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Thermodynamic and transport properties of the PrBr3–MBr binary systems (M = Li, Na)
Journal of Molecular Liquids 148 (2009) 40–44
Contents lists available at ScienceDirect
Journal of Molecular Liquids j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / m o l l i q
Thermodynamic and transport properties of the PrBr3–MBr binary systems (M = Li, Na) Ewa Ingier-Stocka a, Leszek Rycerz a, Madjid Berkani b, Marcelle Gaune-Escard c,⁎ a
Chemical Metallurgy Group, Faculty of Chemistry, Wroclaw University of Technology, Wybrzeze Wyspianskiego 27, 50-370 Wroclaw, Poland Laboratoire des Procédés Catalytiques et Thermodynamique des Matériaux, Département de Génie des Procédés, Faculté des Sciences et des Sciences de l'Ingénieur, Université A. Mira de Béjaïa, 06000 Béjaïa, Algéria c Ecole Polytechnique, IUSTI CNRS UMR 6595, Technopole de Chateau-Gombert 5 rue Enrico Fermi,13453 Marseille Cedex 13, France b
a r t i c l e
i n f o
Article history: Received 24 November 2008 Received in revised form 27 March 2009 Accepted 4 June 2009 Available online 13 June 2009 Keywords: Lanthanide halide Praseodymium bromide Lithium bromide Sodium bromide Phase diagram Electrical conductivity
a b s t r a c t DSC was used to investigate phase equilibrium in the PrBr3–MBr (M = Li, Na) systems. They represent typical examples of simple eutectic systems. The eutectic composition and eutectic temperature, x(PrBr3) = 0.265, Teut = 689 K and x(PrBr3) = 0.409, and Teut = 658 K, where x(PrBr3) denotes the molar fraction of PrBr3, were found for PrBr3–LiBr and PrBr3–NaBr systems, respectively. The electrical conductivity of PrBr3–MBr liquid mixtures, together with that of pure components was measured down to temperatures below solidification. Results obtained are discussed in terms of possible complex formation. © 2009 Elsevier B.V. All rights reserved.
1. Introduction In spite of their technological importance (lanthanide metallurgy, nuclear, lighting, laser, …, industries), and the enormous amount of work performed in the 1960s and 1970s, rare earth halides still need high quality investigations to be characterized properly. It may be said that the literature data on the temperatures and enthalpies of phase transitions of lanthanide halides include significant discrepancies regarding the pure components (temperature and enthalpy) [1–5] or the binary systems. The phase diagrams of binary systems (lanthanide–alkali metal halide) that have been published in literature very often contain serious errors and lack of precision. For example, earlier literature data [6] claimed the congruently melting compound K3LaCl6 in the LaCl3–KCl binary system, whereas a more recent investigation showed that only the congruently melting K2LaCl5 compound exists in this system [7]. Similar discrepancies can be found very often in other binary systems. This situation was the trigger to our systematic investigation program on lanthanide halide-based systems using several techniques to determine thermodynamic properties, structure and electrical conductivity. All the lanthanide–alkali metal chloride binary systems have been examined or re-examined by Seifert [8]. The phase diagrams of the homologous bromide and iodide systems were not fully investigated nor critically assessed yet. Some lanthanide⁎ Corresponding author. E-mail address: [email protected] (M. Gaune-Escard). 0167-7322/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.molliq.2009.06.003
alkali metal bromide systems seem totally erroneous: the TmBr3-RbBr system [9] for instance, in which no congruently melting compound has been reported. Other systems were reported in [10], but as a graphic–only information. Therefore more details would be required to fully characterize those systems. Taking into account the above discrepancies, or lack of data, for most LiBr–LnBr3 binary systems we decided to verify existing data and to investigate the still unexplored lanthanide bromide-based systems. We have measured previously the thermodynamic properties of some bromide systems, i.e. NdBr3–LiBr [11], TbBr3–MBr (M = Na, K, Rb, Cs)[12,13], LaBr3–LiBr [14], CeBr3–MBr (M = Li, Na, K, Rb, Cs) [15–18]. The electrical conductivity of liquid bromide systems i.e. NdBr3–MBr [19] and LaBr3–MBr [20] (where M = Li, Na, K, Rb, Cs) was also reported. Careful analysis of all existing LnX 3 –MX phase diagrams (Ln = lanthanide, M = alkali metal, X = halide) have been performed [13] in order to correlate the phase diagrams topology and the physicochemical properties of the system components. The ionic radii (ri) and/or charges (ei) as also their combination, called “ionic potential”, IP = ei / ri, where ei = Ziε (Zi = valency, ε = elementary charge), were found to be important parameters in this respect. The “ionic potential” is a measure of the electric field intensity at the cation surface, thus accounts for the interaction forces between cations and anions. The ratio of two ionic potentials IP1/IP2 expresses a comparison of the interaction energies. This ionic potential ratio of the alkali metal and lanthanide cations, influences the phase diagram
E. Ingier-Stocka et al. / Journal of Molecular Liquids 148 (2009) 40–44
41
topology of the LnCl3–MCl, LnBr3–MBr and LnI3–MI binary systems. All these systems can be divided into three groups [13]: – simple eutectic systems ( ionic potential ratio bigger or equal to 0.448; 0.325 and 0.330 for chloride, bromide and iodide systems, respectively), – systems including only incongruently melting compounds (ionic potential ratio within the range of 0.416–0.280; 0.315–0.284 and 0.352–0.306 for chloride, bromide and iodide systems, respectively), – systems including both the congruently and incongruently melting compounds (ionic potential ratio equal to or less than 0.256). This above classification will be tested further in the course of our ongoing systematic investigations on unknown LnBr3–MBr binary systems (Ln = lanthanide). The present paper reports the phase diagram and electrical conductivity of the PrBr3–MBr binary systems (M = Li, Na). 2. Experimental 2.1. Chemicals Praseodymium(III) bromide was synthesised from the praseodymium oxide, Pr6O11 (Alfa Aesar, 99.9% (REO)). This oxide was dissolved in hot concentrated HBr acid. Solution was evaporated and PrBr.3xH2O was crystallized. Ammonium bromide was then added and this wet mixture of hydrated PrBr3 and NH4Br was first slowly heated up to 450 and then up to 570 K to remove the water. The resulting mixture was subsequently heated to 650 K for sublimation of NH4Br. Finally, the salt was melted at about 1100 K. Crude PrBr3 was purified by distillation under reduced pressure (∼0.1 Pa) in a quartz ampoule at 1150 K. PrBr3 prepared in this way was of a high purity — min. 99.9 %. Chemical analysis was performed by mercurimetric (bromine) and complexometric (praseodymium) methods. The results were as follows: Pr, 36.96 ± 0.15% (37.02 % theoretical); Br, 63.04 ± 0.11% (62.98 % theoretical). Alkali metal bromides (LiBr and NaBr) were Merck Suprapur reagents (minimum 99.9%, metal basis). Before use, they were progressively heated up to fusion under gaseous HBr atmosphere. Excess of HBr was then removed from the melt by argon bubbling. All chemicals were handled inside a high purity argon atmosphere in a glove box (water content b2 ppm).
Fig. 2. Phase diagram of the PrBr3–NaBr system.
Homogenous mixtures of different compositions were prepared in this way and used in phase diagrams and electrical conductivity measurements. Phase equilibrium in the PrBr3–MBr systems was investigated with a Setaram DSC 121 differential scanning calorimeter. Experimental samples (300–500 mg) were contained in vacuum-sealed quartz ampoules. Experiments were conducted at heating and cooling rates ranging from 1 to 5 K min− 1. Because of the wide experimental temperature range, the determination of the DSC calibration constant and its evolution is crucial. This enthalpy calibration, was performed by “Joule effect”. It was carried out at several defined temperatures over the entire temperature by the so-called “step method” (ΔT = 5 K) and yielded the calorimeter calibration curve, i.e. calorimeter constant dependence on temperature, K(μV/mW) = f(T). This dependence was automatically used during data treatment by the original Setaram software. The sample temperature was measured by a platinum probe located in the calorimetric block. The experimental temperature scale was normalized from temperature calibration experiments performed on several standard reference materials, at various scanning rates. The resulting temperature correction coefficients were introduced into the calorimeter software. The maximum relative experimental error on enthalpy of phase transition did not exceed 1%. This was controlled by the temperature and enthalpy of phase transitions measurements performed on standard substances. The results obtained in this way (differences in
2.2. Measurements Experimental mixture samples, made from the appropriate amounts of PrBr3 and MBr (M = Li or Na), were melted in vacuumsealed quartz ampoules. The melts were homogenised and solidified. These samples were ground in an agate mortar in a glove box.
Table 1 DSC results for PrBr3–LiBr and PrBr3–NaBr binary systems. PrBr3–LiBr
Fig. 1. Phase diagram of the PrBr3–LiBr system.
PrBr3–NaBr
xPrBr3
Teut/K
Tliq/K
xPrBr3
Teut/K
Tliq/K
0.000 0.054 0.101 0.157 0.216 0.319 0.352 0.404 0.455 0.486 0.550 0.617 0.712 0.805 0.855 0.881 0.920 0.952 1.000
– 688 690 689 689 689 689 690 689 688 690 689 688 688 688 689 689 688 –
823 789 781 749 708 721 730 781 791 816 837 872 909 924 932 946 959 960 960
0 0.050 0.100 0.150 0.201 0.251 0.314 0.351 0.400 0.441 0.500 0.548 0.602 0.702 0.801 0.906 1.000
– 656 657 657 659 659 659 657 658 657 659 657 660 660 660 659 –
1020 995 965 919 873 811 753 714 670 705 755 793 842 888 916 942 960
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E. Ingier-Stocka et al. / Journal of Molecular Liquids 148 (2009) 40–44 Table 2 Coefficients of the equation: ln к = A0 + A1 (1000/T) + A2(1000/T)2 and the activation energy of the electrical conductivity (EA) of liquid PrBr3–MBr (M = Li, Na) binary mixtures at 1050 K: к in S m− 1, ln(s) — standard deviation of ln к, n = number of experimental data points. A0 S m − 1
A1 S m− 1K
A2 S m− 1K2
ln(s)
n
EA at 1050 K (kJ/mol)
PrBr3–LiBr 0.000 828–1115 0.098 876–1075 0.198 780–1080 0.298 780–1080 0.387 780–1080 0.495 777–1080 0.561 860–1080 0.598 830–1080 0.696 877–1080 0.784 911–1080 0.837 930–1080 0.884 945–1080 0.918 953–1080 0.956 957–1080 1.000 977–1170
6.1292 6.0294 5.9328 5.9567 5.7213 4.9386 5.1798 5.6279 5.9007 5.5341 4.6824 6.6547 6.6651 6.3983 4.9342
0.8843 0.5883 0.4198 0.1670 0.3917 1.8610 1.3193 0.4657 − 0.1580 0.6217 2.2558 − 1.6756 − 1.7606 − 1.1725 1.6942
− 0.6784 − 0.6296 − 0.6180 − 0.6293 − 0.8153 − 1.6962 − 1.5747 − 1.1184 − 1.0175 − 1.6808 − 2.6031 − 0.7690 − 0.7692 − 1.0988 − 2.6688
0.0083 0.0010 0.0030 0.0038 0.0029 0.0090 0.0087 0.0055 0.0107 0.0105 0.0101 0.0131 0.0093 0.0063 0.0027
2589 399 689 684 688 679 477 579 423 318 354 320 317 288 454
3.391 5.079 6.296 8.577 9.654 11.388 13.968 13.840 17.427 21.449 22.469 26.110 26.819 27.148 28.178
PrBr3–NaBr 0.000 1026–1117 0.049 1003–1090 0.114 970–1080 0.199 896–1080 0.298 792–1080 0.479 767–1080 0.501 775–1080 0.547 793–1080 0.598 823–1090 0.701 868–1080 0.786 911–1080 0.829 932–1080 0.914 953–1080 0.946 965–1080
5.2807 5.6827 5.1484 5.3296 5.3379 4.5283 5.1572 4.7237 5.0176 4.6169 4.6433 3.9326 4.2953 2.4856
1.7775 0.7345 1.7035 0.9531 0.7613 2.2641 1.1229 1.8698 1.3875 2.2350 2.2736 3.6949 2.9729 6.6828
− 1.4020 − 0.8990 − 1.4721 − 1.0895 − 1.0628 − 1.9921 − 1.4782 − 1.8915 − 1.7634 − 2.3861 − 2.6151 − 3.3948 − 3.1467 − 5.0955
0.0003 0.0037 0.0052 0.101 0.0075 0.0039 0.0137 0.0102 0.0092 0.0092 0.0086 0.0048 0.0019 0.0097
220 200 176 452 606 880 738 738 590 442 305 316 294 253
7.424 8.132 9.149 9.330 10.500 12.725 14.074 14.408 16.390 19.205 22.510 23.038 25.116 25.133
x, PrBr3
Fig. 3. Tamman construction for eutectic determination in the PrBr3–MBr systems: open circles and solid lines — PrBr3–LiBr, black circles and broken lines — PrBr3–NaBr.
fusion temperatures less than 1 K, differences in enthalpies of fusion less than 0.5%) confirmed the precision of the calorimeter. Electrical conductivity measurements were carried out in the capillary quartz cells described in details elsewhere [21], and calibrated with molten NaCl [22]. The cells constants varied between 8000 and 9500 m− 1. The change of any individual cell constant was less than 1% after several experiments. The conductivity of the melt was measured by platinum electrodes with the conductivity meter Tacussel CD 810 during increasing and decreasing temperature runs. The mean values of these two runs were used in calculations. Experimental runs were performed at heating and cooling rates 1 K min− 1. Temperature was measured with a Pt/Pt-Rh(10) thermocouple with 1 K accuracy. Temperature and conductivity data acquisition was made with PC computer, interfaced to the conductivity meter. All measurements were carried out under static argon atmosphere. The accuracy of measurements was estimated at ±2%.
3. Results 3.1. Phase diagrams DSC investigations performed on samples with different compositions yielded both the corresponding temperature and fusion enthalpy. Due to supercooling effect, all temperature and enthalpy values reported here were determined from heating curves. Solidus and liquidus temperatures were determined as Tonset and Tpeak of appropriate effects, respectively.
Fig. 4. Electrical conductivity of molten PrBr3 vs. temperature: open circles — experimental data, black circles — literature data [24].
Temp. range (K)
The phase diagrams of the PrBr3–LiBr and PrBr3–NaBr systems are presented in Figs. 1 and 2, respectively, and are of the simple eutectic type. In the whole range of compositions, only two peaks were found in all thermograms, which were ascribed to the eutectic and liquidus effects (Table 1). The eutectic compositions, x = 0.265 ± 0.012 (PrBr3– LiBr system) and x = 0.409 ± 0.004 (PrBr3–NaBr system), were determined accurately from the Tamman plot (Fig. 3) assuming that no solid solutions were formed in the systems. Thus the plot of the eutectic related enthalpy vs. composition included two straight lines that intercept the composition axis at x = 0 and x = 1. This so-called Tamman construction made it possible to evaluate accurately the
Fig. 5. Electrical conductivity isotherms of PrBr3 — MBr liquid mixtures at 1050 K: open circles M = Li, black circles M = Na, solid line — polynomial fitting.
E. Ingier-Stocka et al. / Journal of Molecular Liquids 148 (2009) 40–44
Fig. 6. Activation energy at 1050 K of PrBr3 — MBr liquid mixtures: open circles M = Li, black circles M = Na, solid line — polynomial fitting.
eutectic composition from their intercept. The corresponding equations are: ΔfusHm = 77.31x and ΔfusHm = 27.87 − 27.87x in kJ mol− 1 for the PrBr3–LiBr system and ΔfusHm = 50.79x and ΔfusHm = 35.12 − 35.12x in kJ mol− 1 for the PrBr3–NaBr system. The corresponding eutectic temperature determined from all appropriate DSC curves was 689 K and 658 K, whereas the enthalpy of fusion at the eutectic composition was 20.5 ± 0.9 kJ mol− 1 and 20.8 ± 0.3 kJ mol− 1 for the system with LiBr and NaBr, respectively. The PrBr3–LiBr binary system was investigated for the first time in the present work and accordingly could not be compared with literature data. However, data exist for the PrBr3–NaBr system [23]. Our finding for the eutectic temperature (658 K) differs from those data by 10 K (648 K). Also the eutectic composition determined from our measurements is PrBr3-richer (x = 0.409 and around 0.40 as determined graphically from [23]). Moreover, whereas melting temperatures of NaBr are in a quite good agreement (1020 K and 1018 K), the melting temperature of PrBr3 determined in this work (960 K) is in fairly good agreement with Bredig's reference value (966 K) [1] and somewhat different from 953 K as reported in [23]. These differences might possibly be caused by some impurities in the PrBr3 employed [23]. 3.2. Electrical conductivity Prior to investigation of binary mixtures, we measured the electrical conductivity of pure components. The results obtained for pure PrBr3 agree very well with literature data [24] (difference does not exceed 1.5 % over the whole temperature range where comparison is possible — Fig. 4). The electrical conductivity results related to pure alkali metal bromides were discussed earlier [19,20]. The electrical conductivity of the PrBr3–MBr (M = Li, Na) liquid mixtures was measured for the first time. Experimental determinations for PrBr3–MBr (M = Li, Na) mixtures were conducted over the entire composition range in steps of about 10 mol%. The experimental conductivity, κ, data of the liquid phase were well represented by the equation: 1000 2 1000 + A2 : ð1Þ lnðκÞ = A0 + A1 : T T where A0, A1, and A2 are coefficients determined by the least-squares method. The activation energy, EA, evaluated by analogy to the Arrhenius equation as EA ðTÞ = −R
dlnðκÞ 1000 d
ð2Þ
T
where R is the gas constant, becomes h i 1000 EA = −R A1 + 2A2 T
ð3Þ
43
All Ai coefficients are listed in Table 2, together with the EA values determined at 1050 K for all the PrBr3–MBr (M = Li, Na) mixtures. The experimental conductivity isotherms at 1050 K were plotted against the mole fraction of PrBr3 in Fig. 5. The electrical conductivity decreases with increasing radius of the alkali metal cation i.e. from lithium to sodium. In both systems the specific conductivity decreases with increase of PrBr3 concentration, with significantly larger changes in the alkali bromide-rich region. A similar trend has been already observed in our previous investigations of lanthanide–alkali metal halide binary systems [19,20]. As indicated above, the activation energy for conductivity changes with temperature in both PrBr3–LiBr and PrBr3–NaBr , validating the early statement made by Yaffe and van Artsdalen [25,26] of a correlation with structural changes in melts. Fig. 6 shows the activation energy at 1050 K as function of composition. The activation energy EA varies smoothly with composition in the lithium bromiderich range, similar in that to the behaviour observed in the LaBr3–LiBr, NdBr3–LiBr and CeBr3–LiBr systems [19,20,27]. However, it was shown that a stabilization of EA occurs in the concentration range of 25– 50 mol% of LnBr3 in the LnBr3 systems with heavier alkali metals (K, Rb, Cs) [19,20]. A similar evolution of activation energy is foreseen from preliminary investigations conducted on the PrBr3–KBr binary system [28]. This stabilisation effect can be explained [19,20] as consistent with the predominant LnBr3− (Ln = La, Ce) octahedral 6 complexes in melts rich in KBr, RbBr and CsBr with an increasing amount of polymeric species in the LnBr3-rich melts. As shown in Fig. 6, the concentration evolution of EA appears to be intermediate in the PrBr3–NaBr system, where a stabilisation effect is observed from about 15 mol% up to about 30 mol% PrBr3. Fig. 6 clearly illustrates also that the activation energy increases with the alkali cationic radius particularly in the MBr-rich (M = Li, Na) melts. It is likely that this is due to an increase of the PrBr3− 6 complex concentration in the melt. The radius of the alkali metal cation will therefore govern the complex ion formation in the PrBr3–MBr binary systems. Thus addition of NaBr to PrBr3 favours complex ion formation more than LiBr and results in a larger activation energy for electrical conductivity. 4. Conclusion This phase diagram classification in terms of the ionic potentials ratio (IPM+/IPPr3+) was validated for the PrBr3–LiBr and PrBr3–NaBr investigated in the present work. It will be tested further in the course our future and systematic research on the lanthanide-alkali metal systems. The activation energy for electrical conductivity change with temperature in both PrBr3–LiBr and PrBr3–NaBr is very likely connected with structural modifications in melts. The activation energy increase with the alkali cationic radius (particularly in the MBr-rich mixtures) corresponds to an increase of the PrBr3− 6 complex concentration in the melt. The radius of the alkali metal cation governs the complex ion formation in the PrBr3–MBr binary systems. Acknowledgements Financial support by the Polish Ministry of Science and Higher Education from budget on science in 2007–2010 under the grant N N204 4098 33 is gratefully acknowledged. L.R., E.I-S. and M.B. wish to thank the Ecole Polytechnique de Marseille for hospitality and support during this work. References [1] [2] [3] [4]
A.S. Dworkin, M.A. Bredig, High Temp. Sci. 3 (1) (1971) 81. R.C. Vickery, Chemistry of the lanthanons, Butterworths, London, 1958. G.E. Walden, D.F. Smith, Rep. RI 5859, 1962 (US Bureau of Mines). G. Vogel, A. Schneider, Inorg. Nucl. Chem. Lett. 8 (1972) 513.
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[5] M. Gaune-Escard, L. Rycerz, W. Szczepaniak, A. Bogacz, J. Alloys Comp. 204 (1994) 193. [6] I.C. Sun, I.S. Morozov, Zh. Neorg. Khim. 3 (1958) 1914. [7] H.J. Seifert, H. Fink, G. Thiel, J. Less-Common Metals 110 (1985) 139. [8] H.J. Seifert, J. Thermal. Anal. Calor. 83 (2) (2006) 479 and references therein. [9] A.K. Molodkin, A.M. Karagodina, A.G. Dudareva, A.B. Strekachinskii, Zh. Neorg. Khim. 26 (8) (1981) 2265. [10] R. Blachnik, A. Jaeger-Kasper, Z. Anorg. Allg. Chem. 461 (1980) 74. [11] L. Rycerz, E. Ingier-Stocka, M. Cieslak-Golonka, M. Gaune-Escard, J. Therm. Anal. Cal. 72 (2003) 241. [12] L. Rycerz, High Temperature Characterization of LnX3 and LnX3-AX Solid and Liquid Systems (Ln = Lanthanide, A = Alkali, X = Halide): Thermodynamics and Electrical Conductivity; Ph.D. Thesis, Marseille 2003. [13] L. Rycerz, L. Thermochemistry of lanthanide halides and compounds formed in lanthanide halide-alkali metal halide systems, (in Polish), Scientific Papers of Institute of Inorganic Chemistry and Metallurgy of Rare Elements, Wroclaw University of Technology, Series Monographs 35, Wroclaw (2004). [14] L. Rycerz, E. Ingier-Stocka, B. Ziolek, S. Gadzuric, M. Gaune-Escard, in: H.A. Øye, A. Jagtøyen (Eds.), Proc. Intern. Symp. on Ionic Liquids in honour of Professor Marcelle Gaune-Escard, Carry le Rouet, France, 2003, p. 83, June 26-28. [15] E. Ingier-Stocka, L. Rycerz, S. Gadzuric, M. Gaune-Escard, J. Alloys Comp. 450 (2008) 162.
[16] L. Rycerz, E. Ingier-Stocka, S. Gadzuric, M. Gaune-Escard, Z. Naturforsch. 62a (2007) 197. [17] L. Rycerz, E. Ingier-Stocka, S. Gadzuric, M. Gaune-Escard, J. Alloys Comp. 450 (2008) 175. [18] L. Rycerz, E. Ingier-Stocka, M. Gaune-Escard, J. Thermal Anal. Calor (in press). doi:10.1007/s10973-009-0007-6. [19] S. Gadzuric, E. Ingier-Stocka, L. Rycerz, M. Gaune-Escard, Z. Naturforsch. 59a (2004) 77. [20] B. Ziolek, L. Rycerz, S. Gadzuric, E. Ingier-Stocka, M. Gaune-Escard, Z. Naturforsch. 60a (2005) 75. [21] Y. Fouque, M. Gaune-Escard, W. Szczepaniak, A. Bogacz, J. Chim. Phys. 75 (1978) 360. [22] G.J. Janz, Mat. Sci. Forum 73–75 (1991) 707. [23] G. Vogel, Z. Anorg. Allg. Chem. 388 (11) (1972) 43. [24] A.S. Dworkin, H.R. Bronstein, M.A. Bredig, J. Phys. Chem. 67 (1963) 2715. [25] E.R. van Artsdalen, J.S. Yaffe, J. Phys. Chem. 59 (1955) 118. [26] J.S. Yaffe, E.R. van Artsdalen, J. Phys. Chem. 60 (1956) 1125. [27] E. Ingier-Stocka, L. Rycerz, S. Gadzuric, M. Gaune-Escard, J. Alloys Comp. 450 (2008) 162. [28] E. Ingier-Stocka, L. Rycerz, M. Gaune-Escard, unpublished results.
Contents lists available at ScienceDirect
Journal of Molecular Liquids j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / m o l l i q
Thermodynamic and transport properties of the PrBr3–MBr binary systems (M = Li, Na) Ewa Ingier-Stocka a, Leszek Rycerz a, Madjid Berkani b, Marcelle Gaune-Escard c,⁎ a
Chemical Metallurgy Group, Faculty of Chemistry, Wroclaw University of Technology, Wybrzeze Wyspianskiego 27, 50-370 Wroclaw, Poland Laboratoire des Procédés Catalytiques et Thermodynamique des Matériaux, Département de Génie des Procédés, Faculté des Sciences et des Sciences de l'Ingénieur, Université A. Mira de Béjaïa, 06000 Béjaïa, Algéria c Ecole Polytechnique, IUSTI CNRS UMR 6595, Technopole de Chateau-Gombert 5 rue Enrico Fermi,13453 Marseille Cedex 13, France b
a r t i c l e
i n f o
Article history: Received 24 November 2008 Received in revised form 27 March 2009 Accepted 4 June 2009 Available online 13 June 2009 Keywords: Lanthanide halide Praseodymium bromide Lithium bromide Sodium bromide Phase diagram Electrical conductivity
a b s t r a c t DSC was used to investigate phase equilibrium in the PrBr3–MBr (M = Li, Na) systems. They represent typical examples of simple eutectic systems. The eutectic composition and eutectic temperature, x(PrBr3) = 0.265, Teut = 689 K and x(PrBr3) = 0.409, and Teut = 658 K, where x(PrBr3) denotes the molar fraction of PrBr3, were found for PrBr3–LiBr and PrBr3–NaBr systems, respectively. The electrical conductivity of PrBr3–MBr liquid mixtures, together with that of pure components was measured down to temperatures below solidification. Results obtained are discussed in terms of possible complex formation. © 2009 Elsevier B.V. All rights reserved.
1. Introduction In spite of their technological importance (lanthanide metallurgy, nuclear, lighting, laser, …, industries), and the enormous amount of work performed in the 1960s and 1970s, rare earth halides still need high quality investigations to be characterized properly. It may be said that the literature data on the temperatures and enthalpies of phase transitions of lanthanide halides include significant discrepancies regarding the pure components (temperature and enthalpy) [1–5] or the binary systems. The phase diagrams of binary systems (lanthanide–alkali metal halide) that have been published in literature very often contain serious errors and lack of precision. For example, earlier literature data [6] claimed the congruently melting compound K3LaCl6 in the LaCl3–KCl binary system, whereas a more recent investigation showed that only the congruently melting K2LaCl5 compound exists in this system [7]. Similar discrepancies can be found very often in other binary systems. This situation was the trigger to our systematic investigation program on lanthanide halide-based systems using several techniques to determine thermodynamic properties, structure and electrical conductivity. All the lanthanide–alkali metal chloride binary systems have been examined or re-examined by Seifert [8]. The phase diagrams of the homologous bromide and iodide systems were not fully investigated nor critically assessed yet. Some lanthanide⁎ Corresponding author. E-mail address: [email protected] (M. Gaune-Escard). 0167-7322/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.molliq.2009.06.003
alkali metal bromide systems seem totally erroneous: the TmBr3-RbBr system [9] for instance, in which no congruently melting compound has been reported. Other systems were reported in [10], but as a graphic–only information. Therefore more details would be required to fully characterize those systems. Taking into account the above discrepancies, or lack of data, for most LiBr–LnBr3 binary systems we decided to verify existing data and to investigate the still unexplored lanthanide bromide-based systems. We have measured previously the thermodynamic properties of some bromide systems, i.e. NdBr3–LiBr [11], TbBr3–MBr (M = Na, K, Rb, Cs)[12,13], LaBr3–LiBr [14], CeBr3–MBr (M = Li, Na, K, Rb, Cs) [15–18]. The electrical conductivity of liquid bromide systems i.e. NdBr3–MBr [19] and LaBr3–MBr [20] (where M = Li, Na, K, Rb, Cs) was also reported. Careful analysis of all existing LnX 3 –MX phase diagrams (Ln = lanthanide, M = alkali metal, X = halide) have been performed [13] in order to correlate the phase diagrams topology and the physicochemical properties of the system components. The ionic radii (ri) and/or charges (ei) as also their combination, called “ionic potential”, IP = ei / ri, where ei = Ziε (Zi = valency, ε = elementary charge), were found to be important parameters in this respect. The “ionic potential” is a measure of the electric field intensity at the cation surface, thus accounts for the interaction forces between cations and anions. The ratio of two ionic potentials IP1/IP2 expresses a comparison of the interaction energies. This ionic potential ratio of the alkali metal and lanthanide cations, influences the phase diagram
E. Ingier-Stocka et al. / Journal of Molecular Liquids 148 (2009) 40–44
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topology of the LnCl3–MCl, LnBr3–MBr and LnI3–MI binary systems. All these systems can be divided into three groups [13]: – simple eutectic systems ( ionic potential ratio bigger or equal to 0.448; 0.325 and 0.330 for chloride, bromide and iodide systems, respectively), – systems including only incongruently melting compounds (ionic potential ratio within the range of 0.416–0.280; 0.315–0.284 and 0.352–0.306 for chloride, bromide and iodide systems, respectively), – systems including both the congruently and incongruently melting compounds (ionic potential ratio equal to or less than 0.256). This above classification will be tested further in the course of our ongoing systematic investigations on unknown LnBr3–MBr binary systems (Ln = lanthanide). The present paper reports the phase diagram and electrical conductivity of the PrBr3–MBr binary systems (M = Li, Na). 2. Experimental 2.1. Chemicals Praseodymium(III) bromide was synthesised from the praseodymium oxide, Pr6O11 (Alfa Aesar, 99.9% (REO)). This oxide was dissolved in hot concentrated HBr acid. Solution was evaporated and PrBr.3xH2O was crystallized. Ammonium bromide was then added and this wet mixture of hydrated PrBr3 and NH4Br was first slowly heated up to 450 and then up to 570 K to remove the water. The resulting mixture was subsequently heated to 650 K for sublimation of NH4Br. Finally, the salt was melted at about 1100 K. Crude PrBr3 was purified by distillation under reduced pressure (∼0.1 Pa) in a quartz ampoule at 1150 K. PrBr3 prepared in this way was of a high purity — min. 99.9 %. Chemical analysis was performed by mercurimetric (bromine) and complexometric (praseodymium) methods. The results were as follows: Pr, 36.96 ± 0.15% (37.02 % theoretical); Br, 63.04 ± 0.11% (62.98 % theoretical). Alkali metal bromides (LiBr and NaBr) were Merck Suprapur reagents (minimum 99.9%, metal basis). Before use, they were progressively heated up to fusion under gaseous HBr atmosphere. Excess of HBr was then removed from the melt by argon bubbling. All chemicals were handled inside a high purity argon atmosphere in a glove box (water content b2 ppm).
Fig. 2. Phase diagram of the PrBr3–NaBr system.
Homogenous mixtures of different compositions were prepared in this way and used in phase diagrams and electrical conductivity measurements. Phase equilibrium in the PrBr3–MBr systems was investigated with a Setaram DSC 121 differential scanning calorimeter. Experimental samples (300–500 mg) were contained in vacuum-sealed quartz ampoules. Experiments were conducted at heating and cooling rates ranging from 1 to 5 K min− 1. Because of the wide experimental temperature range, the determination of the DSC calibration constant and its evolution is crucial. This enthalpy calibration, was performed by “Joule effect”. It was carried out at several defined temperatures over the entire temperature by the so-called “step method” (ΔT = 5 K) and yielded the calorimeter calibration curve, i.e. calorimeter constant dependence on temperature, K(μV/mW) = f(T). This dependence was automatically used during data treatment by the original Setaram software. The sample temperature was measured by a platinum probe located in the calorimetric block. The experimental temperature scale was normalized from temperature calibration experiments performed on several standard reference materials, at various scanning rates. The resulting temperature correction coefficients were introduced into the calorimeter software. The maximum relative experimental error on enthalpy of phase transition did not exceed 1%. This was controlled by the temperature and enthalpy of phase transitions measurements performed on standard substances. The results obtained in this way (differences in
2.2. Measurements Experimental mixture samples, made from the appropriate amounts of PrBr3 and MBr (M = Li or Na), were melted in vacuumsealed quartz ampoules. The melts were homogenised and solidified. These samples were ground in an agate mortar in a glove box.
Table 1 DSC results for PrBr3–LiBr and PrBr3–NaBr binary systems. PrBr3–LiBr
Fig. 1. Phase diagram of the PrBr3–LiBr system.
PrBr3–NaBr
xPrBr3
Teut/K
Tliq/K
xPrBr3
Teut/K
Tliq/K
0.000 0.054 0.101 0.157 0.216 0.319 0.352 0.404 0.455 0.486 0.550 0.617 0.712 0.805 0.855 0.881 0.920 0.952 1.000
– 688 690 689 689 689 689 690 689 688 690 689 688 688 688 689 689 688 –
823 789 781 749 708 721 730 781 791 816 837 872 909 924 932 946 959 960 960
0 0.050 0.100 0.150 0.201 0.251 0.314 0.351 0.400 0.441 0.500 0.548 0.602 0.702 0.801 0.906 1.000
– 656 657 657 659 659 659 657 658 657 659 657 660 660 660 659 –
1020 995 965 919 873 811 753 714 670 705 755 793 842 888 916 942 960
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E. Ingier-Stocka et al. / Journal of Molecular Liquids 148 (2009) 40–44 Table 2 Coefficients of the equation: ln к = A0 + A1 (1000/T) + A2(1000/T)2 and the activation energy of the electrical conductivity (EA) of liquid PrBr3–MBr (M = Li, Na) binary mixtures at 1050 K: к in S m− 1, ln(s) — standard deviation of ln к, n = number of experimental data points. A0 S m − 1
A1 S m− 1K
A2 S m− 1K2
ln(s)
n
EA at 1050 K (kJ/mol)
PrBr3–LiBr 0.000 828–1115 0.098 876–1075 0.198 780–1080 0.298 780–1080 0.387 780–1080 0.495 777–1080 0.561 860–1080 0.598 830–1080 0.696 877–1080 0.784 911–1080 0.837 930–1080 0.884 945–1080 0.918 953–1080 0.956 957–1080 1.000 977–1170
6.1292 6.0294 5.9328 5.9567 5.7213 4.9386 5.1798 5.6279 5.9007 5.5341 4.6824 6.6547 6.6651 6.3983 4.9342
0.8843 0.5883 0.4198 0.1670 0.3917 1.8610 1.3193 0.4657 − 0.1580 0.6217 2.2558 − 1.6756 − 1.7606 − 1.1725 1.6942
− 0.6784 − 0.6296 − 0.6180 − 0.6293 − 0.8153 − 1.6962 − 1.5747 − 1.1184 − 1.0175 − 1.6808 − 2.6031 − 0.7690 − 0.7692 − 1.0988 − 2.6688
0.0083 0.0010 0.0030 0.0038 0.0029 0.0090 0.0087 0.0055 0.0107 0.0105 0.0101 0.0131 0.0093 0.0063 0.0027
2589 399 689 684 688 679 477 579 423 318 354 320 317 288 454
3.391 5.079 6.296 8.577 9.654 11.388 13.968 13.840 17.427 21.449 22.469 26.110 26.819 27.148 28.178
PrBr3–NaBr 0.000 1026–1117 0.049 1003–1090 0.114 970–1080 0.199 896–1080 0.298 792–1080 0.479 767–1080 0.501 775–1080 0.547 793–1080 0.598 823–1090 0.701 868–1080 0.786 911–1080 0.829 932–1080 0.914 953–1080 0.946 965–1080
5.2807 5.6827 5.1484 5.3296 5.3379 4.5283 5.1572 4.7237 5.0176 4.6169 4.6433 3.9326 4.2953 2.4856
1.7775 0.7345 1.7035 0.9531 0.7613 2.2641 1.1229 1.8698 1.3875 2.2350 2.2736 3.6949 2.9729 6.6828
− 1.4020 − 0.8990 − 1.4721 − 1.0895 − 1.0628 − 1.9921 − 1.4782 − 1.8915 − 1.7634 − 2.3861 − 2.6151 − 3.3948 − 3.1467 − 5.0955
0.0003 0.0037 0.0052 0.101 0.0075 0.0039 0.0137 0.0102 0.0092 0.0092 0.0086 0.0048 0.0019 0.0097
220 200 176 452 606 880 738 738 590 442 305 316 294 253
7.424 8.132 9.149 9.330 10.500 12.725 14.074 14.408 16.390 19.205 22.510 23.038 25.116 25.133
x, PrBr3
Fig. 3. Tamman construction for eutectic determination in the PrBr3–MBr systems: open circles and solid lines — PrBr3–LiBr, black circles and broken lines — PrBr3–NaBr.
fusion temperatures less than 1 K, differences in enthalpies of fusion less than 0.5%) confirmed the precision of the calorimeter. Electrical conductivity measurements were carried out in the capillary quartz cells described in details elsewhere [21], and calibrated with molten NaCl [22]. The cells constants varied between 8000 and 9500 m− 1. The change of any individual cell constant was less than 1% after several experiments. The conductivity of the melt was measured by platinum electrodes with the conductivity meter Tacussel CD 810 during increasing and decreasing temperature runs. The mean values of these two runs were used in calculations. Experimental runs were performed at heating and cooling rates 1 K min− 1. Temperature was measured with a Pt/Pt-Rh(10) thermocouple with 1 K accuracy. Temperature and conductivity data acquisition was made with PC computer, interfaced to the conductivity meter. All measurements were carried out under static argon atmosphere. The accuracy of measurements was estimated at ±2%.
3. Results 3.1. Phase diagrams DSC investigations performed on samples with different compositions yielded both the corresponding temperature and fusion enthalpy. Due to supercooling effect, all temperature and enthalpy values reported here were determined from heating curves. Solidus and liquidus temperatures were determined as Tonset and Tpeak of appropriate effects, respectively.
Fig. 4. Electrical conductivity of molten PrBr3 vs. temperature: open circles — experimental data, black circles — literature data [24].
Temp. range (K)
The phase diagrams of the PrBr3–LiBr and PrBr3–NaBr systems are presented in Figs. 1 and 2, respectively, and are of the simple eutectic type. In the whole range of compositions, only two peaks were found in all thermograms, which were ascribed to the eutectic and liquidus effects (Table 1). The eutectic compositions, x = 0.265 ± 0.012 (PrBr3– LiBr system) and x = 0.409 ± 0.004 (PrBr3–NaBr system), were determined accurately from the Tamman plot (Fig. 3) assuming that no solid solutions were formed in the systems. Thus the plot of the eutectic related enthalpy vs. composition included two straight lines that intercept the composition axis at x = 0 and x = 1. This so-called Tamman construction made it possible to evaluate accurately the
Fig. 5. Electrical conductivity isotherms of PrBr3 — MBr liquid mixtures at 1050 K: open circles M = Li, black circles M = Na, solid line — polynomial fitting.
E. Ingier-Stocka et al. / Journal of Molecular Liquids 148 (2009) 40–44
Fig. 6. Activation energy at 1050 K of PrBr3 — MBr liquid mixtures: open circles M = Li, black circles M = Na, solid line — polynomial fitting.
eutectic composition from their intercept. The corresponding equations are: ΔfusHm = 77.31x and ΔfusHm = 27.87 − 27.87x in kJ mol− 1 for the PrBr3–LiBr system and ΔfusHm = 50.79x and ΔfusHm = 35.12 − 35.12x in kJ mol− 1 for the PrBr3–NaBr system. The corresponding eutectic temperature determined from all appropriate DSC curves was 689 K and 658 K, whereas the enthalpy of fusion at the eutectic composition was 20.5 ± 0.9 kJ mol− 1 and 20.8 ± 0.3 kJ mol− 1 for the system with LiBr and NaBr, respectively. The PrBr3–LiBr binary system was investigated for the first time in the present work and accordingly could not be compared with literature data. However, data exist for the PrBr3–NaBr system [23]. Our finding for the eutectic temperature (658 K) differs from those data by 10 K (648 K). Also the eutectic composition determined from our measurements is PrBr3-richer (x = 0.409 and around 0.40 as determined graphically from [23]). Moreover, whereas melting temperatures of NaBr are in a quite good agreement (1020 K and 1018 K), the melting temperature of PrBr3 determined in this work (960 K) is in fairly good agreement with Bredig's reference value (966 K) [1] and somewhat different from 953 K as reported in [23]. These differences might possibly be caused by some impurities in the PrBr3 employed [23]. 3.2. Electrical conductivity Prior to investigation of binary mixtures, we measured the electrical conductivity of pure components. The results obtained for pure PrBr3 agree very well with literature data [24] (difference does not exceed 1.5 % over the whole temperature range where comparison is possible — Fig. 4). The electrical conductivity results related to pure alkali metal bromides were discussed earlier [19,20]. The electrical conductivity of the PrBr3–MBr (M = Li, Na) liquid mixtures was measured for the first time. Experimental determinations for PrBr3–MBr (M = Li, Na) mixtures were conducted over the entire composition range in steps of about 10 mol%. The experimental conductivity, κ, data of the liquid phase were well represented by the equation: 1000 2 1000 + A2 : ð1Þ lnðκÞ = A0 + A1 : T T where A0, A1, and A2 are coefficients determined by the least-squares method. The activation energy, EA, evaluated by analogy to the Arrhenius equation as EA ðTÞ = −R
dlnðκÞ 1000 d
ð2Þ
T
where R is the gas constant, becomes h i 1000 EA = −R A1 + 2A2 T
ð3Þ
43
All Ai coefficients are listed in Table 2, together with the EA values determined at 1050 K for all the PrBr3–MBr (M = Li, Na) mixtures. The experimental conductivity isotherms at 1050 K were plotted against the mole fraction of PrBr3 in Fig. 5. The electrical conductivity decreases with increasing radius of the alkali metal cation i.e. from lithium to sodium. In both systems the specific conductivity decreases with increase of PrBr3 concentration, with significantly larger changes in the alkali bromide-rich region. A similar trend has been already observed in our previous investigations of lanthanide–alkali metal halide binary systems [19,20]. As indicated above, the activation energy for conductivity changes with temperature in both PrBr3–LiBr and PrBr3–NaBr , validating the early statement made by Yaffe and van Artsdalen [25,26] of a correlation with structural changes in melts. Fig. 6 shows the activation energy at 1050 K as function of composition. The activation energy EA varies smoothly with composition in the lithium bromiderich range, similar in that to the behaviour observed in the LaBr3–LiBr, NdBr3–LiBr and CeBr3–LiBr systems [19,20,27]. However, it was shown that a stabilization of EA occurs in the concentration range of 25– 50 mol% of LnBr3 in the LnBr3 systems with heavier alkali metals (K, Rb, Cs) [19,20]. A similar evolution of activation energy is foreseen from preliminary investigations conducted on the PrBr3–KBr binary system [28]. This stabilisation effect can be explained [19,20] as consistent with the predominant LnBr3− (Ln = La, Ce) octahedral 6 complexes in melts rich in KBr, RbBr and CsBr with an increasing amount of polymeric species in the LnBr3-rich melts. As shown in Fig. 6, the concentration evolution of EA appears to be intermediate in the PrBr3–NaBr system, where a stabilisation effect is observed from about 15 mol% up to about 30 mol% PrBr3. Fig. 6 clearly illustrates also that the activation energy increases with the alkali cationic radius particularly in the MBr-rich (M = Li, Na) melts. It is likely that this is due to an increase of the PrBr3− 6 complex concentration in the melt. The radius of the alkali metal cation will therefore govern the complex ion formation in the PrBr3–MBr binary systems. Thus addition of NaBr to PrBr3 favours complex ion formation more than LiBr and results in a larger activation energy for electrical conductivity. 4. Conclusion This phase diagram classification in terms of the ionic potentials ratio (IPM+/IPPr3+) was validated for the PrBr3–LiBr and PrBr3–NaBr investigated in the present work. It will be tested further in the course our future and systematic research on the lanthanide-alkali metal systems. The activation energy for electrical conductivity change with temperature in both PrBr3–LiBr and PrBr3–NaBr is very likely connected with structural modifications in melts. The activation energy increase with the alkali cationic radius (particularly in the MBr-rich mixtures) corresponds to an increase of the PrBr3− 6 complex concentration in the melt. The radius of the alkali metal cation governs the complex ion formation in the PrBr3–MBr binary systems. Acknowledgements Financial support by the Polish Ministry of Science and Higher Education from budget on science in 2007–2010 under the grant N N204 4098 33 is gratefully acknowledged. L.R., E.I-S. and M.B. wish to thank the Ecole Polytechnique de Marseille for hospitality and support during this work. References [1] [2] [3] [4]
A.S. Dworkin, M.A. Bredig, High Temp. Sci. 3 (1) (1971) 81. R.C. Vickery, Chemistry of the lanthanons, Butterworths, London, 1958. G.E. Walden, D.F. Smith, Rep. RI 5859, 1962 (US Bureau of Mines). G. Vogel, A. Schneider, Inorg. Nucl. Chem. Lett. 8 (1972) 513.
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[5] M. Gaune-Escard, L. Rycerz, W. Szczepaniak, A. Bogacz, J. Alloys Comp. 204 (1994) 193. [6] I.C. Sun, I.S. Morozov, Zh. Neorg. Khim. 3 (1958) 1914. [7] H.J. Seifert, H. Fink, G. Thiel, J. Less-Common Metals 110 (1985) 139. [8] H.J. Seifert, J. Thermal. Anal. Calor. 83 (2) (2006) 479 and references therein. [9] A.K. Molodkin, A.M. Karagodina, A.G. Dudareva, A.B. Strekachinskii, Zh. Neorg. Khim. 26 (8) (1981) 2265. [10] R. Blachnik, A. Jaeger-Kasper, Z. Anorg. Allg. Chem. 461 (1980) 74. [11] L. Rycerz, E. Ingier-Stocka, M. Cieslak-Golonka, M. Gaune-Escard, J. Therm. Anal. Cal. 72 (2003) 241. [12] L. Rycerz, High Temperature Characterization of LnX3 and LnX3-AX Solid and Liquid Systems (Ln = Lanthanide, A = Alkali, X = Halide): Thermodynamics and Electrical Conductivity; Ph.D. Thesis, Marseille 2003. [13] L. Rycerz, L. Thermochemistry of lanthanide halides and compounds formed in lanthanide halide-alkali metal halide systems, (in Polish), Scientific Papers of Institute of Inorganic Chemistry and Metallurgy of Rare Elements, Wroclaw University of Technology, Series Monographs 35, Wroclaw (2004). [14] L. Rycerz, E. Ingier-Stocka, B. Ziolek, S. Gadzuric, M. Gaune-Escard, in: H.A. Øye, A. Jagtøyen (Eds.), Proc. Intern. Symp. on Ionic Liquids in honour of Professor Marcelle Gaune-Escard, Carry le Rouet, France, 2003, p. 83, June 26-28. [15] E. Ingier-Stocka, L. Rycerz, S. Gadzuric, M. Gaune-Escard, J. Alloys Comp. 450 (2008) 162.
[16] L. Rycerz, E. Ingier-Stocka, S. Gadzuric, M. Gaune-Escard, Z. Naturforsch. 62a (2007) 197. [17] L. Rycerz, E. Ingier-Stocka, S. Gadzuric, M. Gaune-Escard, J. Alloys Comp. 450 (2008) 175. [18] L. Rycerz, E. Ingier-Stocka, M. Gaune-Escard, J. Thermal Anal. Calor (in press). doi:10.1007/s10973-009-0007-6. [19] S. Gadzuric, E. Ingier-Stocka, L. Rycerz, M. Gaune-Escard, Z. Naturforsch. 59a (2004) 77. [20] B. Ziolek, L. Rycerz, S. Gadzuric, E. Ingier-Stocka, M. Gaune-Escard, Z. Naturforsch. 60a (2005) 75. [21] Y. Fouque, M. Gaune-Escard, W. Szczepaniak, A. Bogacz, J. Chim. Phys. 75 (1978) 360. [22] G.J. Janz, Mat. Sci. Forum 73–75 (1991) 707. [23] G. Vogel, Z. Anorg. Allg. Chem. 388 (11) (1972) 43. [24] A.S. Dworkin, H.R. Bronstein, M.A. Bredig, J. Phys. Chem. 67 (1963) 2715. [25] E.R. van Artsdalen, J.S. Yaffe, J. Phys. Chem. 59 (1955) 118. [26] J.S. Yaffe, E.R. van Artsdalen, J. Phys. Chem. 60 (1956) 1125. [27] E. Ingier-Stocka, L. Rycerz, S. Gadzuric, M. Gaune-Escard, J. Alloys Comp. 450 (2008) 162. [28] E. Ingier-Stocka, L. Rycerz, M. Gaune-Escard, unpublished results.