High temperature heat capacity of Nd 2 Zr 2 O 7 and La 2 Zr 2 O 7 pyrochlores

Transcription

1 J. Chem. Thermodynamics 37 (2005) High temperature heat capacity of Nd 2 Zr 2 O 7 and La 2 Zr 2 O 7 pyrochlores D. Sedmidubský a,b, *, O. Beneš a, R.J.M. Konings b a Department of Inorganic Chemistry, Institute of Chemical Technology, Technická 5, Prague, Czech Republic b European Commission, JRC, Institute for Transuranium Elements, P.O. Box 2340, D Karlsruhe, Germany Received 30 November 2004; received in revised form 18 January 2005; accepted 19 January 2005 Available online 19 February 2005 Abstract The enthalpy increment measurements were performed using drop calorimetry on two lanthanide zirconates Ln 2 Zr 2 O 7, Ln = La, Nd, with pyrochlore structure. The temperature dependence of heat capacity in the range (298 to 1550) K was derived by simultaneous linear regression of the measured enthalpies combined with the heat capacity data around ambient temperature. The obtained heat capacity C p ðt Þ is compared to the limit of constant volume lattice C v calculated from the analysis of low temperature specific heat data using a combined Debye Einstein harmonic approximation model. Ó 2005 Elsevier Ltd. All rights reserved. Keywords: Lanthanide pyrochlores; Drop calorimetry; Enthalpy; Heat capacity; Setaram HTC calorimeter 1. Introduction The lanthanide zirconates (Ln 2 Zr 2 O 7 ) belong to the family of ternary metallic oxides frequently adopting a pyrochlore structure (space group Fd 3m). This structure can be derived from the parent fluorite type by substituting one half of metal atoms (Zr) by a rare-earth (Ln) and ordering the two types of cations alternatively along ½110Š and ½ 110Š directions within (001) planes. Since the substitution is heterovalent, the electroneutrality condition requires a formation of 1/8 of oxygen vacancies which are ordered as well. The pyrochlore fluorite type relation is indeed manifested in the phase diagrams of Ln 2 O 3 ZrO 2 systems, where the order disorder transitions between two pertinent phases are frequently observed at high temperatures. The pyrochlore compounds reveal a number of interesting properties such as metal insulator transitions, geometrically frustrated Kagome-type spin lattices, * Corresponding author. Tel.: ; fax: address: sedmidub@vscht.cz (D. Sedmidubský). dielectric, piezo- or ferroelectric properties, as well as fluorescent and phosphorescent behavior. The oxygen vacant sites can be a source of excellent ionic conductivity allowing electrochemical applications (oxygen electrode or solid electrolyte materials) [1]. The notable refractory properties and good chemical resistivity make them prospective candidates for nuclear waste matrices. For many potential applications of these materials the knowledge of their thermal properties is of high importance. In this paper we address two members of Ln 2 Zr 2 O 7 pyrochlore series, namely Ln = La and Nd. Their low temperature heat capacity has been recently measured by Bolech et al. [2] and Lutique et al. [3], respectively. Moreover, the enthalpy increment data up to T = 900 K have been also reported for La 2 Zr 2 O 7 [2] and the heat capacity of Nd 2 Zr 2 O 7 in the range T = (298 to 1600) K obtained by dynamical DSC measurements has been given in [5]. The aim of the present study is to extent the temperature range of heat capacity data for La 2 Zr 2 O 7 up to T = 1600 K and to examine Nd 2 Zr 2 O 7 by an independent technique the heat content measurements using inverse drop calorimetry /$ - see front matter Ó 2005 Elsevier Ltd. All rights reserved. doi: /j.jct

2 D. Sedmidubský et al. / J. Chem. Thermodynamics 37 (2005) Experimental The La 2 Zr 2 O 7 powder was synthesized by solid state reaction from a mixture of La 2 O 3 and ZrO 2 powders at T = 1773 K under purified argon atmosphere for 10 h. The details on the purity and the treatment of starting materials were described elsewhere [2]. The Nd 2 Zr 2 O 7 was prepared by co-precipitation from a solution of ZrOCl 2 Æ8H 2 O and Nd(NO 3 ) 3 in a stoichiometric concentration and heating the resulting powder at T = 1873 K for 72 h [3]. Both thoroughly ground powders of La 2 Zr 2 O 7 and Nd 2 Zr 2 O 7 were analyzed by powder XRD for phase purity, pressed into pellets and sintered at T = 1773 K for 15 h. The sintered pellets of all materials were cut into pieces with typical masses (50 to 90) mg which were subsequently used in calorimetry measurements. The pellets of polycrystalline La 2 O 3 and Nd 2 O 3 used for testing the accuracy of the apparatus were prepared by uniaxial pressing of analytically pure fine powders (Alfa Aesar, and , respectively) and sintering at T = 1673 K for 10 h. Let us note that all measured materials were found relatively sensitive to longer term (several weeks) exposure in normal air atmosphere. In order to preclude the degradation due to a formation of hydration products and/or oxycarbonates, freshly sintered samples stored in dry and CO 2 -free atmosphere had to be used for calorimetric measurements. The heat contents corresponding to the enthalpy increments from ambient temperature to the respective temperature of a given run were determined using Setaram multi-detector high temperature calorimeter (MHTC-96) operating in drop mode. The tubular calorimetric sensor (Al 2 O 3 ) consists of a working chamber (volume 5.3 cm 3 ) with the inserted Pt-crucible and an empty reference chamber positioned vertically below. The sample and reference areas are interconnected by a series of 28 thermocouples covering the whole surface and providing thus an integrated heat exchange at the output signal. In the present work, a detector equipped by Pt-PtRh10 (S-type) thermocouples was employed enabling the operation up to T = 1573 K. The sensor is centered in a gas-tight tube placed in the furnace heated by a single graphite resistance element. All measurements were performed in closed normal air atmosphere. The samples of the measured and reference material are ordered alternatively in the feeding chamber and equilibrated at ambient temperature, which is measured prior to each drop. In the meantime, the detector is maintained at a given temperature and the samples are dropped from the feeding chamber into the working chamber of the sensor every 20 min. This time interval was found to be sufficient for the re-stabilization of both the temperature and the heat flux. The heat flux / (in lv) is monitored as a function of time s and the peak area ò/ ds (after subtracting a baseline / B ) associated with each drop corresponds to the respective enthalpy increment. From the reference material drops, the actual apparatus sensitivity can be determined as R ð/r / S ¼ B Þds R T m T a C p;r dt M R ; m R ð1þ where T a and T m are, respectively, the ambient and sensor temperature, the latter being evaluated as an average from the values taken in a steady state before and after the drop, m R and M R are the reference material mass and molar mass, respectively, and C p;r stands for its molar heat capacity. The enthalpy increment (heat content) corresponding to heating the sample material (denoted as by a subscript S) from T a to T m is given by R ð/s / HðT m Þ HðT a Þ¼ B Þds M S ; ð2þ S m S where one adjacent or a mean value of two adjacent reference measurements is considered for the sensitivity S. Hence, the caloric calibration of the apparatus is performed simultaneously with the sample measurement by alternating the drops of sample and reference materials. In this study the pure platinum rod (2 mm diameter, mass fraction purity Pt, Goodfellow Cambridge Ltd.) cut into pieces of typical masses (180 to 220) mg was employed as a caloric standard. The relevant reference data for the heat capacity of Pt were taken from [6]. All evaluations of background subtraction and peak integration were done by DSCEval software [12]. The temperature calibration was carried out separately by heating pure standard metals (Sn, Pb, Al, Ag and Au) in alumina crucible at various rates (usually r = (1, 2, 5 and 10) KÆmin 1 ) and observing the apparent temperatures of melting (determined as an intersection of the linearly extrapolated background before the peak and the first flex point tangent). The difference between the measured (T m ) and reference temperature (T r ) of melting was expressed as a linear function of heating rate DT ¼ T m T r ¼ DT 0 þ b r; ð3þ where the parameters DT 0 and b were evaluated using, respectively, a linear and quadratic fit with respect to T m. Nonetheless, since the drop measurements are performed in quasi-isothermal conditions (r = 0), only the former equation for DT 0 is used for temperature correction. 3. Results and discussion The accuracy of the calorimeter was tested by measuring the heat contents of La 2 O 3 and Nd 2 O 3 (in their hexagonal A-type forms), whose heat capacities are well established. The reference curve of C pðt Þ for

3 1100 D. Sedmidubský et al. / J. Chem. Thermodynamics 37 (2005) TABLE 1 Heat contents H(T m ) H(T a ) of La 2 O 3 and Nd 2 O 3 measured at temperature T m and referred to the ambient temperature T a T m /K T a /K {H(T m ) H(T a )} r p D n kjæmol 1 kjæmol 1 kjæmol 1 La 2 O TABLE 2 Heat contents H(T m ) H(T a )ofla 2 Zr 2 O 7 and Nd 2 Zr 2 O 7 T m /K T a /K {H(T m ) H(T a )} r p n kjæmol 1 kjæmol 1 La 2 Zr 2 O Nd 2 O Each line corresponds to an average of n single drops performed for one isotherm. The precision is expressed as the respective standard deviation r p. D is the accuracy given as a difference between the experimental and reference value. La 2 O 3 has been assessed from combined results of enthalpy increment measurements performed by [7 9]. Similarly, the heat capacity of Nd 2 O 3 has been derived by simultaneous fit from the heat content data reported by references [7,10]. The results of our measurements including the comparison with the reference data are given in table 1. The values in each line were obtained by averaging the results of (2 to 4) drops in each isothermal run. The overall precision can be expressed as a standard deviation evaluated for a set of all drops and referred to the mean values. We obtained r p ¼ 2:82 kj mol 1 (3.2%) for La 2 O 3 and r p ¼ 2:64 kj mol 1 (2.8%) for Nd 2 O 3. The averaging of all differences D i between the experimental and reference values yields the overall accuracy D ¼ 0:68 kj mol 1 and D ¼ 0:51 kj mol 1 for La 2 O 3 and Nd 2 O 3, respectively. The variance of the individual data points around the reference enthalpy curve can be represented qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi in terms of standard deviation P n r a ¼ i D2 i =ðn 1Þ resulting in the respective values 3.53 kjæmol 1 and 4.45 kjæmol 1. The measured enthalpy increments of La 2 Zr 2 O 7 and Nd 2 Zr 2 O 7 averaged over (4 to 5) sample drops within each isothermal dwell are listed in table 2. The sensitivities for each isothermal run were evaluated from (3 to 4) Pt-standard drops performed between two sample drops. The typical sensitivity values ranged from 0.30 lvæmw 1 for higher temperatures ( ) K to 0.37 lvæmw 1 for lower temperatures ( ) K. The measured enthalpy increment data were analyzed using the simultaneous weighted linear regression of Nd 2 Zr 2 O The symbols T m, T a, n and r p have the same meaning as in table 1. both high temperature enthalpies and heat capacities from the temperature interval (270 to 400) K taken from the literature [2,3]. In the case of La 2 Zr 2 O 7 the enthalpy increment data (10 points) from the interval T = ( ) K [2] were also included. A three parameter polynomial equation for the heat capacity C p ¼ a þ bt þ ct 2 ð4þ and the corresponding integrated form for the enthalpy HðT Þ HðT a Þ¼aðT T a Þþb=2ðT 2 T 2 a Þ cð1=t 1=T aþ ð5þ were employed. The weights calculated as inverse uncertainties (errors) were assigned to individual data points. The selected relative errors 1% and 2.5% were given to low temperature C p and heat contents reported by Bolech et al. [2], respectively. Similarly, the relative errors 1% were given to C p data of Nd 2Zr 2 O 7 reported by Lutique et al. [3]. The standard deviations evaluated for a given isothermal run were considered as errors for enthalpy increments and assigned to all data points within that run. Since the C p data around ambient temperature were included in the fitted data set, no constraint such as the fixed value of C pð298:15 KÞ has been applied. The fitted value at T = 298 K does not indeed differ from the experimental one by more than 0.3 JÆmol 1 ÆK 1. The results of the fitting procedure are summarized in table 3. As seen from figures 1 and 2, the curves calculated from three-parameter polynomial equation fit smoothly

4 D. Sedmidubský et al. / J. Chem. Thermodynamics 37 (2005) TABLE 3 Results of simultaneous linear regression of heat capacity and enthalpy increment data 280 Nd 2 Zr 2 O 7 La 2 Zr 2 O 7 a ± b ± c ± N Cp 18 N H 44 r Cp r H r tot Nd 2 Zr 2 O 7 a ± b ± c ± N Cp 40 N H 55 r Cp r H r tot a,b,c, coefficients in equations (4) and (5); N, number of data points; r, standard deviation. the low temperature C p in both cases, whereas they appropriately describe the high temperature enthalpy increment data (see inset). Our data for La 2 Zr 2 O 7, although more scattered than those reported by Bolech et al. [2], correct for exceedingly high slope of C p ðt Þ dependence obtained if only the latter data are considered, which would result in an unrealistically large C p C V term. Similarly, the DSC data of C p ðnd 2Zr 2 O 7 Þ reported by Lutique et al. [5] lie much higher and have higher slope than our enthalpy increment fit (the difference extends to 24 JÆmol 1 ÆK 1 at T = 1000 K). Regarding the large differences between individual DSC runs and the experimental technique C p / (J.K -1 mol -1 ) La 2 Zr 2 O 7 (H-H 0 ) / (kj mol -1 ) 300 ref. [2] this work T / K FIGURE 1. Heat capacity and relative enthalpy of La 2 Zr 2 O 7 plotted against temperature. ( ) C pðt Þ simultaneous polynomial fit, () the corresponding confidence bands, (- -) analogous fit if only the enthalpy data from [2] are considered, (---) Debye Einstein fit of low temperature C pðt Þ, and (horizontal line) Dulong Petit limit. C p / (J.K -1 mol -1 ) (H-H 0 ) / (kj mol -1 ) ref. [3] this work T / K FIGURE 2. Heat capacity and relative enthalpy of Nd 2 Zr 2 O 7 plotted against temperature. ( ) C pðt Þ simultaneous polynomial fit, () the corresponding confidence bands, (--) DSC data from [5], (---)C V calculated from Debye Einstein using the interpolation scheme between the characteristic temperatures fitted on La 2 Zr 2 O 7 and Gd 2 Zr 2 O 7, and (horizontal line) Dulon Petit limit. used in [5] (dynamical mode), the present enthalpy increment results are believed to be more reliable. Since La 2 Zr 2 O 7 is a diamagnetic insulator with an empty 4f-subshell of La 3+ cation, no electronic or magnetic excitations are anticipated and, accordingly, the heat capacity is merely contributed by crystal lattice dynamics. Hence, we can make use of the available low temperature data [2] and apply a harmonic approximation model to trace the C pðt Þ dependence (provided the anharmonic effects are negligible below T = 300 K). As the atoms in the primitive unit cell of pyrochlore structure occupy 22 sites, the phonon spectrum consists of 66 independent normal modes. For the present purpose we approximate the real phonon spectrum by a triply degenerate Debye mode describing three acoustic branches and three 21-fold degenerate Einstein modes, each represented by a characteristic temperature H D, H E1, H E2 and H E3. The general equations for Debye and Einstein contributions to the lattice heat capacity have been described, e.g. in [11]. The results of this four parameter fit are given in table 4. Let us note that the selection of phonon mode degeneracy ( ) is quite arbitrary and the fit could be likely further improved by releasing this constraint and varying the respective degeneracies. For a comparison, the analogous method was used to model the lattice heat capacity of isostructural Gd 2 Zr 2 O 7 containing Gd 3+ cation with 4f 7 configuration. As such, its free ion ground state term 8 S 7/2 should not be split in crystal field and the heat capacity is supposed to arise purely from lattice vibrations over the temperature range of interest. The temperature range of the thermal anomaly observed below T = 10K [4], whose entropy exactly corresponds to a release of total spin degeneracy, was omitted in the present analysis.

5 1102 D. Sedmidubský et al. / J. Chem. Thermodynamics 37 (2005) TABLE 4 Results of Debye Einstein model fitting of low temperature heat capacity data H D /K H E1 /K H E2 /K H E3 /K Reference La 2 Zr 2 O ± ± ± ± 4 [2] Nd 2 Zr 2 O 7 94 ± ± ± ± 26 [3] a Gd 2 Zr 2 O ± ± ± ± 4 [4] The last column indicates the reference of the data source used in the fit. a Estimated by interpolation. Compared to La 2 Zr 2 O 7, the Debye mode has a lower characteristic temperature, while the first and second Einstein modes are shifted to higher frequencies and the third one is again slightly softened. The enhanced first and second Einstein modes are apparently responsible for lower values of C p and entropy of Gd 2Zr 2 O 7 above T = 200 K due to higher force constants of the relevant phonons. The trivalent neodymium in Nd 2 Zr 2 O 7 reveals a 4 I 9/2 ground state term which is split into five doublets in the crystal field. Moreover, a splitting of the excited state terms 4 I 11/2 and 4 I 13/2 into six and seven doublets should be taken into account to properly describe the excess heat capacity C exs due to electronic excitations [4]. The respective splitting energies for Nd 3+ in pyrochlore structure have been recently proposed by scaling the crystal field parameters from Ho 2 Ti 2 O 7 and Eu 3+ in La 2 Zr 2 O 7 matrix [4]. If these are used to calculate C exs arising from a series of Schottky contributions, the lattice part can be obtained by subtracting C exs from measured C p. However, doing this we obtain exceedingly increased values in an intermediate temperature range ( ) K lying well above both La 2 Zr 2 O 7 and Gd 2 Zr 2 O 7 data. A Debye Einstein fit performed on such a set of data T = (0 to 300) K results in the second and third Einstein mode temperatures being very close to each other and determined with large errors (table 4). Hence, we prefer to estimate the lattice heat capacity of Nd 2 Zr 2 O 7 by interpolating the Debye Einstein parameters fitted for La 2 Zr 2 O 7 and Gd 2 Zr 2 O 7. Using this interpolated set (third line in table 4) we can apply an opposite approach and calculate the contribution of electronic excitations and the anharmonic part of lattice heat capacity which starts to develop above room temperature. The comparison with the calculated Schottky contributions based on the proposed crystal field splitting energy levels [5] clearly shows (see figure 3) that whereas a good agreement is achieved for the low temperature peak arising from the ground state splitting, the excited state levels lie supposedly at lower energies being manifested by a shallow maximum around T = 400 K. The exact interpretation of the excess part of heat capacity would indeed require to employ an FIGURE 3. A plot of the capacity against temperature to show the excess part for Nd 2 Zr 2 O 7 obtained by subtracting the estimated lattice heat capacity C V from the experimental data (s) and compared to Schottky-like anomaly calculated from crystal field splitting energies proposed in [5] ( ). independent experimental and/or theoretical technique, such as spectroscopic measurements or ab initio calculation of crystal field potential around Nd 3+ and the corresponding energy levels. 4. Conclusions The temperature dependence (298 to 1550 K) of heat capacity of two lanthanide pyrochlores, La 2 Zr 2 O 7 and Nd 2 Zr 2 O 7, was derived from the simultaneous analysis of enthalpy increment measurements and the low temperature heat capacity data. If the lattice part of the constant volume heat capacity is modelled by Debye Einstein mode analysis of low temperature C p data, the C p C V difference is only contributed by anharmonic effects in lattice dynamics in the case of La 2 Zr 2 O 7, whereas a huge term arising predominantly from electronic excitations of Nd 3+ is observed in Nd 2 Zr 2 O 7. While its low temperature part can be satisfactorily described by theoretical crystal field splitting energy levels of the 4 I 9/2 ground state, the energy levels of the split exited states 4 I 11/2 and 4 I 13/2 need further refinement. Acknowledgement The authors thank NR6-Petten (Mr. van der Laan) for providing the La 2 Zr 2 O 7 sample. D.S. and O.B. acknowledge the support of the European Commission provided in the frame of the program Training and Mobility of Researchers. References [1] M.A. Subramanian, G. Aravamudan, G.V. Subba Rao, Prog. Solid State Chem. 15 (1983)

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