Ionics (2012) 18:255–265 DOI 10.1007/s11581-011-0624-5
ORIGINAL PAPER
The electrical conductivity of chloride melts Alexander A. Redkin & Elena V. Nikolaeva & Alexander E. Dedyukhin & Yurii P. Zaikov
Received: 5 July 2011 / Revised: 30 August 2011 / Accepted: 5 September 2011 / Published online: 1 October 2011 # Springer-Verlag 2011
Abstract The interrelationship between electrical conductivity, molar volume and enthalpy of mixing was studied for molten chlorides and their mixtures. The dependence of electrical conductivity and activation energy on the molar volume is different for various groups of salts. The dependence of specific conductivity on molar volume obtained for molten alkali chlorides was found to be similar to other chloride salts. The specific conductivity of binary mixtures that lack strong chemical interactions between the components can also be described by the proposed empirical equation. The enthalpy of mixing should be taken into consideration for these chemical interactions. Keywords Molten electrolytes . Chlorides . Electrical conductivity . Molar volume
Introduction More than 20 metals can be produced by molten salt electrolysis [1]. Some of them can be obtained from fluoride electrolytes, but the chloride bath is preferred because of its lower liquidus temperatures. The main component of the chloride electrolyte is a mixture of alkali chlorides. The largest industrial process based on molten chlorides is magnesium electrolysis. In this case, the electrolyte is composed of alkali and alkaline-earth chlorides. The electrical conductivity of a salt bath is an important property for electrolytic processes. Currently, A. A. Redkin (*) : E. V. Nikolaeva : A. E. Dedyukhin : Y. P. Zaikov Institute of High Temperature Electrochemistry, 22 S. Kovalevskaya, Yekaterinburg 620990, Russia e-mail:
[email protected]
there is no reliable model for describing the conductivity of molten salt mixtures. Generally, the conductivity of salt mixtures can be taken as the sum of the individual components. However, this assumption is not correct because electrical conductivity is an extensive property. Some authors have proposed equations for “ideal conductivity” [2, 3], but these equations are only valid for very limited number of molten salt mixtures and cannot be used for multi-component systems. For more than 100 years, the electrical conductivity of chloride melts has been a topic of investigation, and now there are enough data to determine the factors governing electrical conductivity. The first attempt at molten chloride classification based on electrical conductivity was made by Biltz and Klemm [4]. They divided all of the molten chlorides into either good or bad conductors based on the location of the cations in the periodic table. An improved classification was proposed by Antipin [5]. He divided all molten chlorides into four groups. The first one includes good conductors, such as LiCl, NaCl, KCl, RbCl, CsCl, CaCl2, SrCl2, BaCl2 and LaCl3. The equivalent conductivity of these salts near their melting point is higher than 30 S cm2/mol. The second group consists of salts with lower conductivity, such as MgCl2, ScCl3, YCl3 and ThCl4. Their equivalent conductivity is higher than 1 Scm2/mol but lower than 30 Scm2/mol. The third group contains salts that are poor conductors including the following compounds: BeCl2, AlCl3, ZrCl4, HfCl4, NbCl5 and TaCl5.Their equivalent conductivity is lower than 1 Scm2/mol. The chlorides of boron, silicon, titanium and vanadium are insulators. This classification can be explained by the ionic potential of cations (charge/radius). In our previous studies [6, 7], the correlation between electrical conductivity and ionic potential as well as the dependence of electrical conductivity on molar volume was proposed for alkali
256
Ionics (2012) 18:255–265
halides. In this paper, the dependence of electrical conductivity on molar volume is extended to the other chloride salts that exist as liquids at 900–1,200 K.
Source of data Molten chloride properties have been collected by different groups of authors. The most comprehensive set of data are presented in Janz’s reviews [8, 9]. Recently, Minchenko and Stepanov [10] published a book that discusses the density of molten halide salts and their mixtures. The data from this paper are presented in Table 1.
The electrical conductivity, activation energy and molar volume The activation energy plays an important role in the transfer of mass and electricity [22]. It determines the number of particles participating in the process; a higher activation energy leads to a lower fraction of active particles. The activation energy was found to be dependent on the interionic distances [23]. Molar volume reflects the distance between particles in any substance. The dependence of the electrical conductivity and the activation energy on the molar volume for molten alkali chlorides, alkaline-earth chlorides and LaCl3 is shown in Fig. 1. The description will
Table 1 Density (ρ=ρ0 −α T) and electrical conductivity (σ=A exp(−E/RT)) data used for fitting the empirical equation Salts
ΔT/K
ρ0/g cm−3
α 104/g cm−3 K−1
ΔT, K
A/S cm−1
E/J mol−1 6,098
LiCl [9, 10]
894–1,085
1.90
4.46
917–1,056
13.13
NaCl [9, 10]
1,079–1,249
2.15
5.56
1,080–1,290
7.64
6,743
KCl [9, 10] RbCl [9, 10] CsCl [9, 10]
1,073–1,193 998–1,107 934–1,134
2.13 3.12 3.77
5.79 8.77 10.54
1,063–1,198 1,003–1,197 926–1,170
6.95 8.62 11.70
10,100 14,393 17,962
AgCl [9] MgCl2 [9, 10] CaCl2 [9, 10] SrCl2 [9, 10] BaCl2 [9, 10] CrCl2 [11, 12] CoCl2 [13] FeCl2 [14] MnCl2 [15, 16] CdCl2 [9] PbCl2 [9] LaCl3 [10, 17] CeCl3 [10, 18] PrCl3 [10, 17] NdCl3 [10, 17]
760–900 1,123–1,223 1,123–1,223 1,154–1,245 1,244–1,367 1,103–1,273 1,020–1,140 1,000–1,100 967–1,118 840–1,080 789–983 1,150–1,252 1,100–1,370 1,100–1,370 1,050–1,370
5.52 2.06 2.64 3.39 4.33 2.64 3.19 2.97 2.82 4.08 6.11 3.80 3.82 3.86 3.93
9.40 3.79 5.16 5.69 9.84 2.22 7.80 6.58 5.08 8.20 1.50 5.63 6.42 6.58 6.63
753–1,013 987–1,252 1,060–1,291 1,146–1,357 1,233–1,359 1,103–1,173 1,040–1,220 1,000–1,100 942–1,179 845–1,082 773–923 1,120–1,203 1,088–1,182 1,102–1,178 1,033–1,210
8.48 7.37 19.63 17.79 17.48 6.65 14.53 5.86 5.41 6.37 15.55 18.15 13.10 15.75 14.91
4,941 16,314 19,870 20,866 22,067 19,060 24,628 10,848 10,099 8,577 15,184 25,041 22,447 24,365 24,745
SmCl3 [10, 17] EuCl3 [10, 17] GdCl3 [10, 17] TbCl3 [10, 17] DyCl3 [10, 17] HoCl3 [10, 19] ErCl3 [10, 17] TmCl3 [10, 19] YbCl3 [10, 17] LuCl3[10, 19] YCl3 [10, 20] ThCl4 [9] UCl4 [9, 21]
960–1,370 – 900–1,370 870–1,370 950–1,370 1,000–1,370 1,050–1,370 1,100–1,370 1,150–1,370 1,150–1,370 998–1,118 1,050–1,120 891–998
4.12 4.31 4.19 4.19 4.20 4.20 4.11 4.31 4.41 4.44 3.01 4.82 5.63
7.31 8.27 7.06 6.94 6.60 6.21 5.10 6.64 6.63 6.82 5.00 14.00 22.92
932–1,178 867–992 883–1,156 848–1,195 910–1,202 992–1,204 1,047–1,203 1,067–1,265 1,133–1,233 1,157–1,278
29.54 17.10 6.16 21.95 21.86 6.97 22.58 7.62 23.58 24.38 89.83 10.25 5.22
30,008 26,690 14,659 31,375 32,908 17,108 34,816 19,125 36,223 38,516 45,251 25,368 18,104
1,087–1,195 872–1,001
Ionics (2012) 18:255–265 30
25
Activation energy, kJ/mol
Fig. 1 Dependence of the activation energy of electrical conductivity on the molar volume for some molten chlorides at 1,150 K (Data for BaCl2 were extrapolated for the temperature range lower than its melting point.)
257
BaCl 2 20
LaCl 3
SrCl 2 CaCl 2 MgCl 2
CsCl
15 RbCl 10 KCl 5
NaCl LiCl
0 28
38
48
58
68
78
88
Molar volume, cm 3/mol
25 SrCl2 BaCl2
Activation energy, kJ/mol
Fig. 2 Dependence of the activation energy of electrical conductivity on the molar volume for alkali and alkaline-earth chlorides at 1,150 K
20 CaCl2
15
CsCl
KCl RbCl
10 LiCl NaCl 5 25
30
35
40
45
50
55
60
65
70
75
Molar volume, cm3/mol
37
Activation energy, kJ/mol
Fig. 3 Dependence of the activation energy of electrical conductivity on the molar volume for rare earth chlorides at 1,150 K
LuCl 3
YbCl 3 DyCl 3
32
TbCl 3
SmCl 3
27
NdCl 3
PrCl 3 CeCl 3
22
TmCl 3 HoCl 3
17
GdCl 3 12 77
77.5
78
78.5
79
79.5
Molar volume, cm 3/mol
80
80.5
81
258 20
CrCl 2
Activation Energy, kJ/mol
Fig. 4 Dependence of the activation energy of electrical conductivity on the molar volume for transition metal chlorides at 1,150 K
Ionics (2012) 18:255–265
CoCl 2 15
FeCl 2 10
MnCl 2
5 51
52
53
54
55
56
57
58
59
85
25
75
20
65
15
55
10
45
5
35
3
30
Molar volume, cm /mol
Fig. 5 Dependence of the molar volume, activation energy of electrical conductivity on composition for molten mixtures of LiCl+LaCl3 at 1,150 K
Activation Energy, kJ/mol
Molar volume, cm 3/mol
0
0
0.2
0.4
0.6
0.8
1
25
LaCl 3, molar fraction
30
80
25 3
75
Molar volume, cm /mol
Activation ehergy, kJ/mol
Fig. 6 Dependence of the molar volume, activation energy of electrical conductivity on composition for molten mixtures of CsCl+LaCl3 at 1,150 K
20
70 15
10
0
0.2
0.4 0.6 LaCl 3, molar fraction
0.8
1
65
Ionics (2012) 18:255–265
259
be more accurate if the salts are divided into groups based on the location of the cations in the periodic table due to the different dependencies exhibited by the groups and periods. In a group, the activation energy is directly proportional to molar volume but the activation energy decreases with the molar volume in a period. These trends reflect the different processes taking place as the electronic structure changes on going from groups to periods. The dependence of the activation energy on the molar volume for alkali, alkaline-earth, transition metal and rare earth chlorides are shown in Figs. 2, 3 and 4. In the groups (alkali and alkaline-earth chlorides), the dependence
is directly proportional. In the periods (transition and rare earth chlorides), the dependence is reciprocal. The relationship between activation energy and molar volume can also be determined for molten chloride mixtures. The change in the activation energy and the molar volume as a function of the composition of the mixtures is presented in Figs. 5 and 6 for molten mixtures of LiCl–LaCl3 and CsCl–LaCl3. Both parameters change in an additive way for the first system, and they exhibit a positive deviation in the second system. These results could be related to the energetic state of matter, which depends on volume and temperature [24]. The
Table 2 Conductivity σcal calculated according to equation 1 and experimental conductivity σexp (Table 1) of some chlorides T/K=900
T/K=1050
Salt
σexp/S·cm-1
σcal/S·cm-1
k
σexp/S·cm-1
LiCl NaCl
5.81 -
5.81 -
1.00 -
6.53 3.53*
KCl RbCl
-
-
-
CsCl AgCl MgCl2 CaCl2 SrCl2 BaCl2 CrCl2 CoCl2 MnCl2
4.38 -
4.55 -
CdCl2
2.02 2.04 -
PbCl2 FeCl2 YCl3 LaCl3 CeCl3 PrCl3 NdCl3 SmCl3 EuCl3 GdCl3 TbCl3 DyCl3 HoCl3 ErCl3 TmCl3 YbCl3 LuCl3 ThCl4 UCl4
T/K=1150 σcal/S·cm-1
k
σexp/S·cm-1
T/K=1200 σcal/S·cm-1
k
σexp/S·cm-1
σcal/S·cm-1
k
6.45
1.01
-
-
-
-
-
-
2.18* 1.66
3.60 2.12 1.75
0.98 1.03 0.94
3.78 2.42 -
3.92 2.41 -
0.96 1.00 -
3.89 2.52 -
4.06 2.54 -
0.96 0.99 -
0.96 -
1.49 1.14 2.02* 0.70* 0.87 1.70
1.44 1.66 1.87 1.98 1.77 1.76
1.04 0.69 1.08 0.35 0.49 0.97
1.79 1.34 2.46 2.01
1.69 1.96 2.19 1.99
1.06 0.68 1.12 1.01
0.92 1.11 1.88
2.36 2.06 2.07
0.39 0.54 0.91
1.44 2.68 2.20 1.91* 1.00 1.23* -
2.11 2.35 2.15 1.84 2.55 2.20 -
0.68 1.14 1.02 1.04 0.39 0.56 -
1.21 1.09 -
1.68 1.87 -
1.32 0.94
0.67 -
1.43 0.98 0.45 0.77 0.70 0.81 1.00 0.53 0.44 0.86 0.37 0.74 -
1.97 2.02
0.80 -
1.67 1.73 1.11 1.13 1.14 1.17 1.15 1.14 1.14 1.15 1.14 1.15 -
2.60 1.89
0.54 -
2.38 1.69 0.50 0.88 0.80 0.95* 1.15 0.60 0.50 0.98 0.42 0.85* -
1.32 1.21 1.23 1.12 1.05 1.33 0.82 0.70 1.16 0.59 1.03 0.53 0.43
1.40 1.37 1.37 1.38 1.39 1.40 1.40 1.40 1.40 1.41 1.41 1.43 1.42
0.94 0.88 0.90 0.81 0.75 0.95 0.59 0.50 0.83 0.42 0.73 0.37 0.31
1.48 1.36 1.37* 1.25 1.18* 1.42* 0.95 0.81 1.25 0.69 1.12 0.62 0.51
1.53 1.49 1.50 1.51 1.52 1.53 1.52 1.52 1.53 1.54 1.54 1.56 1.55
0.96 0.91 0.92 0.83 0.78 0.93 0.62 0.53 0.82 0.45 0.73 0.40 0.33
0.46
0.84
0.55
0.66 0.56*
1.26 1.59
0.52 0.35
0.72 -
1.89 -
0.38 -
-
-
-
* extrapolation
260
Ionics (2012) 18:255–265
Fig. 7 Correlation between calculated and experimental specific conductivity data
7
6
LiCl
σcalc , S/cm
5
4
NaCl
3
2
MgCl 2
KCl
RbCl
SrCl 2 CaCl 2 CsCl
LaCl 3 BaCl 2
1
0 0
1
2
3
4
5
6
7
σexp , S/cm
activation energy depends on the molar volume, and the electrical conductivity also depends on the molar volume.
is valid for pure alkali chlorides for the temperature range of 900–1,200 K. Equation 1 describes the experimental data for the electrical conductivity of alkali chlorides with an accuracy of 5% in this temperature interval.
Electrical conductivity of molten alkali chlorides The alkali cations have the lowest ionic potentials, and the alkali chlorides possess the greatest specific conductivity values among chloride salts. The dependence of the specific conductivity on the molar volume for molten alkali chlorides is expressed by empirical Eq. 1 [7]:
Electrical conductivity of molten alkaline-earth and other good conducting chlorides Equation 1 can be extended to alkaline-earth, rare earth and other molten chlorides that possess good electrical conductivity. A comparison of the calculated and experimental data is presented in Table 2 and Fig. 7. The coefficient k (σexp/σcal) reflects the difference between calculated and experimental data (Table 1). The value of k is approximately equal to 1 (k= 0.90–1.14) for alkaline-earth chlorides, but the k value is less than 1 (k=0.68–0.70) for molten MgCl2. For the d-metal
s ¼ 4:9 exp½ð2; 747 33; 724=V Þ=T expð53:7=V Þ;
ð1Þ
where V is the molar volume (cm3/mol), σ is the specific conductivity (S/cm), and T is the temperature (K). Equation 1 Fig. 8 Temperature dependence of coefficient k for CdCl2 (filled circles), ThCl4 (filled squares) and UCl4 (filled triangles)
1.8 1.6 1.4
Coefficient k
1.2 1.0 0.8 0.6 0.4 0.2 0.0 850
900
950
1000
1050
T, K
1100
1150
1200
Ionics (2012) 18:255–265
261
LiCl k=1
BeCl2 k<0.1
BCl3
NaCl k=1
MgCl2 k=0.7
AlCl3 k<0.1
KCl k=1
CaCl2 k=1.12
ScCl3 k=0.5
RbCl K=1
SrCl2 k=1
YCl3 k=0.45
CsCl k=1
BaCl2 k=1
LaCl3 k=1
uranium and thorium have much lower k values (0.35–0.55). For most of the molten chlorides, k shows no clear temperature dependence except for CdCl2, ThCl4 and UCl4 (Fig. 8). By sorting the cations according to their location in the periodic table, the salts where k is close to 1 (0.9–1.1) coincide with good conductors, as classified by Antipin [5] (Fig. 9). For less conducting salts, k varies from 0.1 to 1. The coefficient k reflects the specific features of the cations. Thus, it is possible to use Eq. 1 not only for alkali chlorides but also for other chloride salts by including the coefficient k (Table 3): s ¼ 4:9 exp½ð2; 747 33; 724=V Þ=T expð53:7=V Þ k:
ð2Þ
Fig. 9 Dependence of the k values on the position of the cation in the periodic table
chlorides studied, Eq. 1 is valid for MnCl2, FeCl2 and AgCl (k=0.91–0.98). Their equivalent conductivity is higher than 40 Scm2/mol in the temperature range discussed. The equivalent conductivity of chromium and cobalt dichlorides is less than 30 Scm2/mol, and the k coefficient is much lower than 1 (k=0.35–0.56). For heavy metal chlorides (CdCl2 and PbCl2), the value of k is higher than 1. For lanthanide chlorides, Eq. 1 is valid only for the most conductive salts including LaCl3 and GdCl3 (k=0.93–1).The tetrachlorides of Table 3 Calculated values obtained from Eq. 1 (σcalc) and experimental [8] conductivity (σexp) for LiCl+KCl, LiCl+ CsCl, KCl+CsCl and NaCl+ CsCl at 1,100 K
0.00 0.18
6.62 4.65
6.72 4.33
0.10 −0.33
1.47 7.01
0.30 0.42 0.60
3.94 3.47 2.94
3.54 3.17 2.69
−0.40 −0.30 −0.25
10.18 8.53 8.42
0.80 1.00
2.52 2.19
2.43 2.30
−0.09 0.11
3.75 5.22
0.00 0.20 0.42 0.53
6.62 3.82 2.63 2.25
6.72 4.12 2.62 2.17
0.10 0.30 −0.01 −0.08
1.47 7.82 0.34 3.60
0.70 0.80 1.00 0.00 0.25 0.50 0.75 1.00 0.00 0.25 0.50 0.75 1.00
1.90 1.73 1.51 2.19 1.93 1.75 1.60 1.51 3.73 2.63 2.05 1.71 1.51
1.76 1.57 1.53 2.30 1.98 1.77 1.62 1.50 3.65 2.31 1.89 1.63 1.50
−0.14 −0.15 0.03 −0.10 −0.06 −0.02 −0.02 0.00 0.08 0.33 0.15 0.08 0.00
7.22 8.89 1.83 4.77 2.90 1.35 1.52 0.16 2.21 12.36 7.54 4.50 0.16
LiCl(1)+KCl(2)
NaCl(1)+CsCl(2)
(σcalc –σexp)/S cm−1
s calc s exp s exp
σexp/S cm−1
X2
KCl(1)+CsCl(2)
Alkali chloride mixtures can be considered ideal because the change in the molar volume at constant temperature is nearly equivalent to the results obtained from the additive law. The deviations do not exceed 2% [25], which is due to the close ionic potentials of the alkali cations. Thus, the specific conductivity of alkali chloride mixtures can be described by σcalc/S cm−1
System
LiCl(1)+CsCl(2)
Electrical conductivity of ideal chloride mixtures
100
262 Table 4 Calculated values obtained from Eq. 3 and experimental [8] conductivity (σ) for LiCl+KCl, LiCl+CsCl, KCl+ CsCl and NaCl+CsCl at 1,100 K
Ionics (2012) 18:255–265
LiCl(1)+KCl(2)
LiCl(1)+CsCl(2)
NaCl(1)+CsCl(2)
KCl(1)+CsCl(2)
σexp
0.00
6.72
6.72
0.00
0.00
0.18 0.30
5.16 4.38
4.33 3.54
0.84 0.84
19.30 23.60
0.42
3.80
3.17
0.63
19.91
0.60 0.80
3.06 2.57
2.69 2.43
0.38 0.14
14.08 5.91
1.00
2.30
2.30
0.00
0.00
0.00 0.20
6.72 4.47
6.72 4.12
0.00 0.34
0.00 8.32
0.42
3.00
2.62
0.38
14.61
0.53
2.48
2.17
0.32
14.62
0.70 0.80
1.99 1.79
1.76 1.57
0.24 0.21
13.50 13.58
1.00
1.53
1.53
0.00
0.00
0.00 0.25
3.73 2.63
3.73 2.31
0.00 0.36
0.00 15.58
0.50 0.75 1.00
2.05 1.71 1.51
1.89 1.63 1.51
0.16 0.06 0.00
8.63 3.74 0.00
0.00 0.25 0.50
2.30 1.90 1.70
2.30 1.98 1.77
0.00 −0.08 −0.07
0.00 −4.37 −4.16
0.75 1.00
1.58 1.50
1.62 1.50
−0.06 0.00
−3.00 0.00
ð3Þ
where lm is the equivalent conductivity of salt mixture, l1 and l2 are the equivalent conductivity of pure components (l1
7.6
6.6
5.6
σ, S/cm
Fig. 10 Specific conductivity of LiCl+MnCl2 and NaCl+MnCl2 molten systems at 1,100 K: filled circles LiCl+MnCl2 (experimental. Ref. [15]), empty circles LiCl+MnCl2 (calculation), filled squares NaCl+ MnCl2 (experimental, Ref. [15]) and empty squares NaCl+ MnCl2 (calculation)
σcalc −σexp
s calc s exp s exp
σcalc
Eq. 1. A comparison of calculated results obtained from Eq. 1 and the experimental data are given in Table 3. The difference does not exceed 12.5%. The deviations of the experimental equivalent conductivity from the calculated values are comparable to the results obtained by Markov and Shumina [3]. They used the equation of ideal conductivity: lm ¼ x21 l1 þ x22 l2 þ 2x1 x2 l1
100
X2
4.6
3.6
2.6
1.6
0
0.1
0.2
0.3
0.4
0.5
0.6
MnCl 2, molar fraction
0.7
0.8
0.9
1
Ionics (2012) 18:255–265 8 7
LiCl-MgCl 2
6 5
σcalc , S/cm
Fig. 11 Specific conductivity of LiCl+MgCl2 and NaCl+MgCl2 molten systems at 1,100 K: filled triangles LiCl+MgCl2 (experimental, Ref. [8]), filled circles LiCl+MgCl2 (calculation), filled squares NaCl+ MgCl2 (experimental, Ref. [8]) and filled diamonds NaCl+ MgCl2 (calculation)
263
4 3
NaCl-MgCl 2 2 1 0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0.7
0.8
0.9
1
MgCl 2, molar fraction
Fig. 12 Specific conductivity of the CsCl+MnCl2 molten system at 1,100 K: empty circles experimental, Ref. [15] and filled circles calculation
2
1.8
σ, S/cm
1.6
1.4
1.2
1
0.8
0
0.1
0.2
0.3
0.4
0.5
0.6
MnCl 2, molar fraction
30
4.0 3.5
25 3.0 20 2.5 15
2.0 1.5
10 1.0 5 0.5 0
0.0 0
0.1
0.2
0.3
0.4
0.5
0.6
MnCl 2, molar fraction
0.7
0.8
0.9
1
Excess molar volume
Enthalpy of mixing (absolute values), kJ/mol
Fig. 13 Heat of mixing, H [28] and excess molar volume, dV [15], for CsCl+MnCl2 at 1,073 K: filled circles heat of mixing and empty circles dV
0.8
3.0
0.6
2.0
0.4
1.0
0.2
0.0
Deviation of specific conductivity from calculated values, S/cm
4.0
3
Fig. 14 Deviations of the experimental specific conductivity values from the calculated values and the excess molar volume forCsCl+MnCl2 at 1,073 K: empty circles excess specific conductivity and filled circles dV
Ionics (2012) 18:255–265
Excess molar volume, cm /mol
264
0 0
0.2
0.4
0.6
0.8
1
MnCl 2, molar fraction
CsCl–LaCl3 exceeds 5% [10], and it corresponds to a high enthalpy of mixing [26]. In addition, the molar volumes for mixtures of lithium chloride and sodium chloride with lanthanum chloride are nearly additive [8]. A similar behaviour is observed for mixtures of alkaline-earth and rare earth chlorides as well for mixtures of transition metal chlorides with lithium and sodium chlorides. This phenomenon can be explained by the difference in the electronic structure of lithium and sodium cations in comparison to other alkali cations. Light elements (e.g. Li and Na) have fewer electronic shells than other alkali elements, which can affect their interaction with other cations and anions. Thus, the mixtures of lithium and sodium chlorides with other metal chlorides can also be considered nearly ideal. The calculated and experimental conductivity data for LiCl+ MnCl2 and NaCl+MnCl2 are shown in Fig. 10. Equation 1 was used for the calculation. The experimental values of molar volume and specific conductivity were taken from the paper by Kucharski and Flengas [15]. The calculated and experimental values are in good agreement. For the mixtures
s ¼ 4:9 exp½ð2; 747 33; 724=V Þ=T expð53:7=V Þ expðX ln k Þ
ð4Þ
where X is the molar fraction of salt having coefficient k and V is the molar volume of the mixture (cm3/mol). Examples of these systems include molten mixtures of LiCl–MgCl2 and NaCl–MgCl2 (Fig. 11).
Electrical conductivity of non-ideal chloride mixtures The mixtures of potassium, rubidium and caesium chlorides with other metal chlorides are non-ideal due to strong interactions between the components. These interactions result in high positive deviations of the molar volume from the additive values and larger
-5
0
14
16
18
20
22
24
26
-5
-10
-25
-15
-35
-20
-45
-25
•
-1
/%
-15
-55
-30 dIP, nm -1
H, KJ/mol
5
100•
Fig. 15 Maximal relative deviations of experimental specific conductivity values from calculated values and maximal heat of mixing for MCl+LaCl3 (M=Li, Na, K and Cs) at 1,173 K depending on ionic potential differences between La and alkali cations: empty squares excess specific conductivity and filled triangles heat of mixing
of alkali chlorides with other salts having coefficient k deviating from 1, the electrical conductivity–molar volume dependence can be expressed as follows:
Ionics (2012) 18:255–265
negative deviations of specific conductivity from ideal behaviour. These deviations can be explained by the enthalpy of mixing proposed by Hong and Kleppa [27]. They found that the enthalpy of mixing is dependent on the ionic potential difference. The deviations of the experimental electrical conductivity from the calculated values are dependent on the ionic potential difference. The molar volume deviation from the additive values also correlates with the ionic potential difference. An example of a system with strong chemical interactions between its components is CsCl–MnCl2. The calculated and experimental values of the specific conductivity are given in Fig. 12. There are large deviations between the experimental specific conductivity and the calculated values. These deviations have a strong correlation with the enthalpy of mixing [28] (Fig. 13) as well as with the excess molar volume (Fig. 14). Thus, the excess molar volume, the enthalpy of mixing and the negative deviations observed for specific conductivity correlate with each other and are dependent on ionic potential differences. The dependence of the maximal relative deviations of the specific conductivity from the calculated values and the maximal enthalpy of mixing on ionic potential differences are provided in Fig. 15 for MCl–LaCl3 (M=Li, Na, K and Cs).There is a good correlation in the variation of these excess parameters with ionic potential differences, which means that it is possible to evaluate their electrical conductivity based on composition and temperature when the molar volume and enthalpy of mixing are known.
Conclusions 1. The correlation between specific conductivity and molar volume of molten chlorides was proposed. 2. The mutual mixtures of alkali chlorides were found to be systems that are close to ideal because they have a low enthalpy of mixing and an additive change in the molar volume with composition and specific conductivity values in agreement with calculated values. 3. The mixtures of lithium and sodium chlorides with other metal chlorides were shown to be close to ideal. 4. The mixtures of potassium, rubidium and caesium chlorides with other metal chlorides show a strong interaction between components, which influences their molar volume, enthalpy of mixing and electrical conductivity properties.
265 Acknowledgements The work was performed with support from the Ministry of Education and Science of the Russian Federation. State contract 16.525.12.5005.
References 1. 2. 3. 4. 5. 6. 7.
8. 9. 10. 11. 12. 13. 14. 15. 16. 17.
18. 19.
20. 21. 22. 23. 24. 25. 26. 27. 28.
Kroll WJ (1945) J Electrochem Soc 87:551 Markov BF, Shumina LA (1956) Reports SSSR Acad Sci 110:411 Markov BF, Shumina LA (1957) Russian J Phys Chem 31:1767 Biltz W, Klemm W (1926) Z Anorg Alg Chem 152:267 Antipin AN, Vazhenin SFE (1964) Electrochemistry of fused salts. Metallurgizdat, Moscow Redkin A, Tkacheva O, Shuryghin Y, Zaikov Y (2008) Z Naturforsch 63a:462 Redkin A (2002) In: Delong H. C., Bradshaw R. W., Matsunaga M., Stafford G. R., Trulove P. C. (eds) Proceedings of 13th international symposium on molten salts. The Electrochemical Society, Pennington, NJ, p. 453 Janz GJ, Tomkins RP, Allen CB, Downey JR, Gardner HG, Krebs U, Singer S (1975) J Phys Chem Ref Data 4:875 Janz GJ (1988) J Phys Chem Ref Data 17:2 Minchenko VI, Stepanov VP (2008) Ionic melts: elastic and caloric properties. UD RAS, Yekatrinburg Sobchak ES, Shkolnikov SN (1984) Russ J Appl Chem 2:397 Sobchak ES, Shkolnikov SN (1981) Russ J Appl Chem 3:542 Redkin AA, Salyulev AB, Smirnov MB, Khokhlov VA (1995) Z Naturforsch 50A:998 Redkin AA, Salyulev AB, Smirnov MB (1997) Z Naturforsch 52A:420 Kucharski AS, Flengas SN (1979) J Electrochem Soc. 121:1298– 1308 Camichael NR, Flengas SN (1979) J Electrochem Soc 126(2098– 2104):2104–2110 Kulagin NM, Laptev DM, Kulagina NG, Kiseleva TV, Poshevneva AI (1987) In: Abstracts of 9th all-union conference on physical chemistry and electrochemistry of ionic mets and solid electrolytes, USSR Academy of Science, Sverdlovsk, vol. 1, p. 79 Redkin AA, Tkacheva OY, Shishkin VY, Khokhlov VA (1998) High Temperature Material Processes 2: 581 Potapov AM (2009) Transport properties of lanthanide chlorides and their mixtures with alkali chlorides. Doctoral dissertation, Yekatherinberg Mochinaga J, Fukushima K, Iwadate Y, Kuroda H, Kawashima T (1993) J Alloys Comp 193:33 Desyatnik VN, Katyshev SF, Raspopin SP (1978) Atomnaya Energya 42(2):99 Pauling L (1927) J Am Chem Soc 49:765 Chebotin VN (1982) Physical chemistry of solid electrolytes. Khimiya, Moscow Feynman RP, Leighton RB, Sands M (1963) The Feynman Lectures on Physics, vol 1. Adison-Wisley, London Smirnov MV, Stepanov VP (1982) Electrochimica Acta 27(11):1551 Papatheodorou GN, Ostvold T (1974) J Phys Chem 78:181 Hong K, Kleppa O (1978) J Phys Chem 82:1596 Papatheodorou GN, Kleppa O (1971) J Inorg Nucl Chem 33:1249–1278
