Thermal properties of perovskite RCeO3 (R = Ba, Sr)

Thermochimica Acta 614 (2015) 213–217

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Thermal properties of perovskite RCeO3 (R = Ba, Sr) Aarti Shuklaa,* , Vanshree Pareya , Rasna Thakura , Archana srivastavab , N.K. Gaura a b

Department of Physics, Barkatullah University, Bhopal 462026, India Department of Physics, Sri Sathya Sai College for women, Bhopal 462024, India

A R T I C L E I N F O

A B S T R A C T

Article history: Received 16 April 2015 Received in revised form 9 June 2015 Accepted 28 June 2015 Available online 30 June 2015

We have investigated the bulk modulus and thermal properties of proton conducting perovskite RCeO3 (R = Ba, Sr) for the first time by incorporating the effect of lattice distortion in modified rigid ion models (MRIM). The computed bulk modulus, specific heat, thermal expansion coefficient and other thermal properties of BaCeO3 and SrCeO3 reproduce well with the available experimental data. In addition the cohesive energy (f), molecular force constant (f), reststrahlen frequency (n), Debye temperature (uD) and Gruneisen parameter (g ) are also reported and discussed. The specific heat results can further be improved by taking into account the spin and the orbital ordering contribution in the specific heat formulae. ã 2015 Elsevier B.V. All rights reserved.

Keywords: Bulk modulus Elastic properties Thermal expansion Thermodynamic properties

1. Introduction Presently, universal attention is being paid to explore the new ways of energy sources and conversion methods. In this respect, hydrogen energy and solid oxide fuel cell (SOFCS) have been wellknown as excellent energy sources. The proton conducting oxides is one of the best choices to expend such energy source membranes, which is competent of producing pure hydrogen stream. This is an innovative class of materials, exhibits high proton conductivities between 300
C and 800
C, are generally termed as high temperature proton conductor (HTPCS). Additionally, high temperature proton conductor ceramics have gathered broad interest on behalf of their proton conducting appliance. The HTPCs can be used in electrochemical applications such as hydrogen sensors, steam sensors, electrolyte materials for solid oxide fuel cells, hydrogen purification [1,2]. The proton conduction phenomena in proton conducting oxides ABO3 began in the early 1980s by Iwahara et al. [3]. They recognized the main features of the mechanism of proton transport in these oxides. The basis of proton conduction is Grotthus mechanism in protons are located in the crystal lattice close to the oxide ions because of the electrostatic attraction and are capable of rotating as well as migrating between the nearby anions [4–8]. Recently, the simple perovskite-structured rareearth-doped alkaline earth based cerates such as BaCeO3 and SrCeO3 have also attracted great attention because of their highest

* Corresponding author at: Superconductivity Research Lab, Department of Physics, Barkatullah University, Bhopal, 462026, India. Fax: +91 755 2491823. E-mail address: [email protected] (A. Shukla). http://dx.doi.org/10.1016/j.tca.2015.06.032 0040-6031/ ã 2015 Elsevier B.V. All rights reserved.

level of proton conductivity. These cerates easily react with humid atmospheres at high temperatures as a consequence of their thermodynamic instability in such situation [9–11]. The structure of BaCeO3 as a function of temperature was first correctly determined by Knight and reported three types of structural phase transitions in BaCeO3. At comparatively low temperatures up to 563 K, BaCeO3 shows a primitive orthorhombic structure with space group Pnma. Above the temperature 563 K  T  673 K, the structure can be described as body-centered orthorhombic with space group Imma. At 673 K, BaCeO3 transforms into a rhombohedral structure with space group R-3c. Finally, at temperatures over 1200 K, the structure turns to the ideal cubic perovskite pattern with space group Pm-3m [12]. Structural differences are interconnected to the positions of the barium atoms with the oriented of the CeO6 octahedra in BaCeO3. Most neutron diffraction or XRD patterns of SrCeO3 have been interpreted in orthorhombic space group pnma and no high temperature structure phase transition is reported up to 1273 K [13]. Introduction of proton conducting type materials and behavior of protonic defects is an essential part to understand the proton conduction within these materials. These defects usually acquiesce a protonic conductivity, the long-range diffusion of protons resulting from alternative hopping connecting two oxygen atoms and reorientation motion [1,9]. In ABO3 perovskite structures have four types of distortion introduced by Knight, first one is the distortion of the BO6 octahedra, this mechanism identified as the Jahn–Teller distortion observed in LaMnO3 types of perovskite structure. RCeO3 (R = Ba, Sr) are not Jahn–Teller active because of alkaline or rare earth with a considerably larger ionic radius than Ce4+ [12,14]. The second and third mechanism is the displacement

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of the B-site or A-site cation within the octahedron, which is attributes of ferroelectric distortions of the BaTiO3 type of structure. The fourth mechanism is the most common and appropriate in RCeO3 type of perovskite materials. In this mechanism, tilting of the octahedrons when the A-site is too small compared to one another such as Sr and Ba in SrCeO3 and BaCeO3 [12]. Ceramic proton conducting electrolytes are being favored to oxide ion conducting electrolytes in SOFC in the intermediate temperature for their low activation energies than oxide ion conductor. Consequently, to identify with the thermodynamic behavior of these cerates is important to understand to valuable application. The main focus of the present paper is to explore the effect of lattice distortion on cohesive, elastic and thermal properties of BaCeO3 and SrCeO3 between 300 K  T  1300 K using modified rigid ion model (MRIM) that has been successfully characterized the thermal behavior of perovskite manganite, cobalts and vanadates [15–17]. It has been found that MRIM is successful in describing the thermodynamic properties of pure cerates. The necessary of model formalism and the results obtained from its application are presented in Section 2 and 3 respectively.

And using the bulk modulus " # 2 1 d f B ¼ Kr0 9 dr2

(4)

r¼r0

here ro and r are the interionic separations in the equilibrium and pairwise states of the system, respectively. The symbol K is the crystal structure constant. The model parameters obtained from the Eqs. (3) and (4) have been used to compute the thermal properties. The lattice Specific heat is computed using the well known expression  C VðlatticeÞ ¼ 9R

T

3 Q ZD =T

QD

0

ex x 4 dx ex  1

(5)

And at very low temperatures (T
2. Formalism of MRIM The major contribution to pair potential of modified rigid ion model (MRIM) is long-range (LR) Coulomb attractions which are balance by the short-range (SR) Hafemeister–Flygare-type (HF) [18] overlap repulsion effective up to the second nearest neighbor atoms approach. The effective interionic potential corresponding to the MRIM framework is expressed as: e2 X Z k Z k0 r1 0 kk 2 0 kk     3 2 0 rk þ rk0  rkk0 2rk  rkk 0 kk kk n b b exp b n b exp þ i i X6 i i i 7 ri ri 6 7   0 þ 4 5 ni k0 k0; 2rk0  rk0 k0 i þbi bi exp 2 ri

f¼

(1) here the first term is attractive LR coulomb interaction energy and the second term is overlap repulsive energy represented by the Hafemeister–Flygare-type (HF) interaction extended up to the second neighbors. The rkk0 represents the separation between the nearest neighbors while rk0 k and rk0 k0 appearing in the next terms are the second neighbor separation. rk (rk0 ) is the ionic radii of k (k0 ) ion. n (n0 ) is the number of nearest (next nearest neighbor) ions. In ABO3 perovskite structure, k represents cation (A, B) and k0 denotes the (O1, O2) type of ions. The summation is performed over all the kk0 ions. bi and ri are the hardness and range parameters for the ith cation-anion pair (i = 1, 2) respectively, and bkk0 is the Pauling coefficient [19] expressed as: !   Z 0 Z bkk0 ¼ 1 þ k þ k (2) Nk N k0

a¼

g CV

(8)

BT V

here BT,V, CV is the isothermal bulk modulus, unit formula volume and specific heat at constant volume respectively and g is the Gruneisen parameter given as " 000 # r f 0 ðrÞ g ¼  0 kk (9) 00 6 f 0 ðrÞ kk

r¼r0

where r0 is the equilibrium distance between the k th and k0 th ions and the primes in fkk0 (r) denoted the third- order and secondorder derivatives of the fkk0 (r) with respect to the interionic separations (r). The Debye temperature (QD) is given by the expression hv kB

QD ¼

(10)

with h as the Planck constant and n as the reststrahlen frequency  v¼

 1=2 1 f 2p m

(11)

where m is the reduced mass and f is the molecular force constant given by:   1 00 SR 2 0 SR (12) f ¼ fkk0 ðrÞ þ fkk0 ðrÞ 3 r r¼r 0 with fkk0 (r) the short-range nearest neighbor part of f (r). The primes over them denote the first-order and second-order SR

derivatives of the fkk0 (r) with respect to the interonic separations SR

With Zk (Zk0 ) and Nk (Nk0 ) as the valence and number of electrons in the outermost orbit of k (k0 ) ions respectively. The model parameters, hardness (b) and range (r) are determined from the equilibrium condition.   df ¼0 (3) dr r¼r0

(r). 3. Results and discussion 3.1. Model parameter The values of input data similar to unit cell parameter (a, b, c) and other interionic distances are directly in use from Ref. [1,13] for the RCeO3 (R = Ba, Sr) and this data is used for the evaluation of

A. Shukla et al. / Thermochimica Acta 614 (2015) 213–217

model parameters (b1,r1) and (b2,r2) corresponding to the ion pairs Ce3+ O2 and R3+ O2 (R = Ba2+, Sr2+) at a temperature (300 K  T  1300 K) for RCeO3. The ionic radii and atomic compressibility for Ba2+, Sr2+, Ce2+, O2 are taken from Refs. [20,21]. The values of model parameter (b1, r1) and (b2, r2) for BaCeO3 and SrCeO3 are listed in Table 1 and Table 2. 3.2. Cohesive energy The cohesive energy is a measure of strength of the force binding the atoms together in solids. The applicability of the present model is first of all tested by computing the cohesive energy of these compounds using Eq. (1) and the values of cohesive energy of RCeO3 (R = Ba, Sr) are reported in Table 3 and Table 4. The present Cohesive Energy for BaCeO3 at room temperature is 139.24 eV and in cubic phase is 137.77 eV which is closer to the experimental value 136.68 eV [22]. The calculated cohesive energy for SrCeO3 is 140.70 eV which could not be compared due to lack of experimental data on it. This fact is exhibited from our cohesive energy results which follow the similar trend of variation with temperature. The negative values of cohesive energy show the stability of these compounds for the studied temperature range. Additionally, to test the validity of our results, we calculated Table 1 Value of model parameters and bulk modulus based on an AIM theory for BaCeO3 as a function of temperature. T (K)

r1

b1 1019 (J) (Ce–O)

r2

(Å) (Ce–O)

(Å) (Ba–O)

b2  1019 (J) (Ba–O)

B0 (Gpa) (AIM)

300 473 573 773 1223

0.266 0.255 0.254 0.165 0.254

1.828 1.522 1.524 2.815 1.605

0.413 0.476 0.463 0.313 0.464

1.892 2.912 2.923 3.180 1.806

47.69 47.90 48.02 77.88 48.86

Table 2 Values of model parameters and calculated bulk modulus using an AIM theory for SrCeO3 as a function of temperature. T (K)

r1

r2

(Å) (Ce–O)

b1 1019 (J) (Ce–O)

298 373 473 573 673 773 873 973 1073 1173 1273

0.267 0.267 0.269 0.267 0.264 0.261 0.265 0.266 0.264 0.263 0.262

1.383 1.383 1.380 1.381 1.384 1.382 1.384 1.385 1.382 1.382 1.383

(Å) (Sr–O)

b2  1019 (J) (Sr–O)

B0 (Gpa) (AIM)

0.484 0.484 0.484 0.483 0.483 0.482 0.482 0.481 0.480 0.479 0.477

3.510 3.512 3.511 3.511 3.513 3.517 3.520 3.525 3.530 3.537 3.554

63.02 63.02 63.04 63.05 63.10 63.13 63.18 63.24 63.31 63.39 63.49

Table 3 Values of bulk modulus (distorted perovskite), cohesive and thermal properties of BaCeO3 as a function of temperature. T (K)

BT (GPa)

f

f

(eV) (MRIM)

(eV) Kapustinskii Eq.

300 473 573 773 1223

109.71b 110.35 110.71 142.20 108.39

139.24 138.71 138.68 133.32 137.77a

140.08 139.83 139.93 134.83 136.90

a b

Ref. [9]. Ref. [22].

f (N/m)

n (THz) uD

25.21 24.90 25.00 35.43 24.67

6.85 6.79 6.78 8.05 6.70

g

(K) 329.20 326.17 325.92 386.82 321.87

3.11 3.09 3.11 4.08 3.13

215

Table 4 Values of bulk modulus (distorted perovskite), cohesive and thermal properties of SrCeO3 as a function of temperature. T (K)

BT (GPa)

f

f

(eV) (MRIM)

(eV) Kapustinskii Eq.

298 373 473 573 673 773 873 973 1073 1173 1273

111.15a 111.15 111.17 111.22 111.33 111.42 111.55 111.71 111.89 112.08 112.34

140.70 140.70 140.70 140.69 140.69 140.68 140.67 140.66 140.64 140.36 140.61

142.73 142.73 142.73 142.74 142.77 142.78 142.81 142.85 142.88 142.92 142.98

a

f (N/m)

n (THz) uD

24.46 24.46 24.47 24.49 24.52 24.52 24.58 24.63 24.68 24.74 24.81

7.86 7.86 7.86 7.86 7.87 7.87 7.88 7.84 7.89 7.90 7.91

g

(K) 377.57a 377.57 377.63 377.74 377.99 378.18 378.48 376.75 379.24 379.69 380.26

2.92 2.92 2.92 2.92 2.92 2.93 2.93 2.94 2.97 2.96 2.96

Ref. [28].

the cohesive energy of these compounds using the generalized Kapustinskii equation [23]. I¼

t 1X n z2 2 k k k

(13)

where t is the number of types of ions in the formula unit each of number nk and charge zk. In our calculation the value of ionic strength for both BaCeO3 and SrCeO3 is found to be 16. According to generalized Kapustinskii equation the lattice energies of crystal with multiple ions are given as:  X U 1213:9 r 1 ¼   (14) nk zk 2 1 KJmol where = weighted mean cation-anion radius sum (using Goldschmidt radii) and r is taken as the average of our model parameters r1 and r2. The estimated values of lattice energy by the Kapustinskii equation for BaCeO3 and SrCeO3 are mentioned in Table 3 and 4. It can be seen from Table 3 and 4 that the cohesive energy is good agreement with our calculated values which confirms the validity of MRIM. 3.3. Bulk modulus We have calculated the bulk modulus systematically on the basis of atom in molecules (AIM) theory which emphasizes the partitioning of static thermodynamic properties in the condensed system into atom or group contribution. Hence, the inverse of bulk modulus is the simple weighted average of the atomic compressibility’s. k¼

X 1 X 1 f i ki and ¼ fi B Bi i i

(15)

where f i ¼ V i =V We considered that the molar volume V can be written as the sum over atomic volume (Vi), fi is the fractional volume occupancy due to the quantum subsystem i is a unit formula volume, B is the bulk modulus of the compound and k is its compressibility. Here we have considered oxygen atoms as the bulkiest and most compressible and its local compressibility varies according to varying cation volume and their relative occupying factor fi on the lines of Pendas Martin [24]. The obtained values are represented by Bo in Tables 1 and 2. In RCeO3 (R = Ba, Sr) perovskite material, Ce4+ is not exhibiting Jahn-Teller distortion [12]. The tendency of perovskites to undergo tilting transitions is often expressed in p terms of the tolerance factor. (t = (rA + rO)/ 2(rB + rO), Where rA, rB, and rO are the radii of the A-site cation, B-site cation, and the oxygen ion respectively. The value of t = 1 suggests that the perovskite structure is an ideal cubic structure. The tolerance factor t of all

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modulus for undistorted structure calculated on the basis of AIM theory, s m is the size mismatch, s C is the charge mismatch, DJT is a JT distortion of CeO6 octahedral and cosv is the effect of buckling of Ce–O–Ce angle. In the case of BaCeO3 the bulk modulus is increases with the increase in temperature up to 773 K but it start to decrease on further increment of temperature. This might be due to the reason that at above 773 K BaCeO3 transform from rhombohedral to cubic phase. Here it is to be noted, that the volume of rhombohedral phase is larger than cubic phase. The values of bulk modulus (BT) of the distorted structure are presented in Table 3 and 4 as BT. The bulk modulus (BT) calculated on the basis of AIM theory is found to be closer to the experimental value [9] for BaCeO3. Also, the bulk modulus for SrCeO3 is 63.02GPA at room temperature, which is closer to the experimental value [26]. 3.4. Thermal properties Fig. 1. The variation of bulk modulus (Bo and BT) for (a) BaCeO3 and (b) for SrCeO3 as a function of temperature where the solid line with solid square (-&-) and the solid line with the solid circle (-*-) represent Bo and BT respectively.

known perovskite compounds have between the ranges of 0.75–1.00. Here, t < 1 means that the BO bond length is too large with respect to the AO one, and therefore that the octahedral tend to rotate in order to contain the mismatch. The tolerance factor is 0.988 obtained for SrCeO3 and for BaCeO3 is 0.89 [9]. The Bulk Modulus of SrCeO3 obtained by us is larger than that of the calculated value of BaCeO3. At the same time the Debye temperature is expected to increase in temperature corresponds to an increase in bulk modulus (Bo) of BaCeO3 which can be observed from Fig. 1(a). It can be seen from Fig. 1(b) that the bulk modulus of SrCeO3 is constant in the range of 300–1200 K. We considered the effect of charge, size mismatch between A and B as defined [25]. The term for the bulk modulus of the distorted perovskite cerates is: BT ¼

K S B0 s m cosv  exp DJT s C

(16)

where KS is the spin-order-dependent constant of proportionality and its value is less than 1 for ferromagnetic state, B0 is the bulk

In order to investigate the thermodynamic properties of RCeO3 (R = Ba, Sr) compounds, we have computed the molecular force constant (f), reststrahlen frequency (n), Debye temperature (uD) and Gruneisen parameter (g ) for the temperature (300 K  T  1300 K). The frequency of vibration of positive ion lattice with respective to negative ion lattice obtained from this model is represented as reststrahlen frequency and found that the value of reststrahlen frequency increases with the increase of temperature. The value of reststrahlen frequency in the rhombohedral phase of BaCeO3 is sudden increases due to the discontinuous phase transition while the reststrahlen frequency is almost constant up to high temperature in the case of SrCeO3. The reststrahlen frequency and molecular force constant are probably the first report on them, hence our comment on their reliability is restricted until the report of experimental data on them. The concept of Debye temperature has played an important role in determining the thermophysical properties of materials. It is basically a measure of the vibration response of the material and therefore intimately connected with properties like the specific heat, thermal expansion and vibrational entropy. Therefore, we have computed Debye temperature in the temperature range (300 K  T  1300 K). The higher value of the Debye temperature of RCeO3 (R = Ba, Sr) indicates the higher phonon frequency. The present value of Debye temperature is

Fig. 2. The variation of specific heat for (a) BaCeO3 and for (b) SrCeO3 as a function of temperature (300 K  T  1300 K) along with the experimental curve. The inset shows the temperature dependence of the calculated specific heat at very low temperature (0 K  T  20 K) by a solid line with solid square (-&-).

A. Shukla et al. / Thermochimica Acta 614 (2015) 213–217

217

K1 for SrCeO3 [28] . The average volume thermal expansion coefficient for BaCeO3 is 8.42  106 K1 which could not be compared due to lack of experimental data on it. 4. Conclusion In summary, the thermal properties have been thoroughly investigated using the MRIM to reveal the cohesive, elastic and thermal properties of RCeO3 (R = Ba, Sr). Our calculated Debye temperature, specific heat and thermal expansion coefficient are found to be satisfactory agreement with the available experimental data. On the basis of an overall discussion, it may be concluded that MRIM is adequately capable of giving a satisfactory prediction of the bulk modulus, thermal and cohesive properties of the complex proton conducting perovskite structural materials. Finally, we would like to mention that some of the present results on thermal properties may serve as a guide to experimental workers in the future. Acknowledgments

Fig. 3. Variation of volume thermal expansion coefficient for (a) BaCeO3 and (b) for SrCeO3 as a function of temperature (300 K  T  1300 K).

329.20 K and 377.57 K at room temperature for BaCeO3 and SrCeO3 respectively, which are in satisfactory agreement with the obtained by Yamanaka et al. [26]. On inspection of Table 3, it is found that the value of Gruneisen parameter is more than 3 for BaCeO3 which indicate that the enhanced anharmonic effect on temperature (300 K  T  1300 K). The value of the Gruneisen parameter for SrCeO3 (Table 4) obtained by us lie between 2 and 3 for whole temperature (300 K  T  1300 K) which support reported value of Radaelli and Cheong [27]. The specific heat obtained from MRIM for RCeO3 (R = Ba, Sr) at a temperature (300 K  T  1300 K) is displayed in Fig. 2(a,b). It can be seen from Fig. 2(a) that the MRIM specific heat of BaCeO3 is found to be in good agreement with the experimental data of Yamanaka et al. [28]. Also, it is seen from Fig. 2(a) that BaCeO3 change slowly toward the ideal cubic perovskite structure with increasing temperature. Similarly the specific heat values for SrCeO3 shown in Fig. 2(b) at temperature 300 K  T  1300 K found to be in good agreement with the measured data of Yamanaka et al. [29]. Here, is to be noted that the MRIM results on specific heat have followed a trend more or less similar to those exhibited by the experimental curve [26,29]. Our results have shown in Fig. 2(a,b) indicated that the specific heat values near room temperature increases slowly and become constant with the temperature above 300 K. Using the specific heat we have computed the volume thermal expansion coefficient (a = gCv/BV) as a function of temperature. As the temperature is increased, the atoms in the crystal vibrate more and this corresponds to the material expansion as more volume is taken up by the vibration. Similar behavior is observed in the present result on volume thermal expansion coefficient which is displayed in Fig. 3(a,b). It can be observed from Fig. 3(a,b) that the value of volume thermal expansion coefficients at room temperature is high compared to that of low temperature values. Here the present average volume thermal expansion coefficient is 8.39  106 K1 which is closer to the reported value 11.1 106

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