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Thermodynamic study of gaseous CsBO2 by Knudsen effusion mass spectrometry
Journal of Nuclear Materials 491 (2017) 183e189
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Thermodynamic study of gaseous CsBO2 by Knudsen effusion mass spectrometry K. Nakajima a, *, T. Takai b, T. Furukawa b, M. Osaka a a b
Nuclear Science and Engineering Center, Japan Atomic Energy Agency, Tokai-mura, Naka-gun, Ibaraki-ken, Japan Oarai Research and Development Center, Japan Atomic Energy Agency, Oarai-machi, Higashiibaraki-gun, Ibaraki-ken, Japan
h i g h l i g h t s Equilibrium vapor pressures of cesium metaborate, CsBO2, were determined. Gibbs energy function of CsBO2(g) was calculated from its molecular constants. Standard enthalpy of formation of CsBO2(g) was determined. The second and third-law enthalpies of formation agreed within the experimental errors. The existing thermodynamic data agreed well with those evaluated in this study.
a r t i c l e i n f o
a b s t r a c t
Article history: Received 6 July 2016 Received in revised form 1 May 2017 Accepted 1 May 2017 Available online 4 May 2017
One of the main chemical forms of cesium in the gas phase during severe light-water reactor accidents is expected to be cesium metaborate, CsBO2, according to thermodynamic equilibrium calculations considering its reaction with boron. However, the accuracy of the thermodynamic data of the gaseous metaborate, CsBO2(g), has been judged as poor. Thus, Knudsen effusion mass spectrometric measurements of CsBO2 were carried out to obtain reliable thermodynamic data. The evaluated values of the standard enthalpy of formation of CsBO2(g), obtained by the 2nd and 3rd-law treatments, are 700.7 ± 10.7 kJ/mol and 697.0 ± 10.6 kJ/mol, respectively, and agree with each other within the experimental errors, which indicates that our data are reliable. Furthermore, it was found that the existing data of the Gibbs energy function and the standard enthalpy of formation agreed well with the values evaluated in this study, which indicates that the existing thermodynamic data are also reliable. © 2017 Elsevier B.V. All rights reserved.
Keywords: Thermodynamics Gibbs energy function Standard enthalpy of formation Vapor pressure Cesium boron Knudsen cell Mass spectrometry
1. Introduction
considered to be one of the main species of Cs, according to [3]:
Light-water reactors contain large amounts of boron, either as boron carbide, B4C, in control rods (BWR), or as boric acid, H3BO3, dissolved in the primary coolant (PWR). In severe light-water reactor accidents, gaseous cesium metaborate, CsBO2(g), is expected to be formed as one of the main cesium-bearing vapor species according to thermodynamic calculations [e.g., 1,2]. When H3BO3 is released in a severe accident, CsBO2 is thought to be formed by the reaction with gaseous cesium iodide, CsI(g) which is
CsIðgÞ þ H3 BO3 ðgÞ/CsBO2 ðgÞ þ HIðgÞ þ H2 OðgÞ:
* Corresponding author. 2-4 Shirakata, Tokai-mura, Naka-gun, Ibaraki 319-1195, Japan. E-mail address: [email protected] (K. Nakajima). http://dx.doi.org/10.1016/j.jnucmat.2017.05.001 0022-3115/© 2017 Elsevier B.V. All rights reserved.
(1)
However, this paper [3] states that this reaction would not occur thermodynamically, although the experiments have shown that this reaction can proceed to the right and it is considered worthwhile to reinvestigate the thermodynamic properties of CsBO2(g). According to a reference book on critically assessed thermodynamic data for reactor materials and compounds of fission product elements [4], the thermodynamic data of CsBO2(g) is evaluated from the molecular constants and the vapor pressures, and is judged to be poor quality because two sets of data on the equilibrium vapor pressure of CsBO2 reported in the past do not agree [5]. After publication of this reference book [4], new experimental data on the vapor pressure of CsBO2 over the solid and the liquid has
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K. Nakajima et al. / Journal of Nuclear Materials 491 (2017) 183e189
been reported [5]. However, as mentioned in section 3.3, the values of the molar enthalpies of sublimation at 298.15 K, Dsub H298 , calculated using the second-law treatment are found to deviate by more than 5% from the third-law value and uncertainty still remains. New experimental data on the molecular constants of CsBO2 [6] was also reported after publication of the reference book [4]. However, the difference between the values of the Gibbs energy G+ H + function of CsBO2(g), T T 298 , calculated from the CsBO2 ðgÞ
existing [4] and the newly obtained [6] molecular constants, which + are required in the evaluation of Dsub H298 by the second-law and the third-law treatments, was found to be only about 0.1% and was thus negligible as described in section 3.3. So, the vapor pressure is considered to be the principal cause of uncertainty in the thermodynamic data of CsBO2(g). Thus, determination of the equilibrium vapor pressure of CsBO2 was carried out by Knudsen effusion mass spectrometry (KEMS) to obtain reliable thermodynamic data of CsBO2(g) checking their internal consistency. 2. Experimental 2.1. Sample preparation A CsBO2 sample used for KEMS measurement was prepared as follows. Prescribed amounts of Cs2CO3 (99%, Mitsuwa Chemicals Co., Ltd.) and H3BO3 powders originated from B2O3 (99.99%, Alpha Products Inc.), which was checked by XRD to change from B2O3 to H3BO3 due to its hygroscopicity, were put into a platinum crucible, together with a small amount of water. Then the platinum crucible containing the sample was put in a muffle furnace and evaporated to dryness at 423 K. Such a drying process is necessary to avoid explosive boiling during the synthesis of CsBO2. After checking that there was no water left in the crucible, the evaporated sample was heated up to 873 K in the muffle furnace in static air, with no mixing procedure to synthesize CsBO2, which was checked by XRD. Furthermore, the synthesized sample was heated under vacuum with a Knudsen effusion mass spectrometer at 933 K to remove volatile impurities, and these were confirmed to be completely evaporated by this method. The starting materials and synthesized samples were handled in an inert atmosphere glove box, where the moisture content was kept at less than 1 ppm. 2.2. Characterization Both the samples before and after the KEMS measurement were checked by XRD (RINT 2000V, Rigaku Co. Ltd.) using CuKa radiation to identify the crystalline phases present and determine their lattice parameters. A plastic zip bag was used to avoid moisture absorption during the XRD measurements. The lattice parameters were determined by the Cohen's method [7] using the Nelson-Riley extrapolation function [8], and a 95% confidence interval was used as the error index. The B and Cs contents in the samples were analyzed by inductively coupled plasma atomic emission spectrometry (ICP/AES) and mass spectrometry (ICP/MS), respectively.
Corp.) with a box type of ion source and a yttria-coated iridium filament was used. The furnace was evacuated with a turbomolecular pump (HiPace™ 300, Pfeiffer Vacuum Ltd.) to a pressure of less than 104 Pa during the KEMS measurement. According to a study [10] that examined the ionization behavior of CsBO2 by a KEMS method, the detected Csþ ion results from the dissociative ionization of a CsBO2 molecule. Thus, the sample was heated and cooled stepwise in 30 K steps, and the ion current of Csþ ionized under 50 eV electron impact, ICs , was monitored until the end of the KEMS measurement to obtain the vapor pressure of CsBO2, pCsBO2 , by the modified integral method (See Appendix A) using the following equation:
pCsBO2 ðt Þ ¼
Z aL
pffiffiffiffiffiffiffiffiffiffiffi 2p RDWCsBO2 ICs ðt ÞT ðt Þ tend pffiffiffiffiffiffiffiffiffiffi X pffiffiffiffiffiffi ICs ðt 0 Þ Tðt 0 Þdt 0 gi Mi
0
(2)
i
where DWCsBO2 is the weight of the CsBO2 effusing through the orifice, R the gas constant, a the cross section of the effusion orifice, L the Clausing factor [11], T the absolute temperature, i an isotopic species, M the mass number of CsBO2, g the isotopic abundance ratio of CsBO2. In this study, DWCsBO2 is assumed to be the same as the weight difference of the samples before and after the KEMS measurement since the dimer of CsBO2 in the vapor is reported to be less than 1% [5]. The unknown value of aL was determined from the KEMS measurement of silver using the following equation:
aLðt Þ ¼
pffiffiffiffiffiffiffiffiffiffiffi 2p RDWAg IAg ðt ÞT ðt Þ Z tend pffiffiffiffiffiffiffiffiffiffi X pffiffiffiffiffiffi IAg ðt 0 Þ Tðt 0 Þdt 0 gi Mi pref ðT Þ 0
(3)
i i
where pref is the reference vapor pressure of silver [12]. Temperature calibration was also conducted by comparing with the melting point of silver during the KEMS measurement. 3. Results and discussion 3.1. 1Sample preparation and characterization Fig. 1 shows XRD patterns of the samples before and after the KEMS measurement and Table 1 shows the determined lattice parameters together with the chemical analysis results obtained by ICP techniques. This figure suggests that the sample used in the KEMS measurement is almost single-phase CsBO2. But since the chemical analyses show that the B/Cs ratio is larger than one, a trace of boron-rich cesium borate is considered to be present in the KEMS sample based on the phase diagram in the Cs2O-B2O3 system [13,14]. The lattice parameters of the samples before and after the
2.3. Knudsen effusion mass spectrometry The sample was loaded into the KEMS apparatus through the attached glovebox [9] where the moisture content was controlled to be 400e500 ppm with a moisture removing device (GBJPWN0, Glovebox Japan Inc.). The Knudsen cell used is made of platinum with an effusion orifice 1 mm in diameter. A type R (Pt/Pt-13Rh) thermocouple is welded to the bottom of the Knudsen cell. A quadrupole mass spectrometer (M-401QA-MGHY, Canon Anelva
Fig. 1. XRD patterns of the samples before and after the KEMS measurement. * JCPDS card number. The () marks mean the peaks used to determine the lattice parameters.
K. Nakajima et al. / Journal of Nuclear Materials 491 (2017) 183e189 Table 1 Lattice parameters and B/Cs atomic ratios of the samples before and after the KEMS measurement.
Before KEMS After KEMS Schl€ ager & Hoppe [15] a
Lattice parameter (pm)a
B/Csa
a ¼ 1364.8(14), c ¼ 836.2(8) a ¼ 1364.9(10), c ¼ 836.0(6) a ¼ 1363.7(2), c ¼ 836.5(2)
1.04 1.10
The B and Cs contents were determined by ICP/AES and ICP/MS, respectively.
KEMS measurement agree within the experimental errors. On the other hand, the a-axis lattice constant seems to be larger than the reference value [15] although the c-axis values agree within the errors. This difference might be due to the hygroscopic properties of CsBO2 as well as interference originating from the plastic bag. 3.2. Knudsen effusion mass spectrometry þ The main detected ionic species are Csþ, Bþ, BOþ, BOþ 2 , CsO , þ CsBOþ, CsBOþ 2 , and Cs2BO2 ions. The temperature dependences of the ion currents of these ionic species, except for the BOþ and BOþ 2 þ ions, which might be interfered with Nþ 2 and CO2 ions, are plotted in Fig. 2. The ion current of the CsBOþ 2 ion is two orders of magnitude lower than that of the Csþ ion. However, as mentioned in section 2.3, the Csþ ion is considered to be caused by the dissociative ionization of the CsBO2 molecule, so the equilibrium vapor pressures of CsBO2 can be evaluated from the measured ion currents of the Csþ ion. The determined vapor pressures of CsBO2(g) over CsBO2(s) are shown in Table 2 and plotted in Fig. 3 in comparison with the reference data [5,16] and the estimated data from the existing thermodynamic data [4]. As shown in this figure, the determined vapor pressures agree very well with the values calculated from the existing thermodynamic data [4]. The vapor pressure error, dp, is estimated using the following equation, which can be derived from Eq. (2). according to the law of error propagation:
dpCsBO2 pCsBO2
2
¼
dDWCsBO2 DWCsBO2
2
þ
dICs ICs
2
þ
dTCsBO2 TCsBO2
2
þ
daL
185
Table 2 Vapor pressure of CsBO2, Temperature error and Relative errors of ion current of Csþ and vapor pressure of CsBO2. TCsBO2 (K)
pCsBO2 (Pa)
dTCsBO2 (K)
dICs
914.7 912.9 914.5 913.3 913.3 914.7 912.1 915.0 884.0 882.6 883.1 884.0 882.0 884.3 882.2 883.4 852.7 854.3 853.4 853.7 854.4 852.9 855.0 852.2 822.6 825.1 822.7 825.1 822.6 824.6 822.7 792.9 794.6 792.5 794.6 792.4 794.3 792.2
0.3669 0.3715 0.3633 0.3681 0.3770 0.3669 0.3694 0.3599 0.1271 0.1282 0.1261 0.1266 0.1237 0.1224 0.1246 0.1232 0.03255 0.03395 0.03341 0.03309 0.03429 0.03357 0.03365 0.03288 0.008833 0.009004 0.008706 0.008780 0.008513 0.008550 0.008805 0.002230 0.001878 0.002013 0.002142 0.001780 0.001614 0.001780
6.582 6.562 6.579 6.566 6.566 6.582 6.554 6.585 6.254 6.239 6.244 6.254 6.232 6.257 6.234 6.247 5.919 5.936 5.927 5.930 5.938 5.921 5.944 5.914 5.599 5.625 5.600 5.625 5.599 5.619 5.600 5.282 5.300 5.277 5.300 5.276 5.297 5.274
0.02169 0.02130 0.02164 0.02139 0.02139 0.02169 0.02113 0.02175 0.01573 0.01550 0.01558 0.01573 0.01541 0.01578 0.01544 0.01563 0.01295 0.01295 0.01295 0.01295 0.01295 0.01295 0.01295 0.01296 0.01630 0.01582 0.01628 0.01582 0.01630 0.01592 0.01628 0.02387 0.02336 0.02399 0.02336 0.02402 0.02345 0.02408
ICs
dpCsBO2 pCsBO2
0.2216 0.2215 0.2216 0.2216 0.2216 0.2216 0.2215 0.2216 0.2211 0.2211 0.2211 0.2211 0.2210 0.2211 0.2211 0.2211 0.2209 0.2209 0.2209 0.2209 0.2209 0.2209 0.2209 0.2209 0.2211 0.2211 0.2211 0.2211 0.2211 0.2211 0.2211 0.2218 0.2217 0.2218 0.2217 0.2218 0.2217 0.2218
2
sL (4)
where dDW is the error caused by weighing, dI that of the ion current, dT that of the temperature and daL the error in aL. In this study, dICs/ICs is regarded to be equal to the product of the standard deviation of the determined vapor pressures and the natural logarithm of 10, since the vapor pressure, p, is proportional to the product of the measured ion current, I, and the absolute
Fig. 3. Temperature dependence of the vapor pressures of CsBO2. The solid line is estimated from the existing thermodynamic data [4].
temperature, T, (See Appendix A), and the following relation can hold, assuming that the temperature error can be neglected:
vlog p 1 ¼ : vI I ln 10
Fig. 2. Temperature dependence of the ion currents of Csþ, B þ, CsOþ, CsBOþ, CsBOþ 2 and Cs2BOþ 2 ions. The number in the parenthesis of legend indicates mass to charge ratio of the ionic species.
(5)
The dT is assumed to increase linearly with temperature between room temperature and the melting point of silver where the temperature error was estimated to be 10 K from the KEMS measurement of silver. The daL is estimated using the following equation:
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K. Nakajima et al. / Journal of Nuclear Materials 491 (2017) 183e189
daL aL
2 ¼
dDWAg DWAg
!2 þ
dIAg
!2
IAg
þ
dTAg TAg
!2 þ
dpref pref
Table 4 Gibbs energy function of CsBO2(g)b
!2 (6)
which can also be derived from Eq. (3). Both dTAg and dIAg/IAg are estimated in the manner mentioned above. In this study, daL is assumed to be temperature-independent. So, since both dTAg/TAg and dIAg/IAg depend on temperature, these errors are assumed to be equal to those at the temperature corresponding to the average value of 1/TAg. The value of dpref/pref can be regarded as 12% [17]. In this way, daL/aL is estimated to be 0.1870 and the equilibrium pressure errors of CsBO2 can be evaluated from Eq. (4). The dTCsBO2 , dICs/ICs, and temperature-dependent errors of dpCsBO2 =pCsBO2 are also summarized in Table 2.
Temp.(K)
gef(CsBO2,g)Ca
gef(CsBO2,g)E
diff. (%)
298 500 1000 1500 2000 2500 3000
315.727 322.802 349.509 371.647 389.486 404.291 416.908
315.519 322.542 349.154 371.255 389.076 403.870 416.480
0.07 0.08 0.10 0.11 0.11 0.10 0.10
a
The standard state is changed from 1 atm to 1 bar. Suffixes of C and E mean the quantities based on the molecular constants given by Cordfunke and Konings [4] and Ezhov and Komarov [6], respectively. b
following equations to determine Dsub H298 , by the second-law and the third-law methods [17]:
3.3. Thermodynamic evaluation The existing thermodynamic data of CsBO2(g) are evaluated from the molecular constants [4] indicated in Table 3. There are some differences compared with the molecular constants newly obtained by gas phase electron diffractometry and IR spectroscopy [6]. In particular, a nearly 20% difference exists for the moment of G+ H + inertia, IAIBIC. Thus, T T 298 is evaluated at 1 bar
gef ðCsBO2 ; gÞ gef ðCsBO2 ; sÞ R ln pCsBO2 ¼ Fa þ
+ ð2ndÞ Dsub H298
T
;
(7)
+ T gef ðCsBO2 ; gÞ gef ðCsBO2 ; sÞ R ln pCsBO2 ¼ Dsub H298 ð3rdÞ (8)
CsBO2 ðgÞ
assuming a rigid rotor harmonic oscillator model based on the molecular constants given by Cordfunke and Konings [4] and Ezhov and Komarov [6], respectively. The calculated results are shown in Table 4. Hereafter, the Gibbs energy function is abbreviated as gef and the thermodynamic quantities evaluated from the molecular constants given by Cordfunke and Konings [4] and Ezhov and Komarov [6] are added with the suffixes of C and E, respectively. It is found, as shown in this table, that there is only about a 0.1% difference between the gef(CsBO2,g)C and the gef(CsBO2,g)E in spite of the approximately 20% maximum difference at maximum in the molecular constant. Furthermore, Table 5 shows the values calculated by using the
where gef(CsBO2,s) is evaluated from the entropy, S+298 ðCsBO2 ; sÞ, + ðCsBO Þ, given by Cordfunke and the enthalpy increment, HT+ H298 2 + ð2ndÞ are determined by the and Konings [4]. Both Fa and Dsub H298 least squares method. The Fa will be zero for the ideal case where the measured pressures and the free energy functions are completely accurate. + ð2ndÞ and dD + Both of the errors dDsub H298 sub H298 ð3rdÞ are estimated by the law of error propagation from the following equations:
+ dDsub H298 ð2ndÞ2 ¼ dT 2 Rln pCsBO2 Fa þ gef ðCsBO2 ; gÞ gef ðCsBO2 ; sÞ
!
2
þ T 2 R2
dpCsBO2 pCsBO2
2
2
þ dFa þ dgef ðCsBO2 ; gÞ2
þ dgef ðCsBO2 ; sÞ2 ;
(9)
Table 3 Molecular constants of CsBO2.
R(B-O1) [pm] R(B-O2) [pm] R(Cs-O1) [pm] :Cs-O1-B [deg] IAIBIC [kg3m6] n (B-O1) [cm1] n (B-O2) [cm1] n (Cs-O1) [cm1] n (Cs O1B) [cm1] n (O1BO2) [cm1] n (out-of-plane) [cm1] a
Cordfunke and Konings [4]
Ezhov and Komarov [6]
diff. (%)
127 123 265 130 1.43 10134a 1945 1077 206 60 581 576
129.8 121.9 269 125 1.69 10134 1935 1045 233 57 632 588
2.2 0.9 1.5 3.8 18.2 0.5 3.0 13.1 5.0 8.8 2.1
The value of IAIBIC [g3cm6] is written as 1.40 10113 in their compilation.
K. Nakajima et al. / Journal of Nuclear Materials 491 (2017) 183e189
187
Table 5 Gibbs energy function of CsBO2(s) and CsBO2(g) and the values of Eqs. (7). and (8).b T (K)
gef(CsBO2,s)a (J/mol/K)
gef(CsBO2,g)C (J/mol/K)
gef(CsBO2,g)E (J/mol/K)
Eq. (7)C (J/mol/K)
Eq. (7)E (J/mol/K)
Eq. (8)C (J/mol)
Eq. (8)E (J/mol)
914.7 912.9 914.5 913.3 913.3 914.7 912.1 915.0 884.0 882.6 883.1 884.0 882.0 884.3 882.2 883.4 852.7 854.3 853.4 853.7 854.4 852.9 855.0 852.2 822.6 825.1 822.7 825.1 822.6 824.6 822.7 792.9 794.6 792.5 794.6 792.4 794.3 792.2
141.959 141.836 141.945 141.863 141.863 141.959 141.781 141.979 139.877 139.780 139.815 139.877 139.739 139.897 139.753 139.835 137.741 137.852 137.790 137.811 137.859 137.755 137.900 137.707 135.686 135.852 135.693 135.852 135.686 135.818 135.693 133.643 133.761 133.615 133.761 133.608 133.740 133.594
345.205 345.111 345.194 345.132 345.132 345.205 345.070 345.220 343.615 343.542 343.568 343.615 343.510 343.631 343.521 343.584 341.974 342.059 342.011 342.027 342.065 341.985 342.097 341.947 340.383 340.512 340.388 340.512 340.383 340.485 340.388 338.791 338.884 338.769 338.884 338.764 338.867 338.753
344.860 344.766 344.849 344.787 344.787 344.860 344.725 344.875 343.275 343.201 343.227 343.275 343.170 343.290 343.180 343.243 341.638 341.723 341.675 341.691 341.728 341.648 341.760 341.611 340.051 340.180 340.057 340.180 340.051 340.153 340.057 338.464 338.556 338.443 338.556 338.437 338.540 338.426
307.3 307.2 307.4 307.3 307.1 307.3 307.3 307.5 316.6 316.6 316.7 316.6 316.9 316.9 316.8 316.9 328.4 328.1 328.2 328.3 328.0 328.2 328.1 328.4 339.7 339.5 339.9 339.8 340.0 340.0 339.8 351.6 353.0 352.5 351.9 353.5 354.3 353.5
307.0 306.9 307.0 307.0 306.8 307.0 306.9 307.1 316.3 316.2 316.4 316.3 316.5 316.6 316.5 316.5 328.1 327.7 327.9 327.9 327.6 327.8 327.8 328.0 339.4 339.2 339.5 339.4 339.7 339.7 339.4 351.3 352.7 352.2 351.6 353.2 354.0 353.2
281100 280500 281100 280700 280500 281100 280300 281300 279900 279400 279700 279900 279500 280200 279500 279900 280000 280300 280100 280200 280200 279900 280500 279800 279500 280100 279600 280300 279700 280300 279500 278800 280500 279400 279700 280100 281400 280100
280800 280200 280800 280300 280200 280800 280000 281000 279600 279100 279400 279600 279200 279900 279200 279600 279800 280000 279800 280000 279900 279600 280200 279500 279200 279900 279300 280000 279500 280100 279300 278600 280300 279100 279400 279900 281200 279800
a + ðCsBO ; sÞ calculated by using the heat capacity, Cp(CsBO , s), recommended by Cordfunke and The gef(CsBO2,s) is evaluated from the S+298 ðCsBO2 ; sÞ and the HT+ H298 2 2 Konings [4]. b Suffixes of C and E mean the quantities based on the molecular constants given by Cordfunke and Konings [4] and Ezhov and Komarov [6], respectively.
+ dDsub H298 ð3rdÞ2
¼ dT
2
! 2 2 2 2 2 dpCsBO2 2 þ dgef ðCsBO2 ; gÞ þ dgef ðCsBO2 ; sÞ : Rln pCsBO2 þ gef ðCsBO2 ; gÞ gef ðCsBO2 ; sÞ þ T R pCsBO2 (10)
The error in gef(CsBO2,s), d gef(CsBO2,s), is assumed to be 1% because the thermodynamic data of CsBO2(s) is judged as being of good quality [4]. The error in gef(CsBO2,g), d gef(CsBO2,g), is also assumed to be 1%. This is because the values of gef(CsBO2,g)C and gef(CsBO2,g)E agree well each other as shown in Tables 4 and 5 The dFa is assumed to be the same as the standard deviation obtained by using the data obtained using Eq. (7). indicated in Table 5. The + ð2ndÞ , standard enthalpies of sublimation of CsBO2, Dsub H298 C + + + Dsub H298 ð3rdÞC , Dsub H298 ð2ndÞE and Dsub H298 ð3rdÞE evaluated in this way are 276.0 ± 4.4 kJ/mol, 280.1 ± 4.0 kJ/mol, 276.1 ± 4.4 kJ/ mol, and 279.8 ± 4.0 kJ/mol, respectively. These values indicate that the enthalpies based on the molecular constants given by Ezhov and Komarov [6] are preferable. Namely, the difference between + ð2ndÞ and D + Dsub H298 sub H298 ð3rdÞE is smaller than that between E + ð2ndÞ and D + + Dsub H298 H sub 298 ð3rdÞC , and Dsub H298 ð2ndÞE agrees C
+ ð3rdÞ within the error limits. In addition, Fa and Fa with Dsub H298 C E E are calculated to be 4.84 ± 5.90 and 4.38 ± 5.90 by the least squares method using the data obtained from Eq. (7). in Table 5, and FaE is found to be closer to zero than FaC, although both of FaC and FaE can become zero within the error limits. Furthermore, the temperature + ð3rdÞ is found to be weaker than that of dependence of Dsub H298 E + ð3rdÞ , since the slopes of the linear least squares fits to Dsub H298 C the data obtained using Eq. (8).C and Eq. (8).E in Table 5, with respect to temperature, are calculated to be 5.46 103 and 4.80 103, respectively. Consequently, the thermodynamic quantities derived from the molecular constants of Ezhov and Komarov [6] are considered to be preferable. To confirm the accuracy of the thermodynamic quantities obtained from the reported vapor pressures of CsBO2 [5,16], both + ð2ndÞ and D + Dsub H298 sub H298 ð3rdÞ are determined from their vapor pressures by using the existing thermodynamic quantities [4] of
188
K. Nakajima et al. / Journal of Nuclear Materials 491 (2017) 183e189
Table 6 + ðCsBO Þ. Comparison of Dsub H298 2 authors
+ ð2ndÞ (kJ/mol) Dsub H298
+ ð3rdÞ (kJ/mol) Dsub H298
diff. (%)
Biswas and Mukerji [16] for CsBO2(l)a Cordfunke et al. [5] for CsBO2(l)a Cordfunke et al. [5] for CsBO2(s)b This work for CsBO2(s)b
237.5 286.4 289.1 276.1
284.2 270.1 271.9 279.8
16.4 6.0 6.3 1.3
a The values evaluated from vapor pressures over liquid CsBO2 using enthalpy of fusion of CsBO2 and both the heat capacities of solid CsBO2 and liquid CsBO2 recommended by Cordfunke and Konings [4]. b The values evaluated from vapor pressures over solid CsBO2.
gef(CsBO2,s) and gef(CsBO2,l), and the gef(CsBO2,g)E calculated in this study. These results are summarized in Table 6. + ð2ndÞ As shown in this table, the difference between Dsub H298 + and Dsub H298 ð3rdÞ in this work is the smallest and our vapor pressures are believed to be more accurate than those reported in the past. Furthermore, the second and third-law standard en+ ðCsBO ; gÞ thalpies of formation of CsBO2(g), Df H298 2 2nd and + + ð2ndÞ Df H298 ðCsBO2 ; gÞ3rd , derived from Dsub H298 and + ð3rdÞ by using the standard enthalpy of formation of Dsub H298 + ðCsBO ; sÞ, CsBO2(s), Df H298 [4] are calculated to 2 be 700.7 ± 10.7 kJ/mol and 697.0 ± 10.6 kJ/mol where the error + ðCsBO ; sÞ is assumed to be 1%. This is found to agree well in Df H298 2 + ðCsBO ; gÞ, 696.8 kJ/mol. Therefore, the with the existing Df H298 2 existing thermodynamic data are also considered to be reliable, although they were judged as poor quality. Actually, in the experiments [18] referred to in paper [3], the reaction products were not identified as CsBO2(g) and only the deposition profiles of Cs and B were examined after the chemical reaction. This report [18] merely confirms that the obtained results were indicative of a vapor-phase reaction with the formation of cesium borate. Indeed, the Gibbs energy change of the following reaction can become negative:
CsIðgÞ þ H3 BO3 ðgÞ/CsBO2 ðs; lÞ þ HIðgÞ þ H2 OðgÞ:
(11)
It is, therefore, necessary to establish whether the reaction expressed by an equation such as Eq. (11). actually occurs under the same experimental conditions [18].
However, there is no data on the ionization cross-section of Csþ when a CsBO2 molecule fragments into a Csþ ion. So, the modified integral method, which does not require such an ionization crosssection, is applied in this study. The ion current, I, originating from vapor molecules effusing through the orifice, is proportional to the flux, u, and the dwell time of the effusing vapor molecules in the ion source of the mass spectrometer. Since the dwell time is inversely proportional to the velocity of the molecules passing through the ion source of the mass spectrometer, and this velocity, v, is given by the MaxwellBoltzmann velocity distribution, the following relation between the time dependent I(t) and u(t) can hold:
Ij ðtÞ ¼ k
Appendex A Ionization cross-sections are generally required when measured ion currents are converted into absolute vapor pressures [e.g., 19].
(A.1)
pMj
where j is a specific isotopic vapor species, k the factor for instrument geometry, which is independent of vapor species, s the ionization cross section, s the sensitivity of the mass spectrometer, which is dependent on vapor species. On the other hand, according to the kinetic theory of gases, u(t) can be expressed by the following equation:
gj pðtÞNA uj ðtÞ ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi : 2pMj RTðtÞ
(A.2)
where NA is the Avogadro constant. From Eqs (A.1) and (A.2), the following relation can be obtained:
4. Conclusion An almost single-phase CsBO2 sample was prepared and its KEMS measurement was performed in the temperature range of 792e915 K to determine the equilibrium vapor pressures of CsBO2. The Gibbs energy function of CsBO2(g) is not significantly influenced by the difference between the existing and newly obtained molecular constants. However, the thermodynamic quantities derived from the newly obtained molecular constants are found to be preferable. The standard enthalpies of formation of CsBO2(g), determined by the second and third-law methods, are 700.7 ± 10.7 kJ/mol and 697.0 ± 10.6 kJ/mol, respectively. Good agreement within the experimental errors, which suggests reliable thermodynamic data, can be obtained. Furthermore, the existing thermodynamic data, such as the Gibbs energy function and the standard enthalpy of formation of CsBO2(g), almost agree with those evaluated in this study and are also found to be reliable, although the accuracy of the existing data was judged as poor quality.
sj sj ksj sj u ðtÞ ¼ qffiffiffiffiffiffiffiffiffiffiffiuj ðtÞ 8RTðtÞ vj ðtÞ j
pðtÞ ¼
4R I ðtÞTðtÞ: ksj sj NA gj j
(A.3)
When vapor molecules in the gas phase can be regarded as only one vapor species, while allowing any isotopic vapor species, such as the Cs10BO2 and Cs11BO2 molecules in this study, the weight loss, DW, caused by the vapor molecules effusing through the orifice can be related to the u(t) by the following equation:
DW ¼
X i
Ztend ui ðtÞ=NA dt
Mi aL
(A.4)
0
where i is an isotopic vapor species. By substituting Eq. (A.1) into this equation, the following equation can hold:
pffiffiffiffiffiffiffiffiffiffiffiffi tend X aL 8RMi Z pffiffiffiffiffiffiffiffiffi pffiffiffiffi DW ¼ Ii ðtÞ TðtÞdt: p s N ks i i A i
(A.5)
0
When the ionization cross section is assumed to be the same among the isotopes, the following relation can be obtained from Eq. (A.3):
K. Nakajima et al. / Journal of Nuclear Materials 491 (2017) 183e189
Ii ðtÞ ¼
si gi I ðtÞ: sj gj j
(A.6)
By using this relation, Eq. (A.5) can be transformed to the following equation:
pffiffiffiffiffiffi Ztend pffiffiffiffiffiffiffiffiffi X pffiffiffiffiffiffi aL 8R DW ¼ pffiffiffiffi Ij ðtÞ TðtÞdt gi Mi : pksj sj gj NA i
(A.7)
0
Thus, the following equation used in the modified integral method can be obtained from Eqs (A.3) and (A.7) by deleting the unknown factor, ksjsj:
pffiffiffiffiffiffiffiffiffiffiffi 2p RDWIj ðt ÞT ðt Þ : pðt Þ ¼ Z tend pffiffiffiffiffiffiffiffiffiffi X pffiffiffiffiffiffi Ij ðt 0 Þ Tðt 0 Þdt 0 gi Mi aL 0
(A.8)
i
References [1] K. Minato, J. Nucl. Mater 185 (1991) 154, http://dx.doi.org/10.1016/00223115(91)90330-A. [2] S. Miwa, S. Yamashita, M. Osaka, Prog. Nucl. Energ. 92 (2016) 254, http:// dx.doi.org/10.1016/j.pnucene.2016.02.023.
189
[3] E.H.P. Cordfunke, R.J.M. Konings, E.F. Westrum Jr., J. Nucl. Mater 167 (1989) 205, http://dx.doi.org/10.1016/0022-3115(89)90443-1. [4] North Holland, AmsterdamE.H.P. Cordfunke, R.J.M. Konings (Eds.), Thermochemical Data for Reactor Materials and Fission Products, 1990, p. 131. [5] E.H.P. Cordfunke, R.J.M. Konings, R. SASKIA, M. Meyssen, J. Chem. Thermodyn. 23 (1991) 297, http://dx.doi.org/10.1016/S0021-9614(05)80188-0. [6] Yu.S. Ezhov, S.A. Komarov, J. Struct. Chem. 41 (2000) 55, http://dx.doi.org/ 10.1007/BF02684728. [7] B.D. Cullity, Elements of X-ray Diffraction, ADD1SON-WESLEY PUBLISHING COMPANY, Inc, 1956, p. 338. [8] J.B. Nelson, D.P. Riley, Proc. Phys. Soc. Lond. 57 (1945) 160. [9] J. Huang, T. Furukawa, K. Aoto, Thermochim. Acta 405 (2003) 61, http:// dx.doi.org/10.1016/S0040-6031(03)00136-9. [10] M. Asano, Y. Yasue, K. Kubo, J. Nucl. Sci. Technol. 21 (1984) 614, http:// dx.doi.org/10.1080/18811248.1984.9731090. [11] P. Clausing, J. Vac. Sci. Technol. 8 (1971) 636. http://dx.doi.org/10.1116/1. 1316379. [12] O. Kubaschewski, E.L. Evans, C.B. Alock, Metallurgical Thermochemistry, fifth ed., Pergamon Press, New York, 1979, p. 358. [13] A.B. Kaplun, A.B. Meshalkin, J. Crys. Growth 209 (2000) 890, http://dx.doi.org/ 10.1016/S0022-0248(99)00628-4. [14] N. Penin, M. Touboul, G. Nowogrocki, J. Crys. Growth 256 (2003) 334, http:// dx.doi.org/10.1016/S0022-0248(03)01383-6. €ger, R. Hoppe, Z. Anorg. Allg. Chem. 620 (1994) 1867, http:// [15] M. Schla dx.doi.org/10.1002/zaac.19946201106. [16] S.R. Biswas, J. Mukerji, J. Chem. Eng. Data 16 (1971) 336, http://dx.doi.org/ 10.1021/je60050a013. [17] R.C. Paule, J. Mandel, Pure Appl. Chem. 31 (1972) 395. http://dx.doi.org/10. 1351/pac197231030395. [18] B. R. Bowsher and S. Dickinson, AEEW-report R2102 (1986).. [19] M. Miller, K. Armatys, Open Therm. J. 7 (2013) 2, http://dx.doi.org/10.2174/ 1874396X01307010002.
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Journal of Nuclear Materials journal homepage: www.elsevier.com/locate/jnucmat
Thermodynamic study of gaseous CsBO2 by Knudsen effusion mass spectrometry K. Nakajima a, *, T. Takai b, T. Furukawa b, M. Osaka a a b
Nuclear Science and Engineering Center, Japan Atomic Energy Agency, Tokai-mura, Naka-gun, Ibaraki-ken, Japan Oarai Research and Development Center, Japan Atomic Energy Agency, Oarai-machi, Higashiibaraki-gun, Ibaraki-ken, Japan
h i g h l i g h t s Equilibrium vapor pressures of cesium metaborate, CsBO2, were determined. Gibbs energy function of CsBO2(g) was calculated from its molecular constants. Standard enthalpy of formation of CsBO2(g) was determined. The second and third-law enthalpies of formation agreed within the experimental errors. The existing thermodynamic data agreed well with those evaluated in this study.
a r t i c l e i n f o
a b s t r a c t
Article history: Received 6 July 2016 Received in revised form 1 May 2017 Accepted 1 May 2017 Available online 4 May 2017
One of the main chemical forms of cesium in the gas phase during severe light-water reactor accidents is expected to be cesium metaborate, CsBO2, according to thermodynamic equilibrium calculations considering its reaction with boron. However, the accuracy of the thermodynamic data of the gaseous metaborate, CsBO2(g), has been judged as poor. Thus, Knudsen effusion mass spectrometric measurements of CsBO2 were carried out to obtain reliable thermodynamic data. The evaluated values of the standard enthalpy of formation of CsBO2(g), obtained by the 2nd and 3rd-law treatments, are 700.7 ± 10.7 kJ/mol and 697.0 ± 10.6 kJ/mol, respectively, and agree with each other within the experimental errors, which indicates that our data are reliable. Furthermore, it was found that the existing data of the Gibbs energy function and the standard enthalpy of formation agreed well with the values evaluated in this study, which indicates that the existing thermodynamic data are also reliable. © 2017 Elsevier B.V. All rights reserved.
Keywords: Thermodynamics Gibbs energy function Standard enthalpy of formation Vapor pressure Cesium boron Knudsen cell Mass spectrometry
1. Introduction
considered to be one of the main species of Cs, according to [3]:
Light-water reactors contain large amounts of boron, either as boron carbide, B4C, in control rods (BWR), or as boric acid, H3BO3, dissolved in the primary coolant (PWR). In severe light-water reactor accidents, gaseous cesium metaborate, CsBO2(g), is expected to be formed as one of the main cesium-bearing vapor species according to thermodynamic calculations [e.g., 1,2]. When H3BO3 is released in a severe accident, CsBO2 is thought to be formed by the reaction with gaseous cesium iodide, CsI(g) which is
CsIðgÞ þ H3 BO3 ðgÞ/CsBO2 ðgÞ þ HIðgÞ þ H2 OðgÞ:
* Corresponding author. 2-4 Shirakata, Tokai-mura, Naka-gun, Ibaraki 319-1195, Japan. E-mail address: [email protected] (K. Nakajima). http://dx.doi.org/10.1016/j.jnucmat.2017.05.001 0022-3115/© 2017 Elsevier B.V. All rights reserved.
(1)
However, this paper [3] states that this reaction would not occur thermodynamically, although the experiments have shown that this reaction can proceed to the right and it is considered worthwhile to reinvestigate the thermodynamic properties of CsBO2(g). According to a reference book on critically assessed thermodynamic data for reactor materials and compounds of fission product elements [4], the thermodynamic data of CsBO2(g) is evaluated from the molecular constants and the vapor pressures, and is judged to be poor quality because two sets of data on the equilibrium vapor pressure of CsBO2 reported in the past do not agree [5]. After publication of this reference book [4], new experimental data on the vapor pressure of CsBO2 over the solid and the liquid has
184
K. Nakajima et al. / Journal of Nuclear Materials 491 (2017) 183e189
been reported [5]. However, as mentioned in section 3.3, the values of the molar enthalpies of sublimation at 298.15 K, Dsub H298 , calculated using the second-law treatment are found to deviate by more than 5% from the third-law value and uncertainty still remains. New experimental data on the molecular constants of CsBO2 [6] was also reported after publication of the reference book [4]. However, the difference between the values of the Gibbs energy G+ H + function of CsBO2(g), T T 298 , calculated from the CsBO2 ðgÞ
existing [4] and the newly obtained [6] molecular constants, which + are required in the evaluation of Dsub H298 by the second-law and the third-law treatments, was found to be only about 0.1% and was thus negligible as described in section 3.3. So, the vapor pressure is considered to be the principal cause of uncertainty in the thermodynamic data of CsBO2(g). Thus, determination of the equilibrium vapor pressure of CsBO2 was carried out by Knudsen effusion mass spectrometry (KEMS) to obtain reliable thermodynamic data of CsBO2(g) checking their internal consistency. 2. Experimental 2.1. Sample preparation A CsBO2 sample used for KEMS measurement was prepared as follows. Prescribed amounts of Cs2CO3 (99%, Mitsuwa Chemicals Co., Ltd.) and H3BO3 powders originated from B2O3 (99.99%, Alpha Products Inc.), which was checked by XRD to change from B2O3 to H3BO3 due to its hygroscopicity, were put into a platinum crucible, together with a small amount of water. Then the platinum crucible containing the sample was put in a muffle furnace and evaporated to dryness at 423 K. Such a drying process is necessary to avoid explosive boiling during the synthesis of CsBO2. After checking that there was no water left in the crucible, the evaporated sample was heated up to 873 K in the muffle furnace in static air, with no mixing procedure to synthesize CsBO2, which was checked by XRD. Furthermore, the synthesized sample was heated under vacuum with a Knudsen effusion mass spectrometer at 933 K to remove volatile impurities, and these were confirmed to be completely evaporated by this method. The starting materials and synthesized samples were handled in an inert atmosphere glove box, where the moisture content was kept at less than 1 ppm. 2.2. Characterization Both the samples before and after the KEMS measurement were checked by XRD (RINT 2000V, Rigaku Co. Ltd.) using CuKa radiation to identify the crystalline phases present and determine their lattice parameters. A plastic zip bag was used to avoid moisture absorption during the XRD measurements. The lattice parameters were determined by the Cohen's method [7] using the Nelson-Riley extrapolation function [8], and a 95% confidence interval was used as the error index. The B and Cs contents in the samples were analyzed by inductively coupled plasma atomic emission spectrometry (ICP/AES) and mass spectrometry (ICP/MS), respectively.
Corp.) with a box type of ion source and a yttria-coated iridium filament was used. The furnace was evacuated with a turbomolecular pump (HiPace™ 300, Pfeiffer Vacuum Ltd.) to a pressure of less than 104 Pa during the KEMS measurement. According to a study [10] that examined the ionization behavior of CsBO2 by a KEMS method, the detected Csþ ion results from the dissociative ionization of a CsBO2 molecule. Thus, the sample was heated and cooled stepwise in 30 K steps, and the ion current of Csþ ionized under 50 eV electron impact, ICs , was monitored until the end of the KEMS measurement to obtain the vapor pressure of CsBO2, pCsBO2 , by the modified integral method (See Appendix A) using the following equation:
pCsBO2 ðt Þ ¼
Z aL
pffiffiffiffiffiffiffiffiffiffiffi 2p RDWCsBO2 ICs ðt ÞT ðt Þ tend pffiffiffiffiffiffiffiffiffiffi X pffiffiffiffiffiffi ICs ðt 0 Þ Tðt 0 Þdt 0 gi Mi
0
(2)
i
where DWCsBO2 is the weight of the CsBO2 effusing through the orifice, R the gas constant, a the cross section of the effusion orifice, L the Clausing factor [11], T the absolute temperature, i an isotopic species, M the mass number of CsBO2, g the isotopic abundance ratio of CsBO2. In this study, DWCsBO2 is assumed to be the same as the weight difference of the samples before and after the KEMS measurement since the dimer of CsBO2 in the vapor is reported to be less than 1% [5]. The unknown value of aL was determined from the KEMS measurement of silver using the following equation:
aLðt Þ ¼
pffiffiffiffiffiffiffiffiffiffiffi 2p RDWAg IAg ðt ÞT ðt Þ Z tend pffiffiffiffiffiffiffiffiffiffi X pffiffiffiffiffiffi IAg ðt 0 Þ Tðt 0 Þdt 0 gi Mi pref ðT Þ 0
(3)
i i
where pref is the reference vapor pressure of silver [12]. Temperature calibration was also conducted by comparing with the melting point of silver during the KEMS measurement. 3. Results and discussion 3.1. 1Sample preparation and characterization Fig. 1 shows XRD patterns of the samples before and after the KEMS measurement and Table 1 shows the determined lattice parameters together with the chemical analysis results obtained by ICP techniques. This figure suggests that the sample used in the KEMS measurement is almost single-phase CsBO2. But since the chemical analyses show that the B/Cs ratio is larger than one, a trace of boron-rich cesium borate is considered to be present in the KEMS sample based on the phase diagram in the Cs2O-B2O3 system [13,14]. The lattice parameters of the samples before and after the
2.3. Knudsen effusion mass spectrometry The sample was loaded into the KEMS apparatus through the attached glovebox [9] where the moisture content was controlled to be 400e500 ppm with a moisture removing device (GBJPWN0, Glovebox Japan Inc.). The Knudsen cell used is made of platinum with an effusion orifice 1 mm in diameter. A type R (Pt/Pt-13Rh) thermocouple is welded to the bottom of the Knudsen cell. A quadrupole mass spectrometer (M-401QA-MGHY, Canon Anelva
Fig. 1. XRD patterns of the samples before and after the KEMS measurement. * JCPDS card number. The () marks mean the peaks used to determine the lattice parameters.
K. Nakajima et al. / Journal of Nuclear Materials 491 (2017) 183e189 Table 1 Lattice parameters and B/Cs atomic ratios of the samples before and after the KEMS measurement.
Before KEMS After KEMS Schl€ ager & Hoppe [15] a
Lattice parameter (pm)a
B/Csa
a ¼ 1364.8(14), c ¼ 836.2(8) a ¼ 1364.9(10), c ¼ 836.0(6) a ¼ 1363.7(2), c ¼ 836.5(2)
1.04 1.10
The B and Cs contents were determined by ICP/AES and ICP/MS, respectively.
KEMS measurement agree within the experimental errors. On the other hand, the a-axis lattice constant seems to be larger than the reference value [15] although the c-axis values agree within the errors. This difference might be due to the hygroscopic properties of CsBO2 as well as interference originating from the plastic bag. 3.2. Knudsen effusion mass spectrometry þ The main detected ionic species are Csþ, Bþ, BOþ, BOþ 2 , CsO , þ CsBOþ, CsBOþ 2 , and Cs2BO2 ions. The temperature dependences of the ion currents of these ionic species, except for the BOþ and BOþ 2 þ ions, which might be interfered with Nþ 2 and CO2 ions, are plotted in Fig. 2. The ion current of the CsBOþ 2 ion is two orders of magnitude lower than that of the Csþ ion. However, as mentioned in section 2.3, the Csþ ion is considered to be caused by the dissociative ionization of the CsBO2 molecule, so the equilibrium vapor pressures of CsBO2 can be evaluated from the measured ion currents of the Csþ ion. The determined vapor pressures of CsBO2(g) over CsBO2(s) are shown in Table 2 and plotted in Fig. 3 in comparison with the reference data [5,16] and the estimated data from the existing thermodynamic data [4]. As shown in this figure, the determined vapor pressures agree very well with the values calculated from the existing thermodynamic data [4]. The vapor pressure error, dp, is estimated using the following equation, which can be derived from Eq. (2). according to the law of error propagation:
dpCsBO2 pCsBO2
2
¼
dDWCsBO2 DWCsBO2
2
þ
dICs ICs
2
þ
dTCsBO2 TCsBO2
2
þ
daL
185
Table 2 Vapor pressure of CsBO2, Temperature error and Relative errors of ion current of Csþ and vapor pressure of CsBO2. TCsBO2 (K)
pCsBO2 (Pa)
dTCsBO2 (K)
dICs
914.7 912.9 914.5 913.3 913.3 914.7 912.1 915.0 884.0 882.6 883.1 884.0 882.0 884.3 882.2 883.4 852.7 854.3 853.4 853.7 854.4 852.9 855.0 852.2 822.6 825.1 822.7 825.1 822.6 824.6 822.7 792.9 794.6 792.5 794.6 792.4 794.3 792.2
0.3669 0.3715 0.3633 0.3681 0.3770 0.3669 0.3694 0.3599 0.1271 0.1282 0.1261 0.1266 0.1237 0.1224 0.1246 0.1232 0.03255 0.03395 0.03341 0.03309 0.03429 0.03357 0.03365 0.03288 0.008833 0.009004 0.008706 0.008780 0.008513 0.008550 0.008805 0.002230 0.001878 0.002013 0.002142 0.001780 0.001614 0.001780
6.582 6.562 6.579 6.566 6.566 6.582 6.554 6.585 6.254 6.239 6.244 6.254 6.232 6.257 6.234 6.247 5.919 5.936 5.927 5.930 5.938 5.921 5.944 5.914 5.599 5.625 5.600 5.625 5.599 5.619 5.600 5.282 5.300 5.277 5.300 5.276 5.297 5.274
0.02169 0.02130 0.02164 0.02139 0.02139 0.02169 0.02113 0.02175 0.01573 0.01550 0.01558 0.01573 0.01541 0.01578 0.01544 0.01563 0.01295 0.01295 0.01295 0.01295 0.01295 0.01295 0.01295 0.01296 0.01630 0.01582 0.01628 0.01582 0.01630 0.01592 0.01628 0.02387 0.02336 0.02399 0.02336 0.02402 0.02345 0.02408
ICs
dpCsBO2 pCsBO2
0.2216 0.2215 0.2216 0.2216 0.2216 0.2216 0.2215 0.2216 0.2211 0.2211 0.2211 0.2211 0.2210 0.2211 0.2211 0.2211 0.2209 0.2209 0.2209 0.2209 0.2209 0.2209 0.2209 0.2209 0.2211 0.2211 0.2211 0.2211 0.2211 0.2211 0.2211 0.2218 0.2217 0.2218 0.2217 0.2218 0.2217 0.2218
2
sL (4)
where dDW is the error caused by weighing, dI that of the ion current, dT that of the temperature and daL the error in aL. In this study, dICs/ICs is regarded to be equal to the product of the standard deviation of the determined vapor pressures and the natural logarithm of 10, since the vapor pressure, p, is proportional to the product of the measured ion current, I, and the absolute
Fig. 3. Temperature dependence of the vapor pressures of CsBO2. The solid line is estimated from the existing thermodynamic data [4].
temperature, T, (See Appendix A), and the following relation can hold, assuming that the temperature error can be neglected:
vlog p 1 ¼ : vI I ln 10
Fig. 2. Temperature dependence of the ion currents of Csþ, B þ, CsOþ, CsBOþ, CsBOþ 2 and Cs2BOþ 2 ions. The number in the parenthesis of legend indicates mass to charge ratio of the ionic species.
(5)
The dT is assumed to increase linearly with temperature between room temperature and the melting point of silver where the temperature error was estimated to be 10 K from the KEMS measurement of silver. The daL is estimated using the following equation:
186
K. Nakajima et al. / Journal of Nuclear Materials 491 (2017) 183e189
daL aL
2 ¼
dDWAg DWAg
!2 þ
dIAg
!2
IAg
þ
dTAg TAg
!2 þ
dpref pref
Table 4 Gibbs energy function of CsBO2(g)b
!2 (6)
which can also be derived from Eq. (3). Both dTAg and dIAg/IAg are estimated in the manner mentioned above. In this study, daL is assumed to be temperature-independent. So, since both dTAg/TAg and dIAg/IAg depend on temperature, these errors are assumed to be equal to those at the temperature corresponding to the average value of 1/TAg. The value of dpref/pref can be regarded as 12% [17]. In this way, daL/aL is estimated to be 0.1870 and the equilibrium pressure errors of CsBO2 can be evaluated from Eq. (4). The dTCsBO2 , dICs/ICs, and temperature-dependent errors of dpCsBO2 =pCsBO2 are also summarized in Table 2.
Temp.(K)
gef(CsBO2,g)Ca
gef(CsBO2,g)E
diff. (%)
298 500 1000 1500 2000 2500 3000
315.727 322.802 349.509 371.647 389.486 404.291 416.908
315.519 322.542 349.154 371.255 389.076 403.870 416.480
0.07 0.08 0.10 0.11 0.11 0.10 0.10
a
The standard state is changed from 1 atm to 1 bar. Suffixes of C and E mean the quantities based on the molecular constants given by Cordfunke and Konings [4] and Ezhov and Komarov [6], respectively. b
following equations to determine Dsub H298 , by the second-law and the third-law methods [17]:
3.3. Thermodynamic evaluation The existing thermodynamic data of CsBO2(g) are evaluated from the molecular constants [4] indicated in Table 3. There are some differences compared with the molecular constants newly obtained by gas phase electron diffractometry and IR spectroscopy [6]. In particular, a nearly 20% difference exists for the moment of G+ H + inertia, IAIBIC. Thus, T T 298 is evaluated at 1 bar
gef ðCsBO2 ; gÞ gef ðCsBO2 ; sÞ R ln pCsBO2 ¼ Fa þ
+ ð2ndÞ Dsub H298
T
;
(7)
+ T gef ðCsBO2 ; gÞ gef ðCsBO2 ; sÞ R ln pCsBO2 ¼ Dsub H298 ð3rdÞ (8)
CsBO2 ðgÞ
assuming a rigid rotor harmonic oscillator model based on the molecular constants given by Cordfunke and Konings [4] and Ezhov and Komarov [6], respectively. The calculated results are shown in Table 4. Hereafter, the Gibbs energy function is abbreviated as gef and the thermodynamic quantities evaluated from the molecular constants given by Cordfunke and Konings [4] and Ezhov and Komarov [6] are added with the suffixes of C and E, respectively. It is found, as shown in this table, that there is only about a 0.1% difference between the gef(CsBO2,g)C and the gef(CsBO2,g)E in spite of the approximately 20% maximum difference at maximum in the molecular constant. Furthermore, Table 5 shows the values calculated by using the
where gef(CsBO2,s) is evaluated from the entropy, S+298 ðCsBO2 ; sÞ, + ðCsBO Þ, given by Cordfunke and the enthalpy increment, HT+ H298 2 + ð2ndÞ are determined by the and Konings [4]. Both Fa and Dsub H298 least squares method. The Fa will be zero for the ideal case where the measured pressures and the free energy functions are completely accurate. + ð2ndÞ and dD + Both of the errors dDsub H298 sub H298 ð3rdÞ are estimated by the law of error propagation from the following equations:
+ dDsub H298 ð2ndÞ2 ¼ dT 2 Rln pCsBO2 Fa þ gef ðCsBO2 ; gÞ gef ðCsBO2 ; sÞ
!
2
þ T 2 R2
dpCsBO2 pCsBO2
2
2
þ dFa þ dgef ðCsBO2 ; gÞ2
þ dgef ðCsBO2 ; sÞ2 ;
(9)
Table 3 Molecular constants of CsBO2.
R(B-O1) [pm] R(B-O2) [pm] R(Cs-O1) [pm] :Cs-O1-B [deg] IAIBIC [kg3m6] n (B-O1) [cm1] n (B-O2) [cm1] n (Cs-O1) [cm1] n (Cs O1B) [cm1] n (O1BO2) [cm1] n (out-of-plane) [cm1] a
Cordfunke and Konings [4]
Ezhov and Komarov [6]
diff. (%)
127 123 265 130 1.43 10134a 1945 1077 206 60 581 576
129.8 121.9 269 125 1.69 10134 1935 1045 233 57 632 588
2.2 0.9 1.5 3.8 18.2 0.5 3.0 13.1 5.0 8.8 2.1
The value of IAIBIC [g3cm6] is written as 1.40 10113 in their compilation.
K. Nakajima et al. / Journal of Nuclear Materials 491 (2017) 183e189
187
Table 5 Gibbs energy function of CsBO2(s) and CsBO2(g) and the values of Eqs. (7). and (8).b T (K)
gef(CsBO2,s)a (J/mol/K)
gef(CsBO2,g)C (J/mol/K)
gef(CsBO2,g)E (J/mol/K)
Eq. (7)C (J/mol/K)
Eq. (7)E (J/mol/K)
Eq. (8)C (J/mol)
Eq. (8)E (J/mol)
914.7 912.9 914.5 913.3 913.3 914.7 912.1 915.0 884.0 882.6 883.1 884.0 882.0 884.3 882.2 883.4 852.7 854.3 853.4 853.7 854.4 852.9 855.0 852.2 822.6 825.1 822.7 825.1 822.6 824.6 822.7 792.9 794.6 792.5 794.6 792.4 794.3 792.2
141.959 141.836 141.945 141.863 141.863 141.959 141.781 141.979 139.877 139.780 139.815 139.877 139.739 139.897 139.753 139.835 137.741 137.852 137.790 137.811 137.859 137.755 137.900 137.707 135.686 135.852 135.693 135.852 135.686 135.818 135.693 133.643 133.761 133.615 133.761 133.608 133.740 133.594
345.205 345.111 345.194 345.132 345.132 345.205 345.070 345.220 343.615 343.542 343.568 343.615 343.510 343.631 343.521 343.584 341.974 342.059 342.011 342.027 342.065 341.985 342.097 341.947 340.383 340.512 340.388 340.512 340.383 340.485 340.388 338.791 338.884 338.769 338.884 338.764 338.867 338.753
344.860 344.766 344.849 344.787 344.787 344.860 344.725 344.875 343.275 343.201 343.227 343.275 343.170 343.290 343.180 343.243 341.638 341.723 341.675 341.691 341.728 341.648 341.760 341.611 340.051 340.180 340.057 340.180 340.051 340.153 340.057 338.464 338.556 338.443 338.556 338.437 338.540 338.426
307.3 307.2 307.4 307.3 307.1 307.3 307.3 307.5 316.6 316.6 316.7 316.6 316.9 316.9 316.8 316.9 328.4 328.1 328.2 328.3 328.0 328.2 328.1 328.4 339.7 339.5 339.9 339.8 340.0 340.0 339.8 351.6 353.0 352.5 351.9 353.5 354.3 353.5
307.0 306.9 307.0 307.0 306.8 307.0 306.9 307.1 316.3 316.2 316.4 316.3 316.5 316.6 316.5 316.5 328.1 327.7 327.9 327.9 327.6 327.8 327.8 328.0 339.4 339.2 339.5 339.4 339.7 339.7 339.4 351.3 352.7 352.2 351.6 353.2 354.0 353.2
281100 280500 281100 280700 280500 281100 280300 281300 279900 279400 279700 279900 279500 280200 279500 279900 280000 280300 280100 280200 280200 279900 280500 279800 279500 280100 279600 280300 279700 280300 279500 278800 280500 279400 279700 280100 281400 280100
280800 280200 280800 280300 280200 280800 280000 281000 279600 279100 279400 279600 279200 279900 279200 279600 279800 280000 279800 280000 279900 279600 280200 279500 279200 279900 279300 280000 279500 280100 279300 278600 280300 279100 279400 279900 281200 279800
a + ðCsBO ; sÞ calculated by using the heat capacity, Cp(CsBO , s), recommended by Cordfunke and The gef(CsBO2,s) is evaluated from the S+298 ðCsBO2 ; sÞ and the HT+ H298 2 2 Konings [4]. b Suffixes of C and E mean the quantities based on the molecular constants given by Cordfunke and Konings [4] and Ezhov and Komarov [6], respectively.
+ dDsub H298 ð3rdÞ2
¼ dT
2
! 2 2 2 2 2 dpCsBO2 2 þ dgef ðCsBO2 ; gÞ þ dgef ðCsBO2 ; sÞ : Rln pCsBO2 þ gef ðCsBO2 ; gÞ gef ðCsBO2 ; sÞ þ T R pCsBO2 (10)
The error in gef(CsBO2,s), d gef(CsBO2,s), is assumed to be 1% because the thermodynamic data of CsBO2(s) is judged as being of good quality [4]. The error in gef(CsBO2,g), d gef(CsBO2,g), is also assumed to be 1%. This is because the values of gef(CsBO2,g)C and gef(CsBO2,g)E agree well each other as shown in Tables 4 and 5 The dFa is assumed to be the same as the standard deviation obtained by using the data obtained using Eq. (7). indicated in Table 5. The + ð2ndÞ , standard enthalpies of sublimation of CsBO2, Dsub H298 C + + + Dsub H298 ð3rdÞC , Dsub H298 ð2ndÞE and Dsub H298 ð3rdÞE evaluated in this way are 276.0 ± 4.4 kJ/mol, 280.1 ± 4.0 kJ/mol, 276.1 ± 4.4 kJ/ mol, and 279.8 ± 4.0 kJ/mol, respectively. These values indicate that the enthalpies based on the molecular constants given by Ezhov and Komarov [6] are preferable. Namely, the difference between + ð2ndÞ and D + Dsub H298 sub H298 ð3rdÞE is smaller than that between E + ð2ndÞ and D + + Dsub H298 H sub 298 ð3rdÞC , and Dsub H298 ð2ndÞE agrees C
+ ð3rdÞ within the error limits. In addition, Fa and Fa with Dsub H298 C E E are calculated to be 4.84 ± 5.90 and 4.38 ± 5.90 by the least squares method using the data obtained from Eq. (7). in Table 5, and FaE is found to be closer to zero than FaC, although both of FaC and FaE can become zero within the error limits. Furthermore, the temperature + ð3rdÞ is found to be weaker than that of dependence of Dsub H298 E + ð3rdÞ , since the slopes of the linear least squares fits to Dsub H298 C the data obtained using Eq. (8).C and Eq. (8).E in Table 5, with respect to temperature, are calculated to be 5.46 103 and 4.80 103, respectively. Consequently, the thermodynamic quantities derived from the molecular constants of Ezhov and Komarov [6] are considered to be preferable. To confirm the accuracy of the thermodynamic quantities obtained from the reported vapor pressures of CsBO2 [5,16], both + ð2ndÞ and D + Dsub H298 sub H298 ð3rdÞ are determined from their vapor pressures by using the existing thermodynamic quantities [4] of
188
K. Nakajima et al. / Journal of Nuclear Materials 491 (2017) 183e189
Table 6 + ðCsBO Þ. Comparison of Dsub H298 2 authors
+ ð2ndÞ (kJ/mol) Dsub H298
+ ð3rdÞ (kJ/mol) Dsub H298
diff. (%)
Biswas and Mukerji [16] for CsBO2(l)a Cordfunke et al. [5] for CsBO2(l)a Cordfunke et al. [5] for CsBO2(s)b This work for CsBO2(s)b
237.5 286.4 289.1 276.1
284.2 270.1 271.9 279.8
16.4 6.0 6.3 1.3
a The values evaluated from vapor pressures over liquid CsBO2 using enthalpy of fusion of CsBO2 and both the heat capacities of solid CsBO2 and liquid CsBO2 recommended by Cordfunke and Konings [4]. b The values evaluated from vapor pressures over solid CsBO2.
gef(CsBO2,s) and gef(CsBO2,l), and the gef(CsBO2,g)E calculated in this study. These results are summarized in Table 6. + ð2ndÞ As shown in this table, the difference between Dsub H298 + and Dsub H298 ð3rdÞ in this work is the smallest and our vapor pressures are believed to be more accurate than those reported in the past. Furthermore, the second and third-law standard en+ ðCsBO ; gÞ thalpies of formation of CsBO2(g), Df H298 2 2nd and + + ð2ndÞ Df H298 ðCsBO2 ; gÞ3rd , derived from Dsub H298 and + ð3rdÞ by using the standard enthalpy of formation of Dsub H298 + ðCsBO ; sÞ, CsBO2(s), Df H298 [4] are calculated to 2 be 700.7 ± 10.7 kJ/mol and 697.0 ± 10.6 kJ/mol where the error + ðCsBO ; sÞ is assumed to be 1%. This is found to agree well in Df H298 2 + ðCsBO ; gÞ, 696.8 kJ/mol. Therefore, the with the existing Df H298 2 existing thermodynamic data are also considered to be reliable, although they were judged as poor quality. Actually, in the experiments [18] referred to in paper [3], the reaction products were not identified as CsBO2(g) and only the deposition profiles of Cs and B were examined after the chemical reaction. This report [18] merely confirms that the obtained results were indicative of a vapor-phase reaction with the formation of cesium borate. Indeed, the Gibbs energy change of the following reaction can become negative:
CsIðgÞ þ H3 BO3 ðgÞ/CsBO2 ðs; lÞ þ HIðgÞ þ H2 OðgÞ:
(11)
It is, therefore, necessary to establish whether the reaction expressed by an equation such as Eq. (11). actually occurs under the same experimental conditions [18].
However, there is no data on the ionization cross-section of Csþ when a CsBO2 molecule fragments into a Csþ ion. So, the modified integral method, which does not require such an ionization crosssection, is applied in this study. The ion current, I, originating from vapor molecules effusing through the orifice, is proportional to the flux, u, and the dwell time of the effusing vapor molecules in the ion source of the mass spectrometer. Since the dwell time is inversely proportional to the velocity of the molecules passing through the ion source of the mass spectrometer, and this velocity, v, is given by the MaxwellBoltzmann velocity distribution, the following relation between the time dependent I(t) and u(t) can hold:
Ij ðtÞ ¼ k
Appendex A Ionization cross-sections are generally required when measured ion currents are converted into absolute vapor pressures [e.g., 19].
(A.1)
pMj
where j is a specific isotopic vapor species, k the factor for instrument geometry, which is independent of vapor species, s the ionization cross section, s the sensitivity of the mass spectrometer, which is dependent on vapor species. On the other hand, according to the kinetic theory of gases, u(t) can be expressed by the following equation:
gj pðtÞNA uj ðtÞ ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi : 2pMj RTðtÞ
(A.2)
where NA is the Avogadro constant. From Eqs (A.1) and (A.2), the following relation can be obtained:
4. Conclusion An almost single-phase CsBO2 sample was prepared and its KEMS measurement was performed in the temperature range of 792e915 K to determine the equilibrium vapor pressures of CsBO2. The Gibbs energy function of CsBO2(g) is not significantly influenced by the difference between the existing and newly obtained molecular constants. However, the thermodynamic quantities derived from the newly obtained molecular constants are found to be preferable. The standard enthalpies of formation of CsBO2(g), determined by the second and third-law methods, are 700.7 ± 10.7 kJ/mol and 697.0 ± 10.6 kJ/mol, respectively. Good agreement within the experimental errors, which suggests reliable thermodynamic data, can be obtained. Furthermore, the existing thermodynamic data, such as the Gibbs energy function and the standard enthalpy of formation of CsBO2(g), almost agree with those evaluated in this study and are also found to be reliable, although the accuracy of the existing data was judged as poor quality.
sj sj ksj sj u ðtÞ ¼ qffiffiffiffiffiffiffiffiffiffiffiuj ðtÞ 8RTðtÞ vj ðtÞ j
pðtÞ ¼
4R I ðtÞTðtÞ: ksj sj NA gj j
(A.3)
When vapor molecules in the gas phase can be regarded as only one vapor species, while allowing any isotopic vapor species, such as the Cs10BO2 and Cs11BO2 molecules in this study, the weight loss, DW, caused by the vapor molecules effusing through the orifice can be related to the u(t) by the following equation:
DW ¼
X i
Ztend ui ðtÞ=NA dt
Mi aL
(A.4)
0
where i is an isotopic vapor species. By substituting Eq. (A.1) into this equation, the following equation can hold:
pffiffiffiffiffiffiffiffiffiffiffiffi tend X aL 8RMi Z pffiffiffiffiffiffiffiffiffi pffiffiffiffi DW ¼ Ii ðtÞ TðtÞdt: p s N ks i i A i
(A.5)
0
When the ionization cross section is assumed to be the same among the isotopes, the following relation can be obtained from Eq. (A.3):
K. Nakajima et al. / Journal of Nuclear Materials 491 (2017) 183e189
Ii ðtÞ ¼
si gi I ðtÞ: sj gj j
(A.6)
By using this relation, Eq. (A.5) can be transformed to the following equation:
pffiffiffiffiffiffi Ztend pffiffiffiffiffiffiffiffiffi X pffiffiffiffiffiffi aL 8R DW ¼ pffiffiffiffi Ij ðtÞ TðtÞdt gi Mi : pksj sj gj NA i
(A.7)
0
Thus, the following equation used in the modified integral method can be obtained from Eqs (A.3) and (A.7) by deleting the unknown factor, ksjsj:
pffiffiffiffiffiffiffiffiffiffiffi 2p RDWIj ðt ÞT ðt Þ : pðt Þ ¼ Z tend pffiffiffiffiffiffiffiffiffiffi X pffiffiffiffiffiffi Ij ðt 0 Þ Tðt 0 Þdt 0 gi Mi aL 0
(A.8)
i
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