Ionic Transport in Molten Salts

5 Ionic Transport in Molten Salts Isao Okada Tokyo Institute of Technology, Tokyo, Japan

5.1

Introduction

As transport properties of molten salts, diffusion constants and electrolytic conduction may be considered to be the main properties, although viscosity and heat conductivity are also included. This chapter focuses its attention on electrolytic conduction. Most molten salts are composed of ionic species, that is, cations and anions, which interact directly with each other mainly by the coulombic attraction without solvents such as water molecules as intermediators. Between cations and between anions, the coulombic repulsion works. Thus, molten salts may be regarded as the simplest target of “coulombic chemistry.” In this sense, among the various properties of molten salts, one of the most characteristic ones is electrical transport expressed in terms of electric conductivities or mobilities. Collective data on electrical conductance were presented by Janz [1] in 1988.

5.2 5.2.1 l

l l

l

l

Electric Conductance Definition of Some Properties Concerning Electric Conductance

Conductivity {[2]}, k: previously called “specific conductance.” The mark {[]} indicates that the term is given in [2] without definition. Ionic conductivity {[2]}: conductivity of each ionic species. Molar conductivity of an ion {[2]}: For molar quantity, the unit species should be defined so that it is equal to the previously used “equivalent” quantity. Mobility, u: velocity of an ion, v, per electric field, EV, that is, u ¼ v/EV. In molten salts, where there is no distinction between solute and solvent, a problem arises concerning the reference frame. Thus, two kinds of mobilities, that is, external mobility, ue, and internal mobility, ui, are defined. The former is defined for mobility with reference to “laboratory” or actually a porous frit. The latter is defined with reference to the counterion, usually the anion. The internal mobility of the cation in a pure salt and a mixture with a common anion is the sum of the external mobilities of the cation and the anion: ui ¼ ue(cation) þ |ue(anion)|. Transport number {[2]}: In a pure melt MX (M: cation, and X: anion), the external transport numbers, tþ and t, are defined as tþ e ¼ uþ e =ðuþ e þ u e Þ and t e ¼ uþ e =ðuþ e þ u e Þ, while the internal transport number, tM i , is unity. Concerning the reference frame in the external transport number, the same problem arises in external mobility.

For measurement of the external transport number, a kind of the Hittorf method proposed by Chemla’s group [3] seems to be appropriate and practical; in this method, the melt levels Molten Salts Chemistry © 2013 Elsevier Inc. All rights reserved.

80

Molten Salts Chemistry

of the catholyte and the anolyte separated by a porous frit are arranged to be equal, and this method can be applied to multication systems with a common anion. As the theory for external mobility of pure salts, it has been proposed that tþ e ¼ m =ðmþ þ m Þ, where mþ and m are the masses of the cation and the anion, respectively [4,5]. For LiBr, for example, it is estimated to be te Li ¼ 0:92; however, by the aforementioned method, tLi e ¼ 0:78ð750  CÞ, 0.80(650  C), and 0.82(0750  C)[6], and the agreement between their theory and experimental data is poor, while there is a report stating that the external transport number is dependent on the nature of the used frit [7]. Whether the external transport number is the inherent property of molten salts has been argued (e.g., see Lunde´n [8]). At any rate, for elucidation of the electrical transport stated here, the problem of the external transport number can be avoided. Mobility will refer to internal mobility hereafter, unless otherwise stated.

5.2.2

Experimental Method for Internal Mobility Measurement

A countercurrent electromigration method, that is, the Klemm method, has been used for the internal mobility difference of binary mixtures with a common anion; this method was invented originally for the separation of isotopes [9–11]. The principle of the Klemm method is explained briefly using the cell employed for enriching mainly 7Li employed at the anode side by Chemla [12,13](see Figure 5.1), where a mixture of (Li, K)Br is used. A mixture melt of a desired concentration of (Li, K)Br is filled into the separation tube. Then, an electric field is applied between the graphite anode and the cathode. During electrolysis, bromine gas is fully supplied into the cathode compartment. Thus, the otherwise electrodeposited metal (mainly Li in this case) will be brominated (or oxidized) there. At the cathode, Liþ is reduced into Li (metal), which should be followed in the same instance by the reaction Li (metal) þ (1/2)Br2! LiBr. At the anode, bromine gas

Figure 5.1 Principle of a countercurrent migration method. The cell shown is practically the same as the one used for the enrichment of 7Li used originally by Chemla [12].

Ionic Transport in Molten Salts

81

is evolved as a result of electrolysis: Br–! (1/2)Br2. In the part of the separation diaphragm, both cations would electromigrate toward the cathode; however, by the force of gravity and the capillary action of the diaphragm used for suppression of the convection, a countercurrent flow (Cc in Figure 5.1) generates spontaneously in the opposite direction so that the melt levels of the anolyte and the catholyte are kept nearly constant. However, the faster cation (Liþ or Kþ) is to be enriched toward the cathode and the slower one toward the anode. After several hours of electromigration, the separation cell is taken out and the enriched part of the anode side is cut into several 1- to 2-cm fractions (1, 2, 3, . . . ,i in Figure 5.1), and salts toward the anode side are analyzed, where less mobile cations are enriched; the duration of electromigration is usually for several hours for measurement of the relative difference in the internal mobility, e, given by [14] 0X

X

n1i

u1  u2 B e ¼ @ i 0 x1 u1 þ x1 u2 x1



n2i

i

x02

1 C F A Q

(5.1)

where u1 and u2 are the internal mobilities of more mobile and less mobile cations, respectively; x1(¼x01) and x2(¼x02) are the mole fractions before electromigration; Q is the transported charge; and F is the Faraday constant. The sum is taken from fraction 1 to i, where the content of both cations has remained unchanged after electromigration; n1i and n2i are the quantities in mole of cations 1 and 2, respectively, in fraction i. There are some advantages in this method in comparison with other methods [15] such as the electromotive force method, the conventional Hittorf method, and the chromatographic methods; even very small difference in the mobilities of two cations can be measured accurately because the Klemm method was originally devised for the purpose of isotope separations. However, this method does not give any information on external mobilities, while the advanced Hittorf method does, as mentioned previously [3]. The internal mobilities, u1 and u2, are given by u1 ¼

kVm ð1 þ x2 eÞ ¼ L þ x2 eL F

(5.2a)

u2 ¼

kVm ð1  x1 eÞ ¼ L  x1 eL F

(5.2b)

where Vm is the molar volume and L is the molar conductivity; here, the molar quantity has to be defined to be equal to the “equivalent” quantity used previously. The molar volume (i.e., density) can be measured very accurately, and the additivity for the mixtures is known to hold within at most a 1–2 % deviation (e.g., [16]). The electric conductivity can be measured very accurately in mixtures as well as in pure melts. However, the additivity does not hold for k. Thus, when the value of k in a desired concentration is not available, the value has to be measured or interpolated directly from the values at neighboring concentrations (e.g., [17]).

5.2.3

The Chemla Effect and a Standard System for Mobility

Chemla discovered a very surprising phenomenon in 1958 [12], which was named “the Chemla effect” about 20 years after the discovery [18]. In a trial of enriching Li isotopes by the Klemm method, he employed a mixture of LiBr and KBr in order to reduce the running temperature as much as possible. While the chemical ratio of Liþ/Kþ of the anolyte attained

82

Molten Salts Chemistry

to a fixed ratio and did not change any more, 7Li (and 41K) continued to be enriched there. This means that the chemical species are not separated, whereas the isotopes are enriched. Thus, the Chemla effect has been considered to be a key for elucidation of the mechanism of electric conduction in molten salts; therefore, binary cationic systems with a common anion have become the target of investigations for this purpose—the binary systems studied so far are summarized in Okada [19]. The anion Chemla effect has been found in Li(Cl, NO3) experimentally [20] and predicted, for example, in Li(Cl, Br) by molecular dynamics (MD) simulation [21]. It was found rather recently that the binary system (Li, K)Br could be regarded as a standard system in the internal mobilities of the cations [22,23], whereas the original data had been presented by Chemla’s group about 40 years before [6]; the system (Li, K)Br studied there was actually the ternary system containing a trace amount of radioactive 22 Na (t1/2 ¼ 2.60 years). As the external mobilities are given [6], the corresponding internal mobilities are calculated easily. The isotherms in the present system are given at 1023 K in Figure 5.2; the melting points of LiBr, KBr, and the eutectic mixture (xK ¼ 0.4) are 823, 1007, and 601 K, respectively. For (Li, K)Br, an empirical formula [Equation (5.3)] holds well, which was presented originally from alkali nitrates, for example [24,25],   A E uc ¼ exp  ðVm  V0 Þ RT

(5.3)

where Vm is the molar volume, T is the temperature, R is the gas constant; and A, E, and V0 are constants characteristic of the cation of interest, c.

Figure 5.2 Isotherms of the internal mobilities in (Li, K)Br containing a trace amount of 22Naþ at 1023 K [22]. Chemla (crossing) points also exist between uLi and uNa and between uNa and uK.

Ionic Transport in Molten Salts

83

In order to show explicitly that Equation (5.3) holds, one can take the reciprocal of uc as a function of Vm for the isotherm of the internal mobilities: uc 1 ¼ aðVm  V0 Þ ¼ aVm  b

(5.4a)

where a ¼ ð1=AÞ expðE=RT Þ

(5.4b)

b ¼ ðV0 =AÞ expðE=RT Þ

(5.4c)

and

The reciprocals of uLi, uNa, and uK are plotted against the molar volume at 1023 K in Figure 5.3, which demonstrates that the values of uc 1 lie on straight lines as a function Vm except for uK 1 in “pure” LiCl at 1023 K; this slightly lower deviation is accounted for in terms of the agitation effect, as discussed in Section 5.2.7. In particular, the contained Naþ provides very useful information. The molar volume of the mixture of xK ¼ 0.4 (44.2 cm3 mol1) at 1023 K happens to be close to the one of pure NaBr (44.0 cm3 mol1) [1,26], and the internal mobilities of Naþ in (Li, K)Br and in pure NaBr are almost equal: 1.31 107 m2 V1 s1. The findings also support that the isotherms depend on the molar volume, regardless of the coexisting cations in this system.

Figure 5.3 Reciprocals of the internal mobilities shown in Figure 5.2 plotted against molar volumes. The corresponding value of pure NaBr is also presented (), by which the value of the trace amount of Naþ( ) is nearly overlapped [22]. l

84

Molten Salts Chemistry

With regard to the temperature dependence of Equation (5.3), the values are obtained at one concentration at less than 773 K; therefore, A, E, and V0 could not be determined uniquely without any assumptions. Thus, if A and E are assumed to be constant at lower temperatures, that is, below 923 K, V0 can be estimated in the following way. CI and CII are defined as CI  uðVm  V0 Þ

(5.5)

CII  A expðE=RT Þ

(5.6)

From Equations (5.4a) and (5.5), CI ¼ 1=a

(5.7)

If Equation (5.3) holds, CI ¼ CII

(5.8)

From Equation (5.5), uV0 þ CI ¼ uVm

(5.9)

When the values of u and Vm are obtained experimentally at more than two points at a given temperature, V0 and CI are calculated by a least-squares fit. The C I values at 1023 K are shown in Figure 5.4. Although CI can be estimated from “a” also by Equation (5.7), the value obtained from Equation (5.9) is more accurate because the Figure 5.4 CI values vs molar volume in (Li, K)Br at 1023 K [23].

Ionic Transport in Molten Salts

85

Figure 5.5 V0 values vs temperature in (Li, K)Br [23]. The standard deviation can be calculated only for the values at 823, 923, and 1023 K for Liþ and Kþ and at 1023 K for Naþ.

reciprocal values of each measured u are not weighted equally in the calculation from which the value of “a” is estimated. Nevertheless, it is recommended that at the first step of the data analysis, the reciprocal value of u be plotted against the molar volume, Vm. The values of V0, including the ones below 823 K estimated based on the aforementioned assumption, are shown in Figure 5.5. The temperature dependence of CI (¼ CII) is shown in Figure 5.6 [22]. Equation (5.3) indicates the following: (1) The mobility is not expressed by explicit functions of the mass nor the ionic radius. (2) The mobility decreases with an increase of the molar volume. (3) The excellent agreement of uNa in pure NaBr and of a trace amount of Naþ (practically, its concentration is zero) as a function of the molar volume demonstrates that the local environment within the coordination sphere around a cation mainly plays a role for the internal mobility. (4) The original data [6] are considered to be very accurate; as the external mobilities in the mixture were determined by the advanced Hittorf method [3], their method seems to provide accurate data also for the external mobilities in the mixtures.

Further, because the average number density of the common anion is NA/Vm (NA: Avogadro number), the value of V0 may be considered to indicate the deviation from the average density around the cation in the local structure. Therefore, it is reasonable that the sequence of V0 is Liþ > Naþ > Kþ (Figure 5.5), which is in order of strength of the coulomic attraction with the common anion. The temperature dependence of V0 seems to be also reasonable: as temperature decreases, V0 values become larger and approach constant values. As for E values, these are temperature dependent at a higher temperature, particularly for Kþ having a larger size. The value of V0 could become even negative in other systems.

86

Molten Salts Chemistry

Figure 5.6 Temperature dependence of CI values [22].

1023 K

12.8

923 K

823 K 773 K 723 K 673 K 633 K

K+ in pure LiBr

log10 CI/m5 V-1s-1 mol-1

12.6 12.4

Na+

K+

12.2 12.0

Li+

13.8 13.6 1.0

1.2 T

5.2.4

-1/10-3

1.4

1.6

K

Other Charge Symmetric Binary Cation Systems

5.2.4.1 Monovalent Binary Cation Systems with a Common Anion For comparison with data on (Li, K)Br, the u values of (Li, K)Cl at 973 K [17] are shown in Figure 5.7a. The isotherms of both systems appear to be similar; however, if the reciprocal values of u in (Li, K)Cl are taken in Figure 5.7b, the difference becomes distinct. In (Li, K)Cl,

Figure 5.7 Isotherms of (a) internal mobilities, u, vs the mole fraction of Kþ, xK, and of (b) these reciprocals vs the molar volume, Vm, in (Li, K)Cl at 973 K [17]. The value (▪) for pure KCl (m.p.: 1043 K) is the extrapolated one with respect to temperature.

Ionic Transport in Molten Salts

87

there is at least one inflection point (or discontinuous point) in the slope of uLi 1 and uK 1 . The size ratio of the anion/cation is not so large in the chloride mixtures as in the bromide mixtures; therefore, the structure within the coordination sphere around the cations would change at this point in the chloride. This assumption may be supported also from the fact that the inflection point of Kþ appears at a lower Vm than that of Liþ. In contrast, in (Li, Cs)Cl, where the Csþ/Cl size ratio is near unity (0.92; Csþ(VI): 167 pm, Cl (VI):181 pm [27], where (VI) stands for the coordination number of 6), the value of uCs 1 vs the molar volume at 973 K shows a straight line practically over the whole concentration range where the molar volume change is very large (from 28. 98 cm3 mol1(LiCl) to 60.96 (CsCl) cm3 mol1 [1]); however, the slope of uLi 1 shows a very big change [28]. This is presumably because the local structure within the coordination sphere around a large Csþ does not change too much but that around a small Liþ changes with increasing xCs. Molten nitrates of five alkali ions and of Agþ and Tlþ have relatively low melting points (ca. 250–420  C). The internal mobilities of the 21 (7C2 ¼ 7  6/2!) binary mixtures have been measured by the Klemm method in the same laboratory; the isotherms in these systems have so far been cited and discussed elsewhere [19,25,29,30]. The mobility isotherms of even two monovalent cations are not so simple and depend on the nature of the common anion. The case of (Na, K)OH is exemplified here [31]. Whereas the chemical behavior of Naþ and Kþ is generally considered to be highly similar, the isotherms of this system are essentially different as shown in Figure 5.8a. Here, the Chemla effect also manifests itself. The uK decreases with increasing concentration of Naþ. However, the reciprocals of uNa þ shown in Figure 5.8b suggest that such a relation as Equation (5.4a) holds except at a very high concentration of NaOH, where the free-space effect occurs (see Section 5.2.7.3), which is attributable to the hindrance of the rotational motion of the OH ion [30]. Although the OH ion is monovalent, this anion seems to behave like a divalent anion toward the neighboring cations, as the size of H is much smaller than the one of O in OH, and therefore the coulombic interaction with Naþ may be considerably larger than that with Kþ. Thus, a Naþ

Figure 5.8 (a) Mobilities, u, vs xK and (b) these reciprocals vs Vm in (Na, K)OH at 623, 673, and 723 K [31]. As for pure KOH at 623 K (▪)(m.p.: 633 K), see the legend to Figure 5.7.

88

Molten Salts Chemistry

ion acts as the tranquilizing cation on the mobility of Kþ ions; as for the tranquilization effect, see Section 5.2.7.3. Similarly, in the case of (Li, K)F, the interaction Liþ  F is considerably stronger than that of Kþ  F; Liþ causes a tranquilization effect of the mobility of Kþ [32]; see also Section 5.2.7.3. A comparison of the isotherms between (Li, K)(SO4)1/2 [14,33] and (Li, K)(CO3)1/2 [34] is interesting. In the former, the central atom S is surrounded tetrahedrally by four O atoms and therefore the positive charge of S is fully shielded, while in the latter, the C atom is surrounded by three O atoms on a plane, and the positive charge of C is not shielded completely. Thus, the tranquilization effect by Liþ on the mobilities of Kþ is stronger in (Li, K)(SO4)1/2 than in (Li, K)(CO3)1/2, which is revealed in the difference of the isotherms of uK between the two systems.

5.2.4.2 Charge Symmetric Multivalent Binary Systems with a Common Anion 5.2.4.2.1 Divalent Cation System: (Ca, Ba)1/2Cl The isotherms of u at 973 and 1073 K are shown in Figure 5.9a [35]. The melting points of CaCl2 and BaCl2 are 1043 and 1226 K, respectively; the temperature at the eutectic composition (xBa ¼ 0.35) is 873 K. Thus, the temperature and concentration regions of the data are inevitably limited. The mobility of Ba2þ having a heavier mass and larger size is larger than that of Ca2þ. This is probably because the coulombic attraction of Ca2þ  Cl is much stronger than that of Ba2þ  Cl. A similar trend is observed probably with the same reason also in (Li, Na)NO3 [24] and (Li, Na)Cl [36], for example, where uLi < uNa over the measured range. The Chemla effect would not occur; as the slope of the isotherm of Ca2þ is sharper, a crossing point, if any, would appear at a lower temperature, at which the mixture is no more at a molten state. The reciprocals of the isotherms are shown against the molar volume in Figure 5.9b. These linear functions suggest that the mobilities of both cations could be expressed by such an equation as Equation (5.3), although the molar volume range is much more limited (about 3 cm3 mol1) than in the case of (Li, K)Br (about 20 cm3 mol1, see Figure 5.3).

Figure 5.9 (a) Mobilities, u, vs xBa and (b) these reciprocals vs Vm in (Ca, Ba)1/2Cl at 973 and 1073 K [35].

Ionic Transport in Molten Salts

89

5.2.4.2.2 Trivalent Cation Systems: (Y, La)1/3Cl and (Y, Dy)1/3Cl Some properties of Y1/3Cl, La1/3Cl and Dy1/3Cl are compared in Table 5.1. The mobility isotherms of (Y, La)1/3Cl shown in Figure 5.10a [37] are particularly interesting in that the molar volume of the melt increases slightly with an increasing concentration of Y3þ, whereas the ionic radius of La3þ is fairly greater than that of Y3þ[27]. The mobility of the larger cation (La3þ) is larger than that of the smaller one (Y3þ), which is similar to the case in the divalent cation system. The decreasing rate with the molar volume is significantly greater for the larger cation (La3þ) than for the smaller one (Y3þ), which may indicate the tranquilization effect by the trivalent, smaller cation (Y3þ) on the mobility of the fairly larger cation (La3þ). Although the tranquilization effect could not be separated quantitatively from “the negative molar volume effect” indicated by Equation (5.3), the former is Table 5.1 Comparison of Some Properties of Pure Y1/3Cl, La1/3Cl, and Dy1/3Cl [37] Y1/3Cl

La1/3Cl

Dy1/3Cl

Atomic number

39

57

66

Atomic weight of cation

88.91

138.91

162.50

Cation radius (pm)

90.0

103.2

91.2

Crystal structure type

AlCl3

UCl3

AlCl3

Coordination number in the crystal

6

9

6

Coordination number in the melt

6

6

6

987

1150

928

25.46

25.00

25.36

51.2

110.7

56.2

Melting point (K) 3

1

Molar volume at 1073 K (cm mol ) 1

Conductivity at 1073 K (S m )

Figure 5.10 (a) Mobilities, u, vs Vm in (Y, La)1/3Cl and (b) in (Y, Dy)1/3Cl at 1073 K [37].

90

Molten Salts Chemistry

assumed to be larger than the latter. However, in the case of (Ca, Ba)1/2Cl where Vm(Ca) < Vm(Ba), the tranquilization effect decreases with increasing molar volume; the decreasing rate with an increase in the molar volume is slightly greater for the smaller cation, Ca2þ, than for the larger one, Ba2þ. The (Y, Dy)1/3Cl (Figure 5.10b) is of interest for the following points (see Table 5.1): (1) the molar volume of Y1/3Cl is slightly larger than Dy1/3Cl, (2) the order of the cation sizes is reversed, and (3) the atomic weight of Y is much smaller than that of Dy. Whereas the molar volume increase with an increasing concentration of Y1/3 is very small, the mobility decrease is significant; this may be attributable to the tranquilization effect by the smaller Y3þ. This is probably due to the great mass difference that Y3þ, having a smaller ionic radius, is significantly more mobile than Dy3þ.Thus, these two ions behave like two isotopes, in which, however, the mass difference is very large.

5.2.5

Charge Asymmetric Binary Systems with a Common Anion

Here, a problem arises as to the definition of the molar quantity. Which is more essential, Ca1/2Cl or CaCl2, for the mobility of calcium chloride in a mixture, for example, with KCl? For the moment, let us consider that the former, which was previously called “an equivalent quantity,” should be regarded as the molar quantity for the mobility in the mixture with a monovalent cation, partly because Equation (5.1) has been derived on this basis, and mainly because the number of the common anion, which is taken as the reference frame for the mobilities, should be equal in the mixture. At any rate, Equations (5.10) and (5.11) hold between x1 and x1¢, between x2 and x2¢, and between Vm and Vm¢, where the prime “¢” refers to the corresponding quantities when a multivalent cation-containing species (of valency z) such as CaCl2 is regarded as the molar quantity [38,39]: x1 ¢ ¼ zx1 =½1 þ ðz  1Þx1 

(5.10a)

x2 ¢ ¼ x2 =½z þ ð1  zÞx2 

(5.10b)

Vm ¢ ¼ ðx1 ¢=x1 ÞV m ¼ V m =½1 þ ð1=z  1Þx2 

(5.11)

As is also derived from Equations (5.2a) and (5.2b), kVm =F ¼ x1 u1 þ x2 u2

(5.12)

Similarly, it holds kVm ¢=F ¼ x1 ¢u1 ¢ þ x2 ¢u2 ¢

(5.13)

where u1¢ ¼ u1, and u2¢ is the internal mobility of MXz with multivatent cation M, that is, u2¢ ¼ zu2. In the case of a mixture of potassium chloride and calcium chloride, for example, uCa ¼ 2uCa1/2. The mobilities in the mixtures of alkali nitrates and alkaline earth nitrates have been studied systematically for (M1, M2(1/2))NO3, where M1 ¼ alkali ion and M2 ¼ alkaline earth ion [38,39]. Here, the tranquilization effect of the divalent cations on the mobility of alkali ions occurs; the sequence of the tranquilization effect is Ca2þ > Sr2þ > Ba2þ, following the sequence of the coulombic attraction with the common anion NO3  . The isotherms of u at 1073 K in (K, Ca1/2)Cl are shown as a function of Vm in Figure 5.11a [40]. The tranquilization effect of Ca2þ on the uK is very clear. The uCa1/2 appears to be nearly constant. This is affected apparently by the “U-shaped” conductivity isotherms:

Ionic Transport in Molten Salts

91

Figure 5.11 (a) Mobilities, u, vs Vm in (K, Ca1/2)Cl [40] at 1073 K and (b) in (K, Dy1/3)Cl at 1093 K [42].

2.09, 1.64, 1.45, 1.44, 1.68, and 2.23 S cm1 at xK ¼ 0, 0.2, 0.4, 0.6, 0.8, and 1, respectively [41].The isotherm of uCa1/2 may reveal “the molar volume effect” at the low xCa1/2 range and the agitation effect by Kþ at the higher xK range. Thus, the strange isotherms of k may be interpreted in terms of the mobility isotherms of the two cations, if the molar volume effect of uCa1/2 at low xK and the tranquilization effect by Ca2þ at high xK are taken into account. It is not necessary to assume long-lived “complexes” for the mobility. Although uK is very near to uCa1/2 at low xK, the Chemla effect is not observed in the investigated range. Among the charge asymmetric systems studied so far, the Chemla effect has not been found. The isotherms of u at 1093 in (K, Dy1/3)Cl are shown in Figure 5.11b [42]. Quite similar isotherms have been obtained in (K, Nd1/3)Cl [43]. The tranquilization effect manifests itself on uK by Dy3þ (or Nd3þ). It is interesting to note that uDy1/3 is significantly high in the mixture with Kþ at least at higher xDy1/3. In pure DyCl3, the isotope effect on the mobility of Dy3þ is considerably higher [44]. These facts reveal that the electrically conducting species in the present mixture would be Dy3þ (and Cl) and not such species as [DyCl6]3; however, in (K, Ln1/3)Cl (e.g., Ln ¼ La [45] and Y [46]), such species as [LnCl6]3 have been detected by Raman spectroscopy and by X-ray diffraction (e.g., Ln ¼ Er [47]). These two apparently different findings would not contradict each other because the lifetime of the electrically conducting species may be very short or actually zero (cf. Figure 5.13a); in the case of Figure 5.13a, while the cation of interest plays an electrically conducting species by moving along the traced locus, the motion cannot be detected by usual time- and space-averaged diffraction patters. Meanwhile, such a motion of the species could be assumed by mobility measurement and MD.

5.2.6

Calculated Internal Mobility and Self-Exchange Velocity (SEV)

On the basis of the linear response theory, Klemm has derived an equation for calculating internal cation mobilities in binary systems with a common anion by MD [48]: uab ¼

ejz jN kT

ð1 0

Kab ðtÞdt

(5.14a)

92

Molten Salts Chemistry

where Kab ðtÞ ¼ Ca þ Cb þ x1 Ca1 þ x2 Ca2  x1 Cb1  x2 Cb2

(5.14b)

Here, each Cab is the group velocity correlation function between species a and b: Cab ðtÞ ¼

1 1 X 1 X vi ðtÞ vj ð0Þ > < 3 Na iEa Nb jEb

(5.14c)

From Equation (5.14), the mobilities in (Li, Cs)Cl (xCs ¼ 0.90) have been calculated and the Chemla effect has been reproduced; uLi is much smaller than uCs at this concentration [49]. On the basis of Equation (5.14), Ribeiro has calculated the mobilities in some binary nitrate mixtures and pure LiNO3 and KNO3 and concluded that, if the polarizability (named “fluctuating charge model”) is taken into account, the calculated values become higher, resulting in better agreement with the experimental data [50]. Subsequently, he has calculated the mobilities in (Li, K)Cl and (Li, K)F and found that the isotherm of Kþ in the fluoride is quite different from that in the chloride due to the difference in the structural relaxation in a range beyond first-neighbor distances [51]. The findings may correspond to the tranquilization effect in the dynamic dissociation model (see also Section 5.2.7.3). It takes much computational time to calculate the quantities with enough accuracy using Equation (5.14) because the group velocity correlation functions have to be calculated. In order to understand the mobility more simply and by physical intuition, a quantity called the self-exchange velocity has been proposed [52]. The SEV is defined as v ¼ ðR2  < R2 >Þ=t

(5.15)

where R2 is the distance where the radial distribution function between unlike ions crosses unity for the second time, is the average distance of unlike ions with distances < R2, and t is the average time in which ions move from < R2 > to distance R2 (see Figure 5.12). At first, in the calculation of the SEVs in (Li, Rb)Cl (1:1 mixture) using the Tosi-Fumi potentials (rigid ion model) [53], the Chemla effect has been reproduced [52]. Morgan and Madden have calculated both internal mobilities and SEVs in the same MD of (Li, K)Cl at several concentrations at 900, 1000, and 1096 K using polarizable ion potentials as well as rigid-ion model potentials [54]. It is remarkable that the correlation coefficients between the two quantities are as high as 0.96 for both Liþ and Kþ, as given in Table 5.2. This suggests that calculating SEVs may be a good description of the microscopic events that determine internal mobilities; see also Section 5.2.7. In Figure 5.12b, the motion of coordinating cations around an arbitrarily chosen Cl ion is shown with reference to the Cl ion; this is obtained from a MD of pure LiCl [55]. During most of the time, cations oscillate around the Cl (O-process) and then leave (L-process: Liþ ions Nos. (1) and (2) in Figure 5.12b) presumably when the potential barrier becomes low enough (cf. also Figure 5.14). A Liþ ion (No. 1), which has once left, comes back (C-process). It is interesting to note that the velocity during the L-process is proportional to the sum (vc þ va) ffiof the mean velocitiesffi of “ideal-gas like” cations and anions; these pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi are vc ¼ 8RT=pMc and va ¼ 8RT=pMa , where Mc and Ma are the respective masses. In (Li, K)Cl, the slope of the velocity during the L-process vs (vc þ va) has been estimated to be 0.577 0.005 [56]. This means that the L-process is a purely physical process independent of the potentials, that is, regardless of the chemical species, Liþ or Kþ.

Ionic Transport in Molten Salts

93

Figure 5.12 Self-exchange velocity (SEV) in pure LiCl. (a) Radial distribution function, g(r), for the Li  Cl pair. , average distance of all Liþ within R2 [the position where g(r) crosses unity after RM]. (b) Time evolution of distances of four individual Liþ ions located within R2 at t ¼ 0 from a Cl ion chosen arbitrarily. MLi(1) ¼ 6.941 and MLi(2), MLi (3), and MLi (4) ¼ 22.99 (set artificially)[55]. This example reveals that the L-process (or the C-process) occurs rather rarely and that its frequency, that is, the length of the O-process, will be much less mass dependent.

The following apparently anomalous behaviors found in ionic transport have been accounted for in terms of the SEV (the underlined references): (1) (2) (3) (4)

existence of a maximum of electric conductivity as a function of temperature [57,59,60] increase in the electric conductivity of some Liþ salts with increasing pressure [61,62] increase in the isotope effect in electromigration with increasing temperature [55,58,63] the isotope effect in the mobilities between the two isotopically pure melts, that is, 6LiCl and 7LiCl, is greater than that of LiCl having natural abundance (6Li: 7Li ¼ 7.42:92.58)[55,63].

94

Molten Salts Chemistry

Table 5.2 Correlation Coefficients between Calculated Mobilities and SEVsa Total (Li þ K)

0.961 (37)

Total (Li)

0.974 (19)

Li

900 K

1000 K

1096 K

0.969 (7)

0.966 (6)

0.984 (6)

1000 K

1096 K

0.962 (6)

0.974 (6)

0.964 (6)

900 K

1000 K

1096 K

0.901 (13)

0.967 (12)

0.971 (12)

Total (K)

0.966 (18)

K

900 K

Total (Li þ K)

a Data of calculated mobilities vs SEV are from Morgan and Madden [54]. Figures in parentheses indicate number of samples counted.

5.2.7

Dynamic Dissociation Model for Mobilities

As mentioned in Section 5.2.6, the internal mobilities may be strongly related with the separating motion of unlike ion pairs, which is the essence of the dynamic dissociation model. This feature is explained by Figures 5.13 and 5.14. In the real molten system, a cation will move away from its reference anion toward the attracting anion, as shown in Figure 5.13a. Although these three ions do not lie on a straight line in real molten salts, such a schematic picture as Figure 5.13b is drawn so that the potential profile felt by the middle cation located between the two anions can be expressed readily on a plane sheet, as in Figure 5.14. In Figure 5.14, the potential [53] felt by a cation (Liþ or Kþ) between two anions (Br) is shown. For Liþ in Figure 5.14a, the distance between reference Br and attracting Br is ˚ )(600 pm). The height of the kinetic energy (3/2)kT at 1000 K is 0.21  1019 J. d(¼ 6.0 A In this case, the Liþ could transfer from R (reference Br) toward A (attracting Br) nearly without feeling the potential barrier. For Liþ in Figure 5.14a’, d ¼ 700 pm, where the potential barrier is much higher than the kinetic energy, and therefore cannot move away from R (reference Br). For Kþ in Figure 5.14b, d ¼ 600 pm. The Kþ could move away from reference Br, when d becomes larger; this process would start from the situation shown in Figure 5.13b2. For K in Figure 5.14b’, d ¼ 700 pm, Kþ can move away from R without any potential barrier. Thus, at smaller d corresponding to smaller Vm, Liþ is more mobile than Kþ, while at larger d, Kþ is more mobile, and the Chemla effect occurs. Figure 5.14 also explains that, with an increase in d, that is, in Vm, the SEV of Liþ will decrease more sharply than that of Kþ. The Li-Cl distance in molten systems of pure LiCl, (Li, K)Cl and (Li, Cs)Cl have been studied by neutron diffraction [64]. The result shows that as the molar volume increases by the mixed Kþ and Csþ, the nearest Li-Cl distance becomes shorter. This feature will support the different features between Figures 5.14a and 5.14a’. As mentioned in Section 5.2.3, the binary system (Li, K)Br can be regarded as a standard system in that Equation (5.3) holds well practically in all concentrations. Thus, the Chemla effect in (Li, K)Br could be accounted for qualitatively in terms of the potential profiles employed here. An increase of temperature, which leads to an increase in the molar volume, may be more favorable for uK than for uLi, as can be expected also from the potential profiles

Ionic Transport in Molten Salts

95

Figure 5.13 Schematic representation of the dynamic dissociation model. (a) Imagined motion of a cation from the reference anion toward the attracting anion. (b) Process of a cation leaving from the reference anion. (b-1) Tranquilizing cations are shown by dashed line circles (omitted on b-2 and b-3), which are present only when the tranquilization effect occurs.

in Figure 5.14. Therefore, with increasing temperature, the Chemla crossing point shifts toward higher xLi, as has been often pointed out (e.g. [25]). In most cases, however, the internal mobilities deviate more or less from Equation (5.4), as exemplified in Sections 5.2.4 and 5.2.5. It should be mentioned that even in such cases this model could hold, where (1) the agitation effect, (2) the free space effect, and (3) the tranquilization effect are also taken into consideration [19,25,29,30].

5.2.7.1 The Agitation Effect The agitation effect makes the mobility higher than expected from Equation (5.4). The agitation effect has so far been observed for two different cases: (a) An agitation effect may be observed, for example, for uK in practically pure LiBr in the aforementioned (Li, K)Br at higher temperature (significantly at 1023 K and slightly at 923 K, but not at 823 K [22,23]). The vigorous motion of abundant Liþ ions of light mass

96

Molten Salts Chemistry

Figure 5.14 Potentials felt by a cation of interest between two Br ions. (a) Liþ at d ¼ 600 pm, (a’) Liþ at d ¼ 700 pm, (b) Kþ at d ¼ 600 pm, and (b’) Kþ at d ¼ 700 pm.

and small ionic radius would make the diffusional motion of the anions more increased, resulting in an increase of the SEV of the coexisting Kþ. In the system (K, Ca1/2) mentioned in Section 5.2.5, an agitation effect of Kþ on uCa1/2 may be seen at high uK. Usually, an agitation effect of this kind appears not to be so large. (b) Another type of the agitation effect has been found more explicitly for binary nitrates containing Tlþ ions [65]. The high polarizability of Tlþ will lead to an increase in the SEV of coexisting cations from the reference anion. In particular, the isotherms of the mobilities of (K, Tl)NO3 explicitly demonstrate the agitation effect by Tlþ; both uK and uTl increase with an increase in Vm, that is, an increase of xTl, and uK < uTl at all concentrations at 623 K. Thus, the isotherms do not belong to type I nor type II classified previously (e.g., [19]). Also in MD, when the polarizability is taken into account for the anions, transport coefficients such as the self-diffusion coefficients and mobilities become higher than in the case of the rigid ion model [49,54].

5.2.7.2 The Free Space Effect Contrary to the standard system [Equation (5.3)], the mobility decreases with decreasing molar volume under the condition that the free space becomes small enough as compared with the ionic size. Therefore, the free space effect is significantly observed for the mobility of large cations such as Rbþ and Csþ in MNO3 (M ¼ Li and Na) at high concentration (e.g., [25]), where the free space is assumed to be small. Although the free-space effect is found for uCs in (Li, Cs)NO3 [18], this does not occur for uCs in (Li, Cs)Cl [28]. Further, even for uNa in

Ionic Transport in Molten Salts

97

(Na, K)OH, the free space effect is observed explicitly at a high concentration of NaOH, as shown in Figure 5.8b. These facts suggest that the free-space effect at ambient pressure would be caused mainly by the hindered rotation of the poly atomic anions (e.g., [25]). It is obvious that, under high pressure, this effect is large.

5.2.7.3 The Tranquilization Effect The agitation effect þ the tranquilization effect may correspond to the “intercationic drag effect” presented by Klemm [66]. The tranquilization effect occurs in binary mixtures with a common anion, when the interaction of one cation with the common anion is appreciably stronger than that of the other. Therefore, the tranquilization effect has been found clearly in charge asymmetric systems such as (K, Ca1/2)Cl and (K, Dy1/3)Cl and even in monovalent charge symmetric systems such as (Li, K)F [32] and (Na, K)OH[31], (Li, K)(SO4)1/2[33], (Li, K)(CO3)1/2 [34]. For the case that the tranquilizing effect occurs, the tranquilizing ion, “(T)”, is shown by the dashed circle in Figure 5.13b. If the interaction of “T” with “A” is very strong, the approaching motion of “A” toward “C” (Figure 5.13b1) and also the leaving motion (Figure 5.13b3) would be retarded, and consequently the separation motion of “C” from “R” will be retarded. Thus, with an increasing concentration of tranquilizing ions, the tranquilization effect becomes stronger. The ionic size of “T” is usually smaller than the one of “A” or the charge density of “T” is larger than that of “C”; therefore, the coulombic attraction between “T” and “A” is considerably stronger than that between “C” and “R” or between “C” and “A”. Thus, as the concentration of “T” increases, the molar volume decreases, and the approaching (Figure 5.13b1) and leaving (Figure 5.13b3) motion of “A” becomes slower. In this case, the molar volume dependence given by Equation (5.3) does not hold for “the tranquilized ion” (more accurately, the internal mobility of the tranquilized ion, “C”), and the isotherms of the two cation mobilities against the molar volume are “X shaped,” which have been classified into “type II” in previous reviews [19,30]. The existence of such tranquilizing ions may be consistent with the observation by MD through the “intermediate scattering functions” that the structural relaxation in a range beyond first-neighbor distances is an important factor [51]. However, results of the MD of (Li, K)F have shown that the tranquilization effect has not been reproduced by the SEV [67]; in their result, the SEV of Kþ, which is expected to be “the tranquilized ion,” does not decrease with an increase in the concentration of tranquilizing Liþ ion, while the SEV of the tranquilizing Liþ seems to correspond to the calculated internal mobility. When the melt is composed of ions whose coulombic attraction with the counterion is very strong, the melting point is usually high, and therefore, the experiments are considerably difficult; particularly, in fluorides, silicate glasses cannot be used for the cell. From the MD side, the potential curve between cations and anions is very sharp, and even a very small change in the potential parameters will affect the calculated properties. Further development from experiments and MD simulations is desired, particularly for binary systems showing “type II” isotherms.

5.3

Concluding Remarks

In the binary system (Li, K)Br, which may be regarded as the standard system for mobilities, the Chemla effect occurs and the mobilities of both cations decrease with increasing molar volume, which are probably in contrast with our general intuition. These phenomena are

98

Molten Salts Chemistry

caused by the strong electrostatic attraction. For a study of the mechanism of the conductivities, binary systems with a common anion provide much more information than pure melts. It should also be mentioned that the electroconducting species would not be equal to those assumed from a structural study. It is likely that the conducting species are usually monoatomic ions and considerably stable polyatomic ions such as NO3  , OH, and SO4 2 .

References [1] Janz, G.J. (1988). Thermodynamic and transport properties for molten salts: Correlation equations for critically evaluated density, surface tension, electrical conductance, and viscosity data. J. Phys. Chem. Ref. Data, 17(Suppl. 2), 1–309. [2] IUPAC, E.R.Cohen, et al. Quantities, Units and Symbols in Physical Chemistry; Royal Society of Chemistry. [3] Lantelme, F., Chemla, M. (1963). Mobilite´ e´lectrique des ions Naþ et Kþ dans les syste`mes KNO3-NaNO3 fondus. Bull. Soc. Chim. France, 2200–2203. [4] Sundheim, B.R. (1956). Transference numbers in molten salts. J. Phys. Chem., 60, 1381–1383. [5] Koishi, T., Kawase, S., Tamaki, S. (2002). A theory of electrical conductivity of molten salt. J. Chem. Phys., 116, 3018–3026. [6] Mehta, O.P. The`se Universite´ de Paris, 1967. [7] Sjo¨blom, C.-A., Laity, R.W. (1982). Effect of frit material on external transport numbers in molten salts. Z. Naturforsch., 37a, 706–709. [8] Lunde´n, A. (1973). Isotope effect on electromigration of cations in molten nitrates: A comment on the interpretation of some electrophoresis experiments. J. Inorg. Nucl. Chem., 35, 1971–1975. [9] Klemm, A. (1946). Die Pha¨nomenologie zweier Verfahren zur Isotopentrennung. Z. Naturforsch., 1, 252–257. [10] Klemm, A., Hintenberger, H., Hoernes, P. (1947). Anreicherung der schweren Isotope von Li und K durch electrolytische Ionenwanderung in geschmolzenen Chloriden. Z. Naturforsch., 2a, 245–249. [11] Okada, I., Nomura, M., Haibara, T. (2013). High enrichment of 6Li in molten nitrates by the Klemm method. Z. Naturforsch., 68a, 21–38. [12] Chemla, M. (1958). Perfectionnement aux proce´de´s de se´paration isotopique par e´lectromigration en contre-courant dans les sels fondus. 1958, French Patent No. 1 216 418. [13] Pe´rie´, J., Chemla, M., Gignoux, M. (1961). Se´paration d’isotopes par e´lectromigration en contrecourant dans des syste`mes d’haloge´nures fondus. Bull. Soc. Chim. France, ;1249–1256. [14] Ljubimov, V., Lunde´n, A. (1966). Electromigration in molten and solid binary sulfate mixtures: Relative cation mobilities and transport numbers. Z. Naturforsch., 21a, 1592–1600. [15] Ichioka, K., Okada, I., Klemm, A. (1989). Internal cation mobilities in molten (Na, Ag)NO3 remeasured by the column method. Z. Naturforsch., 44a, 747–750. [16] Holm, J.L. (1971). Excess volumes of mixing in liquid binary alkali halide mixtures. Acta Chem. Scand., 25, 3609–3615. [17] Okada, I., Horinouchi, H., Lantelme, F. (2010). A new analysis of internal cation mobilities in molten binary system (Li, K)Cl. J. Chem. Eng. Data, 55, 1847–1854. [18] Okada, I., Takagi, R., Kawamura, K. (1979). Internal cation mobilities in the molten systems (Li-Rb)NO3 and (Li-Cs)NO3. Z. Naturforsch., 34a, 498–503. [19] Okada, I. (1999). The Chemla effect: From the separation of isotopes to the modeling of binary ionic liquids. J. Mol. Liq., 83, 5–22. [20] Endoh, A., Okada, I. (1990). An anion Chemla effect in the mobilities in the molten system Li(Cl, NO3). J. Electrochem. Soc., 137, 933–938. [21] Baluja, S., Endoh, A., Okada, I. (1988). Self-exchange velocities in molten equimolar Li(Cl, Br) predicting an anion Chemla effect. Z. Naturforsch., 43a, 1065–1071. [22] Okada, I., Lantelme, F. (2006). A new interpretation of the original data of Chemla’s group on the mobilities of binary molten system (Li, K)Br. J. New Mat. Electrochem. Systems, 9, 165–174.

Ionic Transport in Molten Salts

99

[23] Okada, I., Lantelme, F. (2008). Application of an empirical mobility equation to the molten binary bromide system (Li, K)Br studied by Chemla’s group. Z. Naturforsch., 63a, 318–320. [24] Yang, C.-C., Takagi, R., Okada, I. (1980). Internal cation mobilities in the molten systems (Li-Na) NO3 and (Na-Cs)NO3. Z. Naturforsch., 35a, 1186–1191. [25] Chemla, M., Okada, I. (1990). Ionic mobilities of monovalent cations in molten salt mixtures. Electrochim. Acta, 35, 1761–1776. [26] Janz, G.J., Tomkins, R.P.T., Allen, C.B., Downey, J.R., Jr, Singer, S.K. (1977). Molten salts: Volume 4, Part 3 Bromides and mixtures; iodides and mixtures. J. Phys. Chem. Ref. Data, 6, 409–596. [27] Shannon, R.D. (1976). Revised effective ionic radii and systematic studies of interatomic distances in halides and chalcogenides. Acta Cryst., A32, 751–767. [28] Okada, I., Horinouchi, H. (1995). The Chemla effect in the mobilities in the molten binary system of lithium chloride and caesium chloride. J. Electoanal. Chem., 396, 547–552. [29] Okada, I. (1999). Electric conduction in molten salts. Electrochemistry, 67, 529–540. [30] Okada, I. (2001). Transport properties of molten salts. In: Modern Aspects of Electrochemistry; Kluwer Academic/Plenum Publishers; Number 34, Chapter 4. [31] Yang, C.-C., Odawara, O., Okada, I. (1989). Internal cation mobilities in the binary system NaOHKOH. J. Electrochem. Soc., 136, 120–125. [32] Matsuura, H., Ohashi, R., Chou, P.-H., Takagi, R. (2006). Internal cation mobilities in molten lithium-potassium fluoride. Electrochemistry, 74, 822–824. [33] Kvist, A. (1966). The electrical conductivity of solid and molten (Li, K)2SO4 and solid Li2SO4 with small quantities of sodium, potassium and rubidium sulphate. Z. Naturforsch., 21a, 1221–1223. [34] Yang, C., Kawamura, K., Okada, I. (1987). Internal cation mobilities in the molten binary system Li2CO3  K2CO3. Electrochim. Acta, 32, 1607–1611. [35] Matsuura, H., Okada, I. (1994). Internal cation mobilities in molten (Ca, Ba)Cl2. Z. Naturforsch., 49a, 690–694. [36] Yang, C.-C., Lee, B.-J. (1993). Internal cation mobilities in the molten binary systems (Li, Na)Cl and (Na, K)Cl. Z. Naturforsch., 48a, 1223–1228. [37] Matsuura, H., Okada, I. (1996). Internal cation mobilities in the molten binary systems (Y, La)Cl3 and (Y, Dy)Cl3. J. Electrochem. Soc., 143, 334–339. [38] Habasaki, J., Yang, C.-C., Okada, I. (1987). Internal cation mobilities in molten binary system KNO3-Ca(NO3)2. Z. Naturforsch., 42a, 695–699. [39] Koura, T., Matsuura, H., Okada, I. (1997). A dynamic dissociation model for internal mobilities in molten alkali and alkaline earth nitrate mixture. J. Mol. Liq., 73–74, 195–208. [40] Matsuura, H., Okada, I. (1993). Internal cation mobilities in the molten binary system (K, Ca1/2) Cl. Denki Kagaku, 61, 732–733. [41] Janz, G.J., Tomkins, R.P.T., Allen, C.B., Downey, J.R., Jr.; Gardner, G.L., Krebs, U., Singer, S.K. (1975). Molten salts: Volume 4, part 2, chlorides and mixtures: Electrical conductance, density, viscosity, and surface tension data. J. Phys. Chem. Ref. Data, 4, 871–1178. [42] Matsuura, H., Okada, I., Takagi, R., Iwadate, Y. (1998). Internal cation mobilities in molten (K, Dy1/3)Cl. Z. Naturforsch., 53a, 45–50. [43] Ohashi, R., Matsumiya, H., Matsuura, H., Takagi, R. (1999). Internal cation mobilities in the molten binary system NdCl3-KCl. Electrochemistry, 67, 550–552. [44] Matsuura, H., Okada, I., Nomura, M., Okamoto, M., Iwadate, Y. (1996). The isotope effect on the internal cation mobility of molten dysprosium chloride. J. Electrochem. Soc., 143, 3830–3832. [45] Maroni, V.A., Hathaway, J.Y., Papatheodorou, G.N. (1974). On the existence of associated species in lanthanum (III) chloride-potassium chloride melts. J. Phys. Chem., 78, 1134–1135. [46] Papatheodorou, G.N. (1977). Raman spectroscopic studies of yttrium(III) chloride-alkali metal chloride melts and of Cs2NaYCl6 and YCl3 solid compounds. J. Chem. Phys., 66, 2893–2900. [47] Iwadate, Y., Fukushima, K., Takagi, R., Gaune-Escard, M. (1999). Complexation and ionic arrangement in Na3ErCl6 and K3ErCl6 and K3ErCl6 melts analyzed by X-ray diffraction. Electrochemistry, 67, 553–562. [48] Klemm, A. (1977). Molten salt ionic mobilities in terms of group velocity correlation functions. Z. Naturforsch., 32a, 927–929.

100

Molten Salts Chemistry

[49] Okada, I., Okazaki, S., Horinouchi, H., Miyamoto, Y. (1991). The Chemla effect in molten (Li, Cs)Cl: Electromigration and MD simulation. Mater. Sci. Forum, 73–75, 175–181. [50] Ribeiro, M.C.C. (2002). On the Chemla effect in molten alkali nitrates. J. Chem. Phys., 117, 266–276. [51] Ribeiro, M.C.C. (2003). Chemla effect in molten LiCl/KCl and LiF/KF mixtures. J. Phys. Chem., B107, 4392–4402. [52] Okada, I., Takagi, R., Kawamura, K. (1980). A molecular dynamics simulation of molten (Li-Rb) Cl implying the Chemla effect of mobilities. Z. Naturforsch., 35a, 493–499. [53] Tosi, M.P., Fumi, F.G. (1964). Ionic sizes and Born repulsive parameters in the NaCl-type alkali halides. II. The generalized Huggins-Mayer form. J. Phys. Chem. Solids, 25, 45–52. [54] Morgan, B., Madden, P.A. (2004). Ion mobilities and microscopic in liquid (Li, K)Cl. J. Chem. Phys., 120, 1402–1413. [55] Okada, I. (1984). MD-simulation of molten LiCl: Self-exchange velocities of Li-Isotopes near Cl--ions. Z. Naturforsch., 39a, 880–887. [56] Okada, I. (1987). MD-simulation of molten (Li, K)Cl at the eutectic composition: Self-exchange velocities of Li- and K-isotopes near the Cl- -ions. Z. Naturforsch., 42a, 21–28. [57] Klemm, A. (1964). Ion mobilities in molten salts. Euratom Report EUR, 2466e, 31–38. [58] Klemm, A. (1987). Ionic mobilities. Advances in Molten Salt Chemistry, Vol. 6, Elsevier pp 1–72. [59] Spedding, P.L. (1973). Diffusion and conduction in melts. Electrochim. Acta, 18, 111–117. [60] Okada, I., Takagi, R. (1981). The maximum of the conductivity of an ionic melt from MD simulations at various temperatures. Z. Naturforsch., 36a, 378–380. [61] Cleaver, B., Smedley, S.I., Spencer, P.N. (1972). Effect of pressure on electrical conductivities of fused alkali metal halides and silver halides. J. Chem. Soc. Faraday Trans., 68, 1720–1733. [62] Okada, I., Endoh, A., Baluja, S. (1991). Effect of pressure on the self-exchange velocities in MD simulations of molten LiCl and LiBr reflecting the anomaly in the conductivities. Z. Naturforsch., 46a, 148–154. [63] Jordan, S., Lenke, R., Klemm, A. (1968). Temperatur- und Konzentrationsabha¨ngigkeit der inneren Beweglichkeiten von 6Li und 7Li in geschmolzenem LiCl und LiNO3. Z. Naturforsch., 23a, 1563–1568. [64] Miyamoto, Y., Okazaki, S., Odawara, O., Okada, I., Misawa, M., Fukunaga, T. (1994). Neutron diffraction study of the Li-Cl distance in molten mixture systems (Li, K)Cl and (Li, Cs)Cl. Mol. Phys., 82, 887–895. [65] Okada, I., Chou, P.-H. (1997). Anomalous behavior of internal mobilities for Ag(I) and Tl(I) ions in molten nitrates. J. Electrochem. Soc., 144, 1332–1339. [66] Klemm, A. (1984). Association in molten salts and mobility isotherms. Z. Naturforsch., 39a, 471–474. [67] Merlet, C., Madden, P.A., Salanne, M. (2010). Internal mobilities and diffusion in an ionic liquid mixture. Phys. Chem. Chem. Phys., 12, 14109–14114.