- Email: [email protected]
Molten rare earth tri-halides: Prediction of surface tension
Journal of Molecular Liquids 200 (2014) 229–231
Contents lists available at ScienceDirect
Journal of Molecular Liquids journal homepage: www.elsevier.com/locate/molliq
Molten rare earth tri-halides: Prediction of surface tension Fathi Aqra Department of Chemistry, Faculty of Science and Technology, Hebron University, P.O. Box 40, Hebron, West Bank, Palestine
a r t i c l e
i n f o
Article history: Received 18 April 2014 Received in revised form 12 October 2014 Accepted 17 October 2014 Available online 18 October 2014 Keywords: Surface tension Lanthanide trihalides
a b s t r a c t Despite the fact that the manuscript targets surface tension as a thermodynamic parameter, the focus of the work is on the examination of a model targeting material properties. The surface tension of about fifty lanthanide(III) trihalide salts, at their corresponding melting points, was determined by a model developed by the author. The equation requires enthalpies of sublimation, molar volume and internuclear distance, with the data available in the literature. The developed idea leads to some worthwhile results. The calculated surface tension values are quite small, for all the salts under study, which lie in the range 55–250 mJ m−2. The presented results are validated by comparison with some of the models that are widely used in the literature, and they agree well with the existing experimental data. © 2014 Elsevier B.V. All rights reserved.
1. Introduction Lanthanide compounds are extensively employed in high temperature technologies, and thus, the thermophysical properties of rare earth halides are of great importance. Investigating such properties is an active modern research, which helps in planning, conducting, and controlling technological processes [1]. The surface tension is a technologically important parameter for industrial applications, but the corresponding data of the molten rare earth trihalides are very limited because the experimental measurement of their surface tension is difficult due to their strong chemical activity. Therefore, theoretical models can compensate for the lack of experimental data of such molten salts. It was considered worthwhile to initiate the current study in a view to calculate the surface tension of the molten rare-earth trihalides by a semi-empirical approach. This paper describes a unique, reasonable and appropriate theoretical method which is capable to predict the surface tension of molten lanthanide trihalides at the melting point. 2. Theory In a previous report [2], an empirical formula was proposed for calculating the surface tension of pure molten alkali metal halides at the melting point. In this formula, the surface tension is proportional to sublimation energy, internuclear distance and molar volume as shown in Eq. (1):
γ ¼ Po
Es D : V
E-mail address: [email protected].
http://dx.doi.org/10.1016/j.molliq.2014.10.020 0167-7322/© 2014 Elsevier B.V. All rights reserved.
ð1Þ
The various parameters are described as follows: γ is the surface tension (J m− 2), V is the molar volume of liquid at the melting point (cm3 mol−1), D is the internuclear distance (m), Po is a fitting parameter constant which is equal to 0.04821 for alkali halides and Es is the heat of sublimation (J mol−1). Eq. (1) gave good values for the surface tension of alkali halides. In continuation of our recent work on the surface tension of molten salts [2–4], Eq. (1) is now applied to predict the surface tension of molten rare earth salts at melting temperatures. The enthalpies of sublimation values of lanthanide trihalides were collected from literature [5–33] while the cationic–anionic internuclear distances were taken from Shannon's work [34]. Eq. (1) is the working equation and it is valid to calculate the surface tension of molten salts at the melting point. Eq. (1) requires a fitting parameter (Po) which is a dimensionless independent temperature constant parameter (a positive fractional number). It was possible to generate numerical data which gives up to 3% variation of available experimental results. The most interesting aspect of the numerical coefficient (0.07 for lanthanide tri-halides, which is said to be a semi-empirical coefficient) is that it is the same for all of the molten rare earth halide salts. In order to give to a reader a visual feeling on how well the correlation (Eq. (1)) works, a figure is drawn as calculated versus experimental data with a dashed 1:1 line. Therefore, Fig. 1 shows a correlation between the calculated surface tension and the experimentally measured data. A straight line is obtained with a good correlation indicating that there is a strong connection between the surface tension and the terms in Eq. (1), and thus, confirming the validity of the proposed model. 3. Discussion The objective of this work is the calculation of the surface tension of lanthanide trihalides, at the melting points. Eq. (1) was checked against
230
F. Aqra / Journal of Molecular Liquids 200 (2014) 229–231 Table 1 Calculated and reported surface tension of lanthanide trihalides at the melting point, and parameters needed for calculations.
104 100
Tm (K)
D γ (Cal.) γ (Rep.) Es Density at Molar (kJ mol−1) (pm) (mJ m−2) (mJ m−2) mass melting (g mol−1) point (g cm−3)
LaF3 CeF3 NdF3 SmF3 DyF3 HoF3 ErF3 TmF3 YbF3 PuF3 LaCl3 CeCl3 PrCl3 NdCl3 SmCl3 GdCl3 TbCl3 DyCl3 HoCl3 ErCl3 TmCl3 YbCl3 LuCl3 LaBr3 CeBr3 PrBr3 NdBr3 SmBr3 GdBr3 TbBr3 DyBr3 HoBr3 ErBr3 TmBr3 YbBr3 LuBr3 LaI3 CeI3 PrI3 NdI3 SmI3 GdI3 TbI3 DyI3 HoI3 ErI3 TmI3 YbI3 LuI3
1766 1691 1647 1579 1633 1416 1623 1431 1325 1669 1131 1090 1059 1031 955 882 831 920 993 1049 1097 976 1178 1056 995 964 957 973 1043 1101 1154 1192 1196 1225 950 1298 1045 1023 1010 1048 1123 1199 1230 1228 1267 1290 1288 1272 1323
5.9 6.16 6.5 6.6 5.948 7.64 7.82 8.0 8.2 9.3 3.84 3.97 4.02 4.13 4.46 4.52 4.35 3.67 3.7 4.1 3.98 4.06 3.98 5.06 5.1 5.1 5.3 5.4 4.6 4.67 4.8 4.85 5.25 5.1 5.0 5.1 5.63 5.0 5.8 5.85 5.9 5.22 5.2 5.0 5.54 5.5 5.2 5.3 5.6
2
cal. (mJ/m )
96 92 88 84 80 76 80
85
90
95
100 2
105
110
exp. (mJ/m ) Fig. 1. Calculated melting point surface tensions versus experimentally measured data, with a dashed 1:1 line, of lanthanide trihalides.
all the rare earth trihalides, at their melting points, using Po = 0.07. The calculated values are illustrated in Table 1. The results are in good agreement with the existing experimental data [35–38]. It is observed that the calculated results agree well with the experimental data, exhibiting a maximum variation of about 3%. Generally, concerning the modeling, it is a practice that if a new model is proposed, it is necessary to validate the new theoretical results by comparison to corresponding experimental data (own or from the literature). At least, one can compare the new theoretical property results using some of well established and widely used models to predict the values of the same property. However, the surface tensions of many molten salts have been compiled by Janz and coworkers [39,40], and the data have been supplemented subsequently by others [41,42]. For a limited set of salts, various correlations of the surface tension with some properties of molten salts have been proposed [43–52]. Therefore, several authors have reported theoretical studies, confined to molten salts, leading to the dependence of the surface tension of molten salts on independent quantities characterizing these salts, such as Reiss et al. [43], Harada et al. [49], Yajima et al. [50] and Kaptay et al. [51,52]. Marcus [37], in his model, correlated the surface tension with the cohesive energy densities of the salts. He has shown the surface tensions of highly ionic molten salts of different types (1:1, 1:2 and 2:1). Unfortunately, a group of molten salts that is excluded from his correlation is the 1:3 molten lanthanide halides. They have quite small surface tension values, in view of their moderately large cohesive energy densities. The reason for this exclusion is not immediately apparent. These salts may not be as highly ionic as may have been thought. The present model, that correlates the surface tension of molten salts with the enthalpy of sublimation, may be considered as the only established correlation that considers the surface tension of all types of salts such as alkali, alkaline earth, transition as well as lanthanide halides. The model (Eq. (1)) requires the knowledge of 3 parameters. However, the model with a smaller number of parameters is a better one. Therefore, D/V could be replaced by V2/3. This was illustrated in a previous paper [53] which provides similar results. Hence, it could be used as an alternative as shown in Eq. (2): γ ¼ Fs
Salt
Es V 2=3
where Fs (0.53 ∗ 10−9 mol1/3) is a semi-empirical fitting parameter.
195.9 197.111 201.237 207.36 219.495 221.93 224.28 225.93 230.04 301.06 245.26 246.48 247.24 250.598 256.76 263.61 265.28 268.86 271.29 273.62 275.29 279.4 281.32 378.62 379.83 380.62 383.95 390.07 396.96 398.64 402.21 404.64 406.97 408.65 412.75 414.68 519.62 520.83 521.62 524.95 531.07 537.96 539.64 543.21 545.64 547.97 549.64 551.77 555.68
440 461 440 437 445 442 448 448 456 413.8 334 335 330 317 306 311 296 305 296 308 296 288 295 308 305 300 298 292 292 288 289 290 293 285 285 285 285 295 278 329 276 295 284 276 303 282 277 302 288
219 236 230 223 189 238 243 245 250 208 104 107 105 102 103 103 93 79 77 87 81 79 78 86 85 83 85 83 69 68 69 70 75 71 68 69 70 64 69 82 68 63 60 55 67 61 57 62 62
– – – – – – – – – – 105 – 106 – 104 – – – – 90 – 81 – – – – – – – – – – – – – – – – – – – – – – – – – – –
4. Conclusion There is always an interest in reliable data on the surface tension of molten rare earth trihalides. At present, the knowledge of these data is not existing. Surface tension is an important thermophysical property, but its measurement and calculation are rather difficult. In this article, an equation was adapted for calculating the surface tension of molten rare earth salts at their corresponding melting point. The sublimation enthalpy is the main model input data. A comparison is done with the existing experimental data and with some of the models that are widely used in the literature. References
ð2Þ
236 234 231 229 224 223 222 221 220 233 284 282 280 279 277 275 273 272 271 270 269 268 267 299 297 295 294 292 290 288 287 286 285 284 283 282 323 321 319 318 316 314 312 311 310 309 308 307 306
[1] [2] [3] [4]
A. Nagashima, Int. J. Thermophys. 11 (1990) 417. F. Aqra, Phys. B Condens. Matter 441 (2014) 54. F. Aqra, Metall. Mater. Trans. A 45 (2014) 2347. F. Aqra, J. Nucl. Mater. 448 (2014) 230.
F. Aqra / Journal of Molecular Liquids 200 (2014) 229–231 [5] R.A. Kent, K.F. Zmbov, A.S. Kana'an, G. Besenbruch, J.D. McDonald, J.L. Margrave, J. Inorg. Nucl. Chem. 28 (1966) 1419. [6] R.D. Wesley, C.W. DeKock, J. Chem. Phys. 55 (1971) 3866. [7] R.W. Mar, A.W. Searcy, J. Phys. Chem. 71 (1967) 888. [8] R.M. Biefeld, H.A. Eick, J. Chem. Thermodyn. 11 (1979) 639. [9] G. Besenbruch, T.V. Charlu, K.F. Zmbov, J.L. Margrave, J. Less Common Met. 12 (1967) 375. [10] R.M. Biefeld, H.A. Eick, J. Less Common Met. 45 (1976) 117. [11] T. Petzel, O. Greis, J. Less Common Met. 46 (1976) 197. [12] B. Brunetti, A.R. Villani, V. Piacente, P. Scardala, J. Chem. Eng. Data 45 (2000) 231. [13] J. Kapała, S. Roszak, S.N. Cesaro, M. Miller, J. Alloys Compd. 345 (2002) 90. [14] A.M. Pogrebnoi, L.S. Kudin, V.B. Motalov, V.F. Goryushkin, Rapid Commun. Mass Spectrom. 15 (2001) 1662. [15] H.B. Skinner, A.W. Searcy, J. Phys. Chem. 72 (1968) 3375. [16] A.R. Villani, P. Scardala, B. Brunetti, V. Piacente, J. Chem. Eng. Data 47 (2002) 428. [17] P. Scardala, A.R. Villani, B. Brunetti, V. Piacente, Mater. Chem. Phys. 78 (2003) 637. [18] C.E. Myers, M.H. Hannay, J. Less Common Met. 70 (1980) 15. [19] V. Piacente, P. Scardala, B. Brunetti, J. Chem. Eng. Data 48 (2003) 637. [20] B. Brunetti, P. Vassallo, V. Piacente, P. Scardala, J. Chem. Eng. Data 44 (1999) 509. [21] V. Piacente, B. Brunetti, P. Scardala, A.R. Villani, J. Chem. Eng. Data 47 (2002) 388. [22] B. Brunetti, V. Piacente, P. Scardala, J. Chem. Eng. Data 48 (2003) 946. [23] B. Brunetti, V. Piacente, P. Scardala, J. Chem. Eng. Data 49 (2004) 832. [24] B. Brunetti, V. Piacente, Paolo Scardala, J. Chem. Eng. Data 50 (2005) 1801. [25] L.S. Kudin, M.F. Butman, V.B. Motalov, A.E. Grishin, A.S. Kryuchkov, G.A. Bergman, High Temp. 46 (2008) 350. [26] S.K. Gupta, J. Chem. Eng. Data 21 (1976) 114. [27] C. Hirayama, F.E. Camp, J. Chem. Eng. Data 17 (1972) 415. [28] C. Hirayama, P.M. Castle, R.W. Liebermann, R.J. Zollweg, F.E. Camp, Inorg. Chem. 13 (1974) 2804.
[29] [30] [31] [32] [33] [34] [35] [36] [37] [38] [39] [40] [41] [42] [43] [44] [45] [46] [47] [48] [49] [50] [51] [52] [53]
231
B. Brunetti, V. Piacente, P. Scardala, J. Chem. Eng. Data 50 (2005) 1646. K. Hilpert, M. Miller, F. Ramondo, Thermochim. Acta 417 (2004) 163. P.D. Kleinschmidt, J. Nucl. Mater. 167 (1989) 131. A.R. Villani, B. Brunetti, V. Piacente, J. Chem. Eng. Data 45 (2000) 1167. A.R. Villani, B. Brunetti, V. Piacente, J. Chem. Eng. Data 45 (2000) 823. R.D. Shannon, Acta Crystallogr. A32 (1976) 751. T. Ueda, T. Tanaka, S. Hara, Z. Metallkd. 90 (1999) 342. K. Igarashi, Y. Iwadate, J. Morinaga, Z. Naturforsch. A 42a (1987) 853. Y. Marcus, Thermochim. Acta 571 (2013) 77. V.I. Shishalov, A.V. Kovalevskii, Russ. J. Phys. Chem. 85 (2011) 108. G.J. Janz, Molten Salts Handbook, Academic Press, New York, 1967. G.J. Janz, G.R. Lakshminarayanan, R.P.T. Tomkins, J. Wong, National Standard Reference Data System, NSRDS-NBS, 1969. 28. G.J. Janz, R.P.T. Tomkins, J. Phys. Chem. Ref. Data 9 (1980) 831. C.S. Dutcher, A.S. Wexledr, S.L. Clegg, J. Phys. Chem. A 114 (2010) 12216. H. Reiss, S.W. Mayer, J.L. Katz, J. Chem. Phys. 35 (1961) 820. H. Blum, The Chemistry of Molten Salts, Benjamin, New York, 1967. S.J. Yosim, B.B. Owens, J. Chem. Phys. 41 (1964) 2032. S. Cantor, D.P. McDermott, L.O. Gilpatrick, J. Chem. Phys. 52 (1970) 4600. Y. Marcus, Thermochim. Acta 495 (2009) 81. Y. Marcus, J. Chem. Thermodyn. 42 (2010) 60. M. Harada, M. Tanigaki, Y. Tada, Ind. Eng. Chem. Fundam. 22 (1983) 116. K. Yajima, H. Moriyama, J. Oishi, J. Phys. Chem. 88 (1984) 4390. G. Kaptay, in: Chen Nianyi, Qiao Zhiyu (Eds.), Proc. 6th Int. Symp. on Molten Salt Chemistry and Technology, Shanghai University Press, 2001, pp. 182–185. P. Baumli, G. Kaptay, Mater. Sci. Eng. A 495 (2008) 192. F. Aqra, J. Non-Cryst. Solids 402 (2014) 49.
Contents lists available at ScienceDirect
Journal of Molecular Liquids journal homepage: www.elsevier.com/locate/molliq
Molten rare earth tri-halides: Prediction of surface tension Fathi Aqra Department of Chemistry, Faculty of Science and Technology, Hebron University, P.O. Box 40, Hebron, West Bank, Palestine
a r t i c l e
i n f o
Article history: Received 18 April 2014 Received in revised form 12 October 2014 Accepted 17 October 2014 Available online 18 October 2014 Keywords: Surface tension Lanthanide trihalides
a b s t r a c t Despite the fact that the manuscript targets surface tension as a thermodynamic parameter, the focus of the work is on the examination of a model targeting material properties. The surface tension of about fifty lanthanide(III) trihalide salts, at their corresponding melting points, was determined by a model developed by the author. The equation requires enthalpies of sublimation, molar volume and internuclear distance, with the data available in the literature. The developed idea leads to some worthwhile results. The calculated surface tension values are quite small, for all the salts under study, which lie in the range 55–250 mJ m−2. The presented results are validated by comparison with some of the models that are widely used in the literature, and they agree well with the existing experimental data. © 2014 Elsevier B.V. All rights reserved.
1. Introduction Lanthanide compounds are extensively employed in high temperature technologies, and thus, the thermophysical properties of rare earth halides are of great importance. Investigating such properties is an active modern research, which helps in planning, conducting, and controlling technological processes [1]. The surface tension is a technologically important parameter for industrial applications, but the corresponding data of the molten rare earth trihalides are very limited because the experimental measurement of their surface tension is difficult due to their strong chemical activity. Therefore, theoretical models can compensate for the lack of experimental data of such molten salts. It was considered worthwhile to initiate the current study in a view to calculate the surface tension of the molten rare-earth trihalides by a semi-empirical approach. This paper describes a unique, reasonable and appropriate theoretical method which is capable to predict the surface tension of molten lanthanide trihalides at the melting point. 2. Theory In a previous report [2], an empirical formula was proposed for calculating the surface tension of pure molten alkali metal halides at the melting point. In this formula, the surface tension is proportional to sublimation energy, internuclear distance and molar volume as shown in Eq. (1):
γ ¼ Po
Es D : V
E-mail address: [email protected].
http://dx.doi.org/10.1016/j.molliq.2014.10.020 0167-7322/© 2014 Elsevier B.V. All rights reserved.
ð1Þ
The various parameters are described as follows: γ is the surface tension (J m− 2), V is the molar volume of liquid at the melting point (cm3 mol−1), D is the internuclear distance (m), Po is a fitting parameter constant which is equal to 0.04821 for alkali halides and Es is the heat of sublimation (J mol−1). Eq. (1) gave good values for the surface tension of alkali halides. In continuation of our recent work on the surface tension of molten salts [2–4], Eq. (1) is now applied to predict the surface tension of molten rare earth salts at melting temperatures. The enthalpies of sublimation values of lanthanide trihalides were collected from literature [5–33] while the cationic–anionic internuclear distances were taken from Shannon's work [34]. Eq. (1) is the working equation and it is valid to calculate the surface tension of molten salts at the melting point. Eq. (1) requires a fitting parameter (Po) which is a dimensionless independent temperature constant parameter (a positive fractional number). It was possible to generate numerical data which gives up to 3% variation of available experimental results. The most interesting aspect of the numerical coefficient (0.07 for lanthanide tri-halides, which is said to be a semi-empirical coefficient) is that it is the same for all of the molten rare earth halide salts. In order to give to a reader a visual feeling on how well the correlation (Eq. (1)) works, a figure is drawn as calculated versus experimental data with a dashed 1:1 line. Therefore, Fig. 1 shows a correlation between the calculated surface tension and the experimentally measured data. A straight line is obtained with a good correlation indicating that there is a strong connection between the surface tension and the terms in Eq. (1), and thus, confirming the validity of the proposed model. 3. Discussion The objective of this work is the calculation of the surface tension of lanthanide trihalides, at the melting points. Eq. (1) was checked against
230
F. Aqra / Journal of Molecular Liquids 200 (2014) 229–231 Table 1 Calculated and reported surface tension of lanthanide trihalides at the melting point, and parameters needed for calculations.
104 100
Tm (K)
D γ (Cal.) γ (Rep.) Es Density at Molar (kJ mol−1) (pm) (mJ m−2) (mJ m−2) mass melting (g mol−1) point (g cm−3)
LaF3 CeF3 NdF3 SmF3 DyF3 HoF3 ErF3 TmF3 YbF3 PuF3 LaCl3 CeCl3 PrCl3 NdCl3 SmCl3 GdCl3 TbCl3 DyCl3 HoCl3 ErCl3 TmCl3 YbCl3 LuCl3 LaBr3 CeBr3 PrBr3 NdBr3 SmBr3 GdBr3 TbBr3 DyBr3 HoBr3 ErBr3 TmBr3 YbBr3 LuBr3 LaI3 CeI3 PrI3 NdI3 SmI3 GdI3 TbI3 DyI3 HoI3 ErI3 TmI3 YbI3 LuI3
1766 1691 1647 1579 1633 1416 1623 1431 1325 1669 1131 1090 1059 1031 955 882 831 920 993 1049 1097 976 1178 1056 995 964 957 973 1043 1101 1154 1192 1196 1225 950 1298 1045 1023 1010 1048 1123 1199 1230 1228 1267 1290 1288 1272 1323
5.9 6.16 6.5 6.6 5.948 7.64 7.82 8.0 8.2 9.3 3.84 3.97 4.02 4.13 4.46 4.52 4.35 3.67 3.7 4.1 3.98 4.06 3.98 5.06 5.1 5.1 5.3 5.4 4.6 4.67 4.8 4.85 5.25 5.1 5.0 5.1 5.63 5.0 5.8 5.85 5.9 5.22 5.2 5.0 5.54 5.5 5.2 5.3 5.6
2
cal. (mJ/m )
96 92 88 84 80 76 80
85
90
95
100 2
105
110
exp. (mJ/m ) Fig. 1. Calculated melting point surface tensions versus experimentally measured data, with a dashed 1:1 line, of lanthanide trihalides.
all the rare earth trihalides, at their melting points, using Po = 0.07. The calculated values are illustrated in Table 1. The results are in good agreement with the existing experimental data [35–38]. It is observed that the calculated results agree well with the experimental data, exhibiting a maximum variation of about 3%. Generally, concerning the modeling, it is a practice that if a new model is proposed, it is necessary to validate the new theoretical results by comparison to corresponding experimental data (own or from the literature). At least, one can compare the new theoretical property results using some of well established and widely used models to predict the values of the same property. However, the surface tensions of many molten salts have been compiled by Janz and coworkers [39,40], and the data have been supplemented subsequently by others [41,42]. For a limited set of salts, various correlations of the surface tension with some properties of molten salts have been proposed [43–52]. Therefore, several authors have reported theoretical studies, confined to molten salts, leading to the dependence of the surface tension of molten salts on independent quantities characterizing these salts, such as Reiss et al. [43], Harada et al. [49], Yajima et al. [50] and Kaptay et al. [51,52]. Marcus [37], in his model, correlated the surface tension with the cohesive energy densities of the salts. He has shown the surface tensions of highly ionic molten salts of different types (1:1, 1:2 and 2:1). Unfortunately, a group of molten salts that is excluded from his correlation is the 1:3 molten lanthanide halides. They have quite small surface tension values, in view of their moderately large cohesive energy densities. The reason for this exclusion is not immediately apparent. These salts may not be as highly ionic as may have been thought. The present model, that correlates the surface tension of molten salts with the enthalpy of sublimation, may be considered as the only established correlation that considers the surface tension of all types of salts such as alkali, alkaline earth, transition as well as lanthanide halides. The model (Eq. (1)) requires the knowledge of 3 parameters. However, the model with a smaller number of parameters is a better one. Therefore, D/V could be replaced by V2/3. This was illustrated in a previous paper [53] which provides similar results. Hence, it could be used as an alternative as shown in Eq. (2): γ ¼ Fs
Salt
Es V 2=3
where Fs (0.53 ∗ 10−9 mol1/3) is a semi-empirical fitting parameter.
195.9 197.111 201.237 207.36 219.495 221.93 224.28 225.93 230.04 301.06 245.26 246.48 247.24 250.598 256.76 263.61 265.28 268.86 271.29 273.62 275.29 279.4 281.32 378.62 379.83 380.62 383.95 390.07 396.96 398.64 402.21 404.64 406.97 408.65 412.75 414.68 519.62 520.83 521.62 524.95 531.07 537.96 539.64 543.21 545.64 547.97 549.64 551.77 555.68
440 461 440 437 445 442 448 448 456 413.8 334 335 330 317 306 311 296 305 296 308 296 288 295 308 305 300 298 292 292 288 289 290 293 285 285 285 285 295 278 329 276 295 284 276 303 282 277 302 288
219 236 230 223 189 238 243 245 250 208 104 107 105 102 103 103 93 79 77 87 81 79 78 86 85 83 85 83 69 68 69 70 75 71 68 69 70 64 69 82 68 63 60 55 67 61 57 62 62
– – – – – – – – – – 105 – 106 – 104 – – – – 90 – 81 – – – – – – – – – – – – – – – – – – – – – – – – – – –
4. Conclusion There is always an interest in reliable data on the surface tension of molten rare earth trihalides. At present, the knowledge of these data is not existing. Surface tension is an important thermophysical property, but its measurement and calculation are rather difficult. In this article, an equation was adapted for calculating the surface tension of molten rare earth salts at their corresponding melting point. The sublimation enthalpy is the main model input data. A comparison is done with the existing experimental data and with some of the models that are widely used in the literature. References
ð2Þ
236 234 231 229 224 223 222 221 220 233 284 282 280 279 277 275 273 272 271 270 269 268 267 299 297 295 294 292 290 288 287 286 285 284 283 282 323 321 319 318 316 314 312 311 310 309 308 307 306
[1] [2] [3] [4]
A. Nagashima, Int. J. Thermophys. 11 (1990) 417. F. Aqra, Phys. B Condens. Matter 441 (2014) 54. F. Aqra, Metall. Mater. Trans. A 45 (2014) 2347. F. Aqra, J. Nucl. Mater. 448 (2014) 230.
F. Aqra / Journal of Molecular Liquids 200 (2014) 229–231 [5] R.A. Kent, K.F. Zmbov, A.S. Kana'an, G. Besenbruch, J.D. McDonald, J.L. Margrave, J. Inorg. Nucl. Chem. 28 (1966) 1419. [6] R.D. Wesley, C.W. DeKock, J. Chem. Phys. 55 (1971) 3866. [7] R.W. Mar, A.W. Searcy, J. Phys. Chem. 71 (1967) 888. [8] R.M. Biefeld, H.A. Eick, J. Chem. Thermodyn. 11 (1979) 639. [9] G. Besenbruch, T.V. Charlu, K.F. Zmbov, J.L. Margrave, J. Less Common Met. 12 (1967) 375. [10] R.M. Biefeld, H.A. Eick, J. Less Common Met. 45 (1976) 117. [11] T. Petzel, O. Greis, J. Less Common Met. 46 (1976) 197. [12] B. Brunetti, A.R. Villani, V. Piacente, P. Scardala, J. Chem. Eng. Data 45 (2000) 231. [13] J. Kapała, S. Roszak, S.N. Cesaro, M. Miller, J. Alloys Compd. 345 (2002) 90. [14] A.M. Pogrebnoi, L.S. Kudin, V.B. Motalov, V.F. Goryushkin, Rapid Commun. Mass Spectrom. 15 (2001) 1662. [15] H.B. Skinner, A.W. Searcy, J. Phys. Chem. 72 (1968) 3375. [16] A.R. Villani, P. Scardala, B. Brunetti, V. Piacente, J. Chem. Eng. Data 47 (2002) 428. [17] P. Scardala, A.R. Villani, B. Brunetti, V. Piacente, Mater. Chem. Phys. 78 (2003) 637. [18] C.E. Myers, M.H. Hannay, J. Less Common Met. 70 (1980) 15. [19] V. Piacente, P. Scardala, B. Brunetti, J. Chem. Eng. Data 48 (2003) 637. [20] B. Brunetti, P. Vassallo, V. Piacente, P. Scardala, J. Chem. Eng. Data 44 (1999) 509. [21] V. Piacente, B. Brunetti, P. Scardala, A.R. Villani, J. Chem. Eng. Data 47 (2002) 388. [22] B. Brunetti, V. Piacente, P. Scardala, J. Chem. Eng. Data 48 (2003) 946. [23] B. Brunetti, V. Piacente, P. Scardala, J. Chem. Eng. Data 49 (2004) 832. [24] B. Brunetti, V. Piacente, Paolo Scardala, J. Chem. Eng. Data 50 (2005) 1801. [25] L.S. Kudin, M.F. Butman, V.B. Motalov, A.E. Grishin, A.S. Kryuchkov, G.A. Bergman, High Temp. 46 (2008) 350. [26] S.K. Gupta, J. Chem. Eng. Data 21 (1976) 114. [27] C. Hirayama, F.E. Camp, J. Chem. Eng. Data 17 (1972) 415. [28] C. Hirayama, P.M. Castle, R.W. Liebermann, R.J. Zollweg, F.E. Camp, Inorg. Chem. 13 (1974) 2804.
[29] [30] [31] [32] [33] [34] [35] [36] [37] [38] [39] [40] [41] [42] [43] [44] [45] [46] [47] [48] [49] [50] [51] [52] [53]
231
B. Brunetti, V. Piacente, P. Scardala, J. Chem. Eng. Data 50 (2005) 1646. K. Hilpert, M. Miller, F. Ramondo, Thermochim. Acta 417 (2004) 163. P.D. Kleinschmidt, J. Nucl. Mater. 167 (1989) 131. A.R. Villani, B. Brunetti, V. Piacente, J. Chem. Eng. Data 45 (2000) 1167. A.R. Villani, B. Brunetti, V. Piacente, J. Chem. Eng. Data 45 (2000) 823. R.D. Shannon, Acta Crystallogr. A32 (1976) 751. T. Ueda, T. Tanaka, S. Hara, Z. Metallkd. 90 (1999) 342. K. Igarashi, Y. Iwadate, J. Morinaga, Z. Naturforsch. A 42a (1987) 853. Y. Marcus, Thermochim. Acta 571 (2013) 77. V.I. Shishalov, A.V. Kovalevskii, Russ. J. Phys. Chem. 85 (2011) 108. G.J. Janz, Molten Salts Handbook, Academic Press, New York, 1967. G.J. Janz, G.R. Lakshminarayanan, R.P.T. Tomkins, J. Wong, National Standard Reference Data System, NSRDS-NBS, 1969. 28. G.J. Janz, R.P.T. Tomkins, J. Phys. Chem. Ref. Data 9 (1980) 831. C.S. Dutcher, A.S. Wexledr, S.L. Clegg, J. Phys. Chem. A 114 (2010) 12216. H. Reiss, S.W. Mayer, J.L. Katz, J. Chem. Phys. 35 (1961) 820. H. Blum, The Chemistry of Molten Salts, Benjamin, New York, 1967. S.J. Yosim, B.B. Owens, J. Chem. Phys. 41 (1964) 2032. S. Cantor, D.P. McDermott, L.O. Gilpatrick, J. Chem. Phys. 52 (1970) 4600. Y. Marcus, Thermochim. Acta 495 (2009) 81. Y. Marcus, J. Chem. Thermodyn. 42 (2010) 60. M. Harada, M. Tanigaki, Y. Tada, Ind. Eng. Chem. Fundam. 22 (1983) 116. K. Yajima, H. Moriyama, J. Oishi, J. Phys. Chem. 88 (1984) 4390. G. Kaptay, in: Chen Nianyi, Qiao Zhiyu (Eds.), Proc. 6th Int. Symp. on Molten Salt Chemistry and Technology, Shanghai University Press, 2001, pp. 182–185. P. Baumli, G. Kaptay, Mater. Sci. Eng. A 495 (2008) 192. F. Aqra, J. Non-Cryst. Solids 402 (2014) 49.