 327 b 342 350 a 363 385 b 407 431 453 487 504 a 520 526 540 565 594 605 785 814 a

∂ωi ∂T p

−1

( ) (cm

K−1)

−0.0076(3) −0.0091(2) −0.0038(3) −0.0104(6)

∂ωi ∂P T

−1

( ) (cm

−0.0085(2) −0.0095(3) −0.0120(3) −0.0092(3) 0.0009(5) −0.015(1) −0.0072(6) −0.009(2) −0.0170(8) −0.018(2) −0.0029(7) −0.0118(5) −0.0101(5) −0.0148(4) −0.0111(6) −0.0179(7) 0.004(1) 0.0070(1) −0.014(2) −0.005(2) −0.0190(9) −0.016(1) −0.023(5) −0.0179(7) −0.0037(8) 0.0010(1) −0.0031(8) −0.0176(9) −0.0167(4) −0.0194(4) −0.014(1) −0.0297(9) 0.0030(6) −0.0022(9)

GPa−1)

γiT

total

implicit

explicit

0.71(6) 0.47(5) 0.75(3)

1.5(1) 0.79(8) 1.13(5)

−12.9 −12.6 −4.7 −12.4

−4.8 −2.5 −3.6

−8.1 −10.1 −1.1

0.12(2) 0.76(7) 0.26(2) 0.87(2) 1.05(5) 0.67(9) 1.14(4) 1.48(3) 2.66(7) 2.3(6) 1.8(1)

0.16(3) 1.01(9) 0.30(3) 0.97(2) 1.105(6) 0.66(9) 1.01(4) 1.08(2) 2.04(5) 1.6(5) 1.22(7)

1.75(3) 1.27(5) 1.22(9) 1.76(5) 1.97(4) 2.1(1) 2.09(9) 2.34(7) 2.97(6)

1.10(2) 0.77(3) 0.68(5) 0.92(3) 0.96(2) 0.97(6) 0.94(4) 1.00(2) 1.15(2)

2.28(7)

0.84(3)

1.77(3) 2.6(1) 3.93(7)

0.61(1) 0.87(3) 1.23(2)

2.2(1) 1.68(7)

0.62(3) 0.45(2)

3.3(2) 3.2(2) 4.10(7) 4.28(9) 3.04(6) 4.61(6) 4.88(4) 4.50(5) 3.86(5)

0.79(5) 0.74(5) 0.94(2) 0.96(2) 0.65(1) 0.94(1) 0.98(1) 0.69(1) 0.57(1)

−9.3 −9.0 −10.4 −6.8 0.6 −8.7 −4.0 −4.8 −8.8 −9.0 −1.3 −5.1 −4.0 −5.7 −4.1 −6.3 1.3 2.2 −4.3 −1.5 −5.4 −4.1 −5.6 −4.1 −0.8 0.2 −0.6 −3.3 −3.1 −3.4 −2.3 −4.9 0.4 −0.3

−0.5 −3.3 −1.0 −3.1 −3.6 −2.1 −3.3 −3.5 −6.6 −5 −3.9

∂ωi ∂P T

−1

( ) (cm

GPa−1)

0 0.6(1) 0.42(6)

−6 −8 −6.8 −3.5 3.5 7.2 −3.7 −0.1

−3.5 −2.5 −2.2 −3.1 −3.1 −3.1 −3.0 −3.2 −3.7

−5.3 −6.5 0.9 −2 −0.9 −2.6 −1.1 −3.1 5

−2.7

−1.6

−2.0 −2.8 −4.0

−3.4

−2.0 −1.4

−2.1 0.6

−2.5 −2.4 −3.0 −3.1 −2.1 −3.1 −3.2 −2.2 −1.8

1.9

1.5(1)

1.1(3) 1.3(6)

−0.1

−0.3 0 −1.3 0.8 −1.7 2.6 1.5

0.5(3)

2.8(3)

2.1(3) 3.3(3)

Represents the extrapolated position at 0 GPa for the modes that appear under pressure. bRepresents extrapolated position at 298 K for the modes

that appear at low temperature. Isothermal Grüneisen parameter γiT = in the monoclinic phase

21

and α = 32.3 × 10

−6

−1 22

B0 ω0

∂ωi ∂P T

( )

is calculated using bulk modulus of La2Ti2O7 which is B0 = 121 GPa

K .

structural change as observed in La2Ti2O7.21 It can be recalled here, earlier energy calculations with molar volume indicates the high symmetric monoclinic P21/m, Cmc21, or Cmcm structures are expected at larger unit-cell volume, while an orthorhombic Pna21 with larger unit-cell parameters due to displacement of cations and anions may be expected at higher pressure.22 The pressure evolution of Raman modes suggests overlapping of modes and discontinuity in pressure depend-

ence. However, because of lack of high-pressure XRD data at present we cannot conclude about the structure of transformed phase. Also it can be suggested that the change in structure might be related to the local structure and/or distortion around the cations. The high-pressure structural studies on La2Ti2O7 by using in situ XRD21 revealed similar unit-cell parameters for high-pressure phase compared to the ambient phase, while the discontinuity in pressure evolution of unit-cell parameters have D

DOI: 10.1021/acs.inorgchem.6b01873 Inorg. Chem. XXXX, XXX, XXX−XXX

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cies. The Raman modes that exist only at low temperatures are the weak modes that broaden and hence merge with other modes at higher temperatures. The vanishing of the Raman modes can be due to temperature-induced broadening and inherent weak intensities of the modes. It may be noted that, of 129 expected Raman-active modes, only 32 distinct peaks are observed in the Raman spectra at ambient conditions. No discontinuous change is observed in the studied temperature range, which indicates that Pr 2Ti2O7 is stable in the temperature range from 77 to 1073 K. Temperature-dependent coefficients of Raman-mode frequencies are shown in Table I. In particular, the mode at 785 cm−1, which is due to stretching of Ti−O bond, shows unusual anomalous temperature dependence. Anomalous behavior of phonons could be a precursor to a structural transition at much lower temperatures. Another possible reason could be anharmonic nature of the phonon without any transition due to the inherent nature of the phase. As phonon anharmonicity has significant effect on thermodynamic properties, it is important to estimate the anharmonicity of individual modes. In the earlier study, it was speculated that this anomaly could be due to symmetrization of the distorted TiO6 octahedra, which may lead eventually to a structural transition at higher temperatures.22 Symmetrization could result in the reduction in some of the bond lengths and increase in some other bond lengths of the TiO6 octahedra. To understand the nature of anomaly, we analyzed the XRD data of Pr2Ti2O7 at different temperatures. d. Temperature-Dependent X-ray Diffraction Studies. A comparison of the XRD data at both low and high temperatures with those recorded at ambient conditions indicates the data are almost similar. The ambient-temperature structural parameters (monoclinic, space group (SG) P21) earlier reported22 by us were used as starting model for the refinement for the presently recorded ambient-temperature data. Only the instrumental errors were corrected for the respective XRD patterns. In all the nonambient XRD patterns, the background, profile, and the unit-cell parameters were refined by using the instrumental correction parameters observed for ambient-temperature data. It may be mentioned here that the background of the XRD data recorded using synchrotron radiation and image plate detector were modeled by using selected points to create a smoothly varying background profile, while the background of the XRD data recorded using Cu Kα radiation and scintillation counter were modeled by fifth-order polynomial functions. In both cases the peak profiles of the XRD data were modeled by using pseudoVoigt profile functions with angle-dependent mixing parameters (η = η0 + X × 2θ, where η0 and X are refinable parameters) of Gaussian and Lorenzian contributions. Further, the position coordinates were also refined for each temperature data. The refined unit-cell parameters of Pr2Ti2O7 and residuals of refinements observed in Rietveld refinements of XRD data recorded at 300 K on image plate are a = 7.7159(3), b = 5.4869(3), c = 12.9936(8) Å, β = 98.59(1)°, and V = 543.93(5) Å3 (Rp: 7.09%, Rwp:11.2%, χ2: 5.62, RB = 5.49%, RF = 3.5%). Similarly, the refined unit-cell parameters observed at 298 K in high-temperature stage are a = 7.7149(2), b = 5.4873(1), c = 12.9993(5) Å, β = 98.56(1)°, V = 544.18(3) Å3; (Rp: 13.6%, Rwp: 18.8%, χ2:2.33, RB: 7.78%, RF: 5.22%). In both cases the ambient-temperature unit-cell parameters are closely in agreement. The refined unit-cell parameters and the position coordinates observed at ambient temperature are in agreement with those reported in the earlier study.22 In an analogous

been attributed to change in local distortion in TiO6 octahedra. In this case also, we expect a possible distortion or rotation of TiO6 octahedra related to the phase transition, as a prominent change in high-frequency stretching modes of TiO6 octahedra are observed at the transition. Experiments have been repeated with different pressure-transmitting media to ensure that the observed changes are not due to the freezing of medium.24 We have not observed any indication of the nonhydrostaticity triggering the phase transition. However, the influence of nonhydrostaticity in triggering the transition cannot be ruled out. Pressure-dependent coefficient for all the Raman modes of Pr2Ti2O7 in both the phases are given in Table I. Isothermal mode Grüneisen parameter is calculated using bulk modulus of isostructural La2Ti2O7.21 Isothermal mode Grüneisen parameter for the Raman modes of Pr2Ti2O7 in ambient condition monoclinic phase is also given in Table I. c. Temperature-Dependent Raman Spectroscopic Studies. To complete the high-temperature Raman data reported earlier, the Raman spectra down to 77 K were recorded, and the Raman spectra at various temperatures are shown in Figure 6. At the lowest temperature (77 K) of

Figure 6. Raman Spectra of Pr2Ti2O7 at various temperatures.

measurement, we observed 45 Raman modes. All the modes show decrease in frequency with increase in temperature except for the modes at 158, 312, 320, 487, and 785 cm−1. Figure 7 shows the temperature dependence of Raman-mode frequen-

Figure 7. Temperature-dependent variation of Raman-mode frequencies. E

DOI: 10.1021/acs.inorgchem.6b01873 Inorg. Chem. XXXX, XXX, XXX−XXX

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cell parameters of Pr2Ti2O7 between 300 and 1473 K is almost linear, and the coefficients of thermal expansion along a-, b-, and c-axes are 10.6 × 10−6, 10.4 × 10−6, and 7.0 × 10−6 K−1, respectively. The average volume thermal expansion is 28.3 × 10−6 K−1, which is comparable to our earlier values. It may be noted that the expansion of c-axis that is parallel to the stacking direction shows lower value compared to other axis. This may be attributed to appreciable reduction in distortion of polyhedra around Pr atoms compared to Ti atoms. To further understand the effect of temperature on structural parameters, the derived parameters are compared. Typical bond lengths between various atoms at some representative temperature are given as Supporting Information. It can be mentioned here that the structure of Pr2Ti2O7 has crystallographically distinct four Pr atoms (Pr1−Pr4), four Ti atoms (Ti1−Ti4), and 14 oxygen atoms (O1−O14), and all are in general positions of SG P21. All the Ti atoms have distorted octahedral coordination, while Pr1 and Pr2 have 10 coordinated polyhedra with oxygen atoms. The Pr3 and Pr4 atoms have distorted polyhedra with coordination number 9 and 8, respectively. With increasing temperature the typical Pr−O and Ti−O bonds show expected increasing trend for typical ionic bonds. The variation of average bond lengths for different coordination polyhedra are shown in Figure 10. Distortion in coordination polyhedra as observed from the variation of bond lengths are shown in Figure 11. It is also observed that the distortion in the coordination polyhedra around all the atoms decreases with temperature, and the decrease is appreciable in the polyhedra

manner, Rietveld refinements of the powder XRD data recorded both at lower and higher temperatures were performed. In all the cases, the diffraction patterns fitted well to the monoclinic (SG P21) structure of Pr2Ti2O7. No anomalous change in the diffraction pattern is observed up to 1473 K. Typical refined XRD patterns at 20 and 1473 K are shown in Figure 8. The refined position coordinates for Pr2Ti2O7 at 20 and 1473 K are given as Supporting Information.

Figure 8. Rietveld refinement plot of the XRD data of Pr2Ti2O7 recorded at 20 and 1473 K. (Residuals of refinements: for 20 K data, Rp: 6.54%; Rwp:10.5%; χ2: 6.31; RBragg: 5.18%; RF: 2.96%, and for 1473 K data, Rp: 13.8%, Rwp: 18.0%, χ2:2.35; RBragg: 8.54%, RF: 6.46%).

The temperature-dependent unit-cell parameters of Pr2Ti2O7 are shown in Figure 9. It can be seen that unit-cell parameters increase nonlinearly between 40 and 1473 K, while an anomalous variation is noticed at lower temperatures (below 40 K). Further it is noticed that the unit-cell parameters show only marginal variation at lower temperatures but an appreciably higher expansion at higher temperatures, which is typical for insulating ceramic materials. The expansion of unit-

Figure 10. Temperature-dependent variation of Pr−O and Ti−O bonds.

Figure 9. Temperature-dependent unit-cell parameters of Pr2Ti2O7. F

DOI: 10.1021/acs.inorgchem.6b01873 Inorg. Chem. XXXX, XXX, XXX−XXX

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frequency (ωi) due to temperature at a particular pressure can be expressed as follows31 ⎛ ∂ωi ⎞ ⎛ ∂ω ⎞ ⎛ ∂V ⎞ ⎛ ∂ω ⎞ ⎜ ⎟ = ⎜ i⎟ ⎜ ⎟ + ⎜ i⎟ ⎝ ∂T ⎠ p ⎝ ∂V ⎠T ⎝ ∂T ⎠ P ⎝ ∂T ⎠V

(3)

Equation 3 can also be simplified as 1 ⎛ ∂ωi ⎞ 1 ⎛ ∂ω ⎞ ⎜ ⎟ = −αγiT + ⎜ i ⎟ ωi ⎝ ∂T ⎠ P ωi ⎝ ∂T ⎠V

The left-hand side of eq 4 gives the temperature-dependent isobaric frequency shift, which is the total anharmonicity as measured in temperature-dependent vibrational phonon frequency experiments. The first term on the right-hand side is the implicit anharmonicity; this is the volume contribution to the phonon frequency shift also known as quasiharmonic contribution. The second term on the right-hand side of eq 4 is the explicit/true anharmonic contribution to the phonon frequency shift, which is the pure-temperature effect and cannot be determined experimentally directly. Though this formalism is strictly valid only for cubic systems, it can be applied to noncubic systems also for separating implicit and explicit/true anharmonicity contributions of phonon-mode frequencies.32−34 In Table I, we separated the implicit and explicit anharmonicity contribution for the Raman-mode frequencies of Pr2Ti2O7 for ambient condition phase. Also it is important to note that none of the Raman modes has shown anomalous behavior with pressure. For many of the low-frequency modes corresponding to Pr−O vibrations and the Ti−O stretching mode around 785 cm −1 , the explicit components of anharmonicity are found to be dominant. Most of the modes with dominant explicit anharmonicity have negative value of explicit anharmonicity, which is the manifestation of dominant three phonon processes. For the modes at 158, 312, and 785 cm−1, explicit anharmonicities have positive value indicating dominant four-phonon process for respective modes, which results in increase in frequency with temperature. Anharmonicity of the Ti−O stretching mode may be also related to the anomaly in structure data at temperatures below 40 K pointing toward structural change at lower temperatures. We further analyzed temperature-dependent shifts for the modes 158, 312, and 785 cm−1 with anomalous behavior. Explicit anharmonicity as denoted by second term on the righthand side of eq 4 arises from a phonon decaying into two phonons (cubic anharmonicity) or three phonons (quartic anharmonicity) or more. This comes from cubic, quartic, and higher-order terms in the expansion of the interatomic potential in powers of the displacements of the atoms from their equilibrium positions.30 While the cubic term produces a decrease in frequency, quartic term produces an increase in frequency. The resultant shift in phonon frequency due to phonon−phonon interaction may be either positive or negative depending on the relative magnitudes of the anharmonic terms in the interatomic potential. The model suggested by Balkanski et al. assumes that each phonon of frequency ω0 decays into phonons of frequency ω0/2 and ω0/3, for cubic and quartic anharmonicities, respectively.35 The resultant temperaturedependent frequency shift due to true anharmonicity is given as

Figure 11. Distortion in coordination polyhedra.

around Pr1, Pr3, and Ti3 atoms. This observation can be related to symmetrization of the coordination polyhedra. Symmetrization around Pr atom is consistent with the observation of lower thermal expansion of c-axis as mentioned earlier. But there is no reduction in any of the bond lengths with increasing temperature. This suggests that the anomaly in Raman modes at higher temperature is predominantly due to anharmonicity of the modes. In the following section, we investigated anharmonicity of some of the prominent phonon modes of Pr2Ti2O7. e. Analysis of Anharmonicity in Pr2Ti2O7. Temperaturedependent phonon-mode frequency has several contributions, which can be written as follows.7 ω(T ) = ω0 + Δωvol(T ) + Δωanh(T ) + Δωel − ph(T ) + Δωsp − ph(T )

(1)

where ω(T) is phonon-mode frequency at temperature T; ω0 is phonon frequency at 0 K, and Δωvol(T) is volume/implicit contribution to frequency shift, which can be expressed as Δωvol(T ) = −

∫0

T

α(T ) ⎛ ∂ω ⎞ ⎜ ⎟ dT χ (T ) ⎝ ∂P ⎠T

(4)

(2)

where α(T) is the volume thermal expansion coefficient, and χ(T) is the compressibility. Δωanh(T) is the true/explicit anharmonic contribution to frequency shift, arises from cubic, quartic, and higher-order terms in the expansion of the interatomic potential in powers of the displacements of the atoms from their equilibrium positions;30 Δωel‑ph(T) is due to the renormalization of the phonon frequency due to coupling with electron; Δωsp‑ph(T) is the shift in phonon frequency due to coupling of spin and phonon arising from the modulation of spin exchange integral by lattice vibration. Terms corresponding to electron−phonon or spin−phonon are generally absent in insulating or nonmagnetic systems. Hence above relation can be simplified by considering only implicit and explicit anharmonicity contribution in the temperature-dependent shift at constant pressure. For an isotropic system, the total change in phonon G

DOI: 10.1021/acs.inorgchem.6b01873 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry ⎛ ⎞ 2 ⎟ Δωanh(T ) = A⎜1 + ℏω /2k T (e 0 B − 1) ⎠ ⎝ ⎛ 3 + B⎜1 + ℏω /3k T 0 B − 1) (e ⎝ +

3 (e

ℏω0 /3kBT

⎞ ⎟ − 1) ⎠ 2

(5a)

where A is the coefficient of cubic anharmonicity, and B is the coefficient of quartic anharmonicity. The broadening of phonon modes at high temperatures is also a consequence of the cubic and/or quartic anharmonicity. Broadening in phonon line width due to three and four phonon decay processes35 at higher temperature is given by ⎛ ⎞ 2 ⎟ Γ(T ) = Γ0 + C ⎜1 + ℏω /2k T (e 0 B − 1) ⎠ ⎝ ⎞ ⎛ 3 3 ⎟ + D⎜1 + ℏω /3k T + ℏω /3k T 2 0 B 0 B − 1) − 1) ⎠ (e (e ⎝ (5b)

The coefficients C and D are the strengths of cubic and quartic anharmonicities, respectively. Explicit anharmonicity estimated from pressure- and temperature-dependent phononmode frequencies are useful in modeling the thermodynamic properties like specific heat and entropy of the geophysically important mantle minerals.30 Study of temperature as well as pressure dependence of phonon-mode frequencies can be used to separate the quasiharmonic and true anharmonic contributions. The role of different normal modes of vibrations in determining the structural stability can be estimated by investigating the anharmonicity of individual vibrations. While computational methods for treating anharmonicity are extremely expensive, experimental methods like Raman spectroscopy provide a simple tool for examining this aspect. While most of the Raman modes of Pr2Ti2O7 exhibit decrease in frequency with temperature, which is due to threephonon process, increase in frequency of some of the modes indicates contribution of quartic anharmonicity also. Figure 12 shows the cubic and quartic anharmonicity analyses for the Raman modes at 158 and 312 cm−1, which are due to Pr−O vibrations and 785 cm−1, which is a Ti−O stretching mode that shows anomaly with temperature. We subtracted volume contribution to temperature-dependent phonon frequency shift using eq 2, and the remaining part, which contains shift in phonon frequency due to explicit anharmonicity, is fitted to eq 5a to find the contribution of cubic and quartic anharmonicity. The FWHM is also fitted using eq 5b. Fitting parameters indicate quartic anharmonicity is significant for Ti− O stretching mode. This approach of incorporating higherorder anharmonicity has been used to explain soft mode behavior in ferroelectrics.36,37 Cubic and quartic anharmonic terms have been found to play an important role in the temperature dependence of Raman modes in many simple systems like MgF2.32 Incorporating techniques to treat anharmonicity computationally has been extremely expensive. Recently individual contribution of cubic and quartic anharmonicity was estimated in TiO2 using molecular dynamics calculations38 and also in a negative thermal expansion material ScF3 in phonon calculations using first principles.39 Present analyses of anharmonicity in Pr2Ti2O7 show the importance of

Figure 12. Temperature dependence of Raman-mode frequency after subtracting the volume contribution and FWHM for (a) 158, (b) 312, and (c) 785 cm−1 modes. Red line represents fitting of temperaturedependent Raman-mode frequency and FWHM to eqs 5a and 5b, respectively.

quartic anharmonicity in explaining the phonon behavior, which needs to be incorporated to estimate thermodynamic properties. Though the higher-order anharmonicity is important for most systems at high temperatures, it is significant even at lower temperatures for some highly anharmonic systems. Feng and Ruan40 have rigorously studied the rates of four-phonon scattering process, which results in quartic anharmonicity in the potential. For weakly anharmonic systems like Si, Ge, and diamond, quartic anharmonicity plays critical role at high temperatures, but for a strongly anharmonic system like bulk argon, quartic anharmonicity is significant even at 80 K. Quartic anharmonicity is known to produce anomalous temperature dependence and soft mode behavior in ferroelectrics like TlBr even at 1 K.36 Computation of physical properties like thermal H

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Inorganic Chemistry

(9) Saha, S.; Muthu, D. V. S.; Singh, S.; Dkhil, B.; Suryanarayanan, R.; Dhalenne, G.; Poswal, H. K.; Karmakar, S.; Sharma, S. M.; Revcolevschi, A.; Sood, A. K. Low-temperature and high-pressure Raman and x-ray studies of pyrochlore Tb2Ti2O7: Phonon anomalies and possible phase transition. Phys. Rev. B: Condens. Matter Mater. Phys. 2009, 79, 134112. (10) Mishra, A. K.; Poswal, H. K.; Sharma, S. M.; Saha, S.; Muthu, D. V. S.; Singh, S.; Suryanarayanan, R.; Revcolevschi, A.; Sood, A. K. The study of pressure induced structural phase transition in spin-frustrated Yb2Ti2O7 pyrochlore. J. Appl. Phys. 2012, 111, 033509. (11) Kumar, R. S.; Cornelius, A. L.; Somayazulu, M.; Errandonea, D.; Nicol, M. F.; Gardner, J. High pressure structure of Tb2Ti2O7 pyrochlore at cryogenic temperatures. Phys. Status Solidi B 2007, 244, 266−269. (12) Scott, P. R.; Midgley, A.; Musaev, O.; Muthu, D. V. S.; Singh, S.; Suryanarayanan, R.; Revcolevschi, A.; Sood, A. K.; Kruger, M. B. Highpressure synchrotron X-ray diffraction study of the pyrochlores: Ho2Ti2O7, Y2Ti2O7 and Tb2Ti2O7. High Pressure Res. 2011, 31, 219− 227. (13) Winkler, B.; Friedrich, A.; Morgenroth, W.; Haussuhl, E.; Milman, M.; Stanek, C. R.; McClellan, K. J. Compression behavior of Sm2Ti2O7-pyrochlore up to 50 GPa: single-crystal X-ray diffraction and density functional theory calculations. Chin. Sci. Bull. 2014, 59, 5278−5282. (14) Surble, S.; Heathman, S.; Raison, E.; Bouexiere, B.; Popa, K.; Caciuffo, R. Pressure-induced structural transition in Ln2Zr2O7 (Ln = Ce, Nd, Gd) pyrochlores. Phys. Chem. Miner. 2010, 37, 761−767. (15) Dong, L.; Li, Y.; Devanathan, R.; Gao, F. Molecular dynamics simulation of the structural, elastic, and thermal properties of pyrochlores. RSC Adv. 2016, 6, 41410. (16) Li, H.; Li, Y.; Li, N.; Zhao, Y.; Zhu, H.; Zhu, P.; Wang, X. A comparative study of high pressure behaviors of pyrochlore-type and thortveitite-type In2Ge2O7. RSC Adv. 2015, 5, 44121−44127. (17) Salamat, A.; Hector, A. L.; McMillan, P. F.; Ritter, C. Structure, Bonding, and Phase Relations in Bi2Sn2O7 and Bi2Ti2O7 Pyrochlores: New Insights from High Pressure and High Temperature Studies. Inorg. Chem. 2011, 50, 11905−11913. (18) Zhao, Y.; Yang, W.; Li, N.; Li, Y.; Tang, R.; Li, H.; Zhu, H.; Zhu, P.; Wang, X. Pressure-enhanced insulating state and trigonal distortion relaxation in geometrically frustrated pyrochlore Eu2Sn2O7. J. Phys. Chem. C 2016, 120, 9436−9442. (19) Barisic, N.; Forro, L.; Mandrus, D.; Jin, R.; He, J.; Fazekas, P. Electrical properties of Cd2Re2O7 under pressure. Phys. Rev. B: Condens. Matter Mater. Phys. 2003, 67, 245112. (20) Saha, S.; Prusty, S.; Singh, S.; Suryanarayanan, R.; Revcolevschi, A.; Sood, A. K. Pyrochlore dynamic spin-ice Pr2Sn2O7 and monoclinic Pr2Ti2O7: A comparative temperature-dependent Raman study. J. Solid State Chem. 2011, 184, 2204−2208. (21) Zhang, F. X.; Lian, J.; Becker, U.; Ewing, R. C.; Wang, L. M.; Hu, J.; Saxena, S. K. Structural change of layered perovskite La2Ti2O7 at high pressures. J. Solid State Chem. 2007, 180, 571−576. (22) Patwe, S. J.; Katari, V.; Salke, N. P.; Deshpande, S. K.; Rao, R.; Gupta, M. K.; Mittal, R.; Achary, S. N.; Tyagi, A. K. Structural and electrical properties of layered perovskite type Pr2Ti2O7: experimental and theoretical investigations. J. Mater. Chem. C 2015, 3, 4570−4584. (23) Klotz, S.; Chervin, J.-C.; Munsch, P.; Le Marchand, G. Hydrostatic limits of 11 pressure transmitting media. J. Phys. D: Appl. Phys. 2009, 42, 075413. (24) Errandonea, D.; Munoz, A.; Gonzalez-Platas, J. Comment on “High-pressure x-ray diffraction study of YBO3/Eu3+, GdBO3, and EuBO3: Pressure-induced amorphization in GdBO3. J. Appl. Phys. 2014, 115, 216101. (25) Sinha, A. K.; Sagdeo, A.; Gupta, P.; Upadhyay, A.; Kumar, A.; Singh, M. N.; Gupta, R. K.; Kane, S. R.; Verma, A.; Deb, S. K. Angle dispersive X-ray diffraction beamline on Indus-2 synchrotron radiation source: Commissioning and first results. J. Phys.: Conf. Ser. 2013, 425, 1−4.

expansion and conductivity need to take into account of anharmonicity.41 The present studies provide understanding of lattice anharmonicity in the ferroelectric system and enable us to identify instabilities that may affect the system and to provide insights to design high-performance materials.

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SUMMARY We have performed Raman spectroscopic measurements at high pressures on Pr2Ti2O7 up to 23 GPa. It undergoes a subtle reversible transition around 15 GPa. Temperature-dependent Raman spectroscopic investigations revealed that explicit anharmonicity is dominant over implicit anharmonicity for low-frequency modes. Some of the Raman-active modes, particularly the Ti−O stretching mode, show interesting anharmonic behavior. We have correlated the Raman spectroscopic data with temperature-dependent X-ray diffraction data and interpreted that the anharmonicity is due to phonon−phonon interactions.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.inorgchem.6b01873. Listing of refined structural parameters and interatomic distances of Pr2Ti2O7 at various temperatures (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Authors are thankful to Dr. S. Basu, Head, Solid State Physics Division and Dr. V. K. Jain, Head, Chemistry Division for support and encouragement to this work.

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REFERENCES

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