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Implication of aliovalent cation substitution on structural and thermodynamic stability of Gd2Ti2O7: Experimental and theoretical investigations
Journal of Alloys and Compounds xxx (xxxx) xxx
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Implication of aliovalent cation substitution on structural and thermodynamic stability of Gd2Ti2O7: Experimental and theoretical investigations M. Jafar a, b, S.B. Phapale a, b, S. Nigam a, b, S.N. Achary a, b, *, R. Mishra a, b, C. Majumder a, b, A.K. Tyagi a, b a b
Chemistry Division, Bhabha Atomic Research Centre, Trombay, Mumbai 400085, India Homi Bhabha National Institute, Anushaktinagar, Mumbai 400094, India
a r t i c l e i n f o
a b s t r a c t
Article history: Received 3 August 2020 Received in revised form 28 October 2020 Accepted 30 October 2020 Available online xxx
Multi-cation substituted pyrochlores are potential matrices for immobilization of long-lived high level nuclear waste. In this paper, we report, the structural and thermodynamic stabilities of aliovalent multi cation substituted Gd2Ti2O7 pyrochlore compounds determined by experimental and theoretical methods. A series of cubic pyrochlore-type Gd2-2xCaxZrxTi2O7 (0.0 x 0.4) compounds were synthesized and characterized by XRD and Raman spectroscopy techniques. It is observed that incorporation of Ca2þ and Zr4þ at Gd3þ site does not significantly alter crystal lattice of Gd2Ti2O7. Calorimetric studies were carried out to determine the thermodynamic stability of Gd2-2xCaxZrxTi2O7 compounds. The observed data indicate that standard molar enthalpy of formation of Gd2-2xCaxZrxTi2O7 decreases steadily with increasing dopant concentration which has been attributed to increasing distortion of the polyhedra around the cations. These inferences were further supported by DFT calculations. © 2020 Elsevier B.V. All rights reserved.
Keywords: Aliovalent substitution Pyrochlore Gd2Ti2O7 XRD Raman spectroscopy Calorimetry DFT
1. Introduction Long lived minor actinides such as Np, Am, Cf, etc. Present in high level nuclear waste (HLW) are the main source of long-term radio toxicity. It is therefore necessary to immobilize nuclear HLWs in thermodynamically stable and long-lasting immobilization matrices [1]. Presently borosilicate glasses are being used as primary waste immobilization matrix all over the world [2]. However, glass being a metastable material has some limitations like low solubility of minor actinides, lower activity loading, possible devitrification and hence deterioration in stability, etc. [3e5]. In view of these shortcomings of glass matrices, Ringwood et al. [6] proposed ceramic composites or aggregates of mineral analogous titanates, termed as SYNROC as futuristic and potential matrices for immobilization of nuclear HLW [6]. SYNROC is a composite material and mostly consists of zirconolite, perovskite,
* Corresponding author. Chemistry Division, Bhabha Atomic Research Centre Mumbai-400085, India E-mail address: [email protected] (S.N. Achary).
hollandite, pyrochlore and rutile type phases [6e9]. Pyrochlore, which is an important constituent phases of SYNROC, can be represented by a general formula A2B2O7, where A and B cations form AO8 and BO6 polyhedra with oxygen atom respectively, in its crystal structure [10]. Depending upon the rA/rB, where rA and rB represent the ionic radii of the cations in their respective coordination numbers, the pyrochlore structure (symmetry: Fd3m) has an ability to transform into either a cation ordered perovskite type (symmetry: C2/c) structure or a cation disordered defect-fluorite type structure (symmetry: Fm-3m) [11]. In general, for A2Ti2O7 with rare earth ions (A) having ionic radii smaller than Sm3þ generally form an ordered cubic pyrochlore structure, whereas ions having larger ionic radii than Sm3þ form perovskite related monoclinic structures [12,13]. The ability to accommodate a wider range of ions without significant alteration in the structure makes pyrochlore a potential candidate for immobilization of minor actinides present in nuclear HLW [11e15]. Thus, structural and thermodynamic stabilities of a number of pyrochlore-type compounds have been explored under extreme conditions such as temperature, pressure, higher radiation field, etc. [16e21]. Most of these studies are limited either to host lattices or single cation
https://doi.org/10.1016/j.jallcom.2020.157781 0925-8388/© 2020 Elsevier B.V. All rights reserved.
Please cite this article as: M. Jafar, S.B. Phapale, S. Nigam et al., Implication of aliovalent cation substitution on structural and thermodynamic stability of Gd2Ti2O7: Experimental and theoretical investigations, Journal of Alloys and Compounds, https://doi.org/10.1016/ j.jallcom.2020.157781
M. Jafar, S.B. Phapale, S. Nigam et al.
Journal of Alloys and Compounds xxx (xxxx) xxx
720]. The details of the calorimetry experimental procedures are explained in our earlier reports [20,21]. Solvent used for calorimetric studies, a mixture of Na2O and MoO3 (3:4 M ratio), was synthesized by heating appropriate amounts of dried Na2CO3 (BDH, reagent grade) and MoO3 (BDH, reagent grade) at 986K. At this temperature, Na2CO3 decomposes to Na2O, and that form a eutectic mixture with MoO3. The mixture was kept for 6 h at 986 K for complete homogenization and then cooled to room temperature. The solvent powder was characterized for stoichiometry by chemical analysis and XRD study. No impurity element and only Na and Mo of desired stoichiometry were observed in the solvent mixture. Around 7 g of Na2O þ MoO3 solvent were added to platinum tubes placed inside the alumina assembly and the assembly is slowly lowered into the calorimeter. The temperature was maintained at 986 ± 0.05 K during the whole experiment. Reaction tubes were equilibrated till a steady base line for heat flux was obtained. Sample pellets of about few milligrams were dropped into the solvent and the characteristic heat change effects were recorded by integration of heat flow signal with respect to time. In a similar manner heat change effects for the constituent reagents like ZrO2, CaO and TiO2 were also recorded.
incorporated lattices. However, the structural perturbations induced by doping of diverse cations into pyrochlore lattices are not well explored in literature. The effects of aliovalent substitution and multi cation substitution on the stabilities of pyrochlore structure need to be well understood before qualifying them as waste immobilization matrices. To understand structural and thermodynamic stabilities of aliovalent multi cation substituted Gd2Ti2O7 pyrochlore, detailed investigations on divalent (Ca2þ) and tetravalent (Zr4þ) cation substituted at trivalent cation (Gd3þ) site were carried out. The choice of this system was based on our earlier studies in zirconolite-pyrochlore based systems wherein the formation of single phase pyrochlore or zirconolite by co-doping has been revealed [11,12,22]. The observations from experimental investigations and theoretical validations on the structure and stabilities of co-doped Gd2Ti2O7 pyrochlore system are presented in the manuscript. 2. Experimental A series of compounds having nominal composition Gd2(0.0 x 0.4) was prepared by solid state reaction route. Binary oxides such as ZrO2 (Sigma Aldrich, purity 99.0%), TiO2 (Sigma Aldrich, purity 99.5%), Gd2O3 (Indian Rare Earths Ltd., purity 99.9%) were preheated overnight at 1173K to remove adsorbed water and oxy-carbonate residues. CaCO3 (Sigma Aldrich, St. Louis, MO, USA, purity >99.0%) was dried at 473K for 4h. Calculated amounts of the dried reactants were homogenized in acetone medium, pelletized and then heated at 1473K for 24 h. The heat-treated pellets were crushed, homogenized and again kept at the same temperature for another 24 h. The above process was repeated once more. The obtained products after this heat treatment were crushed and repelletized and then sintered at 1573K for 24 h. Products obtained after each heat treatment were characterized by powder x-ray diffraction (XRD) data recorded on a Panalytical X-pert Pro diffractometer using Cu Ka (l ¼ 1.5406 and 1.5444 Å) radiation. The powder XRD data were recorded in the two-theta range of 10e90 with step width and time of 0.02 and 1.20s, respectively as mentioned in our earlier reports [11,12,22]. Structural investigations of the nominal compositions were carried out using Rietveld refinement method using Fullprof-2000 program [23]. Raman spectra of the prepared samples were recorded using HeeNe laser (wavelength of 632 nm) as excitation source using a LabRAM HR800 Raman spectrometer (Horiba Jobin Yvon, France). Powder samples were smeared on a glass slide and the scattered radiations were collected at 180 scattering geometry using a CCD (Synapse) based monochromator together with an edge filter. The operating power of the laser was kept at 10 mW and spot size of the sample was 0.5 mm in diameter. Raman band at 520 cm1 corresponding to a silicon wafer was used for calibration of the instrument. The accuracy of the spectral measurement was estimated to be close to ~1 cm1. 2xCaxZrxTi2O7
2.2. Computational details All the calculations were carried out using spin-polarized DFT with a plane-wave basis set implemented in the Vienna Ab-initio Simulation Package (VASP) [24e26]. Electron-ion interactions were described by the projector augmented wave (PAW) method [27]. To calculate the exchangeecorrelation energy, the spinpolarized generalized gradient approximation using the PerdeweBurkeeErnzerhof (PBE) functional has been used [28]. The cut-off energy for the plane-wave basis set was fixed at 400 eV. Geometry optimization was performed by ionic relaxation using a conjugate gradient minimization. A MonkhorstePack k-point grid of 2 2 x 2 was employed to map the first Brillouin zone. Geometries were considered to be converged when the force on each ion became 0.01 eV Å or less. The total energy convergence was tested with respect to the sizes of the plane-wave basis set and the simulation cell and the total energy was found to be accurate to within 1 meV. 3. Results and discussions 3.1. Structural studies Phase formation in Gd2-2xCaxZrxTi2O7 (0.0 x 0.4) was examined by analysing the powder XRD patterns of the products obtained after each heat treatment. Completion of reaction was observed after sintering the sample at 1573K as per our earlier studies [11,12,22]. Powder XRD patterns of the Gd2-2xCaxZrxTi2O7 (0.0 x 0.4) compounds obtained after heat treatment at 1573K are shown in Fig. 1. XRD pattern for the parent compound Gd2Ti2O7 (x ¼ 0.0) agrees quite well with the standard cubic pyrochlore type structure (Fd-3m symmetry, PCPDF card no. 73e1698) with superstructure at 2q ~15.06 , 29.09 , 46.30 and 65.39 corresponding to (111), (311), (511) and (711) planes, respectively. Presence of these superstructure peaks in XRD patterns of Gd2Ti2O7 and all other compositions indicates cubic pyrochlore structure for all of them. However, a gradual decreasing trend for intensity of super structure peaks with increasing Ca2þ and Zr4þ concentrations are observed. The relative intensities of the (222) superstructure peak with respect to the (111) main peak as a function of concentration of Ca2þ and Zr4þ ions are shown in Fig. 2. This decreasing trend can be attributed to the increasing randomization of ions incorporated
2.1. Calorimetric measurements Standard molar enthalpy of formation of the compounds with compositions Gd2-2xCaxZrxTi2O7 (0.0 x 0.4) were determined by measuring the enthalpy of dissolution of the compounds as well as the constituent binary oxides such Gd2O3(s), CaO(s), ZrO2(s) and TiO2(s) in liquid Na2O þ MoO3 solvent (3:4 M ratio) at 986 K employing a high-temperature Calvet calorimeter (Setaram model HT-1000). The calorimeter consists of an isothermal alumina block containing two equal alumina tubes surrounded by a series of thermopiles composed of PtePt 10% Rh thermocouple having a measurement accuracy of ±0.1 K. Calibration of heat flow in the instrument was carried out by using synthetic sapphire [NIST SRM2
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Fig. 1. Powder X-ray diffraction patterns of the series Gd2-2xCaxZrxTi2O7 (0.0 x 0.4).
Fig. 2. Representative Rietveld refinement plot of Gd1.6Ca0.2Zr0.2Ti2O7 (x ¼ 0.2) composition.
3
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Table 1 Refined structural parameters of the series Gd2-2xCaxZrxTi2O7 (0.0 x 0.4). x
0.00
0.10
0.20
0.30
0.40
Composition
Gd2.00Ti2O7
Gd1.80Ca0.10Zr0.10Ti2O7
Gd1.60Ca0.20Zr0.20Ti2O7
Gd1.40Ca0.30Zr0.30Ti2O7
Gd1.20Ca0.40Zr0.40Ti2O7
Crystal System. a (Å) V (Å3) O1 (x) parameter u v w Rp Rwp Chi2 A-O1 (Å) A-O2 (Å)
Cubic, Fd-3m 10.1841(1) 1056.25(2) 0.433(1) 0.0214(4) 0.021(4) 0.012(1) 12.2 19.5 1.99 2.205(1) 2 2.593(6) 4 2.593(8) 2 45.414 1.924(8) 4 1.924(4) 2 0.001
Cubic, Fd-3m 10.1762(2) 1053.79(3) 0.431(2) 0.057(8) 0.070(9) 0.034(3) 16.2 27.0 1.99 2.203(1) 2 2.577(6) 4 2.577(10) 2 42.435 1.930(10) 4 1.930(6) 2 0.000
Cubic, Fd-3m 10.1629(1) 1049.68(2) 0.432(1) 0.033(7) 0.042(8) 0.027(2) 17.5 24.8 1.65 2.200(1) 2 2.577(8) 4 2.577(6) 2 43.170 1.926(7) 4 1.926(4) 2 0.001
Cubic, Fd-3m 10.1533(1) 1046.71(2) 0.432(1) 0.0400(5) 0.036(5) 0.015(1) 14.6 20.4 1.60 2.198(1) 2 2.579(5) 4 2.579(7) 2 44.060 1.922(7) 4 1.922(4) 2 0.001
Cubic, Fd-3m 10.1356(1) 1041.24(2) 0.425(1) 0.045(6) 0.055(6) 0.024(2) 16.3 22.0 1.90 2.194(1) 2 2.525(5) 4 2.525(7) 2 34.307 1.944(7) 4 1.944(4) 2 0.001
Distortion in AO8 ( 104) TieO (Å) Distortion in TiO6 ( 104) (A ¼ Gd3þ/Ca2þ/Zr4þ).
Rietveld refinement plot of Gd1.6Ca0.2Zr0.2Ti2O7 (x ¼ 0.2) is shown in Fig. 3. Since all the compositions exhibited superstructure peaks, the patterns were refined considering the substitution of both Ca2þ and Zr4þ ions into Gd3þ site only. The rationale in favour for the above assumption can also be supported by the ionic radii of the different constituent ions in the in different coordination number (see Table 2 [29]). From the table, it can also be noticed that sum of ionic radii of two Gd3þ is 2.106 Å whereas the sum of the ionic radii of substituent ions (Ca2þ and Zr4þ) is 1.96 Å. Thus, a negative deviation of ionic radii from the combined substituent at ‘A’ site of pyrochlore structure comes out to be ~6%. In accordance with this, the unit cell parameters of the compositions show a decreasing trend with the increase in substituent concentration i.e. the x
into the pyrochlore structure. Keeping these things in mind, Rietveld refinement of all these compositions were carried out. The background of obtained XRD data was fitted with a sixth order polynomial relation and the scale factor adjusted to match intensity. All the observed diffraction peaks were fitted with pseudoVoigt profile function where the half width parameters (u, v, and w) were refined. No absorption or displacement corrections were used for the refinement of the experimental data. The unit cell parameters obtained for Gd2Ti2O7 (x ¼ 0.0) are a ¼ 10.1841(1) Å and V ¼ 1056.25(2) Å3, and they are in agreement with the literature values (PCPDF card no. 73e1698). The details of refined structural and residual parameters are given in Table 1. In a similar manner the XRD patterns of other compositions were refined, and the details of refined parameters are included in Table 1. Representative
Fig. 3. Relative peak intensity (%) of (111) superstructure peak with respect to the strongest (222) peak of pyrochlore structure. 4
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Gd2Ti2O7 (x ¼ 0.0) exhibited five discrete bands centred at ~ 310 cm1, 450 cm1, 520 cm1, 570 cm1 and 690 cm1. The strongest band centred around 310 cm1 can be attributed to O-GdO bending mode, which is an amalgamation of two Raman modes (Eg and F2g) [30e32]. The weak band at around 450 cm1 can be assigned to TieO stretching vibration. An intense band was also observed at around 520 cm1 which can be assigned to GdeO stretching vibration (A1g mode). Two weak bands around 570 cm1 and 690 cm1 were observed which are the characteristics of TieO stretching vibrations of TiO6 polyhedra respectively. No new bands were observed in any compositions which is also a support for the conclusion on monophasic system concluded from XRD studies throughout the composition range. Further it can be noticed that Raman bands are broadened progressively with increasing the value of x of the nominal compositions. Such broadening of Raman bands can also be observed in pyrochlore to defect fluorite transformation. However, the observed Raman spectrum of the highest substituted composition also show signature bands of pyrochlore phase. It can be mentioned here that the fully cation disordered lattice invariably shows only one broad peak centred around 450-500 cm1. At the same time the intensity of mode observed at 570 cm1 becomes more prominent with increasing x in the studied compositions. This suggests that the TiO6 octahedra remain almost unaffected by the substitution. Thus, the broadening of the Raman bands can be attributed to the increasing disordering in the pyrochlore structure, which is due to involvement of ions having different ionic radius and valency. Hence, it can be concluded that the disturbance in the GdO8
Table 2 Ionic radii of the constituent ions in different coordination number. Atoms
Coordination No.
Ionic radii (Å)
Gd3þ
8 6 8 6 8 6 8 6
1.053 0.938 0.84 0.72 0.74 0.605 1.12 1.00
Zr4þ Ti4þ Ca2þ
values of the compositions. Unit cell parameter as calculated from Rietveld refinement steadily decreases from a ¼ 10.1841(1) Å, V ¼ 1056.25(2) Å3 for Gd2Ti2O7 (x ¼ 0.0) to a ¼ 10.1356(1) Å, V ¼ 1041.24(2) Å3 for Gd1.20Ca0.40Zr0.40Ti2O7 (x ¼ 0.4). However, the “x” parameter for 48f oxygen atoms (O1) also remains almost similar (~0.43), viz. 0.433(1) to 0.431(1) for x ¼ 0.0 to x ¼ 0.3, while a slight decreasing value of “x” parameter for the composition with x ¼ 0.4 (“x” ¼ 0.425(1)) indicates a tendency towards randomization cations leading to a disordered form or phase segregation. The segregation of secondary phase beyond this limit has been evidenced in our earlier reports [11,12,22]. Further characterization on the internal strictures of the pyrochlore phases are carried out by Raman spectroscopy. Raman spectra of the nominal compositions Gd2-2xCaxZrxTi2O7 (0.0 x 0.4) were recorded in the range of 200e800 cm1, and they are shown in Fig. 4. Raman spectra of the parent compound
Fig. 4. Raman spectra for the Gd2-2xCaxZrxTi2O7 (0.0 x 0.4) nominal compositions. 5
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polyhedra in substituted samples are due to incorporation of Ca2þ and Zr4þ and that leads to different types of bonds, like CaeO, ZreO, and GdeO in the A site of pyrochlore structure. From the aforesaid structural details, it can be inferred that the cubic pyrochlore structure is retained in the studied compositions but the substitution of Ca2þ and Zr4þ together in the lattice renders a contraction in unit cell due to the average ionic radius of Ca2þ þ Zr4þ couple which is smaller compared to Gd3þ ions. Further a decreasing trend in the intensity of superstructure peak and “x” parameter of oxygen O1 atoms suggests for a cation disorder site. Both Rietveld refinement and Raman spectroscopy indicate the incorporation of Ca2þ and Zr4þ in the Gd3þ site of Gd2Ti2O7.
can be either exothermic or endothermic depending upon the characteristics of solute-solvent interactions. It was observed that endothermic heat flow signals were observed for TiO2(s) and ZrO2(s), whereas, exothermic ones were obtained for dissolution of CaO(s), Gd2O3(s) and the Gd2-2xCaxZrxTi2O7 compositions. Cumulative heat effect of dissolution of the species in solvent was calculated using SETSOFT software. The values of molar enthalpies of dissolution of Gd2-2xCaxZrxTi2O7(s) (0.0 x 0.4), CaO(s), ZrO2(s), Gd2O3(s) and TiO2(s) in liquid Na2O þ MoO3 (3:4) melt maintained at 986K are tabulated in Table 3. The standard molar enthalpy of formation of (0.0 x 0.4) was derived using thermo-chemical cycles represented in Table 4. The values obtained for molar enthalpy of dissolution of Gd2-2xCaxZrxTi2O7(s), CaO(s), ZrO2(s), Gd2O3(s) and TiO2(s) were combined with auxiliary data such as standard molar enthalpies of formation of CaO(s), ZrO2(s), Gd2O3(s) and TiO2(s) from reported literature values [33e35] to derive the standard molar enthalpy of formation of the nominal compositions respectively as depicted in Fig. 6. The standard molar enthalpies of formation (in kJ.mol1) for Gd22xCaxZrxTi2O7 compositions are found to be 3751.26 ± 17.14 (for x ¼ 0.0), 3718.47 ± 16.32 (for x ¼ 0.1), 3686.88 ± 15.46 (for x ¼ 0.2), 3652.53 ± 14.54 (for x ¼ 0.3) and 3618.28 ± 13.57 (for x ¼ 0.4). A systematic decreasing trend in standard molar enthalpies of formation with compositions is evident from these values and that suggests a gradual decreasing trend in stability with increasing the Ca2þ and Zr4þ concentrations. However, the decrease in relative stability is only about 3.5% till the complete saturation limit. Hence it can be concluded that there is no significant destabilization of the parent Gd2Ti2O7 lattice upon incorporation of charge compensatory co-dopants Ca2þ and Zr4þ. As mentioned above, the standard molar enthalpy of formation
3.2. Calorimetric results Standard molar enthalpies of formation of the nominal compositions Gd2-2xCaxZrxTi2O7 (0.0 x 0.4) were derived from the enthalpy of dissolution values of the nominal compositions along with the constituent reagents. Fig. 5 exhibits the heat flow signal of the nominal compositions for a time period of 3600 s wherein a steady base line was obtained and there after the system became ready for the next dropping. Special precaution was taken for dropping of CaO(s) pellets into the solvent as reported in our earlier study [20]. Dropping for each of the species were carried out four times and heat change in J/g was calculated. The change in heat flow during dropping of sample into the solvent can be attributed to heating of the sample from 298K to 986 K, dissociation of lattice of the species, and the dissolution of the species into the solvent. The first two processes are generally endothermic in nature and hence an endothermic heat change is observed. However, dissolution of chemical species in the solvent
Fig. 5. Normalized heat flow curves for nominal compositions Gd2-2xCaxZrxTi2O7 (0.0 x 0.4). 6
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decreases progressively with increase with substitution of Ca2þ and Zr4þ ion pairs at the Gd3þ site. The lowering of enthalpy of formation indicate lowering of stability which can be due to randomization of ions, formation vacancies, as well as overall lattice energy due to the involvement of this ions pair. As the ionic radii of Ca2þ (1.12 Å) and Zr4þ (0.84 Å) are different from Gd3þ (1.05 Å), they are likely to have bonds with different bond length and force constants. Due to aliovalent and difference in the electropositive characters of the cations in A site of pyrochlore lattice a local disordering of anion sites is obviously expected, and that in turn can also influence neighbouring bonds of adjacent AO8 and BO6 polyhedra. Such differences can induce internal strain within the lattice and hence lowering the stability of the lattice. This is predominantly reflected in the decrease of enthalpy of formation of the substituted pyrochlore phases compared to the parent lattice. Further the progressively increasing of such local distortion resulted in the gradual decreasing trend in the enthalpy of formation, and that subsequently can result in a transformed or disproportionated phases. This observation is further supported by theoretical calculations.
Table 3 Heat of Dissolution of Gd22xCaxZrxTi2O7 (0.0 x 0.4) and their component oxides. Compounds
Mass (m) (mg)
DH (J/g)
DHT (kJ mol1)
Gd2Ti2O7(s) Mol. Wt. ¼ 522.24 x ¼ 0.0
22.6 30.9 67.5 51.1
189.30 198.13 199.11 192.54
Gd1.8Ca0.1Zr0.1Ti2O7(s) Mol. Wt. ¼ 503.92 x ¼ 0.1
27.8 24.7 11.5 10.9
218.85 208.65 210.48 213.46
Gd1.6Ca0.2Zr0.2Ti2O7(s) Mol. Wt. ¼ 485.60 x ¼ 0.2
11.6 14.4 16.2 7.6
225.96 229.32 239.21 224.91
Gd1.4Ca0.3Zr0.3Ti2O7(s) Mol. Wt. ¼ 467.28 x ¼ 0.3
24.8 12.1 8.7 12.5
255.34 257.26 252.63 251.43
Gd1.6Ca0.4Zr0.4Ti2O7(s) Mol. Wt. ¼ 448.96 x ¼ 0.4
34.4 22.0 23.3 28.3
279.53 277.73 284.12 278.85
Gd2O3(s) Mol. Wt. ¼ 362.50
15.1 21.0 17.9 12.5
652.44 654.98 659.72 658.37
CaO (s) Mol. Wt. ¼ 56.08
11.2 18.1 15.0 9.5
1608.95 1599.68 1627.14 1619.29
ZrO2(s) Mol. Wt. ¼ 123.22
15.1 9.8 10.1 13.7
357.13 358.68 359.42 358.77
TiO2 (s) Mol. Wt. ¼ 79.87
14.2 13.1 17.5 15.4
558.16 576.06 564.29 563.16
98.86 103.47 103.98 100.55 Avg: 101.72 ± 2.43 110.28 105.14 106.07 107.57 Avg: 107.27 ± 2.25 109.73 111.36 116.16 109.22 Avg: 111.62 ± 3.16 119.32 120.21 118.05 117.49 Avg: 118.77 ± 1.23 125.50 124.69 127.56 125.19 Avg: 125.74 ± 1.26 236.51 237.43 239.15 238.66 Avg: 237.94 ± 1.2 90.23 89.71 91.25 90.81 Avg: 90.50 ± 0.67 44.01 44.20 44.29 44.21 Avg: 44.18 ± 0.12 44.58 46.01 45.07 44.98 Avg: 45.16 ± 0.61
3.3. Computational results To rationalize the experimental results and to get more insights in the local structure and energetic due to aliovalent substitution, theoretical calculations were carried under density functional theory (DFT) formalism on Gd2Ti2O7 and its doped variants. The three-dimensional periodic boundary conditions were applied to approximate a bulk solid (i.e. the pyrochlore (Fd-3m) phase of Gd2Ti2O7). A conventional cubic unit cell (a ¼ b ¼ g ¼ 90 ) containing 88 atoms (16 Gd, 16 Ti and 56 O) was used for calculations. Structural optimization was performed with respect to atomic coordinates and unit cell parameters. The unit cell parameters of the relaxed structure are: a ¼ b ¼ c ¼ 10.177 Å, which is reasonably close to experimental value (a ¼ 10.1841(1) Å). In the case of doped Gd2Ti2O7, out of the 16 Gd/Ti atoms in the unit cell, appropriate number of atoms were replaced with Ca2þ/Zr4þ to nearly approximate the studied Gd2-2xCaxZrxTi2O7 (0.0 x 0.4) compositions. For example, the replacement of two Gd atoms out of 16 Gd atoms by one Ca and one Zr atom can result in composition with x ¼ 0.125, i.e. Gd1.75Ca0.125Zr0.125Ti2O7. Although the theoretical compositions
Table 4 Thermochemical cycles for enthalpy of formation of Gd22xCaxZrxTi2O7 (0.0 x 0.4). DfH 298(Gd22xCaxZrxTi2O7 (s)) ¼ -DH1i þ (1-x) DH2 þ xDH3 þ xDH4 þ 2DH5 þ (1-x) DH6 þ xDH7 þ x DH8 þ 2DH9. Reaction
DHi
DHdissolution (kJ mol1)
Gd2Ti2O7 (s,298K) þ (sln) ¼ Gd2O3(sln) þ 2TiO2(sln) Gd1.8Ca0.1Zr0.1Ti2O7(s) (s,298K) þ (sln) ¼ 0.9Gd2O3(sln) þ 0.1CaO(sln) þ 0.1ZrO2(sln) þ 2TiO2(sln) Gd1.6Ca0.2Zr0.2Ti2O7(s) (s,298K) þ (sln) ¼ 0.8Gd2O3(sln) þ 0.2CaO(sln) þ 0.2ZrO2(sln) þ 2TiO2(sln) Gd1.4Ca0.3Zr0.3Ti2O7(s) (s,298K) þ (sln) ¼ 0.7Gd2O3(sln) þ 0.3CaO(sln) þ 0.3ZrO2(sln) þ 2TiO2(sln) Gd1.2Ca0.4Zr0.4Ti2O7(s) (s,298K) þ (sln) ¼ 0.6Gd2O3(sln) þ 0.4CaO(sln) þ 0.4ZrO2(sln) þ 2TiO2(sln) Gd2O3(s,298K) þ(sln) ¼ Gd2O3(sln) CaO(s,298K) þ (sln) ¼ CaO(sln) ZrO2(s,298K) þ (sln) ¼ ZrO2(sln) TiO2(s,298K) þ (sln) ¼ TiO2(sln) 2Gd(s,298K) þ 3/2O2(g) ¼ Gd2O3(s) Ca(s,298K) þ 1/2O2(g) ¼ CaO(s) Zr(s,298K) þ O2(g) ¼ ZrO2(s) Ti(s,298K) þ O2(g) ¼ TiO2(s) 2Gd(s,298K) þ 2Ti(s,298K) þ 3.5 O2(g) ¼ Gd2Ti2O7 (s,298K) (x ¼ 0.0) 1.8Gd(s,298K) þ 0.1Ca(s,298K) þ 0.1Zr(s,298K) þ 2Ti(s,298K) þ 3.5 O2(g) ¼ Gd1.8Ca0.1Zr0.1Ti2O7 (s,298K) 1.6Gd(s,298K) þ 0.2Ca(s,298K) þ 0.2Zr(s,298K) þ 2Ti(s,298K) þ 3.5 O2(g) ¼ Gd1.6Ca0.2Zr0.2Ti2O7 (s,298K) 1.4Gd(s,298K) þ 0.3Ca(s,298K) þ 0.3Zr(s,298K) þ 2Ti(s,298K) þ 3.5 O2(g) ¼ Gd1.4Ca0.3Zr0.3Ti2O7 (s,298K) 1.2Gd(s,298K) þ 0.4Ca(s,298K) þ 0.4Zr(s,298K) þ 2Ti(s,298K) þ 3.5 O2(g) ¼ Gd1.2Ca0.4Zr0.4Ti2O7 (s,298K)
DH1a DH1b DH1c DH1d DH1e DH2 DH3 DH4 DH5 DH6 DH7 DH8 DH9 DfH 298
101.72 ± 2.43 107.27 ± 2.25 111.62 ± 3.16 118.74 ± 1.23 125.75 ± 1.26 237.94 ± 1.20 90.50 ± 0.67 44.18 ± 0.12 45.16 ± 0.61 1815.86 ± 16.74 634.29 ± 1.67 1100.81 ± 2.09 944.75 ± 1.67 3751.26 ± 17.14 3718.47 ± 16.32 3686.88 ± 15.46 3652.53 ± 14.54 3618.28 ± 13.57
7
(x (x (x (x
¼ ¼ ¼ ¼
0.1) 0.2) 0.3) 0.4)
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Fig. 6. Variation of experimental and theoretically calculated standard molar enthalpy of formation of Gd2-2xCaxZrxTi2O7 (0.0 x 0.4) with composition.
The net cohesive energy for Gd2Ti2O7 (7.13eV/atom) is in agreement with that reported by Jun and Bin (7.224 eV/atom [36]. Similarly, the calculated values of DHf for x ¼ 0.125, 0.25, 0.315, 0.375 are found to be 7.14, 7.13, 7.11 and 7.09 eV/atom, respectively. The calculated values of DHf indicate a systematically decreasing trend with increasing the dopant concentrations, and they are in line with the experimental observations presented in Fig. 6. For better comparison the calculated enthalpies of formation of all the compositions are converted to kJ/mol in Fig. 6. From the figure, it is clear that both experimental and theoretical calculation values show a similar trend with variation in compositions. However, the absolute values show differences for each compositions. The differences can be attributed to the difference in compositions used for calculations for computational simplicity in DFT, methods used for DFT calculations, temperature of calculations (0 K) and experimental (298 K), as well as defects and microstructural contributions in the experimental results. The steady decrease in heat of formation with increasing dopant concentration can be attributed to the smaller ionic size of dopant (total ionic radius of Ca2þ and Zr4þ) in comparison to host Gd3þ ion (2 ionic radius of Gd3þ ion) as well as difference in oxidation states of substituted ions. Thus, they are also resulted in significant change in the polyhedron around the cations as shown in Fig. 7. Further from the analyses of local structural parameters, shown in Fig. 7, it is clearly observed that the substitution of Ca2þ and Zr4þ in Gd2Ti2O7 not only effect the substituted sites but also adjacent polyhedra. This is expected due to the differences in charge as well as radii of the substituted ions. In the parent Gd2Ti2O7, the calculated GdeO bond lengths in GdO8 units are 2.51 Å 6 and 2.20 Å 2 while TieO bond lengths in TiO6 units are 1.97 Å 6. Upon substitution of the Ca2þ and Zr4þ, the GdeO and TieO bonds respectively in GdO8 and TiO6 are dispersed widely, creating a distorted polyhedra around Gd3þ and Ti4þ. These are due to the incorporation smaller ZrO8 polyhedra in the structure (Fig. 7). This
are not exactly same to that of experimental compositions, it is expected that set of nearby composition can rationalize the experimental trends. First to find out the energetic preference for substitution of Ca2þ/Zr4þ at either Gd site or Ti site calculations were carried out for three cases, viz. (i). both Ca2þ and Zr4þ replacing the Gd3þ ions, (ii). Ca2þ substituting the Gd3þ ion and Zr4þ replacing the Ti4þ ion, and (iii). both Ca2þ and Zr4þ replacing the Ti4þ ion in the lattice. It was found that the replacement of Gd3þ by both Ca2þ and Zr4þ together is energetically most favourable situation than the substitution of Ca2þ in Gd3þ site and Zr4þ in Ti4þ site or substitution of both Ca2þ and Zr4þ in the Ti4þ sites. The net energy of case-2 and case-3 are 0.28 and 0.81 eV higher than that of the case-1. This order of relative energy suggests that the substitution of Ca2þ and Zr4þ at the Gd3þ is energetically preferred over the fully or partially substituted Ti4þ sites. This energetic preference is in line with ionic radius criteria of substitutional solid solution (see. Table 2). Further calculations for higher dopant concentration, like x ¼ 0.25, 0.315, 0.375, were also carried out by considering the substitution at Gd3þ site only. For x ¼ 0.25, 0.375 the calculations were performed with single unit cell containing 88 atoms, however for x ¼ 0.315, the calculations were performed with a supercell having two unit-cells together containing 178 atoms. The heat of formation (DHf) for different aliovalent doping concentrations at Gd-sites was calculated using the following relation. DHf ¼ {E (Gd2-2xCaxZrxTi2O7) e no. of Gd atoms E(Gd) e no. of Ti atoms E(Ti) eno. of Ca atoms E(Ca) e no. of Zr atoms E(Zr)}/total number of atoms.Where E (Gd2-2xCaxZrxTi2O7) is the total energy of doped supercell, and E(Gd), E(Ti), E(Ca) and E(Zr) are atom correction energy for a single Gd, Ti, Ca, and Zr atom respectively. In the case of Gd2Ti2O7, the net cohesive energy calculated as per the above relation can be represented as: 918.97163458 e {16 x 10.21945436 þ 16 x 2.61943856 þ 56 x 1.53478333} ¼ 627.6014814 -627.6014814/88 ¼ 7.13 eV/atom. 8
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Fig. 7. GdO8 and TiO6 polyhedra in the structure of doped and undoped Gd2Ti2O7.
increasingly disordered cation sublattice. Higher disorder in the surroundings of Gd site compared to that at the Ti sites is concluded from Raman spectroscopic studies as well as dentistry functional calculations. Calorimetric investigations indicated a gradually decreasing trend in the enthalpy of formation with increasing substitution, which is also indicated by density functional theory calculations. From the joint experimental and theoretical calculations, it could be concluded that the relative stability of multiple aliovalent cation substituted pyrochlore type Gd2Ti2O7 are lower than the undoped systems. Both experimental characterization and theoretical calculations indicate the substation of Ca2þ and Zr4þ are favoured at Gd3þ sites. Also, from density functional calculation further indicates the expansion of TieO bonds and increased distortions in the AO8 and BO6 polyhedra of the pyrochlore lattice. That in turn lower the stability of the lattice. This study indicates, despite the formation of single-phase cation substituted pyrochlore
also indicates a relative expansion of TieO bonds in Gd2-2xCaxZrxTi2O7 compared to those in Gd2Ti2O7. Thus, an appreciable weakening of ZreO and TieO bonds and incorporation of ionic CaeO bonds decrease the stability in comparison to the unsubstituted Gd2Ti2O7 lattice. This result is in accordance with the overall decrease of DHf for the doped Gd2Ti2O7 observed experimentally. 4. Conclusions Following the electroneutrality considerations, single phase solid solution compositions containing two aliovalent cations while maintaining the oxygen stoichiometry could be prepared. From both XRD and Raman spectroscopic studies, it is concluded that about 40% of Gd3þ of Gd2Ti2O7 can be replaced by Ca2þ and Zr4þ cations together. No distortion was observed in the unit cell but a decreasing tendency of super structure peaks indicates an 9
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phase in the complete range of compositions, the relative stability decreases by substitution. However, the decrease in relative stability is about 3.5% compared to unsubstituted phase, suggesting the Gd2Ti2O7 type pyrochlore lattices are promising matrices to accommodate multiple aliovalent cations related to nuclear waste immobilization.
609e616. [12] M. Jafar, P. Sengupta, S.N. Achary, A.K. Tyagi, Phase evolution and microstructural studies in CaZrTi2O7 (zirconolite)eSm2Ti2O7 (pyrochlore) system, J. Eur. Ceram. Soc. 34 (2014) 4373e4381. [13] B.P. Mandal, N. Garg, S.M. Sharma, A.K. Tyagi, Preparation, XRD and Raman spectroscopic studies on new compounds RE2Hf2O7 (RE ¼ Dy, Ho, Er, Tm Yb, Lu, Y): pyrochlores or defect-fluorite? J. Solid State Chem. 179 (2006) 1990e1994. [14] M. Lang, F. Zhang, J. Zhang, J. Wang, J. Lian, W.J. Weber, B. Schuster, C. Trautmann, R. Neumann, R.C. Ewing, Review of A2B2O7 pyrochlore response to irradiation and pressure, Nucl. Instrum. Methods B 268 (2010) 2951e2959. [15] S.X. Wang, L.M. Wang, R.C. Ewing, G.S. Was, G.R. Lumpkin, Ion irradiationinduced phase transformation of pyrochlore and zirconolite, Nucl. Instrum. Methods B 148 (1999) 704e709. [16] R.S. Kumar, A.L. Cornelius, M. Somayazulu, D. Errandonea, M.F. Nicol, J. Gardner, High pressure structure of Tb2Ti2O7 pyrochlore at cryogenic temperatures, phys. stat. solidi. B 244 (2007) 266e269. [17] H.Y. Xiao, F. Gao, W.J. Weber, Ab initio investigation of phase stability of Y2Ti2O7 and Y2Zr2O7 under high pressure, Phys. Rev. B 80 (2009) 212102. n, R. Shukla, [18] D. Errandonea, R.S. Kumar, S.N. Achary, O. Gomis, F.J. Manjo A.K. Tyagi, New high-pressure phase and equation of state of Ce2Zr2O8, J. App. Phys. 111 (2012), 053519. [19] H. Li, Q. Tao, N. Li, R. Tang, Y. Zhao, H. Zhu, P. Zhu, X. Wang, Pressure-induced structural transition of Y2Zr2O7, J. Alloys Compd. 660 (2016) 446e449. [20] M. Jafar, S.B. Phapale, B.P. Mandal, R. Mishra, A.K. Tyagi, Preparation and structure of uranium-incorporated Gd2Zr2O7 compounds and their thermodynamic stabilities under oxidizing and reducing conditions, Inorg. Chem. 54 (2015) 9447e9457. [21] M. Jafar, S.B. Phapale, S.N. Achary, R. Mishra, A.K. Tyagi, High-temperature crystallographic and thermodynamic investigations on synthetic zirconolite (CaZrTi2O7), J. Therm. Anal. Calorim. 131 (2018) 2709e2718. [22] M. Jafar, S.N. Achary, N.P. Salke, A.K. Sahu, R. Rao, A.K. Tyagi, X-ray diffraction and Raman spectroscopic investigations on CaZrTi2O7-Y2Ti2O7 system: delineation of phase fields consisting of potential ceramic host materials, J. Nucl. Mater. 475 (2016) 192e199. [23] J. Rodriguez-Carjaval, “Multi Pattern Rietveld Refinement Program, Fullprof 2k” Version 1, 6 July 2000. [24] G. Kresse, J. Hafner, Ab initio molecular dynamics for liquid metals, Phys. Rev. B 47 (1993) 558e567. [25] G. Kresse, J. Furthmuller, Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set, Phys. Rev. B 54 (1996) 11169. [26] G. Kresse, J. Furthmuller, Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set, Comput. Mater. Sci.Comput. Mater. Sci. 6 (1996) 15e50. [27] G. Kresse, J. Joubert, From ultrasoft pseudopotentials to the projector augmented-wave method, Phys. Rev. B 59 (1999) 1758e1775. [28] J.P. Perdew, K. Burke, M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77 (1996) 3865e3868. [29] R.D. Shannon, Revised effective ionic radii and systematic studies of interatomic distances in halides and chalcogenides, Acta Cryst. A 32 (1976) 751e767. [30] F.X. Zhang, B. Manoun, S.K. Saxena, Mater. Lett. 60 (2006) 2773e2776. [31] Ashkan Salamat, Paul F. McMillan, Steven firth, katherine woodhead, andrew L. Hector, gaston garbarino, martin C. Stennett and neil C. Hyatt,, Inorg. Chem. 52 (2013) 1550e1558. n, C. Guglieri, S. Díaz-Moreno, G. Aquilanti, A.F. Fuentes, L. Olivi, [32] M.L. Sanjua J. Chaboy, Raman and x-ray absorption spectroscopy study of the phase evolution induced by mechanical milling and thermal treatments in R2Ti2O7 pyrochlores, Phys. Rev. B 84 (2011) 104207. [33] C.H. Shomatte, A method for evaluating and correlating thermodynamic data, J. Phys. Chem. 58 (1954) 368e371. [34] S. Phapale, R. Mishra, D. Das, Standard enthalpy of formation and heat capacity of compounds in the pseudo-binary Bi2O3eFe2O3 system, J. Nucl. Mater. 373 (2008) 137e141. [35] David R. Lide (Ed.), CRC Handbook of Chemistry and Physics, CRC Press, Boca Raton, FL, 2005. Internet Version 2005, http://www.hbcpnetbase.com. [36] C.Z. Jun, T.D.- Bin, First-principles study of disordering tendencies in Gd2B2O7 (B ¼ Ti, Sn, Zr) compounds Chin, Phys. B 19 (2010) 127101.
CRediT authorship contribution statement M. Jafar: Prepared the sample, characterized by XRD, Raman spectroscopy, participated in calorimetric measurements and analyses of data, wrote the manuscript, Formal analysis, Data curation. S.B. Phapale: Carried out the calorimetric measurements and analyses of data, Formal analysis, Data curation. S.N. Achary: Conceived the problem, coordinated the experiments and calculations, analysed and interpreted the data, wrote the manuscript, edit the manuscript and prepared the final manuscript, Formal analysis, Data curation. R. Mishra: Carried out the calorimetric measurements and analyses of data, wrote the manuscript, Formal analysis, Data curation. C. Majumder: Carried out DFT calculations and wrote the manuscript. A.K. Tyagi: Proof read and edited the manuscript. Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. References rus, V. Aubin-Chevaldonnet, I. Bardez, [1] D. Caurant, P. Loiseau, O. Maje A. Quintas, in: “Glasses, GlasseCeramics and Ceramics for Immobilization of Highly Radioactive Nuclear Wastes”, Nova Science Publishers, New York, 2009. [2] M.I. Ojovan, W.E. Lee, An Introduction to Nuclear Waste Immobilization, Elsevier Ltd, Oxford, UK, 2005, pp. 213e267. [3] M.I. Ojovan, W.E. Lee, An Introduction to Nuclear Waste Immobilization, Elsevier Ltd, Oxford, UK, 2005, pp. 213e267. rus, P. Loiseau, I. Bardez, N. Baffier, J.L. Dussossoy, Crys[4] D. Caurant, O. Maje tallization of neodymium-rich phases in silicate glasses developed for nuclear waste immobilization, J. Nucl. Mater. 354 (2006) 143e162. [5] P. Loiseau, D. Caurant, O. Majerus, N. Baffier, C. Fillet, Crystallization study of (TiO2, ZrO2)-rich SiO2-Al2O3-CaO glasses. Part II. Surface and internal crystallization processes investigated by differential thermal analysis (DTA), J. Mater. Sci. 38 (2003) 843e852. [6] A.E. Ringwood, S.E. Kesson, N.G. Ware, W. Hibberson, Immobilisation of high level nuclear reactor wastes in, SYNROC” Nature 278 (1979) 219e223. [7] R.C. Ewing, Nuclear waste forms for actinides, Proc. Natl. Acad. Sci. U.S.A. 96 (1999) 3432e3439. [8] E.R. Vance, G.R. Lumpkin, M.L. Carter, D.J. Cassidy, C.J. Ball, R.A. Day, B.D. Begg, Incorporation of uranium in zirconolite (CaZrTi2O7), J. Am. Ceram. Soc. 85 (2002) 1853e1859. [9] R.C. Ewing, W.J. Weber, J. Lian, “Nuclear waste disposaldpyrochlore A2B2O7: nuclear waste form for the immobilization of plutonium and ‘‘minor’’ actinides, J. Appl. Phys. 95 (2004) 5929e5971. [10] M.A. Subramanian, G. Aravamudan, G.V. Subba Rao, Oxide pyrochlores -A review”, Prog. Solid State Chem. 15 (1983) 55e143. [11] M. Jafar, P. Sengupta, S.N. Achary, A.K. Tyagi, Phase evolution and microstructural studies in CaZrTi2O7eNd2Ti2O7 system, J. Am. Ceram. Soc. 97 (2014)
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Journal of Alloys and Compounds journal homepage: http://www.elsevier.com/locate/jalcom
Implication of aliovalent cation substitution on structural and thermodynamic stability of Gd2Ti2O7: Experimental and theoretical investigations M. Jafar a, b, S.B. Phapale a, b, S. Nigam a, b, S.N. Achary a, b, *, R. Mishra a, b, C. Majumder a, b, A.K. Tyagi a, b a b
Chemistry Division, Bhabha Atomic Research Centre, Trombay, Mumbai 400085, India Homi Bhabha National Institute, Anushaktinagar, Mumbai 400094, India
a r t i c l e i n f o
a b s t r a c t
Article history: Received 3 August 2020 Received in revised form 28 October 2020 Accepted 30 October 2020 Available online xxx
Multi-cation substituted pyrochlores are potential matrices for immobilization of long-lived high level nuclear waste. In this paper, we report, the structural and thermodynamic stabilities of aliovalent multi cation substituted Gd2Ti2O7 pyrochlore compounds determined by experimental and theoretical methods. A series of cubic pyrochlore-type Gd2-2xCaxZrxTi2O7 (0.0 x 0.4) compounds were synthesized and characterized by XRD and Raman spectroscopy techniques. It is observed that incorporation of Ca2þ and Zr4þ at Gd3þ site does not significantly alter crystal lattice of Gd2Ti2O7. Calorimetric studies were carried out to determine the thermodynamic stability of Gd2-2xCaxZrxTi2O7 compounds. The observed data indicate that standard molar enthalpy of formation of Gd2-2xCaxZrxTi2O7 decreases steadily with increasing dopant concentration which has been attributed to increasing distortion of the polyhedra around the cations. These inferences were further supported by DFT calculations. © 2020 Elsevier B.V. All rights reserved.
Keywords: Aliovalent substitution Pyrochlore Gd2Ti2O7 XRD Raman spectroscopy Calorimetry DFT
1. Introduction Long lived minor actinides such as Np, Am, Cf, etc. Present in high level nuclear waste (HLW) are the main source of long-term radio toxicity. It is therefore necessary to immobilize nuclear HLWs in thermodynamically stable and long-lasting immobilization matrices [1]. Presently borosilicate glasses are being used as primary waste immobilization matrix all over the world [2]. However, glass being a metastable material has some limitations like low solubility of minor actinides, lower activity loading, possible devitrification and hence deterioration in stability, etc. [3e5]. In view of these shortcomings of glass matrices, Ringwood et al. [6] proposed ceramic composites or aggregates of mineral analogous titanates, termed as SYNROC as futuristic and potential matrices for immobilization of nuclear HLW [6]. SYNROC is a composite material and mostly consists of zirconolite, perovskite,
* Corresponding author. Chemistry Division, Bhabha Atomic Research Centre Mumbai-400085, India E-mail address: [email protected] (S.N. Achary).
hollandite, pyrochlore and rutile type phases [6e9]. Pyrochlore, which is an important constituent phases of SYNROC, can be represented by a general formula A2B2O7, where A and B cations form AO8 and BO6 polyhedra with oxygen atom respectively, in its crystal structure [10]. Depending upon the rA/rB, where rA and rB represent the ionic radii of the cations in their respective coordination numbers, the pyrochlore structure (symmetry: Fd3m) has an ability to transform into either a cation ordered perovskite type (symmetry: C2/c) structure or a cation disordered defect-fluorite type structure (symmetry: Fm-3m) [11]. In general, for A2Ti2O7 with rare earth ions (A) having ionic radii smaller than Sm3þ generally form an ordered cubic pyrochlore structure, whereas ions having larger ionic radii than Sm3þ form perovskite related monoclinic structures [12,13]. The ability to accommodate a wider range of ions without significant alteration in the structure makes pyrochlore a potential candidate for immobilization of minor actinides present in nuclear HLW [11e15]. Thus, structural and thermodynamic stabilities of a number of pyrochlore-type compounds have been explored under extreme conditions such as temperature, pressure, higher radiation field, etc. [16e21]. Most of these studies are limited either to host lattices or single cation
https://doi.org/10.1016/j.jallcom.2020.157781 0925-8388/© 2020 Elsevier B.V. All rights reserved.
Please cite this article as: M. Jafar, S.B. Phapale, S. Nigam et al., Implication of aliovalent cation substitution on structural and thermodynamic stability of Gd2Ti2O7: Experimental and theoretical investigations, Journal of Alloys and Compounds, https://doi.org/10.1016/ j.jallcom.2020.157781
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720]. The details of the calorimetry experimental procedures are explained in our earlier reports [20,21]. Solvent used for calorimetric studies, a mixture of Na2O and MoO3 (3:4 M ratio), was synthesized by heating appropriate amounts of dried Na2CO3 (BDH, reagent grade) and MoO3 (BDH, reagent grade) at 986K. At this temperature, Na2CO3 decomposes to Na2O, and that form a eutectic mixture with MoO3. The mixture was kept for 6 h at 986 K for complete homogenization and then cooled to room temperature. The solvent powder was characterized for stoichiometry by chemical analysis and XRD study. No impurity element and only Na and Mo of desired stoichiometry were observed in the solvent mixture. Around 7 g of Na2O þ MoO3 solvent were added to platinum tubes placed inside the alumina assembly and the assembly is slowly lowered into the calorimeter. The temperature was maintained at 986 ± 0.05 K during the whole experiment. Reaction tubes were equilibrated till a steady base line for heat flux was obtained. Sample pellets of about few milligrams were dropped into the solvent and the characteristic heat change effects were recorded by integration of heat flow signal with respect to time. In a similar manner heat change effects for the constituent reagents like ZrO2, CaO and TiO2 were also recorded.
incorporated lattices. However, the structural perturbations induced by doping of diverse cations into pyrochlore lattices are not well explored in literature. The effects of aliovalent substitution and multi cation substitution on the stabilities of pyrochlore structure need to be well understood before qualifying them as waste immobilization matrices. To understand structural and thermodynamic stabilities of aliovalent multi cation substituted Gd2Ti2O7 pyrochlore, detailed investigations on divalent (Ca2þ) and tetravalent (Zr4þ) cation substituted at trivalent cation (Gd3þ) site were carried out. The choice of this system was based on our earlier studies in zirconolite-pyrochlore based systems wherein the formation of single phase pyrochlore or zirconolite by co-doping has been revealed [11,12,22]. The observations from experimental investigations and theoretical validations on the structure and stabilities of co-doped Gd2Ti2O7 pyrochlore system are presented in the manuscript. 2. Experimental A series of compounds having nominal composition Gd2(0.0 x 0.4) was prepared by solid state reaction route. Binary oxides such as ZrO2 (Sigma Aldrich, purity 99.0%), TiO2 (Sigma Aldrich, purity 99.5%), Gd2O3 (Indian Rare Earths Ltd., purity 99.9%) were preheated overnight at 1173K to remove adsorbed water and oxy-carbonate residues. CaCO3 (Sigma Aldrich, St. Louis, MO, USA, purity >99.0%) was dried at 473K for 4h. Calculated amounts of the dried reactants were homogenized in acetone medium, pelletized and then heated at 1473K for 24 h. The heat-treated pellets were crushed, homogenized and again kept at the same temperature for another 24 h. The above process was repeated once more. The obtained products after this heat treatment were crushed and repelletized and then sintered at 1573K for 24 h. Products obtained after each heat treatment were characterized by powder x-ray diffraction (XRD) data recorded on a Panalytical X-pert Pro diffractometer using Cu Ka (l ¼ 1.5406 and 1.5444 Å) radiation. The powder XRD data were recorded in the two-theta range of 10e90 with step width and time of 0.02 and 1.20s, respectively as mentioned in our earlier reports [11,12,22]. Structural investigations of the nominal compositions were carried out using Rietveld refinement method using Fullprof-2000 program [23]. Raman spectra of the prepared samples were recorded using HeeNe laser (wavelength of 632 nm) as excitation source using a LabRAM HR800 Raman spectrometer (Horiba Jobin Yvon, France). Powder samples were smeared on a glass slide and the scattered radiations were collected at 180 scattering geometry using a CCD (Synapse) based monochromator together with an edge filter. The operating power of the laser was kept at 10 mW and spot size of the sample was 0.5 mm in diameter. Raman band at 520 cm1 corresponding to a silicon wafer was used for calibration of the instrument. The accuracy of the spectral measurement was estimated to be close to ~1 cm1. 2xCaxZrxTi2O7
2.2. Computational details All the calculations were carried out using spin-polarized DFT with a plane-wave basis set implemented in the Vienna Ab-initio Simulation Package (VASP) [24e26]. Electron-ion interactions were described by the projector augmented wave (PAW) method [27]. To calculate the exchangeecorrelation energy, the spinpolarized generalized gradient approximation using the PerdeweBurkeeErnzerhof (PBE) functional has been used [28]. The cut-off energy for the plane-wave basis set was fixed at 400 eV. Geometry optimization was performed by ionic relaxation using a conjugate gradient minimization. A MonkhorstePack k-point grid of 2 2 x 2 was employed to map the first Brillouin zone. Geometries were considered to be converged when the force on each ion became 0.01 eV Å or less. The total energy convergence was tested with respect to the sizes of the plane-wave basis set and the simulation cell and the total energy was found to be accurate to within 1 meV. 3. Results and discussions 3.1. Structural studies Phase formation in Gd2-2xCaxZrxTi2O7 (0.0 x 0.4) was examined by analysing the powder XRD patterns of the products obtained after each heat treatment. Completion of reaction was observed after sintering the sample at 1573K as per our earlier studies [11,12,22]. Powder XRD patterns of the Gd2-2xCaxZrxTi2O7 (0.0 x 0.4) compounds obtained after heat treatment at 1573K are shown in Fig. 1. XRD pattern for the parent compound Gd2Ti2O7 (x ¼ 0.0) agrees quite well with the standard cubic pyrochlore type structure (Fd-3m symmetry, PCPDF card no. 73e1698) with superstructure at 2q ~15.06 , 29.09 , 46.30 and 65.39 corresponding to (111), (311), (511) and (711) planes, respectively. Presence of these superstructure peaks in XRD patterns of Gd2Ti2O7 and all other compositions indicates cubic pyrochlore structure for all of them. However, a gradual decreasing trend for intensity of super structure peaks with increasing Ca2þ and Zr4þ concentrations are observed. The relative intensities of the (222) superstructure peak with respect to the (111) main peak as a function of concentration of Ca2þ and Zr4þ ions are shown in Fig. 2. This decreasing trend can be attributed to the increasing randomization of ions incorporated
2.1. Calorimetric measurements Standard molar enthalpy of formation of the compounds with compositions Gd2-2xCaxZrxTi2O7 (0.0 x 0.4) were determined by measuring the enthalpy of dissolution of the compounds as well as the constituent binary oxides such Gd2O3(s), CaO(s), ZrO2(s) and TiO2(s) in liquid Na2O þ MoO3 solvent (3:4 M ratio) at 986 K employing a high-temperature Calvet calorimeter (Setaram model HT-1000). The calorimeter consists of an isothermal alumina block containing two equal alumina tubes surrounded by a series of thermopiles composed of PtePt 10% Rh thermocouple having a measurement accuracy of ±0.1 K. Calibration of heat flow in the instrument was carried out by using synthetic sapphire [NIST SRM2
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Fig. 1. Powder X-ray diffraction patterns of the series Gd2-2xCaxZrxTi2O7 (0.0 x 0.4).
Fig. 2. Representative Rietveld refinement plot of Gd1.6Ca0.2Zr0.2Ti2O7 (x ¼ 0.2) composition.
3
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Table 1 Refined structural parameters of the series Gd2-2xCaxZrxTi2O7 (0.0 x 0.4). x
0.00
0.10
0.20
0.30
0.40
Composition
Gd2.00Ti2O7
Gd1.80Ca0.10Zr0.10Ti2O7
Gd1.60Ca0.20Zr0.20Ti2O7
Gd1.40Ca0.30Zr0.30Ti2O7
Gd1.20Ca0.40Zr0.40Ti2O7
Crystal System. a (Å) V (Å3) O1 (x) parameter u v w Rp Rwp Chi2 A-O1 (Å) A-O2 (Å)
Cubic, Fd-3m 10.1841(1) 1056.25(2) 0.433(1) 0.0214(4) 0.021(4) 0.012(1) 12.2 19.5 1.99 2.205(1) 2 2.593(6) 4 2.593(8) 2 45.414 1.924(8) 4 1.924(4) 2 0.001
Cubic, Fd-3m 10.1762(2) 1053.79(3) 0.431(2) 0.057(8) 0.070(9) 0.034(3) 16.2 27.0 1.99 2.203(1) 2 2.577(6) 4 2.577(10) 2 42.435 1.930(10) 4 1.930(6) 2 0.000
Cubic, Fd-3m 10.1629(1) 1049.68(2) 0.432(1) 0.033(7) 0.042(8) 0.027(2) 17.5 24.8 1.65 2.200(1) 2 2.577(8) 4 2.577(6) 2 43.170 1.926(7) 4 1.926(4) 2 0.001
Cubic, Fd-3m 10.1533(1) 1046.71(2) 0.432(1) 0.0400(5) 0.036(5) 0.015(1) 14.6 20.4 1.60 2.198(1) 2 2.579(5) 4 2.579(7) 2 44.060 1.922(7) 4 1.922(4) 2 0.001
Cubic, Fd-3m 10.1356(1) 1041.24(2) 0.425(1) 0.045(6) 0.055(6) 0.024(2) 16.3 22.0 1.90 2.194(1) 2 2.525(5) 4 2.525(7) 2 34.307 1.944(7) 4 1.944(4) 2 0.001
Distortion in AO8 ( 104) TieO (Å) Distortion in TiO6 ( 104) (A ¼ Gd3þ/Ca2þ/Zr4þ).
Rietveld refinement plot of Gd1.6Ca0.2Zr0.2Ti2O7 (x ¼ 0.2) is shown in Fig. 3. Since all the compositions exhibited superstructure peaks, the patterns were refined considering the substitution of both Ca2þ and Zr4þ ions into Gd3þ site only. The rationale in favour for the above assumption can also be supported by the ionic radii of the different constituent ions in the in different coordination number (see Table 2 [29]). From the table, it can also be noticed that sum of ionic radii of two Gd3þ is 2.106 Å whereas the sum of the ionic radii of substituent ions (Ca2þ and Zr4þ) is 1.96 Å. Thus, a negative deviation of ionic radii from the combined substituent at ‘A’ site of pyrochlore structure comes out to be ~6%. In accordance with this, the unit cell parameters of the compositions show a decreasing trend with the increase in substituent concentration i.e. the x
into the pyrochlore structure. Keeping these things in mind, Rietveld refinement of all these compositions were carried out. The background of obtained XRD data was fitted with a sixth order polynomial relation and the scale factor adjusted to match intensity. All the observed diffraction peaks were fitted with pseudoVoigt profile function where the half width parameters (u, v, and w) were refined. No absorption or displacement corrections were used for the refinement of the experimental data. The unit cell parameters obtained for Gd2Ti2O7 (x ¼ 0.0) are a ¼ 10.1841(1) Å and V ¼ 1056.25(2) Å3, and they are in agreement with the literature values (PCPDF card no. 73e1698). The details of refined structural and residual parameters are given in Table 1. In a similar manner the XRD patterns of other compositions were refined, and the details of refined parameters are included in Table 1. Representative
Fig. 3. Relative peak intensity (%) of (111) superstructure peak with respect to the strongest (222) peak of pyrochlore structure. 4
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Gd2Ti2O7 (x ¼ 0.0) exhibited five discrete bands centred at ~ 310 cm1, 450 cm1, 520 cm1, 570 cm1 and 690 cm1. The strongest band centred around 310 cm1 can be attributed to O-GdO bending mode, which is an amalgamation of two Raman modes (Eg and F2g) [30e32]. The weak band at around 450 cm1 can be assigned to TieO stretching vibration. An intense band was also observed at around 520 cm1 which can be assigned to GdeO stretching vibration (A1g mode). Two weak bands around 570 cm1 and 690 cm1 were observed which are the characteristics of TieO stretching vibrations of TiO6 polyhedra respectively. No new bands were observed in any compositions which is also a support for the conclusion on monophasic system concluded from XRD studies throughout the composition range. Further it can be noticed that Raman bands are broadened progressively with increasing the value of x of the nominal compositions. Such broadening of Raman bands can also be observed in pyrochlore to defect fluorite transformation. However, the observed Raman spectrum of the highest substituted composition also show signature bands of pyrochlore phase. It can be mentioned here that the fully cation disordered lattice invariably shows only one broad peak centred around 450-500 cm1. At the same time the intensity of mode observed at 570 cm1 becomes more prominent with increasing x in the studied compositions. This suggests that the TiO6 octahedra remain almost unaffected by the substitution. Thus, the broadening of the Raman bands can be attributed to the increasing disordering in the pyrochlore structure, which is due to involvement of ions having different ionic radius and valency. Hence, it can be concluded that the disturbance in the GdO8
Table 2 Ionic radii of the constituent ions in different coordination number. Atoms
Coordination No.
Ionic radii (Å)
Gd3þ
8 6 8 6 8 6 8 6
1.053 0.938 0.84 0.72 0.74 0.605 1.12 1.00
Zr4þ Ti4þ Ca2þ
values of the compositions. Unit cell parameter as calculated from Rietveld refinement steadily decreases from a ¼ 10.1841(1) Å, V ¼ 1056.25(2) Å3 for Gd2Ti2O7 (x ¼ 0.0) to a ¼ 10.1356(1) Å, V ¼ 1041.24(2) Å3 for Gd1.20Ca0.40Zr0.40Ti2O7 (x ¼ 0.4). However, the “x” parameter for 48f oxygen atoms (O1) also remains almost similar (~0.43), viz. 0.433(1) to 0.431(1) for x ¼ 0.0 to x ¼ 0.3, while a slight decreasing value of “x” parameter for the composition with x ¼ 0.4 (“x” ¼ 0.425(1)) indicates a tendency towards randomization cations leading to a disordered form or phase segregation. The segregation of secondary phase beyond this limit has been evidenced in our earlier reports [11,12,22]. Further characterization on the internal strictures of the pyrochlore phases are carried out by Raman spectroscopy. Raman spectra of the nominal compositions Gd2-2xCaxZrxTi2O7 (0.0 x 0.4) were recorded in the range of 200e800 cm1, and they are shown in Fig. 4. Raman spectra of the parent compound
Fig. 4. Raman spectra for the Gd2-2xCaxZrxTi2O7 (0.0 x 0.4) nominal compositions. 5
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polyhedra in substituted samples are due to incorporation of Ca2þ and Zr4þ and that leads to different types of bonds, like CaeO, ZreO, and GdeO in the A site of pyrochlore structure. From the aforesaid structural details, it can be inferred that the cubic pyrochlore structure is retained in the studied compositions but the substitution of Ca2þ and Zr4þ together in the lattice renders a contraction in unit cell due to the average ionic radius of Ca2þ þ Zr4þ couple which is smaller compared to Gd3þ ions. Further a decreasing trend in the intensity of superstructure peak and “x” parameter of oxygen O1 atoms suggests for a cation disorder site. Both Rietveld refinement and Raman spectroscopy indicate the incorporation of Ca2þ and Zr4þ in the Gd3þ site of Gd2Ti2O7.
can be either exothermic or endothermic depending upon the characteristics of solute-solvent interactions. It was observed that endothermic heat flow signals were observed for TiO2(s) and ZrO2(s), whereas, exothermic ones were obtained for dissolution of CaO(s), Gd2O3(s) and the Gd2-2xCaxZrxTi2O7 compositions. Cumulative heat effect of dissolution of the species in solvent was calculated using SETSOFT software. The values of molar enthalpies of dissolution of Gd2-2xCaxZrxTi2O7(s) (0.0 x 0.4), CaO(s), ZrO2(s), Gd2O3(s) and TiO2(s) in liquid Na2O þ MoO3 (3:4) melt maintained at 986K are tabulated in Table 3. The standard molar enthalpy of formation of (0.0 x 0.4) was derived using thermo-chemical cycles represented in Table 4. The values obtained for molar enthalpy of dissolution of Gd2-2xCaxZrxTi2O7(s), CaO(s), ZrO2(s), Gd2O3(s) and TiO2(s) were combined with auxiliary data such as standard molar enthalpies of formation of CaO(s), ZrO2(s), Gd2O3(s) and TiO2(s) from reported literature values [33e35] to derive the standard molar enthalpy of formation of the nominal compositions respectively as depicted in Fig. 6. The standard molar enthalpies of formation (in kJ.mol1) for Gd22xCaxZrxTi2O7 compositions are found to be 3751.26 ± 17.14 (for x ¼ 0.0), 3718.47 ± 16.32 (for x ¼ 0.1), 3686.88 ± 15.46 (for x ¼ 0.2), 3652.53 ± 14.54 (for x ¼ 0.3) and 3618.28 ± 13.57 (for x ¼ 0.4). A systematic decreasing trend in standard molar enthalpies of formation with compositions is evident from these values and that suggests a gradual decreasing trend in stability with increasing the Ca2þ and Zr4þ concentrations. However, the decrease in relative stability is only about 3.5% till the complete saturation limit. Hence it can be concluded that there is no significant destabilization of the parent Gd2Ti2O7 lattice upon incorporation of charge compensatory co-dopants Ca2þ and Zr4þ. As mentioned above, the standard molar enthalpy of formation
3.2. Calorimetric results Standard molar enthalpies of formation of the nominal compositions Gd2-2xCaxZrxTi2O7 (0.0 x 0.4) were derived from the enthalpy of dissolution values of the nominal compositions along with the constituent reagents. Fig. 5 exhibits the heat flow signal of the nominal compositions for a time period of 3600 s wherein a steady base line was obtained and there after the system became ready for the next dropping. Special precaution was taken for dropping of CaO(s) pellets into the solvent as reported in our earlier study [20]. Dropping for each of the species were carried out four times and heat change in J/g was calculated. The change in heat flow during dropping of sample into the solvent can be attributed to heating of the sample from 298K to 986 K, dissociation of lattice of the species, and the dissolution of the species into the solvent. The first two processes are generally endothermic in nature and hence an endothermic heat change is observed. However, dissolution of chemical species in the solvent
Fig. 5. Normalized heat flow curves for nominal compositions Gd2-2xCaxZrxTi2O7 (0.0 x 0.4). 6
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decreases progressively with increase with substitution of Ca2þ and Zr4þ ion pairs at the Gd3þ site. The lowering of enthalpy of formation indicate lowering of stability which can be due to randomization of ions, formation vacancies, as well as overall lattice energy due to the involvement of this ions pair. As the ionic radii of Ca2þ (1.12 Å) and Zr4þ (0.84 Å) are different from Gd3þ (1.05 Å), they are likely to have bonds with different bond length and force constants. Due to aliovalent and difference in the electropositive characters of the cations in A site of pyrochlore lattice a local disordering of anion sites is obviously expected, and that in turn can also influence neighbouring bonds of adjacent AO8 and BO6 polyhedra. Such differences can induce internal strain within the lattice and hence lowering the stability of the lattice. This is predominantly reflected in the decrease of enthalpy of formation of the substituted pyrochlore phases compared to the parent lattice. Further the progressively increasing of such local distortion resulted in the gradual decreasing trend in the enthalpy of formation, and that subsequently can result in a transformed or disproportionated phases. This observation is further supported by theoretical calculations.
Table 3 Heat of Dissolution of Gd22xCaxZrxTi2O7 (0.0 x 0.4) and their component oxides. Compounds
Mass (m) (mg)
DH (J/g)
DHT (kJ mol1)
Gd2Ti2O7(s) Mol. Wt. ¼ 522.24 x ¼ 0.0
22.6 30.9 67.5 51.1
189.30 198.13 199.11 192.54
Gd1.8Ca0.1Zr0.1Ti2O7(s) Mol. Wt. ¼ 503.92 x ¼ 0.1
27.8 24.7 11.5 10.9
218.85 208.65 210.48 213.46
Gd1.6Ca0.2Zr0.2Ti2O7(s) Mol. Wt. ¼ 485.60 x ¼ 0.2
11.6 14.4 16.2 7.6
225.96 229.32 239.21 224.91
Gd1.4Ca0.3Zr0.3Ti2O7(s) Mol. Wt. ¼ 467.28 x ¼ 0.3
24.8 12.1 8.7 12.5
255.34 257.26 252.63 251.43
Gd1.6Ca0.4Zr0.4Ti2O7(s) Mol. Wt. ¼ 448.96 x ¼ 0.4
34.4 22.0 23.3 28.3
279.53 277.73 284.12 278.85
Gd2O3(s) Mol. Wt. ¼ 362.50
15.1 21.0 17.9 12.5
652.44 654.98 659.72 658.37
CaO (s) Mol. Wt. ¼ 56.08
11.2 18.1 15.0 9.5
1608.95 1599.68 1627.14 1619.29
ZrO2(s) Mol. Wt. ¼ 123.22
15.1 9.8 10.1 13.7
357.13 358.68 359.42 358.77
TiO2 (s) Mol. Wt. ¼ 79.87
14.2 13.1 17.5 15.4
558.16 576.06 564.29 563.16
98.86 103.47 103.98 100.55 Avg: 101.72 ± 2.43 110.28 105.14 106.07 107.57 Avg: 107.27 ± 2.25 109.73 111.36 116.16 109.22 Avg: 111.62 ± 3.16 119.32 120.21 118.05 117.49 Avg: 118.77 ± 1.23 125.50 124.69 127.56 125.19 Avg: 125.74 ± 1.26 236.51 237.43 239.15 238.66 Avg: 237.94 ± 1.2 90.23 89.71 91.25 90.81 Avg: 90.50 ± 0.67 44.01 44.20 44.29 44.21 Avg: 44.18 ± 0.12 44.58 46.01 45.07 44.98 Avg: 45.16 ± 0.61
3.3. Computational results To rationalize the experimental results and to get more insights in the local structure and energetic due to aliovalent substitution, theoretical calculations were carried under density functional theory (DFT) formalism on Gd2Ti2O7 and its doped variants. The three-dimensional periodic boundary conditions were applied to approximate a bulk solid (i.e. the pyrochlore (Fd-3m) phase of Gd2Ti2O7). A conventional cubic unit cell (a ¼ b ¼ g ¼ 90 ) containing 88 atoms (16 Gd, 16 Ti and 56 O) was used for calculations. Structural optimization was performed with respect to atomic coordinates and unit cell parameters. The unit cell parameters of the relaxed structure are: a ¼ b ¼ c ¼ 10.177 Å, which is reasonably close to experimental value (a ¼ 10.1841(1) Å). In the case of doped Gd2Ti2O7, out of the 16 Gd/Ti atoms in the unit cell, appropriate number of atoms were replaced with Ca2þ/Zr4þ to nearly approximate the studied Gd2-2xCaxZrxTi2O7 (0.0 x 0.4) compositions. For example, the replacement of two Gd atoms out of 16 Gd atoms by one Ca and one Zr atom can result in composition with x ¼ 0.125, i.e. Gd1.75Ca0.125Zr0.125Ti2O7. Although the theoretical compositions
Table 4 Thermochemical cycles for enthalpy of formation of Gd22xCaxZrxTi2O7 (0.0 x 0.4). DfH 298(Gd22xCaxZrxTi2O7 (s)) ¼ -DH1i þ (1-x) DH2 þ xDH3 þ xDH4 þ 2DH5 þ (1-x) DH6 þ xDH7 þ x DH8 þ 2DH9. Reaction
DHi
DHdissolution (kJ mol1)
Gd2Ti2O7 (s,298K) þ (sln) ¼ Gd2O3(sln) þ 2TiO2(sln) Gd1.8Ca0.1Zr0.1Ti2O7(s) (s,298K) þ (sln) ¼ 0.9Gd2O3(sln) þ 0.1CaO(sln) þ 0.1ZrO2(sln) þ 2TiO2(sln) Gd1.6Ca0.2Zr0.2Ti2O7(s) (s,298K) þ (sln) ¼ 0.8Gd2O3(sln) þ 0.2CaO(sln) þ 0.2ZrO2(sln) þ 2TiO2(sln) Gd1.4Ca0.3Zr0.3Ti2O7(s) (s,298K) þ (sln) ¼ 0.7Gd2O3(sln) þ 0.3CaO(sln) þ 0.3ZrO2(sln) þ 2TiO2(sln) Gd1.2Ca0.4Zr0.4Ti2O7(s) (s,298K) þ (sln) ¼ 0.6Gd2O3(sln) þ 0.4CaO(sln) þ 0.4ZrO2(sln) þ 2TiO2(sln) Gd2O3(s,298K) þ(sln) ¼ Gd2O3(sln) CaO(s,298K) þ (sln) ¼ CaO(sln) ZrO2(s,298K) þ (sln) ¼ ZrO2(sln) TiO2(s,298K) þ (sln) ¼ TiO2(sln) 2Gd(s,298K) þ 3/2O2(g) ¼ Gd2O3(s) Ca(s,298K) þ 1/2O2(g) ¼ CaO(s) Zr(s,298K) þ O2(g) ¼ ZrO2(s) Ti(s,298K) þ O2(g) ¼ TiO2(s) 2Gd(s,298K) þ 2Ti(s,298K) þ 3.5 O2(g) ¼ Gd2Ti2O7 (s,298K) (x ¼ 0.0) 1.8Gd(s,298K) þ 0.1Ca(s,298K) þ 0.1Zr(s,298K) þ 2Ti(s,298K) þ 3.5 O2(g) ¼ Gd1.8Ca0.1Zr0.1Ti2O7 (s,298K) 1.6Gd(s,298K) þ 0.2Ca(s,298K) þ 0.2Zr(s,298K) þ 2Ti(s,298K) þ 3.5 O2(g) ¼ Gd1.6Ca0.2Zr0.2Ti2O7 (s,298K) 1.4Gd(s,298K) þ 0.3Ca(s,298K) þ 0.3Zr(s,298K) þ 2Ti(s,298K) þ 3.5 O2(g) ¼ Gd1.4Ca0.3Zr0.3Ti2O7 (s,298K) 1.2Gd(s,298K) þ 0.4Ca(s,298K) þ 0.4Zr(s,298K) þ 2Ti(s,298K) þ 3.5 O2(g) ¼ Gd1.2Ca0.4Zr0.4Ti2O7 (s,298K)
DH1a DH1b DH1c DH1d DH1e DH2 DH3 DH4 DH5 DH6 DH7 DH8 DH9 DfH 298
101.72 ± 2.43 107.27 ± 2.25 111.62 ± 3.16 118.74 ± 1.23 125.75 ± 1.26 237.94 ± 1.20 90.50 ± 0.67 44.18 ± 0.12 45.16 ± 0.61 1815.86 ± 16.74 634.29 ± 1.67 1100.81 ± 2.09 944.75 ± 1.67 3751.26 ± 17.14 3718.47 ± 16.32 3686.88 ± 15.46 3652.53 ± 14.54 3618.28 ± 13.57
7
(x (x (x (x
¼ ¼ ¼ ¼
0.1) 0.2) 0.3) 0.4)
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Fig. 6. Variation of experimental and theoretically calculated standard molar enthalpy of formation of Gd2-2xCaxZrxTi2O7 (0.0 x 0.4) with composition.
The net cohesive energy for Gd2Ti2O7 (7.13eV/atom) is in agreement with that reported by Jun and Bin (7.224 eV/atom [36]. Similarly, the calculated values of DHf for x ¼ 0.125, 0.25, 0.315, 0.375 are found to be 7.14, 7.13, 7.11 and 7.09 eV/atom, respectively. The calculated values of DHf indicate a systematically decreasing trend with increasing the dopant concentrations, and they are in line with the experimental observations presented in Fig. 6. For better comparison the calculated enthalpies of formation of all the compositions are converted to kJ/mol in Fig. 6. From the figure, it is clear that both experimental and theoretical calculation values show a similar trend with variation in compositions. However, the absolute values show differences for each compositions. The differences can be attributed to the difference in compositions used for calculations for computational simplicity in DFT, methods used for DFT calculations, temperature of calculations (0 K) and experimental (298 K), as well as defects and microstructural contributions in the experimental results. The steady decrease in heat of formation with increasing dopant concentration can be attributed to the smaller ionic size of dopant (total ionic radius of Ca2þ and Zr4þ) in comparison to host Gd3þ ion (2 ionic radius of Gd3þ ion) as well as difference in oxidation states of substituted ions. Thus, they are also resulted in significant change in the polyhedron around the cations as shown in Fig. 7. Further from the analyses of local structural parameters, shown in Fig. 7, it is clearly observed that the substitution of Ca2þ and Zr4þ in Gd2Ti2O7 not only effect the substituted sites but also adjacent polyhedra. This is expected due to the differences in charge as well as radii of the substituted ions. In the parent Gd2Ti2O7, the calculated GdeO bond lengths in GdO8 units are 2.51 Å 6 and 2.20 Å 2 while TieO bond lengths in TiO6 units are 1.97 Å 6. Upon substitution of the Ca2þ and Zr4þ, the GdeO and TieO bonds respectively in GdO8 and TiO6 are dispersed widely, creating a distorted polyhedra around Gd3þ and Ti4þ. These are due to the incorporation smaller ZrO8 polyhedra in the structure (Fig. 7). This
are not exactly same to that of experimental compositions, it is expected that set of nearby composition can rationalize the experimental trends. First to find out the energetic preference for substitution of Ca2þ/Zr4þ at either Gd site or Ti site calculations were carried out for three cases, viz. (i). both Ca2þ and Zr4þ replacing the Gd3þ ions, (ii). Ca2þ substituting the Gd3þ ion and Zr4þ replacing the Ti4þ ion, and (iii). both Ca2þ and Zr4þ replacing the Ti4þ ion in the lattice. It was found that the replacement of Gd3þ by both Ca2þ and Zr4þ together is energetically most favourable situation than the substitution of Ca2þ in Gd3þ site and Zr4þ in Ti4þ site or substitution of both Ca2þ and Zr4þ in the Ti4þ sites. The net energy of case-2 and case-3 are 0.28 and 0.81 eV higher than that of the case-1. This order of relative energy suggests that the substitution of Ca2þ and Zr4þ at the Gd3þ is energetically preferred over the fully or partially substituted Ti4þ sites. This energetic preference is in line with ionic radius criteria of substitutional solid solution (see. Table 2). Further calculations for higher dopant concentration, like x ¼ 0.25, 0.315, 0.375, were also carried out by considering the substitution at Gd3þ site only. For x ¼ 0.25, 0.375 the calculations were performed with single unit cell containing 88 atoms, however for x ¼ 0.315, the calculations were performed with a supercell having two unit-cells together containing 178 atoms. The heat of formation (DHf) for different aliovalent doping concentrations at Gd-sites was calculated using the following relation. DHf ¼ {E (Gd2-2xCaxZrxTi2O7) e no. of Gd atoms E(Gd) e no. of Ti atoms E(Ti) eno. of Ca atoms E(Ca) e no. of Zr atoms E(Zr)}/total number of atoms.Where E (Gd2-2xCaxZrxTi2O7) is the total energy of doped supercell, and E(Gd), E(Ti), E(Ca) and E(Zr) are atom correction energy for a single Gd, Ti, Ca, and Zr atom respectively. In the case of Gd2Ti2O7, the net cohesive energy calculated as per the above relation can be represented as: 918.97163458 e {16 x 10.21945436 þ 16 x 2.61943856 þ 56 x 1.53478333} ¼ 627.6014814 -627.6014814/88 ¼ 7.13 eV/atom. 8
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Fig. 7. GdO8 and TiO6 polyhedra in the structure of doped and undoped Gd2Ti2O7.
increasingly disordered cation sublattice. Higher disorder in the surroundings of Gd site compared to that at the Ti sites is concluded from Raman spectroscopic studies as well as dentistry functional calculations. Calorimetric investigations indicated a gradually decreasing trend in the enthalpy of formation with increasing substitution, which is also indicated by density functional theory calculations. From the joint experimental and theoretical calculations, it could be concluded that the relative stability of multiple aliovalent cation substituted pyrochlore type Gd2Ti2O7 are lower than the undoped systems. Both experimental characterization and theoretical calculations indicate the substation of Ca2þ and Zr4þ are favoured at Gd3þ sites. Also, from density functional calculation further indicates the expansion of TieO bonds and increased distortions in the AO8 and BO6 polyhedra of the pyrochlore lattice. That in turn lower the stability of the lattice. This study indicates, despite the formation of single-phase cation substituted pyrochlore
also indicates a relative expansion of TieO bonds in Gd2-2xCaxZrxTi2O7 compared to those in Gd2Ti2O7. Thus, an appreciable weakening of ZreO and TieO bonds and incorporation of ionic CaeO bonds decrease the stability in comparison to the unsubstituted Gd2Ti2O7 lattice. This result is in accordance with the overall decrease of DHf for the doped Gd2Ti2O7 observed experimentally. 4. Conclusions Following the electroneutrality considerations, single phase solid solution compositions containing two aliovalent cations while maintaining the oxygen stoichiometry could be prepared. From both XRD and Raman spectroscopic studies, it is concluded that about 40% of Gd3þ of Gd2Ti2O7 can be replaced by Ca2þ and Zr4þ cations together. No distortion was observed in the unit cell but a decreasing tendency of super structure peaks indicates an 9
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phase in the complete range of compositions, the relative stability decreases by substitution. However, the decrease in relative stability is about 3.5% compared to unsubstituted phase, suggesting the Gd2Ti2O7 type pyrochlore lattices are promising matrices to accommodate multiple aliovalent cations related to nuclear waste immobilization.
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CRediT authorship contribution statement M. Jafar: Prepared the sample, characterized by XRD, Raman spectroscopy, participated in calorimetric measurements and analyses of data, wrote the manuscript, Formal analysis, Data curation. S.B. Phapale: Carried out the calorimetric measurements and analyses of data, Formal analysis, Data curation. S.N. Achary: Conceived the problem, coordinated the experiments and calculations, analysed and interpreted the data, wrote the manuscript, edit the manuscript and prepared the final manuscript, Formal analysis, Data curation. R. Mishra: Carried out the calorimetric measurements and analyses of data, wrote the manuscript, Formal analysis, Data curation. C. Majumder: Carried out DFT calculations and wrote the manuscript. A.K. Tyagi: Proof read and edited the manuscript. Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. References rus, V. Aubin-Chevaldonnet, I. Bardez, [1] D. Caurant, P. Loiseau, O. Maje A. Quintas, in: “Glasses, GlasseCeramics and Ceramics for Immobilization of Highly Radioactive Nuclear Wastes”, Nova Science Publishers, New York, 2009. [2] M.I. Ojovan, W.E. Lee, An Introduction to Nuclear Waste Immobilization, Elsevier Ltd, Oxford, UK, 2005, pp. 213e267. [3] M.I. Ojovan, W.E. Lee, An Introduction to Nuclear Waste Immobilization, Elsevier Ltd, Oxford, UK, 2005, pp. 213e267. rus, P. Loiseau, I. Bardez, N. Baffier, J.L. Dussossoy, Crys[4] D. Caurant, O. Maje tallization of neodymium-rich phases in silicate glasses developed for nuclear waste immobilization, J. Nucl. Mater. 354 (2006) 143e162. [5] P. Loiseau, D. Caurant, O. Majerus, N. Baffier, C. Fillet, Crystallization study of (TiO2, ZrO2)-rich SiO2-Al2O3-CaO glasses. Part II. Surface and internal crystallization processes investigated by differential thermal analysis (DTA), J. Mater. Sci. 38 (2003) 843e852. [6] A.E. Ringwood, S.E. Kesson, N.G. Ware, W. Hibberson, Immobilisation of high level nuclear reactor wastes in, SYNROC” Nature 278 (1979) 219e223. [7] R.C. Ewing, Nuclear waste forms for actinides, Proc. Natl. Acad. Sci. U.S.A. 96 (1999) 3432e3439. [8] E.R. Vance, G.R. Lumpkin, M.L. Carter, D.J. Cassidy, C.J. Ball, R.A. Day, B.D. Begg, Incorporation of uranium in zirconolite (CaZrTi2O7), J. Am. Ceram. Soc. 85 (2002) 1853e1859. [9] R.C. Ewing, W.J. Weber, J. Lian, “Nuclear waste disposaldpyrochlore A2B2O7: nuclear waste form for the immobilization of plutonium and ‘‘minor’’ actinides, J. Appl. Phys. 95 (2004) 5929e5971. [10] M.A. Subramanian, G. Aravamudan, G.V. Subba Rao, Oxide pyrochlores -A review”, Prog. Solid State Chem. 15 (1983) 55e143. [11] M. Jafar, P. Sengupta, S.N. Achary, A.K. Tyagi, Phase evolution and microstructural studies in CaZrTi2O7eNd2Ti2O7 system, J. Am. Ceram. Soc. 97 (2014)
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