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Thermodynamic stability of Cs2ZrO3 by Knudsen effusion technique
Journal of Alloys and Compounds 314 (2001) 96–98
L
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Thermodynamic stability of Cs 2 ZrO 3 by Knudsen effusion technique M. Ali (Basu)a , R. Mishra a , S.R. Bharadwaj a , A.S. Kerkar a , K.N.G. Kaimal a , S.C. Kumar b , a, D. Das * b
a Applied Chemistry Division, Bhabha Atomic Research Centre, Trombay, Mumbai 400 085, India Analytical Chemistry Division, Bhabha Atomic Research Centre, Trombay, Mumbai 400 085, India
Received 5 August 2000; accepted 26 August 2000
Abstract Thermodynamic stability of cesium zirconate was determined by measuring the vapour pressure of Cs 2 O using Knudsen effusion forward collection technique. Cs 2 ZrO 3 (s) vaporized incongruently according to the reaction Cs 2 ZrO 3 (s) 5 ZrO 2 (s) 1 Cs 2 O( g) The Gibbs energy of formation of Cs 2 ZrO 3 obtained from the vapour pressure of Cs 2 O and other auxiliary data could be given by the equation Df G8 (Cs 2 ZrO 3 , s) (618.0 kJ / mol) 5 2 1671.6 1 0.440T
(1142 # T /K # 1273)
2001 Elsevier Science B.V. All rights reserved. Keywords: Cesium zirconate; Chemical synthesis; X-ray diffraction; Thermodynamic properties; Thermal analysis
1. Introduction Thermochemistry of the compounds of cesium plays an important role in the nuclear applications. The fission product iodine which is formed in significant amounts combines with another fission product cesium giving CsI [1–3] inside the nuclear fuel pin. In the presence of oxygen, even at its low potential of about 2400 kJ / mol, CsI dissociates to form ternary compounds of cesium such as Cs 2 U 4 O 12 , Cs 2 UO 4 , Cs 2 ZrO 3 , etc. and releases elemental iodine [1–3]. The migration of the released iodine to the clad surface and its subsequent reaction with clad material (e.g. zircalloy) causes stress corrosion cracking [1–3] which is detrimental to the long-term stability of the nuclear fuel pins. In this context the knowledge of thermochemistry of the compounds of Cs with the other fission products, fuel matrix and the clad materials are important. In this paper, we give our results on the
*Corresponding author. Tel.: 191-22-550-5151; fax: 191-22-5519613. E-mail address: [email protected] (D. Das).
vaporization behaviour of cesium zirconate which has not been reported so far.
2. Experimental Cs 2 ZrO 3 was prepared by sol–gel method through citrate–nitrate route. The chemicals used for the preparation of the compound were Cs 2 CO 3 (99.99% purity, Aldrich, USA), ZrOCl 2 ?xH 2 O (AR Grade), citric acid (AR grade), AR-grade HNO 3 and NH 4 OH solutions. In the first step zirconium nitrate solution, prepared by dissolving chloride-free precipitate of zirconium hydroxide in nitric acid, was mixed with cesium nitrate solution prepared by dissolving Cs 2 CO 3 in HNO 3 in a 1:2 molar ratio. To the above resulting solution citric acid amounting to 2.5 times the number of moles of the total metal ion content was added. The solution was slowly heated in an open beaker at 808C in a fumehood until it formed a gel, which was then transformed into a solid powder on prolonged heating. The solid powder was vacuum dried and transferred to a platinum boat placed in a furnace under dry flowing
0925-8388 / 01 / $ – see front matter 2001 Elsevier Science B.V. All rights reserved. PII: S0925-8388( 00 )01180-4
M. Ali ( Basu) et al. / Journal of Alloys and Compounds 314 (2001) 96 – 98
97
oxygen gas and then ignited at 4008C for 1 h and then at 6008C for 6 h under similar conditions to increase the crystallinity of the product. The compound was cooled to room temperature in gas flow condition and was immediately transferred to a vacuum desiccator. The compound was characterized by X-ray diffraction studies, chemical analysis and thermogravimetry and differential thermal analysis (TG-DTA). Vapour pressure measurement of the compound was done, using a Knudsen effusion forward collection apparatus described elsewhere [4]. Experimental details involving the measurement of temperature and collection of vapor of Cs 2 O on targets are given in Refs. [4,5]. The vapour deposits on the targets were analysed chemically by bringing them into solution and measuring the concentration by atomic emission spectrometry. Fig. 1. ln( pCs 2 O / Pa) versus reciprocal temperature.
3. Results and discussion The literature data for the gaseous cesium oxides indicates that at an oxygen partial pressure of 10 28 –10 29 atm, cesium vaporizes predominantly as Cs 2 O(g) [6]. From the above observation it is concluded that Cs 2 ZrO 3 vaporizes incongruently in the Knudsen cell to Cs 2 O(g) and ZrO 2 (s) and the vaporization reaction can be given the equation, Cs 2 ZrO 3 (s) 5 ZrO 2 (s) 1 Cs 2 O(g)
(1)
The vapour pressure expression for Cs 2 O in the Knudsen cell using the kinetic theory of the gas and the geometry for vapour collection can be given by the relation,
ln[ p(Cs 2 O) / Pa] (60.04) 5 2 31597.0 /T 1 25.87 (1142 # T /K # 1273)
pCs 2 O 5 (1 /A) 3 (w Cs 2 O /t) 3 [(r 2 1 d 2 ) /r 2 ] 3 [2p RT /MCs 2 O ] 1 / 2
where w Cs 2 O is the amount of Cs 2 O that effused out of the orifice of area A and collected during the time t. R is the gas constant and T is the temperature of the Knudsen cell monitored during the vapour collection. MCs 2 O is the molecular weight of Cs 2 O and [(r 2 1 d 2 ) /r 2 ] is the geometric factor, r being the radius of the vapour collimator and d the distance between the orifice and collimator. The vapour pressure of Cs 2 O was calculated from the experimentally determined parameters involved in the Eq. (2) and are represented in Table 1 for all runs. The linear least-square fit of ln p versus 1 /T plot (see Fig. 1) for the experimental results can be represented by the relation
(2)
(3)
The incongruent vaporization of Cs 2 ZrO 3 giving
Table 1 Vaporization data and the Gibbs energy of formation of Cs 2 ZrO 3 (s) Temp. (K)
Time (s)
Mass collected w(Cs 2 O)310 9 (kg)
Pressure (Pa)
Gibbs energy of formation Df G8(Cs 2 ZrO 3 , s) (kJ / mol)
Third law of enthalpy DH8 298.15 a (kJ / mol)
1142 1156 1171 1184 1198 1214 1225 1241 1259 1273
2400 2000 1500 1200 900 600 600 300 300 304
14.4 15.7 16.0 18.0 18.0 16.0 22.6 15.0 21.0 29.0
0.176 0.231 0.316 0.447 0.600 0.805 1.142 1.526 2.152 2.949
21167.9 21161.7 21155.1 21149.4 21143.2 21136.2 21131.3 21124.3 21116.3 21110.2
304.84 305.59 306.09 305.71 306.00 306.67 305.57 306.11 306.42 306.07
a
DH8 298.15 refers to enthalpy change for the vaporization reaction, viz., Cs 2 ZrO 3 (s)5ZrO 2 (s)1Cs 2 O(g). Mean third law value for DH8 298.15 5 305.91615.0 kJ mol 21 . Mean second law value for DH8 298.15 5291.3618.0 kJ mol 21 . The indicated deviations from the respective mean values are mainly due to the uncertainties in the thermal functions; the contribution from experimental uncertainties are very small in comparison.
M. Ali ( Basu) et al. / Journal of Alloys and Compounds 314 (2001) 96 – 98
98
Cs 2 O(g) and ZrO 2 (s) is given by Eq. (1). Therefore the Gibbs energy change for the vaporization reaction can be given by, DG8r 5 Df G8(Cs 2 O(g)) 1 Df G8(ZrO 2 (s)) 2 Df G8(Cs 2 ZrO 3 (s))
(4)
where Df G8s are Gibbs energy change for formation of the compounds from the elements in their standard states at 1 atm pressure and DG8r is the standard Gibbs energy change for the reaction. The standard Gibbs energy change for the reaction in equilibrium condition can equated to 2 RT ln Keq which in turn is equal to 2 RT ln p(Cs 2 O) for this reaction. Eq. (4) can be rearranged to give the standard Gibbs energy of formation of Cs 2 ZrO 3 by the relation Df G8(Cs 2 ZrO 3 (s)) 5 Df G8(ZrO 2 (s)) 1 Df G8(Cs 2 O(g)) 1 RT ln p(Cs 2 O)
(5)
The standard Gibbs energies of formation of Df G8(ZrO 2 (s)) and Df G8(Cs 2 O(g)) can be obtained from literature [7] and therefore the standard Gibbs energy of formation can be calculated using Eqs. (3) and (5). The equation describing the temperature dependence of Gibbs energy of formation of Cs 2 ZrO 3 is given by Df G8(Cs 2 ZrO 3 (s)) (618.0 kJ / mol) 5 2 1671.6 1 0.440 T (1142 # T /K # 1273)
(6)
Table 1 also gives the second law and third law enthalpies for the vaporization reaction. The thermal functions required for these calculations have been taken from Refs. [7,8]. The uncertainties of 615 and 618 kJ / mol assigned to the third law and second law enthalpies in Table 1 come from the data for Cs 2 O(g) species. The thermal functions of Cs 2 O(g) given by Scharm et al. [8] are based on the molecular parameters estimated by Lamoreaux and Hildenbrand [6], which differs from Barin’s selection [9].
4. Conclusion The Gibbs energy of formation for the compound Cs 2 ZrO 3 at 1200 K derived from the vapour measurements
was found to be 2(1143.6618.0) kJ / mol. This value is in agreement with the Gibbs energy of formation of Cs 2 ZrO 3 at 1200 K reported by Scharm et al. [8] from the standard enthalpy of formation and heat capacity measurements, viz., 2(1163.1615) kJ / mol, within the uncertainty limits. Similarly, the standard molar enthalpy of formation of Cs 2 ZrO 3 , (Df H8 298.15 ) reported by Scharm et al. [8], 2(1584.6561.9) compares well with the Df H8 298.15 derived from the third law enthalpy of vaporization reaction, viz., 2(1565.2620.0) kJ / mol.
Acknowledgements This work was carried out under IAEA-CRP on, ‘Establishment of a thermophysical Property database for LWR and HWR Contract No. 10631. The authors thank Dr. J.P. Mittal, Director, Chemistry and Isotope Group, BARC and Dr. N.M. Gupta, Head, Applied Chemistry Division for their support and interest in this work.
References [1] P. Hofmann, J. Spino, J. Nucl. Mater. 127 (1985) 205. [2] R. Kohli, W. Lacom, IAEA Tech. Committee Meeting on Fuel Rod Internal Chemistry and Fission Products Behaviour, Karlshruhe, Germany, Nov. 11–15 (1985) (IWGFPT / 25). [3] O. Gotzmann, J. Nucl. Mater. 107 (1982) 185. [4] R. Mishra, M. Ali (Basu), S.R. Bharadwaj, A.S. Kerkar, D. Das, S.R. Dharwadkar, J. Alloys Comp. 290 (1999) 97. [5] D. Das, M.S. Chandrasekharaiah, High Temp. Sci. 21 (1987) 161. [6] R.H. Lamoreaux, D.L. Hildenbrand, J. Phys. Chem. Ref. Data 13 (1984) 151. [7] E.H.P. Cordfunke, R.J.M. Konings (Eds.), Thermochemical Data for Reactor Materials and Fission Products, North Holland, Amsterdam, 1990. [8] R.P.C. Scharm, V.M. Smit-Groen, E.H.P. Cordfunke, J. Chem. Ther. 31 (1999) 43. [9] I. Barin, in: Thermochemical Data of Pure Substances, 3rd Edition, VCH, Weinheim, 1995.
L
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Thermodynamic stability of Cs 2 ZrO 3 by Knudsen effusion technique M. Ali (Basu)a , R. Mishra a , S.R. Bharadwaj a , A.S. Kerkar a , K.N.G. Kaimal a , S.C. Kumar b , a, D. Das * b
a Applied Chemistry Division, Bhabha Atomic Research Centre, Trombay, Mumbai 400 085, India Analytical Chemistry Division, Bhabha Atomic Research Centre, Trombay, Mumbai 400 085, India
Received 5 August 2000; accepted 26 August 2000
Abstract Thermodynamic stability of cesium zirconate was determined by measuring the vapour pressure of Cs 2 O using Knudsen effusion forward collection technique. Cs 2 ZrO 3 (s) vaporized incongruently according to the reaction Cs 2 ZrO 3 (s) 5 ZrO 2 (s) 1 Cs 2 O( g) The Gibbs energy of formation of Cs 2 ZrO 3 obtained from the vapour pressure of Cs 2 O and other auxiliary data could be given by the equation Df G8 (Cs 2 ZrO 3 , s) (618.0 kJ / mol) 5 2 1671.6 1 0.440T
(1142 # T /K # 1273)
2001 Elsevier Science B.V. All rights reserved. Keywords: Cesium zirconate; Chemical synthesis; X-ray diffraction; Thermodynamic properties; Thermal analysis
1. Introduction Thermochemistry of the compounds of cesium plays an important role in the nuclear applications. The fission product iodine which is formed in significant amounts combines with another fission product cesium giving CsI [1–3] inside the nuclear fuel pin. In the presence of oxygen, even at its low potential of about 2400 kJ / mol, CsI dissociates to form ternary compounds of cesium such as Cs 2 U 4 O 12 , Cs 2 UO 4 , Cs 2 ZrO 3 , etc. and releases elemental iodine [1–3]. The migration of the released iodine to the clad surface and its subsequent reaction with clad material (e.g. zircalloy) causes stress corrosion cracking [1–3] which is detrimental to the long-term stability of the nuclear fuel pins. In this context the knowledge of thermochemistry of the compounds of Cs with the other fission products, fuel matrix and the clad materials are important. In this paper, we give our results on the
*Corresponding author. Tel.: 191-22-550-5151; fax: 191-22-5519613. E-mail address: [email protected] (D. Das).
vaporization behaviour of cesium zirconate which has not been reported so far.
2. Experimental Cs 2 ZrO 3 was prepared by sol–gel method through citrate–nitrate route. The chemicals used for the preparation of the compound were Cs 2 CO 3 (99.99% purity, Aldrich, USA), ZrOCl 2 ?xH 2 O (AR Grade), citric acid (AR grade), AR-grade HNO 3 and NH 4 OH solutions. In the first step zirconium nitrate solution, prepared by dissolving chloride-free precipitate of zirconium hydroxide in nitric acid, was mixed with cesium nitrate solution prepared by dissolving Cs 2 CO 3 in HNO 3 in a 1:2 molar ratio. To the above resulting solution citric acid amounting to 2.5 times the number of moles of the total metal ion content was added. The solution was slowly heated in an open beaker at 808C in a fumehood until it formed a gel, which was then transformed into a solid powder on prolonged heating. The solid powder was vacuum dried and transferred to a platinum boat placed in a furnace under dry flowing
0925-8388 / 01 / $ – see front matter 2001 Elsevier Science B.V. All rights reserved. PII: S0925-8388( 00 )01180-4
M. Ali ( Basu) et al. / Journal of Alloys and Compounds 314 (2001) 96 – 98
97
oxygen gas and then ignited at 4008C for 1 h and then at 6008C for 6 h under similar conditions to increase the crystallinity of the product. The compound was cooled to room temperature in gas flow condition and was immediately transferred to a vacuum desiccator. The compound was characterized by X-ray diffraction studies, chemical analysis and thermogravimetry and differential thermal analysis (TG-DTA). Vapour pressure measurement of the compound was done, using a Knudsen effusion forward collection apparatus described elsewhere [4]. Experimental details involving the measurement of temperature and collection of vapor of Cs 2 O on targets are given in Refs. [4,5]. The vapour deposits on the targets were analysed chemically by bringing them into solution and measuring the concentration by atomic emission spectrometry. Fig. 1. ln( pCs 2 O / Pa) versus reciprocal temperature.
3. Results and discussion The literature data for the gaseous cesium oxides indicates that at an oxygen partial pressure of 10 28 –10 29 atm, cesium vaporizes predominantly as Cs 2 O(g) [6]. From the above observation it is concluded that Cs 2 ZrO 3 vaporizes incongruently in the Knudsen cell to Cs 2 O(g) and ZrO 2 (s) and the vaporization reaction can be given the equation, Cs 2 ZrO 3 (s) 5 ZrO 2 (s) 1 Cs 2 O(g)
(1)
The vapour pressure expression for Cs 2 O in the Knudsen cell using the kinetic theory of the gas and the geometry for vapour collection can be given by the relation,
ln[ p(Cs 2 O) / Pa] (60.04) 5 2 31597.0 /T 1 25.87 (1142 # T /K # 1273)
pCs 2 O 5 (1 /A) 3 (w Cs 2 O /t) 3 [(r 2 1 d 2 ) /r 2 ] 3 [2p RT /MCs 2 O ] 1 / 2
where w Cs 2 O is the amount of Cs 2 O that effused out of the orifice of area A and collected during the time t. R is the gas constant and T is the temperature of the Knudsen cell monitored during the vapour collection. MCs 2 O is the molecular weight of Cs 2 O and [(r 2 1 d 2 ) /r 2 ] is the geometric factor, r being the radius of the vapour collimator and d the distance between the orifice and collimator. The vapour pressure of Cs 2 O was calculated from the experimentally determined parameters involved in the Eq. (2) and are represented in Table 1 for all runs. The linear least-square fit of ln p versus 1 /T plot (see Fig. 1) for the experimental results can be represented by the relation
(2)
(3)
The incongruent vaporization of Cs 2 ZrO 3 giving
Table 1 Vaporization data and the Gibbs energy of formation of Cs 2 ZrO 3 (s) Temp. (K)
Time (s)
Mass collected w(Cs 2 O)310 9 (kg)
Pressure (Pa)
Gibbs energy of formation Df G8(Cs 2 ZrO 3 , s) (kJ / mol)
Third law of enthalpy DH8 298.15 a (kJ / mol)
1142 1156 1171 1184 1198 1214 1225 1241 1259 1273
2400 2000 1500 1200 900 600 600 300 300 304
14.4 15.7 16.0 18.0 18.0 16.0 22.6 15.0 21.0 29.0
0.176 0.231 0.316 0.447 0.600 0.805 1.142 1.526 2.152 2.949
21167.9 21161.7 21155.1 21149.4 21143.2 21136.2 21131.3 21124.3 21116.3 21110.2
304.84 305.59 306.09 305.71 306.00 306.67 305.57 306.11 306.42 306.07
a
DH8 298.15 refers to enthalpy change for the vaporization reaction, viz., Cs 2 ZrO 3 (s)5ZrO 2 (s)1Cs 2 O(g). Mean third law value for DH8 298.15 5 305.91615.0 kJ mol 21 . Mean second law value for DH8 298.15 5291.3618.0 kJ mol 21 . The indicated deviations from the respective mean values are mainly due to the uncertainties in the thermal functions; the contribution from experimental uncertainties are very small in comparison.
M. Ali ( Basu) et al. / Journal of Alloys and Compounds 314 (2001) 96 – 98
98
Cs 2 O(g) and ZrO 2 (s) is given by Eq. (1). Therefore the Gibbs energy change for the vaporization reaction can be given by, DG8r 5 Df G8(Cs 2 O(g)) 1 Df G8(ZrO 2 (s)) 2 Df G8(Cs 2 ZrO 3 (s))
(4)
where Df G8s are Gibbs energy change for formation of the compounds from the elements in their standard states at 1 atm pressure and DG8r is the standard Gibbs energy change for the reaction. The standard Gibbs energy change for the reaction in equilibrium condition can equated to 2 RT ln Keq which in turn is equal to 2 RT ln p(Cs 2 O) for this reaction. Eq. (4) can be rearranged to give the standard Gibbs energy of formation of Cs 2 ZrO 3 by the relation Df G8(Cs 2 ZrO 3 (s)) 5 Df G8(ZrO 2 (s)) 1 Df G8(Cs 2 O(g)) 1 RT ln p(Cs 2 O)
(5)
The standard Gibbs energies of formation of Df G8(ZrO 2 (s)) and Df G8(Cs 2 O(g)) can be obtained from literature [7] and therefore the standard Gibbs energy of formation can be calculated using Eqs. (3) and (5). The equation describing the temperature dependence of Gibbs energy of formation of Cs 2 ZrO 3 is given by Df G8(Cs 2 ZrO 3 (s)) (618.0 kJ / mol) 5 2 1671.6 1 0.440 T (1142 # T /K # 1273)
(6)
Table 1 also gives the second law and third law enthalpies for the vaporization reaction. The thermal functions required for these calculations have been taken from Refs. [7,8]. The uncertainties of 615 and 618 kJ / mol assigned to the third law and second law enthalpies in Table 1 come from the data for Cs 2 O(g) species. The thermal functions of Cs 2 O(g) given by Scharm et al. [8] are based on the molecular parameters estimated by Lamoreaux and Hildenbrand [6], which differs from Barin’s selection [9].
4. Conclusion The Gibbs energy of formation for the compound Cs 2 ZrO 3 at 1200 K derived from the vapour measurements
was found to be 2(1143.6618.0) kJ / mol. This value is in agreement with the Gibbs energy of formation of Cs 2 ZrO 3 at 1200 K reported by Scharm et al. [8] from the standard enthalpy of formation and heat capacity measurements, viz., 2(1163.1615) kJ / mol, within the uncertainty limits. Similarly, the standard molar enthalpy of formation of Cs 2 ZrO 3 , (Df H8 298.15 ) reported by Scharm et al. [8], 2(1584.6561.9) compares well with the Df H8 298.15 derived from the third law enthalpy of vaporization reaction, viz., 2(1565.2620.0) kJ / mol.
Acknowledgements This work was carried out under IAEA-CRP on, ‘Establishment of a thermophysical Property database for LWR and HWR Contract No. 10631. The authors thank Dr. J.P. Mittal, Director, Chemistry and Isotope Group, BARC and Dr. N.M. Gupta, Head, Applied Chemistry Division for their support and interest in this work.
References [1] P. Hofmann, J. Spino, J. Nucl. Mater. 127 (1985) 205. [2] R. Kohli, W. Lacom, IAEA Tech. Committee Meeting on Fuel Rod Internal Chemistry and Fission Products Behaviour, Karlshruhe, Germany, Nov. 11–15 (1985) (IWGFPT / 25). [3] O. Gotzmann, J. Nucl. Mater. 107 (1982) 185. [4] R. Mishra, M. Ali (Basu), S.R. Bharadwaj, A.S. Kerkar, D. Das, S.R. Dharwadkar, J. Alloys Comp. 290 (1999) 97. [5] D. Das, M.S. Chandrasekharaiah, High Temp. Sci. 21 (1987) 161. [6] R.H. Lamoreaux, D.L. Hildenbrand, J. Phys. Chem. Ref. Data 13 (1984) 151. [7] E.H.P. Cordfunke, R.J.M. Konings (Eds.), Thermochemical Data for Reactor Materials and Fission Products, North Holland, Amsterdam, 1990. [8] R.P.C. Scharm, V.M. Smit-Groen, E.H.P. Cordfunke, J. Chem. Ther. 31 (1999) 43. [9] I. Barin, in: Thermochemical Data of Pure Substances, 3rd Edition, VCH, Weinheim, 1995.