Article pubs.acs.org/IC
Phase Transformation, Vibrational and Electronic Properties of K2Ce(PO4)2: A Combined Experimental and Theoretical Study Samatha Bevara,†,‡ Karuna Kara Mishra,§ Sadeque Jahedkhan Patwe,† T. R. Ravindran,§ Mayanak K. Gupta,∥ Ranjan Mittal,∥ P. Siva Ram Krishna,∥ Anil K. Sinha,‡,⊥ S. Nagabhusan Achary,*,†,‡ and Avesh Kumar Tyagi†,‡ †
Chemistry Division and ∥Solid State Physics Division, Bhabha Atomic Research Centre, Trombay, Mumbai 400085, India ‡ Homi Bhabha National Institute, Anushakti Nagar, Mumbai 400094, India § Condensed Matter Physics Division, Indira Gandhi Centre for Atomic Research, Kalpakkam 603102, India ⊥ Indus Synchrotrons Utilization Division, Raja Ramanna Centre for Advanced Technology, Indore 452013, India S Supporting Information *
ABSTRACT: Herein we report the high-temperature crystal chemistry of K2Ce(PO4)2 as observed from a joint in situ variable-temperature X-ray diffraction (XRD) and Raman spectroscopy as well as ab initio density functional theory (DFT) calculations. These studies revealed that the ambient-temperature monoclinic (P21/n) phase reversibly transforms to a tetragonal (I41/amd) structure at higher temperature. Also, from the experimental and theoretical calculations, a possible existence of an orthorhombic (Imma) structure with almost zero orthorhombicity is predicted which is closely related to tetragonal K2Ce(PO4)2. The high-temperature tetragonal phase reverts back to ambient monoclinic phase at much lower temperature in the cooling cycle compared to that observed at the heating cycle. XRD studies revealed the transition is accompanied by volume expansion of about 14.4%. The lower packing density of the high-temperature phase is reflected in its significantly lower thermal expansion coefficient (αV = 3.83 × 10−6 K−1) compared to that in ambient monoclinic phase (αV = 41.30 × 10−6 K−1). The coexistences of low- and hightemperature phases, large volume discontinuity in transition, and large hysteresis of transition temperature in heating and cooling cycles, as well as drastically different structural arrangement are in accordance with the first-order reconstructive nature of the transition. Temperature-dependent Raman spectra indicate significant changes around 783 K attributable to the phase transition. In situ low-temperature XRD, neutron diffraction, and Raman spectroscopic studies revealed no structural transition below ambient temperature. Raman mode frequencies, temperature coefficients, and reduced temperature coefficients for both monoclinic and tetragonal phases of K2Ce(PO4)2 have been obtained. Several lattice and external modes of rigid PO4 units are found to be strongly anharmonic. The observed phase transition and structures as well as vibrational properties of both ambientand high-temperature phases were complimented by DFT calculations. The optical absorption studies on monoclinic phase indicated a band gap of about 2.46 eV. The electronic structure calculations on ambient-temperature monoclinic and hightemperature phases were also carried out. studies.10 Salvado et al. reported a series of such hydrated phosphates with K, Rb, Cs, and NH4 ions and investigated the detailed crystal structure from powder XRD studies.11,12 The crystal structures of these hydrated phosphates have been explained by either an orthorhombic (Imma) or a tetragonal (I41/amd) lattice where the distorted cubic CeO8 and tetrahedral PO4 units form the building blocks and the H2O and M+ ions are occupied in the tunnels formed by these units.11,12 Differential thermal analysis studies of Xu et al. on hydrothermally prepared K2Ce(PO4)2H2O indicated a dehydrated phase at higher temperature (HT) which undergoes a phase transition before its decomposition.10 However, no
I. INTRODUCTION Complex phosphates of Ce(IV) have been a challenging subject of research owing to their metastable nature and difficulty in preparation. Due to these reasons, only a few phosphates of Ce(IV) have been reported since the first reported example, Ce(IV)P2O7, by Herman and Clearfield in the early 1970s.1 Ce(IV)P2O7 has been of interest for its symmetry and negative thermal expansion behavior.2 Later, the existence of Ce(IV) in hydrated phosphates and hypophosphite lattices were reported in the literature.3−8 Xu et al. reported a complex hydrated phosphate as (NH4)2Ce(PO4)2H2O with Ce(IV) by hydrothermal reaction of the CeO2−NH3−P2O5−H2O system.8,9 Later, Xu et al. also reported a similar hydrated phosphate, K2Ce(PO4)2H2O, by hydrothermal reactions and assigned an orthorhombic lattice from powder X-rays diffraction (XRD) © 2017 American Chemical Society
Received: November 26, 2016 Published: March 6, 2017 3335
DOI: 10.1021/acs.inorgchem.6b02870 Inorg. Chem. 2017, 56, 3335−3348
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Inorganic Chemistry
sample was cooled to 60 K and allowed to equilibrate for about 1 h. The XRD pattern at several temperatures between 60 and 300 K was recorded by heating the sample to the desired temperature. For hightemperature XRD studies a small amount of sample was spread over a thin quartz plate placed on a custom-made resistive heater, and data were recorded while heating the sample from ambient temperature to a specified temperature. Data were also recorded while cooling the sample from high temperature. The temperature of the heater was controlled by a Eurotherm temperature controller, and a stability of ±1 K is ensured prior to measurement of diffraction data. The diffraction data collected on the image plate were integrated by using FIT2D software to obtain 1D diffraction patterns.22 All XRD patterns were analyzed by the Rietveld method using the Fullprof-2K software package.23 Raman spectroscopic studies were carried out using a Renishaw micro-Raman Spectrometer (model InVia). Using a 20×-long working distance objective, the 514.5 nm laser excitation line was focused to a ∼1 μm spot size on the sample. Raman spectra between 83 and 853 K were recorded by using a Linkam heating/cooling stage with a temperature stability of ±0.1 K. Data acquisition time and laser power were optimized to obtain a good signal-to-noise ratio in the Raman spectra. Spectra were analyzed with Lorentzian line shapes using PeakFit software (JANDEL).
details on the structure of hydrated, dehydrated, or transformed phases have been reported by them.10−12 Ogorodnyk et al.13 prepared a complex phosphate with mixed tetravalent cations, K4CeZr(PO4)4, by a high-temperature molten flux method, and a tetragonal (I41/amd) structure with orientationally disordered PO43− ions and random distribution of Ce4+ and Zr4+ ions has been assigned to it. The orientational disorder of the PO43− ions in this structure has been attributed to the local variation of coordination number around the tetravalent ions, i.e., due to a random distribution of ZrO6 and CeO8 polyhedra.13 Popa et al. studied a number of complex phosphates of the tetravalent cation and concluded that such complexes with Ce4+ are nonexistent due to transformation of Ce4+ to Ce3+ during the preparation procedure.14 Recently, an anhydrous phase of K2Ce(PO4)2 was prepared by us from a controlled hightemperature reaction with CeO2.15 The tetravalent Ce4+ is confirmed from both X-ray photoelectron and X-ray absorption spectroscopic studies, and a monoclinic (P21/n) structure with distorted cubic CeO8 and tetrahedral PO4 units as structural building units is revealed. Differential scanning calorimetry (DSC) and preliminary HTXRD studies on this anhydrous phase indicated a phase transition at a temperature similar to that reported by Xu et al.,10 while details of the hightemperature phase still remain unsolved due to the limitation of high-temperature XRD data as well as decomposition of the sample at higher temperature.15 As the complex phosphates of tetravalent cerium are ideal to simulate the thermophysical properties of tetravalent Pu and other minor actinides16,17 as well as for materials with mixed ionic and electronic conduction and redox catalyst due to the ease of fluctuation of the oxidation state of cerium, their structural and high-temperature properties bear significant importance.18−21 In order to understand the temperaturedependent structural properties as well as the stability of K2Ce(PO4)2, we investigated the detailed structure of the hightemperature phase from in situ HTXRD data using synchrotron radiation and established that the ambient monoclinic phase reversibly transforms to a tetragonal phase. Also, this study revealed a significant disorder in the K+ ions in the structure compared to the PO43− ions. The HT phase shows appreciably lower expansion compared to the ambient-temperature phase. The structure of the HT phase and phase transition are also supported by ab initio density functional theoretical calculations and in situ temperature-dependent Raman spectroscopic studies. Also, we have commented on the electronic properties of the phases from both experimental studies as well as electronic structure calculations.
III. THEORETICAL CALCULATIONS The calculations were performed using the ab initio density functional theory (DFT)24−26 method implemented in the Vienna ab initio simulation package (VASP).27,28 Projected augmented wave (PAW) potentials with the generalized gradient approximation (GGA)29,30 were used to calculate the total energy and band structure. The PAW method combines both pseudopotential and all-electron methods in an optimized manner. PAW creates a pseudopotential that adjusts the instantaneous electronic structure and charge transferability problems of the pseudopotential method.29,30 The GGA was formulated by the Perdew−Burke−Ernzerhof (PBE) density functional. The numbers of valence electrons of O, P, K, and Ce used in pseudopotential generation are 6, 5, 9, and 12, respectively. A plane wave kinetic energy cut off of 840 eV was used for electronic structure and equation of state calculations. Brillouin zone integrations were sampled using a Monkhorstpack method31,32 on a fine mesh. The convergence criteria for total energy and ionic forces were set to 10−7 and 10−3, respectively. All possible structures inferred from the XRD studies and reported structures for similar compositions were relaxed using the conjugate gradient algorithm. The band structure and electronic density of states were calculated using a very fine mesh. The zone center phonon frequencies were calculated using the density functional perturbation method.33,34
II. EXPERIMENTAL METHODS
IV. RESULTS AND DISCUSSION The phase purity and structure of prepared K2Ce(PO4)2 sample were confirmed by Rietveld refinement of the XRD data recorded at 300 K. The ambient-temperature XRD patterns recorded on the heating stage as well as in the cooling assembly were used for correction of the instrumental parameters for the data of the respective experimental run. Our earlier reported structural details for K2Ce(PO4)215 were used as initial parameters for the model structure. The background of the diffraction patterns recorded on the image plate (low T) were refined by linear interpolation of selected points to create a smoothly varying background profile, while those collected by scintillation counter or strip detector (high T) were modeled using fifth-order polynomial functions. The Bragg peaks of the
The ambient-temperature monoclinic phase of K2Ce(PO4)2 was prepared by our earlier reported synthesis method.15 The yellow product was characterized by powder XRD, Raman, and combined thermogravimetric and differential thermal analyses (TG-DTA) prior to further temperature-dependent structural studies. The powder XRD data of the sample were recorded using synchrotron radiation on the ADXRD beamline (BL-12) of the Indus-2 (2.5 GeV, 200 mA) Synchrotron Radiation (SR) Source at the Raja Ramanna Centre for Advanced Technology (RRCAT), Indore, India. The XRD patterns at low temperature (up to 60 K) were recorded in transmission mode by using an image plate (mar 345), while the data above ambient temperature were recorded in reflection mode using a scintillation counter or a Mythen strip detector. For low-temperature studies, wellground sample was placed between two Kapton films and placed between two copper blocks connected to a liquid helium cryostat. The 3336
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Inorganic Chemistry Table 1. Experimental and Theoretical Unit Cell Parameters of Different Structural Models of K2Ce(PO4)2a III: tetragonal I41/amd (No. 141)
I: monoclinic P21/n (No. 14) DFT 0K a (Å) b (Å) c (Å) β (deg) Z V (Å)3 Rp, Rwp (%) χ2 RB, RF E (eV/fu) a
9.2889 11.0347 7.7894 110.767 4 746.549
expt.
DFT
60 K
300 K
885 K
9.0755(1) 10.7823(2) 7.5994(1) 111.142(1) 4 693.58(2) 5.08, 6.88 2.81 3.91, 3.25
9.1020(1) 10.8132(1) 7.6231(1) 111.14(1) 4 699.78(2) 9.87, 12.7 5.34 8.58, 4.50
9.1761(2) 10.8571(2) 7.7096(2) 111.289(2) 4 715.66(3) 9.20, 11.8 6.22 11.7, 8.68
−92.3040
0K 6.9184 6.9184 17.9441 90 4 858.882
−92.3105
expt. 885 K 6.83658(3) 6.83658(3) 17.5091(1) 90 4 818.35(1) 9.20, 11.8 6.22 7.42, 4.77
II: orthorhombic Imma (No. 74) DFT 0K 6.9181 6.9187 17.9440 90 4 858.881
−92.3106
expt.
IV: monoclinic C2/c
V: monoclinic P21/c
DFT
DFT
885 K
0K
0K
6.8363(3) 6.8369(3) 17.5090(1) 90 4 818.35(5) 9.33, 12.0 6.41 7.79, 4.26
7.6266 22.4226 9.5032 113.441 8 1491.010
7.6648 25.5439 9.3702 108.707 8 1737.659
−92.2070
−91.7631
DFT-calculated unit cell parameters are at 0 K.
XRD patterns were modeled by a split-Pearson profile or pseudo-Voigt profile function with angle-dependent mixing parameters (η) defined as η = η0 + X × 2θ, where η0 and X are refinable parameters. Further, the scale, unit cell parameters, and position coordinates followed by isotropic thermal parameters were refined. Some of the weak peaks attributable to monazite-type CePO4 were observed in some XRD patterns. The complete diffraction pattern recorded at 300 K could be explained by this considered model, and the refined structural parameters are in agreement with those reported earlier by us.15 The refined unit cell parameters and residuals of refinement of the ambient-temperature phase are given in Table 1. The final Rietveld refinement plot for the XRD data of K2Ce(PO4)2 at 300 K is shown in Figure 1. Details of the structural parameters of the ambient-temperature phase are given in the Supporting Information (Table S1). In an analogous manner, the XRD pattern recorded at 60 K could be satisfactorily refined by using the observed structural parameters at 300 K. It is observed that the unit cell parameters decrease only marginally with decreasing temperature up to 60 K, the lowest temperature of the present XRD studies. The typical Rietveld refinement plot for the XRD data recorded at 60 K is included in Figure 1, and the refined position coordinates observed at 60 K are given in the Supporting Information (Table S1). No significant changes or splitting of any peaks are observed in the low-temperature data, which suggests the absence of any structural change at lower temperature. It may be mentioned here that we also carried out low-temperature neutron diffraction studies up to 6 K using a CCR-based cryostat on a 5-Linear PSD-based powder neutron diffractometer at the Dhruva nuclear reactor, BARC, Mumbai. The analyses of powder neutron diffraction data also suggest the absence of structural change up to 6 K. The typical Rietveld refinement plot of the neutron diffraction pattern recorded at 6 K and the corresponding refined structural parameters are given as Supporting Information (Table S2, Figure S1). Details of the structural arrangement in monoclinic K2Ce(PO4)2 have been explained in our earlier report.15 The typical crystal structure of monoclinic K2Ce(PO4)2 is shown in Figure 2. The structure of the monoclinic phase has distorted eight-coordinated CeO8 polyhedra and nearly regular PO4 tetrahedra as structure building units. The CeO8 units are connected to two PO4 units by sharing its two nearby edges while to four other PO4 units by sharing other corner oxygen atoms. The anionic clusters formed by such arrangement are
Figure 1. Rietveld refinement plots for the XRD data of K2Ce(PO4)2 recorded at 300 and 60 K. Vertical ticks in both panels indicates Bragg positions: upper row for monoclinic (P21/n) K2Ce(PO4)2 phase and lower row for monoclinic monazite-type CePO4.
Figure 2. Crystal structure of K2Ce(PO4)2 in monoclinic (P21/n) and tetragonal (I41/amd) structures. CeO8 and PO4 polyhedra are shown. Isolated spheres are K atoms in both structures.
linked together forming a three-dimensional structure containing tunnel-like open space. The K+ ions are occupied in these 3337
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Figure 3. Powder XRD data of K2Ce(PO4)2 recorded at different temperatures while heating (a) and cooling (b).
transition was proposed from the DSC study.15 This suggests that the phase transformation, though reversible, depends on the heating protocol. The large hysteresis in reverting back to ambient phase and the coexistence of phases in a wider temperature range may be attributed to the kinetically hindered reconstructive transition, which has been subsequently explained from the detailed structural analyses of the hightemperature phase. In order to understand the temperature-induced structural changes, the XRD patterns recorded at different temperatures were analyzed. The unit cell parameters and structure of the monoclinic phase could be successfully accounted for all of the high-temperature XRD patterns. Complete structural analyses of high-temperature phase were carried out from the XRD data recorded at 885 K in the heating cycle due to its higher resolution, and they were used as initial structural parameters for refinement of all other temperatures. Excluding the peaks attributable to monoclinic phase, all other peaks observed in the XRD pattern recorded at 885 K are attributed to the hightemperature phase and can be accounted for a tetragonal as well as a feebly distorted pseudo-orthorhombic lattice. The observed unit cell parameters are close to the reported tetragonal lattices for (NH4)2Ce(PO4)2H2O,12 K4CeZr(PO4)4,13 and orthorhombic lattice for (NH4)2Ce(PO4)2H2O.11 The reported structural details of these materials were used as initial models for refinement of XRD data. Rietveld refinements with model structures based on tetragonal12 and orthorhombic11 (NH4)2Ce(PO4)2H2O can successfully explain the reflections as well as peak intensities of the high-temperature phase of K2Ce(PO4)2. It is also revealed that about 33 wt % of monoclinic phase coexists at this temperature. In the tetragonal model structure one cerium (Ce1), one K (K1), and one P (P1) are, respectively, occupied in 4a, 8d, and 8e sites of the space group I41/amd, while two oxygen atoms (O1 and O2) are occupied in 16h sites. Similarly, in the orthorhombic (space group Imma) model, one Ce at 4c, two K (K1 and K2 at 4a and 4d, respectively), two P (P1 and P2 at 4e and 4e, respectively), and four oxygens (O1, O1a, O2, and O2a at 8h, 8i, 8h, and 8i, respectively) are considered. The
open tunnels of the structure. It is mentioned here that the structure of analogous complex phosphates of thorium, like Na2Th(XO4)2 (X = P and As), has been reported with closely similar monoclinic lattices but with different unit cell parameters.35,36The lowering of symmetry and doubling of the unit cell in the later structures are not only due to the splitting of the sites of tetravalent ions but also due to the differences in the linkages of the ThO8 and PO4 units.15 In the present case, none of the XRD patterns recorded at lower temperature down to 60 K or powder neutron diffraction data at 6 K indicate any feature attributable to lowering of symmetry (see Supporting Information, Tables S3 and S4 and Figure S2). Thus, we concluded that the ambient-temperature monoclinic phase remains unchanged at lower temperature. Contrary to the low-temperature studies, the high-temperature structural studies on K2Ce(PO4)2 indicated distinct temperature dependencies. The HTXRD patterns were recorded in different sequences, namely, while heating from ambient temperature to about 885 K and while cooling the sample after heating up to 993 K. Some representative XRD patterns recorded in these two sequences are shown in Figure 3. A comparison of the XRD patterns recorded at a temperature of around 885 K while heating the sample indicates clearly distinguishable additional reflections compared to those recorded at lower temperatures. This is in accordance with the phase transition reported earlier by DSC10,15 and preliminary HTXRD studies.15 Similarly, the XRD patterns recorded while cooling the sample show a change in the XRD pattern at and below 673 K onward. In both cases, the XRD pattern recorded at ambient temperature (300 K) are in agreement with the monoclinic phase of K2Ce(PO4)2 while the patterns at higher temperature are in agreement with a new transformed phase. It can also be noticed that the ambienttemperature monoclinic phase coexists with the transformed phase even at 885 K in the heating runs. However, upon cooling, the high-temperature phase exists as a single phase up to 798 K, coexists with monoclinic phase even at 673 K, and thereafter completely vanishes in the XRD patterns recorded below 423 K. Earlier, the first-order nature of this phase 3338
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of the thermal parameters of K atoms significantly, which indicates that the K+ ions are disordered in the lattice and have 1/2 occupancy in the 16h site. This also suggests the K+ ions are of dynamic nature, in particular, at higher temperature. The typical crystal structure of orthorhombic K2Ce(PO4)2 is shown in the Supporting Information (Figure S4). Similar structural analyses, for a possible disorder of the tetrahedral PO4 group in the structure, were also carried out using the model structure based on parameters reported by Ogorodnyk et al.13 It has been mentioned earlier that the tetragonal structure reported by Ogorodnyk et al. for K4CeZr(PO4)413 differed from the tetragonal structure reported by Salvado et al. for (NH4)2Ce(PO4)2H2O12 and also from the present tetragonal structure in the linkages of PO4 units with the polyhedra around the tetravalent cation. In the case of tetragonal structure of (NH4)2Ce(PO4)2H2O, the Ce4+ ions have distorted eight-coordinated CeO8 polyhedra, while in K4CeZr(PO4)4, due to the larger difference in ionic radii of Ce4+ and Zr4+ ions, they form CeO8 and ZrO6 polyhedra, respectively. The statistical distribution of these CeO8 and ZrO6 polyhedra resulted in an orientationally disordered PO4 sublattice. Although such scenario is not expected in the present case due to the presence of only one type of tetravalent ion, we attempted to refine the XRD pattern in the expectation of orientational disorder due to the temperature effect. In this model, Ce and K are occupied in 4b and 8c sites of space group I41/amd while P atoms are occupied statistically in 8e and 16h sites in the ratio of 1:1. The oxygen atoms are distributed over four different sites, namely, 16h, 16h, 8e, and 16h with occupancies 1, 0.5, 0.5, and 0.25, respectively. A good match between the experimental and the calculated diffraction data is observed in this case also. The typical refined structural parameters and final Rietveld refinement plot for this model are given as Supporting Information (Table S6 and Figure S5). The differences in [Ce(PO4)2]2− of the ordered and disordered tetragonal structure of K2Ce(PO4)2 is shown in the Supporting Information (Figure S6). However, despite having a larger number of free parameters, the residuals are not better than those obtained for the ordered tetragonal structure. Thus, the structure of the present high-temperature phase does not have disorder in the PO4 group; rather, it has disorder in K+ sites. Analyses of the structural parameters of K2Ce(PO4)2 in the tetragonal structure (Table 2 and Table S7) indicate that the phosphorus atoms have a tetrahedral PO4 configuration with two O1 and two O2, while Ce atoms have an eight-coordinated distorted cubic CeO8 configuration with four O1 and four O2.
refined unit cell parameters and residuals of refinement of these two models are as follows: tetragonal, I41/amd, a = b = 6.83658(3) Å, c = 17.5091(1) Å, V = 818.35(1) Å3, Rp = 9.20%, Rwp = 11.8%, χ2 = 6.22, RB = 7.42, RF = 4.77%; orthorhombic, Imma, a = 6.8363(3) Å, b = 6.8369(3) Å, c = 17.5090(1) Å, V = 818.35(5) Å3, Rp = 9.33%, Rwp = 12.0%, χ2 = 6.41, RB = 7.79%, RF = 4.26%. The typical orthorhombicity (|b − a|/|b + a|) is estimated as 4.3 × 10−5, which is almost zero; thus, the lattice can be treated as a tetragonal lattice. In addition, the residuals obtained for tetragonal lattice are relatively lower as compared to those observed for orthorhombic lattice. From the point of view of a higher symmetric lattice and relatively better residuals, it is logical to accept the tetragonal structure as the structure of the high-temperature phase. The typical Rietveld refinement plot of the XRD pattern of K2Ce(PO4)2 refined with tetragonal symmetry is shown in Figure 4. Refined structural parameters
Figure 4. Rietveld refinement plot of the XRD pattern of K2Ce(PO4)2 refined with tetragonal (I41/amd) symmetry. (Lower vertical ticks are for monoclinic P21/n phase of K2Ce(PO4)2.)
of the high-temperature phase obtained by using the tetragonal model are given in Table 2. The structural parameters for the orthorhombic model and final Rietveld refinement plot of the XRD data are given as Supporting Information (Table S5 and Figure S3). It should be mentioned here that the tetragonal (I41/amd) and orthorhombic (Imma) lattices are related by group−subgroup transformation, where the K1, P1, O1, and O2 sites split into two distinguishable sets. Further, it is noticed that the shifting of the potassium (K1) atoms from the special positions 8c to 16h in I41/amd structure reduces the amplitudes
Table 2. Refined Position Coordinates for High-Temperature Phase of K2Ce(PO4)2a atoms
wyc.
occ
x
y
z
Ce1
4a 4a 8d 16h 8e 8e 16h 16h 16h 16h
1 1 1 0.5 1 1 1 1 1 1
0.5 0.5 0.75 0.763(2) 0.5 0.5 0.5 0.5 0.3203 0.3258(9)
0.25 0.25 0.75 0.75 0.75 0.75 0.57193 0.5745(7) 0.75 0.75
0.625 0.625 0.75 0.7364(7) 0.55056 0.5579(3) 0.60335 0.6112(4) 0.49894 0.5026(3)
K1 * P1 O1 O2
Uiso (Å2) 0.0031(6) 0.037(2 0.0283(17) 0.047(3) 0.088(4)
Temperature 885 K. Tetragonal, I41/amd. DFT-calculated values at 0 K are given in the first row. *K1 atoms are displaced from the 8d sites to 16h sites in experimental data. a
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Figure 5. Polyhedral connections of K2Ce(PO4)2 in monoclinic (P21/n), tetragonal (I41/amd), and orthorhombic (Imma) structures (digits are typical bond lengths).
third-order Birch−Murnaghan (BM-III) equation of state. The calculated bulk moduli for the P21/n, I41/amd, and Imma structures are 45.18, 64.98, and 64.98 GPa, respectively. The pressure derivatives (K′) and reference volumes (V0) of the phases are 5.10 and 747.04 Å3 (for P21/n), 5.04 and 847.32 Å3 (for I41/amd), and 5.62 and 856.36 Å3 (for Imma). The calculated bulk moduli are closely similar to those experimentally observed for the bulk modulus of complex phosphates containing alkali metal ions.40,41 In addition, they are appreciably lower compared to the zircon- or monazite-type phosphates.42,43 Despite the lower packing of the hightemperature structures, they show a relatively higher bulk modulus compared to the ambient-temperature phases. This can be attributed to the zircon-type connections of polyhedra in the later structures compared to that in the monoclinic P21/n structure. However, the calculations indicated that the orthorhombic and tetragonal structures have almost similar energy and that both are relatively more stable compared to Na2Th(PO4)2-type monoclinic lattices. It is mentioned here that in the present material the Na2Th(PO4)2-type monoclinic P21/c structure is expected only at larger volume and hence that may crystallize with larger tetravalent cations. However, the transition may not occur due to the intervening stable orthorhombic or tetragonal structures as well as instability of the structure due to reduction of Ce4+ ions at higher temperature as concluded earlier.15 The formation of Na2Th(PO4)2 can thus be related to the larger ionic radii of Th4+ ions compared to Ce4+. Though the equilibrium molar volume of the monoclinic C2/c structure is comparable to that in the monoclinic P21/n structure, the structure is not experimentally observed in K2Ce(PO4)2 down to 60 K by XRD and down to 6 K by PND. Essentially the Na2Th(PO4)2-type structures have two different types of [Th(PO4)2] 2− clusters: one equivalent to that in the monoclinic phase, while the other is equivalent to that in high-temperature tetragonal or orthorhombic phases. Thus, these Na2Th(PO4)2-type monoclinic structures can be considered as intermediate structures between the hightemperature and the ambient-temperature structures of K2Ce(PO4)2. The variations of lattice energy with molar volume for different structures are shown in Figure 6. From Figure 6, it can be seen that the expansion of molar volume of the monoclinic (P21/n) phase of K2Ce(PO4)2 by about 8% will destabilize the lattice and will transform to orthorhombic or tetragonal
The CeO8 units are linked to two PO4 units by sharing the edges along the c axis while to four other PO4 units by sharing corners along the ab plane forming a cluster with composition [Ce(PO4)2]2−. The structural arrangement of CeO8 and PO4 units forms tunnel-like empty space along the ⟨100⟩ direction which are occupied by the K+ ions, and they balance the net negative charge of [Ce(PO4)2]2− in the lattice. The typical crystal structure of HT tetragonal K2Ce(PO4)2 is shown in Figure 2. The typical linkages of CeO8 and PO4 units in [Ce(PO4)2]2− in the monoclinic and tetragonal structures are shown in Figure 5. For comparison, CeO8 and PO4 units in the considered orthorhombic structure are also included in Figure 5. It can be mentioned here that the local surroundings of the CeO8 as well as PO4 units are more distorted in the orthorhombic structure compared to that in the tetragonal structure; however, in both cases the distortions are found to be lower than the ambient monoclinic structure (Table S7). These features are reflected in their expansion behavior, which are explained later in this manuscript. Further, to understand the crystal structure and phase transition in K2Ce(PO4)2, ab initio density functional theory (DFT) calculations were performed. The equilibrium structure of K2Ce(PO4)2 for different structural models, namely, monoclinic (P21/n, P21/c, and C2/c), orthorhombic (Imma), and tetragonal (I41/amd) structures, were calculated. The calculated unit cell parameters and the energy per formula unit are given in Table 1. As explained earlier, the structural parameters calculated on symmetry P21/c and C2/c equivalent to the Na2Th(PO4)2 structure cannot explain the experimentally observed data either at lower or at higher temperature and thus are excluded from further consideration. As expected the equilibrium volume of monoclinic (P21/n) lattice for ambienttemperature phase is overestimated by about 7.6% due to the underestimation of the cohesion energy in the GGA formalism.32,37−39 The calculated position coordinates for the ambient-temperature monoclinic phase (included in Table S1) are in close agreement with the experimental results. A comparison of the equilibrium lattice energy for different structures suggests that the monoclinic (P21/n) lattice is the stable lattice for K2Ce(PO4)2 compared to all other considered lattices. From the pressure-dependent equilibrium volume of the equilibrium monoclinic (P21/n), tetragonal, and orthorhombic structures, the bulk modulus was obtained by using the 3340
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the present experimental studies are in favor of tetragonal structure. Further comparison of the ambient monoclinic (P21/n) phase and high-temperature tetragonal (I41/amd) phase (Figure 2 and 5) indicates that even though both have CeO8 and PO4 polyhedra they have different topology in their linkages. It is mentioned here that in the monoclinic phase two of the PO4 tetrahedra are connected to CeO8 by sharing two nearby edges of the later and thus lead to a distorted and compact lattice, while in the later case they are connected by sharing two opposite edges of CeO8. The arrangement of CeO8 and PO4 polyhedra in the tetragonal phase is similar to that in zircon-type structures. In zircon-type structures, the infinite chains of edge-shared MO8 and PO4 units propagate along the c direction which is equivalent to the c axis of the present tetragonal phase. However, the unit cell is doubled in the c axis of the tetragonal K2Ce(PO4)2 structure due to the variation of periodicity arising from the disruption of chains at every clustered unit of two tetrahedra and one CeO8 bisdisphenoid, i.e., every alternate CeO8 unit. Moreover, this structural transformation does not change the net tunnel-type structure of ambient monoclinic phase. In both cases the empty tunnels are occupied by K+ ions, which are along the ⟨100⟩ and ⟨101⟩ direction in the monoclinic phase while along the ⟨100⟩ and ⟨010⟩ direction in the tetragonal phase. The restructuring of the local arrangement around CeO8 cannot be explained by a simple rotation of polyhedra, while they are restructured by reconstruction of the PO4 and CeO8 polyhedra. The expansion of the CeO8 polyhedra thus relaxes the structure to a higher symmetric structure, while at temperature above 1123 K the sample is found to decompose due to the unstable nature of Ce4+ in phosphate matrix.15
Figure 6. Variation of lattice energy with unit cell volume of K2Ce(PO4)2 for monoclinic (P21/n) phase, tetragonal (I41/amd), and orthorhombic (Imma) structures.
structure. In Table 2, the calculated equilibrium position coordinates for tetragonal (I41/amd) lattice are compared with those observed from XRD data. A similar comparison of calculated position coordinates of orthorhombic structure are given in the Supporting Information (Table S5). From the calculations it can be suggested that the tetragonal structure has marginally higher stability compared to the orthorhombic structure. Thus, it can be inferred that the temperature has an important role for stabilization of these structures. No significant improvement in the residual in Rietveld refinements and no additional reflections due to a lowering of symmetry in
Figure 7. Variation of unit cell parameters of monoclinic (P21/n) and tetragonal (I41/amd) phases of K2Ce(PO4)2 with temperature (subscripts m and t indicate monoclinic and tetragonal structures, respectively). 3341
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metastable, the spectroscopic details, in particular, their vibrational properties, are mostly obscure in the literature. In order to study the temperature-induced change in local structures and phase transition, Raman spectroscopic investigations were carried out as they are often reflected in their phonon behaviors.48−50 Raman spectroscopy is often used as a complementary technique to XRD for studying the thermodynamic and structural properties as it probes in the microscopic length scale compared to macroscopic probing of the XRD. The phase transition or structural distortions that occurs due to a change in symmetry or movement of ions at microscopic length scale can thus be obtained from the Raman spectroscopic studies more accurately. In order to complement the observed spectroscopic finding, the Raman and IR modes for all considered structures such as monoclinic (P21/n), tetragonal (I41/amd), and orthorhombic (Imma) phases were calculated. The calculated Raman modes for monoclinic (P21/ n) and tetragonal (I41/amd) structures are given in the Supporting Information (Tables S9−11). For comparison, those calculated for the considered orthorhombic structure are also in included in Tables S10 and S11. The presence of PO4 units and absence of water in the structure have been confirmed in our earlier study.15 As mentioned earlier, the structure of ambient-temperature monoclinic K2Ce(PO4)2 (apace group P21/n) has four formula units per primitive unit cell (Z = 4). Therefore, one can expect a total of 156 vibrational degrees of freedom which are distributed as optical and acoustic phonon modes at the Brillouin zone center (q = 0). From factor group analyses,51 the total irreducible representation can be obtained as Γ = 39Ag + 39Au + 39Bg + 39Bu, out of which the total irreducible representation for an optical phonon is Γoptic = 39Ag + 38Au + 39Bg + 37Bu and that for acoustic is Γacoustic = Au + 2Bu. Therefore, 78 Raman active modes (39Ag + 39Bg) and 75 infrared active modes (38Au + 37Bu) are expected. Figure 8 shows a Raman spectrum recorded at ambient temperature (300 K). At ambient temperature, the major Raman bands are located at 199, 269, 397, 624, 982, and 1127 cm−1. A total of 26 peaks are precisely obtained using peak fitting. The
In order to compare the expansion behavior of K2Ce(PO4)2, the unit cell parameters of monoclinic and tetragonal phase at different temperatures are obtained; they are shown in Figure 7. It can be seen from Figure 7 that the unit cell parameters of the monoclinic phase smoothly increase from the lowest temperature and can be explained by second-order polynomial relations. However, the temperature-dependent unit cell parameters of the tetragonal phase show anomalous behavior, viz. expansion along the a and b axes while a contraction along the c axis. The coefficients of typical second-order polynomial relations obtained by fitting the temperature-dependent unit cell parameters of both monoclinic and tetragonal phases are given in the Supporting Information (Table S8). The coefficients of the average thermal expansion of monoclinic phases in the temperature range from 60 to 885 K are αa = 13.71 × 10−6 K−1, αb = 8.46 × 10−6 K−1, αc = 19.28 × 10−6 K−1, αβ = 2.04 × 10−6 K−1, and αV = 41.30 × 10−6 K−1, while those of the tetragonal phase between 400 and 900 K are αa = 9.61 × 10−6 K−1, αc = −15.3 × 10−6 K−1, and αV = 3.83 × 10−6 K−1. The large negative thermal expansion along the c axis resulted in a significantly lower volume thermal expansion in the tetragonal structure. As seen from the variation of the unit cell volume with temperature (Figure 7), the transition from monoclinic P21/n to tetragonal I41/amd structure is accompanied by about a 14.4% rise in volume, which is also in accordance with the volume difference calculated by DFT. The resulted open structure of the high-temperature phase is more prone to exhibit either lower or negative thermal expansion. Phase transitions accompanied by such larger volume discontinuity exhibiting lower or negative thermal expansion have been reported earlier on several systems.44,45 A similar difference in thermal expansion has been observed in the ambient-temperature pseudocubic (triclinic) and high-temperature cubic phase of CeP2O7.2 The triclinic to cubic phase transition occurs with a rise in volume of about 0.6%, and the transformed phase shows negative thermal expansion (αV = −5.7 × 10−6 K−1 between 445 and 805 °C), while the ambienttemperature phase shows a normal positive expansion (αV = 19.5 × 10−6 K−1 between 25 and 115 °C).2 Negative thermal expansion is also observed in the high-temperature cubic phase of various actinide phosphates, like AP2O7 (A = Th, U, Np, Pu).46 The ambient-temperature triclinic phase of such actinide diphosphate transforms to the cubic phase with a large expansion of the unit cell volume. The abrupt increase in unit cell volume at the transition leads to a relatively open structure having a lower packing density which allows lower or negative expansion in the lattice. However, as mentioned earlier, the bulk modulus of the tetragonal phase is relatively higher compared to the monoclinic phase of K2Ce(PO4)2. This can be due to the zircon-type arrangements where the CeO8 polyhedra share two opposite edges by incompressible and rotationally hindered PO4 tetrahedra. Also, analyses of temperature-dependent Ce−O and P−O bond lengths of monoclinic and tetragonal structures of K2Ce(PO4)2 indicate only marginal variation in the P−O bonds compared to the Ce−O bonds (Table S7 and Figure S7). This is a common observation for the tetrahedrally or octahedrally coordinated polyhedra of cations with high positive charge like P5+, V5+, S6+, W6+, Mo6+, etc., which often act like a rigid unit and hence show lower expansion as well as larger bulk modulus.43−45,47 Further accounts on structural changes are obtained from the in situ variable-temperature Raman spectroscopic studies. Since the phosphates of tetravalent Ce4+ are relatively unknown and
Figure 8. Raman spectra of K2Ce(PO4)2 at ambient temperatures. Solid curves are the Lorentzian least-squares fits to the data including a suitable background. Blue tick marks indicate the Raman bands at 300 K. 3342
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Figure 9. Raman spectra of K2Ce(PO4)2 at different temperatures: (a) low-frequency region showing the lattice and bending modes of PO4 ion, (b) high-frequency region showing the stretching modes of PO4 ion. Blue tick marks indicate the Raman bands at 83 K. Solid curves are the Lorentzian least-squares fits to the data including a suitable background.
Figure 10. Raman mode frequencies of K2Ce(PO4)2 as a function of temperature: (a) low-frequency lattice and bending modes of PO4 ion, (b) highfrequency stretching modes of PO4 ion. Solid lines through the data are a linear least-squares fit. Several modes exhibit the usual negative slope, while the lattice mode at 81 cm−1 and bending mode at 396 and 447 cm−1 have positive slopes. Vertical dashed line indicates the transition temperature.
calculated mode frequencies along with their assignments are presented in Table S9. Most of the observed and calculated Raman frequencies show good matching with each other within a maximum of ∼4% mismatch, which can be due to the difference between the experimental and the relaxed unit cell volume obtained from first-principle calculations. As pointed out earlier, the tunnel structured K2Ce(PO4)2 consists of edge- and corner-shared network of CeO8 polyhedra and stiffest PO4 tetrahedra. K+ ions are located in the empty space of the tunnel. Since the PO4 units are tightly bound, they can be treated as rigid units; hence, one can expect internal modes resulting from the vibration of the oxygen ion against the central phosphate ion in the oxygen cage. On the other hand, the comparatively loosely bound CeO8 polyhedra contributes only lattice modes associated with the Ce4+ ion translational vibration in the potential well formed by the surrounding oxygen cage. Similarly, the K+ ions can contribute only lattice translation modes. Therefore, in the present Raman spectra of K2Ce(PO4)2, the lattice modes involving Ce4+ and K+ ions can be seen in the low-frequency region, whereas the vibrations involving PO4 units are expected in the highfrequency region. Using the assignments reported earlier for
experimental Raman spectrum and the total Lorentzian leastsquares fit pattern with individual Raman band positions are shown in Figure 8. The observed mode frequencies are close to our earlier reported frequencies.15 Due to an increase in the phonon lifetime at lower temperature, the Raman modes generally become narrow; hence, the overlapping modes are often resolved at lower temperature. Thus, the initial analyses of Raman modes were carried out from the spectrum recorded at 83 K. The deconvolution of peaks of this spectrum using multi-Lorentzian profile shape yields 35 modes. These mode frequencies are presented in Table S9, and the locations of the mode positions are marked in Figure 9. There are no modes observed in the spectral range 660−920 cm−1 in the Raman spectra. The lower number of observed modes than expected from group theoretical analyses may be due to either weak intensity arising from the small polarizability of several modes or accidental degeneracy-related overlapping.52 Assignments of the observed modes are carried out by using the computed eigenvectors obtained from our DFT calculations. The observed band frequencies close to those obtained from calculation for zone center phonons are assigned to the corresponding eigenvector symmetry. The observed and 3343
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Inorganic Chemistry K2Ce(PO4)2,15 the observed modes are assigned in Table S9. The internal modes are assigned in the range 390−1130 cm−1. Raman modes observed in the high-requency range 940−1130 cm−1 are attributed to the stretching mode of the PO4 units, while the bending modes are in the frequency range 390−627 cm−1. The lattice translational mode related to K+ and Ce4+ ions and librational modes involving the PO4 rigid unit are observed in the low-frequency range 80−313 cm−1. In order to examine the changes in phonon behavior at elevated temperature, we measured in situ Raman spectra of K2Ce(PO4)2 using a Linkam stage up to 853 K. Figure 9 shows representative Raman spectra between 83 and 853 K. Upon increasing temperature, most of the Raman bands soften continuously and their intensities decrease. A few Raman bands located at 81, 396, and 446 cm−1 show abnormal hardening (Figure 9a). Under the influence of temperature, mode frequencies are normally expected to decrease due to expansion of bonds. Sometimes a few bands may show opposite behavior which can be attributed to the stiffening of bonds resulting from steepening of the potential well associated with their atomic vibration. The hardening behaviors of vibrational modes have been reported in several systems.48,49 With increasing temperature the line width of several Raman bands of K2Ce(PO4)2 are broadened, which is normally due to enhanced phonon scattering processes. Figure 9b shows the significant broadening of internal modes at 853 K, which appears like only 4 Raman bands. The modes at 446 and 457 cm−1 and 1024 and 1039 cm−1 were merged at 783 K, and they appeared as broad bands centered at 453 and 1138 cm−1, respectively. These new bands continue to appear above this temperature. Raman bands centered at 81, 110, 562, and 999 cm−1 disappeared at 783 K. Some of the bands disappeared even below 783 K. At the highest temperature, 853 K, only 11 bands were observed (Table S10 and Figure 10). The merging of modes and disappearance of several modes at ∼783 K suggest the transition is accompanied by an increase in symmetry. As the ambient monoclinic phase transforms to the HT phase, the temperature dependency of internal modes of PO4 units shows a change in slope, which is clearly observed at around 783 K (Figure 10). The observed modes of the high-temperature phase and their assignments are given in Table S10. In addition, between 783 and 853 K, phonon modes of both the monoclinic and the highly symmetric phase are observed in the spectra, suggesting a coexistence of the phases in this temperature range, which is consistent with the findings, from the present Tdependent XRD studies. Group theoretical analyses for the structure of the hightemperature tetragonal structure (I41/amd; Z = 4) predict 78 vibrational degrees of freedom. Excluding the acoustic phonons, factor group analyses of the tetragonal structure (without consideration of disorder in K+ atoms) indicates the total irreducible representations of optical phonons are Γoptics = 5A1g + 3A1u + 2A2g + 7A2u + 6B1g + 3B1u + 2B2g + 7B2u + 11Eu (doubly degenerate) + 9Eg (doubly degenerate). Thus, there are 18 distinct IR modes with irreducible representation Γoptic (IR) = 7Au + 11Eu, and 22 distinct Raman modes with irreducible representation Γoptic (R) = 5A1g + 6Bg + 2B2g + 9Eg are expected. Similar analyses for the orthorhombic (Imma; Z = 4) phases indicate a total of 75 optical phonons with representations Γoptic = 11Ag + 6Au + 4B1g + 14B1u + 9B2g + 11B2u + 9B3g + 11B3u. Out of these representations, there are 36 modes that are IR active (Γoptic (IR) = 14B1u + 11B2u + 11B3u) and 33 modes that are Raman active (Γoptic (R) = 11Ag + 4B1g +
9B2g + 9B3g). The calculated Raman modes for both tetragonal and orthorhombic structures are listed in Table S10. The lower number of observed modes at higher temperature is an indication of the higher symmetry of the high-temperature phase and most favorably a tetragonal structure. Figure S10 shows the temperature dependences of band frequencies. Several bands of the monoclinic phase have disappeared, and a few merged together because of the transformation to tetragonal phase. From Table S11, it can be seen that several of the IR mode frequencies of the high-temperature tetragonal phase of K2Ce(PO4)2 have negative frequencies (viz. Eu, −42.87 cm−1), which suggest this structure is dynamically unstable with respect to the ambient-temperature monoclinic (P21/n) structure. These modes are essentially the rotational motion of PO4 tetrahedra and largely by translational motion of the K+ ions (Supporting Information Figure S8). This is in accordance with the unstable nature of the tetragonal structure at lower temperature, and hence, it reverts back to ambient phase on cooling. The temperature coefficients (χ) of the Raman bands in the monoclinic phase are obtained by fitting the ω vs T plot (Figure 10) using the linear equation ω(T) = ω0 + χT, where ω0 are mode frequencies at absolute zero temperature (Table S9). To avoid contribution from higher order temperature coefficients, we fitted the data in the low-temperature range 1 dω (83−500 K). The reduced slopes, ω dT , are calculated for all 35 observed Raman bands at 83 K and are included in Table S9. Similarly, the reduced slopes of the identified modes of transformed high-temperature phases are obtained by linear fitting, and they are included in Table S10. This reduced slope essentially represents the total anharmonicity of phonon modes and is contributed by two effects,44,45,49 viz. (a) a pure temperature effect related to phonon−phonon interaction (explicit contribution) and (b) a change in the volume of the lattice (implicit contribution). Furthermore, a comparison of the magnitude of the total anharmonicity of phonon modes indicates the low-frequency lattice and external modes such as 81, 152, 178, 213, 234, 272, and 313 cm−1 indeed have large anharmonicities. These large values indicate a large contribution to thermal expansion and that these modes are flexible and sensitive to temperature. On the other hand, the high-frequency internal modes of phosphate ions are not strongly anharmonic. These results indicate that the internal modes involving the PO4 unit are less sensitive to temperature, suggesting the strong bonding in the PO4 tetrahedral unit, as observed in our XRD analysis, and thus implying its covalent bonding character. The thermal Grüneisen parameters as obtained from the temperature coefficients of the mode frequencies are included in Table S9. It is observed that the low-frequency modes are mainly contributing to the thermal expansion and differences in the magnitude of thermal expansion of both ambient- and hightemperature phases. As mentioned earlier, the change in mode frequencies with temperature is a consequence of anharmonicity. In fact, the cubic, quartic, and even higher order terms present in the expansion of interatomic interaction potential that arise from atomic displacement from their mean equilibrium position contribute to the shift in mode frequencies. Due to the cubic and quartic anharmonicity,48,49,53 a phonon of frequency ω0 decays into two phonons of frequency ω0/2 or three phonons of frequency ω0/3, respectively. Therefore, the resulting contribution to the shift in mode frequencies can be analyzed 3344
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Figure 11. Variation of mode frequencies (ω) of some modes (below 400 cm−1) with temperature. Continuous curves are fitted lines. Lattice mode at 81 cm−1 is fitted with only the quartic part.
band structures for the other two considered monoclinic lattices are given in the Supporting Information (Figure S9). As can be seen, the electronic structures are nearly similar for all three (P21/n, I41/amd, and Imma) structures. The valence bands for all structures are mainly comprised from the oxygen 2p orbitals. The conduction band of the compound ranged from above 1.3 eV, and the bottom of the conduction band is mainly due to the 4d orbitals of cerium. The calculated band gap (1.41 eV) is found to be lower than the band gap (2.46 eV, see Supporting Information Figure S10) measured from diffuse reflectance spectra. The observation of such difference is common in the DFT calculation since it usually underestimates the band gap energy.39,55,56 The partial electronic densities of state for the considered three structures are shown in Supporting Information Figure S11. From Figure 12, it can be seen that the top of the valence band remains at the E point in the ambient-temperature monoclinic structure, while they are located at R and N points in orthorhombic and tetragonal structures, respectively. The E → A indirect band gap around 1.41 eV is observed from the electronic structure of the monoclinic phase, and an additional Γ → Γ direct band gap with an almost similar energy is also seen in this case. As the structure changes from monoclinic to tetragonal or orthorhombic, the top of the valence band maxima shifts to R and N points, respectively. In all cases, the electronic transition is found to be mainly from the filled oxygen levels to the empty d or f orbital of the Ce ion.
by using a cubic and quartic anharmonicity formal⎡ ⎤ 2 ism48,49,51,53,54 using relation ω = ω0+ A⎢⎣1 + exp(x) − 1 ⎥⎦ + ⎡ ⎤ 3 3 B⎣⎢1 + exp(y) − 1 + ⎥, where ω0 is the frequency at (exp(y) − 1)2 ⎦ absolute zero temperature, x = ℏω0/kBT, A is the coefficient of cubic anahramonicity, y = ℏω0/3kBT, and B is the coefficient of quartic anharmonicity. Some of the observed mode frequencies (lattice and external modes) obtained in our analysis, which are highly anharmonic, are fitted using the above expression. The fitted parameters ω0, A, and B are given in Figure 11. A comparison of these parameters suggests that cubic anharmonicity dominates over quartic anharmonicity in several modes. However, the lattice mode at 81 cm−1, which is hardening with temperature, can be fitted with the quartic part alone (Figure 11). This is due to the fact that the lattice mode at 81 cm−1 shows an abnormal hardening with increasing temperature, implying that the contribution of quartic anharmonicity is dominant over the cubic anharmonicity. Hence, the cubic anharmonicity contribution to the change in frequency for this mode can be neglected. If we add the cubic part during analysis of mode frequency with temperature the fitted parameter A (coefficient of cubic anharmonicity) turns out to have a positive value, which is unrealistic,53,54 and hence, only a quartic term is used for analysis. As expected, the hardening of the mode with temperature is due to steepening of the interatomic potential well, and they are essentially contributed by the quartic term. Hence, dominance of four-phonon processes is evident in the monoclinic structure. However, due to the limited range of measurement temperature at higher temperature, complete anharmonic analyses for the high-temperature phases could not be carried out. Finally, we comment on the electronic structure of ambient and HT phases from DFT calculations and optical properties of ambient-temperature monoclinic phase as observed from the diffuse reflectance measurements. The calculated band structures for the ambient-temperature P21/n phase are depicted in Figure 12. For comparison, the band structures calculated for tetragonal (I41/amd) and orthorhombic (Imma) structures are included in Figure 12. The calculated electronic
V. CONCLUSION The in situ variable-temperature XRD studies on K2Ce(PO4)2 in a wider range of temperatures revealed that the ambienttemperature monoclinic phase remains unchanged at lower temperature while it transforms to a tetragonal structure with large (∼14.4%) expansion of the unit cell volume at higher temperature. The high-temperature phase reverts back to ambient phase with a larger hysteresis in temperature and also coexists with monoclinic phase in a wider range of temperature. The detailed structural analyses of the ambient and hightemperature phases suggest a reconstructive first-order-type phase transition. The highly open and loosely packed structure 3345
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quartic anharmonicity. In addition to lattice modes at 81 cm−1, several other librational modes of PO4 tetrahedral units are observed to be strongly anharmonic. Optical absorption studies on the monoclinic phase of K2Ce(PO4)2 indicate a band gap of 2.46 eV.
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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.6b02870. Details of XRD analyses in other models structures, neutron diffraction, and DRUV spectrum, band structure of Na2Th(PO4)2-type monoclinic phase, and partial electron density of states of ambient and high-temperature phases of K2Ce(PO4)2 (PDF) (CIF) (CIF) (CIF) (CIF)
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AUTHOR INFORMATION
Corresponding Author
*Phone: 0091-22-25592328. Fax: 0091-22-25505151. E-mail
[email protected]; acharysn@rediffmail.com. ORCID
S. Nagabhusan Achary: 0000-0002-2103-1063 Author Contributions
The manuscript was written through contributions of all authors. All authors have equal contribution to this manuscript. All authors have given approval to the final version of the manuscript. Notes
The authors declare no competing financial interest.
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REFERENCES
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Figure 12. Electronic band structures of K2Ce(PO4)2 in equilibrium P21/n, I41/amd, and Imma structures.
of HT tetragonal phase shows anisotropic thermal expansion with a larger negative thermal expansion along the c axis (−15.3 × 10−6 K−1), and that in turn resulted in an appreciable lowvolume thermal expansion (3.83 × 10−6 K−1) as compared to that observed in ambient-temperature monoclinic phase (41.30 × 10−6 K−1). Temperature-dependent Raman spectroscopic studies indicate the onset of structural transition from monoclinic to a high-symmetry tetragonal phase at 783 K. The phonon frequencies in the monoclinic phase which are highly anharmonic are identified. Several mode frequencies in this compound are dominated by three-phonon contributions. Abnormal hardening of 81 cm−1 lattice mode arises from 3346
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