Thermodynamic and transport properties of the PrBr3-RbBr binary system

Article abstract of DOI:10.1016/j.jallcom.2010.04.087

Phase equilibrium in the PrBr₃RbBr binary system was established by differential scanning calorimetry (DSC). This system, investigated for the first time, includes Rb₃PrBr₆, Rb₂PrBr ₅ and RbPr₂Br₇ compounds, and three eutectics located at molar fraction of PrBr₃ (x = 0.136; 865 K), (x = 0.488; 765 K) and (x = 0.679; 834 K), respectively. Rb3PrBr6 undergoes a solidsolid phase transition at 704K and melts congruently at 995 K. Rb2PrBr5 melts incongruently at 803K and finally RbPr2Br7 melts congruently at 852 K. The electrical conductivity of PrBr₃RbBr liquid mixtures was measured over an extended temperature range down to temperatures below solidification and over the whole composition range. Results obtained are discussed in terms of possible complex formation.

Full text of DOI:10.1016/j.jallcom.2010.04.087

Journal of Alloys and Compounds 501 (2010) 269–274
Contents lists available at ScienceDirect
Journal of Alloys and Compounds
journal homepage: www.elsevier.com/locate/jallcom
Thermodynamic and transport properties of the PrBr3–RbBr binary system
Leszek Rycerza, Ewa Ingier-Stockaa, Madjid Berkanib, Marcelle Gaune-Escardc,∗
a Chemical Metallurgy Group, Faculty of Chemistry, Wroclaw University of Technology, Wybrzeze Wyspianskiego 27, 50-370 Wroclaw, Poland
b Laboratoire de Génie de l’Environnement, Département de Chimie, Faculté des Sciences Exactes, Université A. Mira, Béjaïa 06000, Algeria
c Ecole Polytechnique, IUSTI CNRS UMR 6595, Technopole de Chateau-Gombert, 5 rue Enrico Fermi, 13453 Marseille Cedex 13, France
a r t i c l e i n f o
a b s t r a c t
Article history:
Phase equilibrium in the PrBr3–RbBr binary system was established by differential scanning calorimetry
(DSC). This system, investigated for the first time, includes Rb3PrBr6, Rb2PrBr5 and RbPr2Br7 compounds,
and three eutectics located at molar fraction of PrBr3 (x = 0.136; 865 K), (x = 0.488; 765 K) and (x = 0.679;
834 K), respectively. Rb3PrBr6 undergoes a solid–solid phase transition at 704 K and melts congruently
at 995 K. Rb2PrBr5 melts incongruently at 803 K and finally RbPr2Br7 melts congruently at 852 K. The
electrical conductivity of PrBr3–RbBr liquid mixtures was measured over an extended temperature range
down to temperatures below solidification and over the whole composition range. Results obtained are
discussed in terms of possible complex formation.
Received 27 October 2009
Received in revised form 8 April 2010
Accepted 14 April 2010
Available online 24 April 2010
Keywords:
Inorganic materials
Electrical transport
Phase diagrams
© 2010 Elsevier B.V. All rights reserved.
Thermodynamic properties
Calorimetry
Thermal analysis
1. Introduction
understanding and hence prediction of tungsten corrosion, silica
corrosion and spectral output. The data are also needed for pre-
Lanthanide halides play a very important role in many tech-
nological applications. They are extensively used in optical and
scintillation [1–5] devices and are attractive components for doses
in high-intensity discharge lamps and new highly efficient light
sources with energy saving features [6]. The wide band gap mate-
rials like fluorides and other halides co-doped by lanthanide ions
provide valuable insight into many aspects of luminescence cen-
ters and have wide applications [7]. The development of new
phosphors for vacuum ultraviolet (VUV) excitation is an impor-
tant new challenge in the field of luminescence materials research.
The phosphors excited in the VUV can be used in a new gener-
ation of lamps or in gas plasma discharge devices for flat color
display panels. Praseodymium and cerium compounds seem to
be promising for these purposes [7]. In spite of the techno-
logical importance, the properties of many lanthanide halides,
however, are poorly characterised. Bromides have received even
less attention in scientific literature than chlorides and iodides.
Comprehensive thermochemical parameters for the lanthanide tri-
bromides are not available in any of the standard compilations of
thermodynamic properties. These properties are required for the
calculation of the chemical composition in the lamp to assist in the
dicting the behaviour of doses by modelling multicomponent metal
halide systems [8].
In connection with our research program on lanthanide halides
and their systems with alkali metal halides, aiming to deter-
mine the physicochemical properties of these poorly characterised
LnX3–MX systems, we have investigated the binary system of
praseodymium(III) bromide with rubidium bromide.
In addition to investigating one more system in this system-
atic research program, our goal was also to further test systematic
rules evidenced recently [9] from our own investigations and lit-
erature data regarding the topology of related phase diagrams.
As reported previously [9] a relation between the phase dia-
gram topology and the physicochemical properties of components
was established in the LnX3–MX systems. The so-called “ionic
potential”, IP = ei/ri, where ri = ionic radius, ei = Ziε (Zi = valency and
ε = elementary charge), was found to be an important parameter in
this respect. The “ionic potential” is a measure of the electric field
intensity at the cation surface, therefore accounting for interaction
forces between cations with anions. The ratio of ionic potential
of the alkali metal cation and the lanthanide cation, IPM+/IPLn3+
,
expresses a comparison of the interaction energies and influences
the phase diagram topology of LnX3–MX binary systems. When
IPM+/IPLn3+ ≤ 0.256, both incongruently and congruently melting
compounds are present in the systems.
This had been previously tested on the CeBr3–MBr binary sys-
tems (M = Li, Na, K, Rb), still unknown at that time. Indeed it
was found that CeBr3–LiBr and CeBr3–NaBr are simple eutec-
∗
Corresponding author. Tel.: +33 4 91 10 68 87; fax: +33 4 91 11 74 39.
E-mail addresses: leszek.rycerz@pwr.wroc.pl (L. Rycerz),
berkanima@yahoo.fr (M. Berkani), marcelle.gaune-escard@polytech.univ-mrs.fr,
molten.salts@polytech.univ-mrs.fr (M. Gaune-Escard).
0925-8388/$ – see front matter © 2010 Elsevier B.V. All rights reserved.
doi:10.1016/j.jallcom.2010.04.087

270
L. Rycerz et al. / Journal of Alloys and Compounds 501 (2010) 269–274
tic systems [10] (IPM+/IPCe3+ = 0.465 and 0.366, respectively),
whereas in the system CeBr3–KBr [11] two congruently melt-
ing compounds, namely K3CeBr6 and K2CeBr5 exist in agreement
with the above observation (IPK+/IPCe3+ = 0.249). Therefore the
CeBr3–RbBr binary system followed the expected behaviour and
since IPRb+/IPCe3+ = 0.231, three compounds are formed accordingly
in this system [12]. One of them (Rb2CeBr5) melts incongruently,
whereas the other two (Rb3CeBr6 and RbCe2Br7) melt congru-
ently. PrBr3-based bromide systems follow this trend. The binary
systems with LiBr and NaBr are of simple eutectic-type [13]
(IPM+/IPPr3+ = 0.456 and 0.330, respectively). In the system with
KBr [14], the congruently melting compound, K3PrBr6 and two
incongruently melting compounds (K2PrBr5 and KPr2Br7) were
found (IPK+/IPPr3+ = 0.244). It can be expected that the system with
rubidium bromide (IPRb+/IPPr3+ = 0.227) would be characterised by
analogous compounds.
All chemicals were handled inside a high purity argon atmosphere in a glove
box (water content < 2 ppm).
2.2. Measurements
Experimental mixture samples, made from the appropriate amounts of PrBr3
and RbBr (Table 1) were melted in vacuum-sealed quartz ampoules. The melts were
homogenised and solidified. These samples were ground in an agate mortar in a
glove box. Homogenous mixtures of different compositions were prepared in this
way and used in phase diagram measurements.
Phase equilibria in the PrBr3–RbBr system were 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 heat-
ing and cooling rates ranging 1–5 K min−1. Details of experimental procedures and
apparatus calibration were given previously [13]. The maximum relative experi-
mental error on enthalpy of phase transition did not exceed 1%. Temperature was
measured with precision 1 K.
Electrical conductivity measurements were carried out in the capillary quartz
cells described in detail elsewhere [15], and calibrated with molten NaCl [16]. Exper-
imental mixture samples, made from the appropriate amounts of PrBr3 and RbBr
were placed in capillary cells and melted under argon atmosphere. The melts were
homogenised by argon bubbling during 30 min. The cells constants varied between
11 000 and 12 500 m−1. The change of any individual cell constant was less than
1% after several experiments. The conductivity of the melt was measured by plat-
inum electrodes with the conductivity meter Tacussel CD 810 during increasing and
decreasing temperature runs. The mean values of these two runs were used in calcu-
In addition the electrical conductivity of PrBr3–RbBr liquid
binary mixtures was measured over the whole composition range
and a wide temperature range.
2. Experimental
lations. Experimental runs were performed at heating and cooling rates 1 K min−1
.
2.1. Chemicals
Temperature was measured with a Pt/Pt–Rh(10) thermocouple with 1 K accuracy.
Temperature and conductivity data acquisition were made with PC computer, inter-
faced to the conductivity meter. All measurements were carried out under static
argon atmosphere. The accuracy of measurements was estimated at 2%.
Praseodymium(III) bromide was synthesised from the praseodymium oxide,
Pr6O11. The main steps of this synthesis include: dissolution of oxide in hot con-
centrated HBr acid, crystallisation of PrBr3·nH2O, its dehydration in the presence of
ammonium bromide, sublimation of NH4Br, melting of crude PrBr3 and its purifica-
tion by distillation under reduced pressure (∼0.1 Pa) in a quartz ampoule at 1150 K.
The details of this synthesis were described elsewhere [13]. PrBr3 prepared in this
way was of a high purity – minimum 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).
3. Results and discussion
3.1. Phase diagram
DSC investigations, performed on 35 samples with different
compositions, yielded both the corresponding temperature and
enthalpy. Due to a frequent supercooling effect, all temperature
and enthalpy values reported here were determined from heat-
ing curves. Solidus and liquidus temperatures were determined as
Tonset and Tpeak of appropriate effects, respectively.
Rubidium bromide was a Merck Suprapur reagent (minimum 99.9%). Before use,
it was progressively heated up to fusion under gaseous HBr atmosphere. Excess of
HBr was then removed from the melt by argon bubbling.
Table 1
Compositions of PrBr3–RbBr mixtures used in DSC measurements.
Fig. 1 shows the heating thermograms for samples with molar
fraction of PrBr3, x = 0.050, 0.250, 0.297, 0.373, 0.665 and 0.796,
Sample no.
m(PrBr3) (g)
m(RbBr) (g)
x(PrBr3)
1
2
3
4
5
6
7
8
9
0.0971
0.2233
0.1937
0.4109
0.2567
0.5325
0.4777
0.7647
0.5973
0.2010
0.4832
0.5073
0.7381
0.6959
0.6812
0.6073
0.7493
0.6789
0.7044
0.7707
0.7428
0.8535
0.7804
0.7430
1.0058
0.7741
0.8021
0.7694
0.8798
1.3528
1.4042
1.9080
2.4464
1.6340
1.8463
1.0206
1.600
0.025
0.050
0.076
0.100
0.127
0.149
0.177
0.200
0.237
0.250
0.271
0.297
0.313
0.350
0.373
0.395
0.426
0.462
0.501
0.523
0.544
0.577
0.600
0.625
0.652
0.665
0.666
0.677
0.741
0.796
0.850
0.899
0.949
respectively, obtained with heating rate 5 K min−1
.
In all thermograms, the endothermic effect observed at the high-
est temperature corresponds to liquidus. In the composition range
0 < x ≤ 0.250, where x is the PrBr3 molar fraction, two additional
endothermic peaks were present in all heating thermograms (with
the exception of compositions very close to the eutectic). The first
one, at 865 K (mean value from measurements), is observable in all
thermograms up to x < 0.250. Its disappearance at x = 0.250 suggests
the existence of the Rb3PrBr6 compound. It can be undoubtedly
ascribed to the RbBr–Rb3PrBr6 eutectic. The eutectic composi-
tion was determined accurately from the Tamman plot (Fig. 2a).
The analysis of this experimental enthalpy vs. composition plot
evidences that no solid solutions form in the system. Thus the cor-
responding straight lines intercept the composition axis at x = 0 and
0.250. The eutectic composition, x = 0.136 0.005, was determined
from the intercept of the two linear parts in Fig. 2a. The eutec-
tic temperature determined from all appropriate DSC curves was
found to be 865 1 K, whereas the enthalpy of fusion at the eutectic
0.7694
1.3254
0.9614
1.3311
0.8330
0.2620
0.5654
0.5210
0.7026
0.5623
0.4972
0.4044
0.4380
0.3429
0.3052
0.3059
0.2707
0.2717
0.2264
0.1940
0.2337
0.1693
0.1743
0.1592
0.1335
0.1505
0.1076
0.0934
0.0570
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
composition was 15.3 0.3 kJ mol−1
.
The second thermal effect at 704 K (mean value for samples
of different compositions) in samples with composition range
0 < x ≤ 0.250 was also observed in all samples with PrBr3 molar
fraction up to x < 0.333, composition at which it disappears. The
Tamman construction for this effect (Fig. 2b) evidences that
it is related to the Rb3PrBr6 compound. The molar enthalpy
related to this effect (calculated for the Rb3PrBr6 compound),
ꢀHm = 8.0 0.4 kJ mol−1
, is in excellent agreement with the

L. Rycerz et al. / Journal of Alloys and Compounds 501 (2010) 269–274
271
Fig. 1. DSC heating curves for PrBr3–RbBr mixtures of different compositions obtained with heating rate 5 K min−1, x = 0.050, 0.250, 0.297, 0.373, 0.665 and 0.796 (x denotes
mole fraction of PrBr3).
enthalpy observed previously [9] for many M3LnX6 compounds
(M = Rb, Cs; Ln = lanthanide) and ascribed to a solid–solid phase
transition. Accordingly, this effect at 704 K was attributed to a
solid–solid phase transition in Rb3PrBr6.
Two thermal events were observed at 704 K and 995 K for the
sample of composition x = 0.250 and were related to a solid–solid
phase transition (from low-temperature (LT) to high-temperature
(HT) modification) and the congruent melting of the Rb3PrBr6 com-
pound.
This thermal event at about 704 K was not detected in
samples with x ≥ 0.333, suggesting the existence of another com-
pound, namely Rb2PrBr5. Indeed, an additional thermal effect
at 803 K, which appears for samples in the composition range
0.250 < x ≈ 0.402 corresponds to the incongruent melting of
Rb2PrBr5, which leads to the formation of liquid phase and solid
Rb3PrBr6. Tamman diagram construction (enthalpy related to the
effect at 803 K vs. PrBr3 molar fraction) (Fig. 2c) yields the value
x = 0.332 0.024, which is in excellent agreement with the theo-
retical value x = 0.333 for Rb2PrBr5.
One or two endothermic peaks in addition to liquidus were
observed on heating thermograms for the samples in the compo-
sition range 0.250 < x < 0.666. The first one, at 803 K (as mentioned
above), corresponds to the incongruent melting of Rb2PrBr5. The
second one, observable at about 765 K, disappears at composi-
tions x ≥ 0.666, thus suggesting the existence of another compound,
namely RbPr2Br7. Thus it can be ascribed to the Rb2PrBr5–RbPr2Br7
eutectic. The enthalpy-composition plot in Fig. 2d resulted in the
eutectic composition, x = 0.488 0.009. This eutectic mixture melts
at 765 K, with the related enthalpy ꢀfusHm = 20.5 0.7 kJ mol−1
.
Only one endothermic effect was observed on heating DSC
curves for the mixture of composition x = 0.666 at 852 K. It corre-
sponds to the congruent melting of the RbPr2Br7 compound.
Fig. 2. Tamman constructions for the PrBr3–RbBr system: description in the text.

272
L. Rycerz et al. / Journal of Alloys and Compounds 501 (2010) 269–274
Table 2
DSC results for PrBr3–RbBr binary system.
Sample no.
x(PrBr3)
T/K
Rb3PrBr6 phase
transition
RbBr–Rb3PrBr6
eutectic
Rb2PrBr5
decomposition
Rb2PrBr5–RbPr2Br7
eutectic
RbPr2Br7–PrBr3
eutectic
Liquidus
0
1
2
3
4
5
6
7
8
0.000
0.025
0.050
0.076
0.100
0.127
0.149
0.177
0.200
0.237
0.250
0.271
0.297
0.313
0.350
0.373
0.395
0.426
0.462
0.501
0.523
0.544
0.577
0.600
0.625
0.652
0.665
0.666
0.677
0.741
0.796
0.850
0.899
0.949
1.000
–
701
704
704
704
703
704
705
704
703
704
702
704
700
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
864
865
866
866
864
865
866
865
863
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
838
838
839
837
833
817
–
967
959
945
927
904
879
883
921
958
989
995
986
970
955
916
880
813
798
778
776
797
810
828
839
844
853
851
852
851
878
894
934
941
958
960
9
–
–
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
800
806
803
799
807
806
–
––
–
–
–
–
–
–
–
–
–
–
–
749
768
767
768
768
766
766
766
766
768
762
760
761
–
–
–
–
–
–
–
–
–
–
–
–
–
–
Finally, one effect in addition to the liquidus was observable at
about 834 K in mixtures in the range x > 0.666. It undoubtedly cor-
responds to the RbPr2Br7–PrBr3 eutectic. The enthalpy vs. molar
fraction PrBr3 (Fig. 2e) gives x = 0.679 0.004 as the eutectic com-
position. This eutectic mixture melts at 834 K with the related
enthalpy 28.5 0.7 kJ mol−1. It should be pointed out that the Tam-
man diagram for the RbPr2Br7–PrBr3 eutectic (Fig. 2e) suggests the
existence of solid solutions. Accordingly, the straight line on the
right hand side does not cross the composition axis at x = 1. The
PrBr3 molar fractions at which solid solutions may exist at 834 K
were found as x ≥ 0.975.
where R is the gas constant, becomes
ꢄ
ꢀ
ꢁꢅ
1000
T
EA = −R A1 + 2A2
(3)
All Ai coefficients are listed in Table 3, together with the EA
values determined at 1050 K for all the PrBr3–RbBr mixtures.
The experimental conductivity isotherm at 1050 K was plotted
against the mole fraction of PrBr3 in Fig. 4. Conductivity decreases
with the increase of PrBr3 composition, with significantly larger
changes in the rubidium bromide-rich region.
All the results of DSC investigations are presented in Table 2,
and the complete phase diagram is shown in Fig. 3.
3.2. Electrical conductivity
The electrical conductivity of the PrBr3–RbBr liquid mixtures
was measured for the first time. Experimental determinations were
conducted over the entire composition range in steps of about
10 mol% and on an extended temperature range.
The experimental conductivity, Ä, data of the liquid phase were
well represented by the equation:
ꢂ
ꢃ
2
ꢀ
ꢁ
1000
T
1000
T
ln Ä = A0 + A1
( )
+ A2
(1)
Fig. 3. Phase diagram of the PrBr3–RbBr binary system. Description of phase equilib-
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
rium areas: A: RbBr(s) + liquid; B: HT-Rb3PrBr6(s) + liquid; C: RbBr(s) + HT-Rb3PrBr6(s)
D: RbBr(s) + LT-Rb3PrBr6(s); E: HT-Rb3PrBr6(s) + liquid; F: HT-Rb3PrBr6(s) + Rb2PrBr5(s)
;
;
G: LT-Rb3PrBr6(s) + Rb2PrBr5(s)
J: Rb2PrBr5(s) + RbPr2Br7(s) K: solid solution + liquid; L: solid solution; M:
RbPr2Br7(s) + solid solution, and N: RbPr2Br7(s) + liquid.
; H: Rb2PrBr5(s) + liquid; I: RbPr2Br7(s) + liquid;
;
d
ln(K)
EA(T) = −R d(1000/T)
(2)

L. Rycerz et al. / Journal of Alloys and Compounds 501 (2010) 269–274
273
Table 3
Coefficients of the electrical conductivity equation: lnк= A0 + A1(1000/T) + A2(1000/T)2 and the activation energy of the electrical conductivity (EA) of liquid PrBr3–RbBr binary
mixtures at 1050 K: к in S m−1, ln(s) = standard deviation of ln к, and n = number of experimental data points.
x(PrBr3)
Temperature range (K)
A0 (S m−1
)
A1 (S m−1K)
A2 (S m−1K2)
ln(s)
n
EA at 1050 K (kJ/mol)
0.000
0.105
0.202
0.305
0.431
0.537
0.636
0.718
0.847
0.945
1.000
993–1124
983–1150
957–1150
964–1140
840–1150
842–1150
845–1150
912–1150
975–1150
984–1150
977–1170
5.7114
4.7608
4.6902
5.7835
5.0893
4.4403
4.1941
4.0724
4.7829
4.7276
4.9342
−0.4031
1.5330
1.4596
−1.1299
0.1843
1.7218
2.5414
2.9421
1.8151
2.0123
1.6942
−0.5083
−1.6720
−1.7755
−0.4408
−1.1487
−2.0230
−2.6468
−2.9510
−2.5374
−2.7467
−2.6688
0.0009
0.0030
0.0024
0.0060
0.0028
0.0036
0.0066
0.0039
0.0024
0.0011
0.0027
386
361
397
366
657
659
642
510
379
386
454
11.325
13.733
15.982
16.375
16.659
17.721
20.786
22.273
25.091
26.767
28.178
Fig. 5 shows the activation energy at 1050 K as a function of
composition. For comparison, the data on activation energy for the
analogous system with LiBr [13] are also included in Fig. 5. Whereas
in the system with LiBr the activation energy increases smoothly
with PrBr3 concentration, in the system with RbBr it increases up
to about 15 mol% of PrBr3 and becomes almost stable up to about
55 mol% of PrBr3. This plateau can be explained in terms of coex-
istence of different forms of complexes as evidenced by Raman
spectroscopy [17]. These investigations showed that octahedral
formed. The activation energy for electrical conductivity increases
with alkali metal cationic radius (from lithium to rubidium). It
is likely that this is due to the complex concentration increase
in the melt. This observation is in agreement with preliminary
mixing enthalpy measurements [18] that also indicate that forma-
3−
tion enthalpy, attributed to the PrBr6
complex ions formation,
increases with ionic radius of alkali metal cation. Thus the presence
of RbBr in mixtures with PrBr3 favours complex ion formation more
than addition of LiBr and results in a larger enthalpy of formation,
larger activation energy for conductivity, etc.
3−
LnBr6 ions are formed in LnBr3–MBr liquid mixtures. These ions
constitute the predominant species in the MBr-rich liquid mixtures.
As the LnBr3 concentration increases distorted octahedral species
occur, which are bridged by bromide anions. Complex formation
in the melt influences the activation energy for electrical conduc-
tivity, which should increase with increasing amount of complex
4. Conclusions
Phase equilibrium in the PrBr3–RbBr binary system was estab-
lished for the first time by differential scanning calorimetry (DSC).
This system includes the Rb3PrBr6, Rb2PrBr5 and RbPr2Br7 com-
pounds and three eutectics. Rb3PrBr6 undergoes a solid–solid phase
transition at 704 K and melts congruently at 995 K. Rb2PrBr5 melts
incongruently at 803 K with formation of solid Rb3PrBr6 and finally
RbPr2Br7 melts congruently at 852 K. The electrical conductivities
of PrBr3–RbBr liquid mixtures measured over an extended temper-
ature range and on the whole composition range are indicative of
3−
octahedral PrBr6 complexes formation.
Acknowledgements
Financial support by the Polish Ministry of Science and Higher
Education from budget on science in 2007–2010 under the grant
No. N204 4098 33 is gratefully acknowledged.
L.R., M.B. and E.I.-S. wish to thank the Ecole Polytechnique de
Marseille for hospitality and support during this work.
Fig. 4. Electrical conductivity isotherms of PrBr3–RbBr liquid mixtures at 1050 K:
(open circles) experimental results; and (solid line) polynomial fitting.
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