George J. Janz Rensseloer Polytechnic Institute Troy, N e w York
I
Physical Properties and Structure
Underlying the development of modern theoretical treatments of molten salts as molten electrolytes, ionic solvents, and the liquid st.at,e, arc t,he experimental investigations of fused salts. The melting points for some typical substances are found in Table 1. It is readily apparent t,hat ionic meks afford an opportunity to study theoretical problems in both thc physics and chemistry of t,he liquid state over a wide t,emperature range and for a very large variety of syst,ems in which the constituents vary from simple molecular, to purely ionic, and to highly polymeric species. The classification of molten salt research as an aspect of high temperature chemistry is also readily apparent from this viewpoint. Table 1. Melting Points of Some Typical Substances Molecular Solids Ne A H1
N1
H CI CO, CCI, HSO Mtlals
Hg
Na AhAu Pt Nh
studies of the physical properties and st,ructnre, to provide the data essential t,o develop the broad unifying concepts of knowledge for ionic mcks, are now recognized as part of a well-defined area in molteu salt chemist,ry. The need for such data, and indirect reflection of the current status of the art, is conveniently illustrated by a specific example. Molten carbonates are examples of the interesting class of electrolytes in which the anionic species are planar polyatomic disc-shaped ions as distinct from the molten alkali halides in which both species are spherical monatomic ions. I n the course of work currently in progress ( 2 ) on the mechanism of electrical conductance, not only the conductivity, but the densities, surface tensions, and viscosities had to he investigated since the published data were practically non-existent. Two values were the only data available for the surface tcnsions of moltcn Na2C03: 179 found by Quincke (1869) (S), and 210 by Traube (1891) (4),both for temperatures "just a t the melting points." Evaluation of these in the light of the recent careful measurements ( f )shows the former to be seriously in error, whereas the latter corresponds to the exact value for NarCOa at 891°C (mp 858°C). An interesting aspect of Traube's experimental work was the use of the principle of the drop-weight method for surface tension (that is now known by his name) at high temperatures by means of a suitable capillary tipped platinum funnel.
An indication of the research activity in this arca is gained from a correlation of publicat,ions for the t,imc interval, 1900 to the present date, as illustrated in Figure 1. The analysis is based on a recent bibliography (I) which embraced some 2000 references covering both the domestic and international research journals. The enhanced interest in the chemist,ryof molten saks over the period of t,he past t,wn decades may he at,trihntcd, in no small part, in the problems raised hy the inadequate knowledge of lligh-t,emperat~i~.r chemistry. It is also apparent from this survey that, only a small fraction of these investigations were directed to studies of physical properties, and that relatively few of the contributions of this fract.ion meet the limits of accuracy and precision imposed by the requirements of modern theoretical treatmenk Careful Presented as Part of the S ~ m ~ o s i u On m Recent Advances in the Chemistry of Fused Salts before the Division of Chemical Education at the 139th ACS National Meeting, St. Louis, March, 1YG1.
P ~ b i i ~ a t i oPeriod o Figure 1. Survey of research publications in molten salts. The 1958 ordinate indicates contributions in phyrico~ .tructure only in that yeor.
Volume 39, Number 2, February 1962 / 59
Techniques of High Temperature Experimentation
The preceding example illustrates yet another feature of molten salt chemistry. The main differences from the experimental point, relative to conventional systems, are the high temperature and the reactivity of the constituents in molten salt chemistry. Temperature homogeneity and temperature measurements are important considerations where precise values are required. Many of the classical physico-chemical techniques, such as cryoscopy, conductimetry, densitometry, viscometry, calorimetry, measurement of liquid diffusivity, transference numbers, solubility, refractive indices, electrode potentials, cell emf's, surface tensions, and vapor pressures have been employed. These have been complemented more recently by the modern techniques of infrared, Raman, visible, and ultraviolet spectroscopy, X-ray and neutron diffraction, nuclear magnetic and electron paramagnetic resonance, and ultrasonic velocity measurements. The methods have been summarized in Table 2 under the general headings spectroscopic, thermodynamic, transport, and electrical. The vast majority of the investigations have been devoted to melts of simple ionic salt,s and their mixtures. The experimental assemblies adapting the classical techniques of density, surface tension, and electrical conductance, may be used to illustrate the approach in fused salt measurements. Table 2.
Status of Experimental Techniques for Molten Salt Studies
Technique
Statusa
Teehniaue
Status*
1 1 3
Electrical Conductance Polnrography Dielectric constant
1 2 3
Molten Salts a n d Conventional Systems
Thermodynamic Cam~ressibilitv
1
A comparison of the properties of density, surface tensions, viscosity, and equivalent conductance for
Spectroscopic X-ray diffraction Neutron diffraction Microwave Nuclear magnetic re~onance Electron paramagnetic resonance Ramsn Infrared Visible and ultraviolet Transuort Difhsion Electrical transport Viscosity Thermal
3 2 2 2 2
1 2 1 1
crvdscouv
"
DensityElectromotive force Heet of fusion, rcaction Heat capacity Phase equilibria Refractive index Surface tension .
a
function of the viscosity of the medium. By adding weights to the balance pan, the additional property of viscosity can be obtained. This principle has been used (fin i) the recent measurements for borate and silicate melts a t temperaturesup to 1800°C. A conductance cell for molten salts is illustrated in Figure 2c where the twin capillary design has been used to attain a path of sufficient lcngth in the highly conducting melts to permit precise measurement of this property. An attractive feature is that the capillaries can readily be exchanged to gain a cell constant in a range suitable for the salt being investigated. For highly reactive salts such as molten carbonates, these capillaries were made from sing13 crystal magnesium oxide (7). The detail shown in Figure 2c illustrates the refractory capillaries, D, suspended from an Au-Pd block, E, and the position of the electrode contacts, F, through alundum insulators to the bridge circuit. Corrections for polarization errors are important, as in aqueous electrolytes, since the ac frequency range normally is extended to 20 kc/sec for this purpose in molten salts. With suitably high cell constants, this correction is readily reduced to less than 0.1%, which compares favorably with the corresponding measurements in aqueous systems. About 50% of the more common salts melt below 500°C; only about 30% melt above 900°C. If the molten salts can be contained in Pyrex or Vycor glass, without reaction or attack on the glass, the problems of experimcntal design are greatly reduced. Two recent monographs (8, 9) in the area of experimental mcthods at high temperatures provide useful sources for information on such practical problems in this area of high temperature chemistry.
1 1
1 1 1
1 1
1
.
1, established; 2, potential being explored; 3, untried or
potential not yet tested.
An assembly for the precise measurement of surface tension and density of melts in one apparat,us simult,aneously is illustrated in Figures 23, and 2b. The essent,ial feat,ures are the density bob, A , of sprcial shape to permit precise cont,act wit,h tthe melt, a cont,inuously variable height cn~cihle arrangement, R and C, and a visual scale recording analytical balance. This arrangement has been used (5) with molten alkali metal salts a t temperatures up to 1000°C. The detail of the surface tension density bob is shown in Figure lb. The bob is machined from a massive block of metal to avoid all cracks and tapped threads which, on expansion, might retain some of the molten salt and introduce errors in measurements. It is of interest to note that in the Archimedian principle of density measurements, the rate of motion of the bob in the melt is a 60 1 Journal of Chemical Education
Figure 2. Experimental orrtmblies for precire measurement of wrfoce tension, demity, and electrical conductance of molten raltr.
some molten salts with more conventionally known liquids (carbon tetrachloride and water) is shown in Table 3. Potassium chloride, for which the evidence is in support of a completely ionized melt, thus forms a liquid somewhat more viscous, and of somewhat greater surface tension, than water, and with density greater than carbon tetrachloride but with an electrical conductance markedly different from either of these two liquids. Lithium carbonate, for example, is a liquid of similar density to KCI, but of much greater surface tension than water, or molten KCI. Mercuric bromide, it was found, melts to form a liquid of high density, of moderate fluidity, and extremely low equivalent conductance. The evidence here is in support of a molecular type melt; i.e., when HgBrp melts, the lattice breaks down to give a liquid essentially molecular in nature, and only incipiently ionized. Table 3.
Comparison of Properties of Some Molten Salts, CCl,, and HpO
Density (g e c L )
LilCO, HgBn KC1 CCI, HsO
1.812 4.41 1.977 1.592 1.000
Surface tension (dyne cm-') 240
Viscosity
...
Electrical conductance ( mho 1 99.0
98.4 28.07 71.97
2.52 1.21 0 969 0.894
114 0.00 10-
...
(CP)
The salient features of molten electrolytes have been developed elsewhere in detail (10). The term electrolyte has a meaning here different from that in the conventional systems; in one case it is merely an ionized solute, and in the other, the whole of the system. In Table 4 is found a short summary of the values for A, for the recognized strong electrolytes compared with the values for the equivalent salts in the molten state. Table 4.
Comparison of Conductance: Molten Salts and Aqueous Solutions
Equivalent conduetmce, A (mho) Aqueous solution LiCl NaCl KC1
Inf. Dil.
0.10 N
Molten salt
115.03 126.45 149.86
95.86 106.74 128.96
170 143 114
The limiting equivalent conductance, &, of an electrolyte is that conductance which would be observed for a measurement on a hypothetical solution containing 1 equivalent. of solute (salt) in an infinitely large volume of solvent. The value is obtained by a study of the concentration dependence of A, and by various mathematical techniques, extrapolating to infinite dilution. The significance of this value is theoretical. It is the electrical conductance that would be observed if the ions did not suffer any of the long-range electrostatic ionic interactions (Coulombic) which contribute to the observed decrease in mobility with increasing concentration (cf. A, and A,.,, Table 4). The pure molten salt by contrast corresponds to a state in which the solvent to solute ratio is now 1.0/ m , i.e., the anions and cations are in intimate contact. It is
readily apparent that the concepts based on consideration of the long-range ionic interactions, successful in the theoretical treatment of strong electrolytes in dilute aqueous solutions, would not be too helpful since the molten salts present the extreme of concentrated electrolytes. The most fruitful theoretical contributions have come by focusing attention on the fact that the kinetic properties of fused salt electrolytes are more appropriately discussed by extension of the defect solid state theory. An interesting feature for ionic melts is seen in the data summarized in Table 5. On comparison with the pure metal halides, normally classed as simple ionic melts, it. is readily apparent that molten carbonates form highly ionized molten electrolytes. The relatively large increase in conductance in the alkali halide series in the change from K + to Li+ has been interpreted as due to a predominant contribution by the more mobile alkali metal cationic species to electrical transport in these molten electrolytes. The relatively small change noted in the molten alkali carbonates, i.e., +12 ohm-' equiv.-', is in marked contrast. It is apparent that molten electrolytes such as the carbonates, in which the anions are disc-shaped polyatomic species rather than simple spheres as in the molten alkali halides, present additional problems to the fundamental interpretation of physical properties and structure of these liquids. Toble 5. Electrical Conductances for a Series of Alkali Metal Halides and Carbonates in the Molten State
Physical Properties a n d Structure
In Figure 3 the crystal lattices for some simple salts are illustrated. Sodium chloride and cesium chloride are well-known examples of ionic crystals containing ions of inert gas structure, and are examples of the facecentered and body-centered cubic structures. Cadmium chloride illustrates an ionic layer type structure in which the halide atoms are found in an unsymmetrical cationic environment. While long-range crystalline order is entirely absent in the liquid state resulting from fusion, and liquid structure cannot be referred to a space lattice (ll),it is apparent that the properties of ionic salts in the liquid state will be characterized, statistically, by the short-range ion-core and ioncoulomb interactions that arise by virtue of the charges on the ions. The type of information gained from a study of the properties of fused salts by the experimental techniques listed in Table 2 may be illustrated by
Volume 39, Number 2, February 1962
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61
the following examples of recent contributions in this area.
Table 7.
Densities and Thermal Expansion Coefficients of Molten Halides a t T = 1 . I OT,
X-Roy and Neutron Diffraction (Spectroscopic)
Diffraction studies can furnish useful information about the atomic structure of ionic melts. The information is provided in the form of a pair radial distribution function, giving the probability that pairs of atoms are t o be found separated by a given distance. The nearest gegen-ion distances from a recent study (12) are listed in Table 6. The crystal state distances were those a t the melting points, also gained by X-ray diffraction; the gas state distances were from microwave spectroscopy. The liquid state distance is the "most frequent" distance; the broad character of the first peak of the pair radial distribution function supports the view that gegen-ion species are found as Table 6.
Nearest Gegen-Ion Distances for Alkali Halides (12)
Ion and ionic radius (A)
Distances in Compounds (A) C r y ~ t t ~ l Liquid Gas
"pairs" at distances significantly closer (as well as greater) than the values in Table 6. The values for the "shortest distances" was estimated (12) as very nearly equal to those found in the gaseous state for the monomeric molecular pair species. Two other points illustrate the information to be gained from such studies. It was noted that the like-ion distances in the liquid state for these ionic salts were nearly always larger than in the crystalline state, and the coordination number for the iirst shell of nearest neighbors was always less on the molten salt than that for the crystalline state. I n the molten alkali halides, in which the ions are spherical and of the inert gas type, the ionic interactions in the molten state lead to a statistical configuration in which, compared with the solid, t,here is a collapsed array of anions and cations, but an expanded array of the like-ion species.
variables such as density and temperature, it may be used to calculate the thermodynamic functions of the fluid (IS). Finally, knowledge of the change in volume on fusion provides a direct correlation between the usually known structure of the solid substance and that of the liquid. I n Table 7 are listed values of the density, d, and thermal expansion coefficient, a,for a number of molten halides a t "corresponding temperatures," i.e., a t equal fractions above their normal melting points (22).' The values of a for the molten mercuric halides are two to three times greater than those for the ionic halides of the Group I-A and Group II-A metal cations, but are less than those for typical nou-polar liquids (e.g., A, 02, CHa). This indicates that the cohesive forces in mercuric halide melts are weaker than the Coulombic forces which predominate in simple ionic melts, but are greater in strength than the London dispersion forces acting in purely non-polar liquids. Liquids may rationally he divided into a number of classes determined by the differences in type and symmetry of the intermolecular forces among the constituent particles. The molten mercuric halides may be regarded, on the basis of this classification, as polar liquids, the physical properties of which are governed by dispersion and multipole forces. Heat and Entropy o f Fusion (Thermodynamic)
Densitometry (Thermodynamic)
The latent heat of fusion, AH,, is essentially the cnergy required to overcome the attractive intermolecular forces which tend to produce the ordered arrangement of the crystal. When the lattice is expanded during fusion, these ordering forces are weakened and the system tends t o a more disordered state. The magnitude of AHr evidently depends upon the type of int,ermolerular forces involved in cryst.al binding and varies over several orders of magnitude for different t,yprs of crystals. The variat,ion of the ent,ropy of fusion, AS,, however, varies by less than olle order of magnitude for nearly all substances. Since the free energy of the system remains constant during the fusion
Knowledge of the densities and molar volumes of molten electrolytes is a prerequisite for interpretation of conductivity, viscosity, and diffusivity measurements on these systems. Partial molar volumes and thermal expansion coefficients are reflective of the structure and intermolecular forces in the melts. When the radial distribution function is found in terms of the intermolecular potential and two thermodynamic
In view of the uncertainties in boiling point temperatures and the more accurate knowledge of melting point temperatures far salts, the concept of a "corresponding state" suitable for comparison of physical properties of a molten salt has been praposed (88) as given by 8 = Ts/T,, where the temperatures Te are selected such that B has the same value for the salts to he compared. Values of B = 1.05 and 1.10 have been used most frequently.
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process, the temperature of fusion is determined by the relation:
T I=
=
Fusion Parameters of Some Typical Substances
AKrlASt
The principal mechanisms contributing to randomization in melting have been classified (14) as follows: (a) increase in vibrational entropy due to looser packing and a consequent decrease of characteristic frequencies in the melt; (6) increase of orientational randomization due to the marked reduction of repulsion barriers accompanying the expansion in volume on melting; (c) increase in positional disorder on melting, giving rise to the concept of the communal entropy term; (d) randomization of the internal configuration of molecules or ions containing flexible groups; (e) changes of association or chemical bonding on melting. The over-all entropy change on fusion may thus be written: As,
Table 8.
a", +,AS,,iSn. . + AS
,...+
AS.,r.
+ ASs8.,.
For crystals containing monatomic particles, positional randomization is the principal contribution to AS,. In Table 8, fusion parameters are collected for a number of different types of substances. For ionic crystals containing ions of the inert gas structure, ASr = 2-3 cal deg-' g-ion-'. This is expressed in the similitude rule (18): the increase of randomization on melting is the same for crystals of similar structure. The similitude rule is only approximately obeyed by such salts, since differences in the radius ratio of the ions and their polarizahilities lead to systematic variations on the short range interactions observed as electrostatic "ion pair" association, as noted by the spectroscopic methods. Further, it is evident (18) that not all "sites" in an ionic melt are equivalent. From inspection of the data in Table 8 for the 1 : l and 2:l salts, the magnitude of such interactions may be seen, in the first approximation in the deviations from the values for AS,predicted for these ionic melts, assuming complete ionization. The mercuric halides, as already noted (Table 3), form melts of exceedingly low electrical conductance, compared with the alkali halides. The entropies of fusion for the mercuric halides (Table 8) are intermediate between those for 1 : l and 1:2 type ionic salts, and compare more closely with the values for molecular liquids (cf. C02,9.2 eu, Clz,9.6 eu). Cryascopy (Thermodynamic)
Freezing-point measurements on molten salts can In phase-rule studies the range of composition studies is usually from 0-100% of added constituent, the temperature often being measured with an accuracy of only plus or minus several degrees. Analyses of the solid phases which separate out on freezing the liquid are also often made. For cryoscopy (or, more correctly cryometry) the concentration range studied is usually low, usually up to about 0.1 mole-fraction, and the freezing points are measured with an accuracy of usually *O.l°C or better. Freezing-point measurements yield information about the natures and activities of the molecular and ionic species and the modes and degrees of dissociation occurring in a solute-solvent system (15). Data such as heats and entropies of fusion can also be derived'for be divided into two overlapping groups.
Ne A NsCl KC1 MgCL CdCL CdBr, ZnCL HgCI. HgBrl HKI. NnNOa Adi01
use in elucidating the structures of the melts. In molten salt mixtures, the freezing-point depression in the dilute solute concentration range is given by: AT, = nkm,
where k is the cryoscopic constant, mzis the molality, and n is the number of "foreign" particles produced per molecule of solute (i.e., the total number minus the number of particles "common" to the solvent species). Thus in molten NaCl as solvent, n is found equal to 1 in the addition of solutes such as NaF, KCI, NarSOd, hut equal to 2 and 3 for solutes as K F and BaF2 respectively. The successful prediction of the cryoscopic behaviour of many types of solute-solvent systems has led to the use of the cryoscopy as a diagnostic procedure. This approach, thus, has been used to establish association-dissociation equilibria in molten salt mixtures. The reactions:
+
=
CdClz 2CI[CdClrl (in molten NaNOI as solvent)
and KnTiF.
=(in2Kt + ( T i F P 2 TiF, + 2Fmolten NsCl as solvent)
are illustrative examples. Viscosity (Transport)
The viscosity of the different types of liquids and its temperature dependence vary over an extremely wide range, and, accordingly, may be used to characterize the nature of the liquid state. For most non-polar and polar liquids, metals, and ionic melts, the viscosities near the melting point have values, within one order of magnitude, of 0.01 poise; for net-work like liquids (glass forming) the viscosities are much higher, having values of lo2 to 104 poise at the liquidus temperature. An experimental temperature dependence: = Ae-BdRT
has been observed for a large number of liquids, includmg many molten electrolytes. Typical values of E,, the energy of activation for viscous flow, are summarized in Table 9. For ionic melts, the empirical activation energy, E,, calculated from a plot of in v versus 1/T, is always found to be greater than the corresponding activation energy of conductance, En, the ratio EJEn usually lying in the range 2.04.0. This ratio has been interpreted as indicating that viscous flow involves a much greater configurational change than does the Volume 39, Number 2, February 1962
/
63
Table 9.
Activation Energies for Viscous Flow for Different Classes of Liquids
Range of values of E, (kcal mole-')
Group Non-polar liquids Polar liquids Hydrogen bonds Metals Ionic liauida Glasses ' Quautum liquids (He 11)
ionic migration caused by an applied electrical field. Whereas electrical conduction may be primarily uni-ionic, the smaller or more mobile ion carrying the current, electrical neutrality requires movement of both ions during viscous flow and the rate is governed by the larger ion. The approximate equality of EA and E, observed for some melts (e.g., molten nitrates) has been considered as indication that the structural units involved in conduction are larger than the simple ion, and more nearly comparable in size to the units involved in viscous flow. A marked decrease in activation energy with increasing temperature is observed for highly associated vitreous melts (18) (e.g., SiOz, GeOz, BeF2, ZnCL). Highly associated liquids exhibit large values of E,, since structural bonds must be broken before flow can occur. The decrease of E, with increasing temperature provides an indication of decreased coordination or a breakdown in ''network" structure. Electrical Conductance
Measurements of the electrical conductance of molten salt systems are probably among the most numerous for molten salts. The magnitude of the electrical conductance is a measure of the electrovalency of the molten salt and provides a ready parameter for the comparison of salts as molten electrolytes. A summary of some of the equivalent conductances for a series of molten chlorides, arranged in the order of the Periodic Table of the elements is shown in Table 10. The "stepladder" Table 10. Equivalent Conductonces for the Molten State (A),and the Freezing Points (Tr, 'C) of Some Chlorides in the Order of the Periodic Tables of the Elements
CuCl 94 430 RbCl (A) 94 (Tt) 717
(A) (Tr)
ZnCln 0.02 275 SrCI, 69 875
AgCl CdCL 118 75g! 455 CsCl B&ll (A) 86 (TI) 645 962 AuCl HgClr 3 X lo-" (A) ( T r ) libid.) 277 (A) (Tr)
64
/
GaCb
.
124
1
GeCb 0 -49.05
700
InCls
2
1
k
194
=
Axe-
EdRT
are applicable. In Table 11 are found the values (22) for the molten akali chlorides. Since electrical transport occurs at constant pressure, the empirical activation energy for conductance, En, may be identified with the enthalpy of activation AHA$, in the absolute rate theory. The entropy of activiation, ASAX, is included in the pre-exponential term, AA, and requires a knowledge of the dielectric constant of the melt for its evaluation. No experimental measurements of the latter for molten salts have been reported; values for this parameter of 3.0-5.0 have been assumed (22) empirically in these calculations. For simple ionic salts, a decrease in MA$ with increasing temperature is usually interpreted in terms of structural changes in the melt or a reduction height of the energy barriers controlling ionic migration, owing to thermal expansion of the liquid. It should be noted, however, that on the basis of this interpretation, the simple Arrhenius expressions are strictly applicable only when the conduction is uniionic. Applied to all the ionic species, the expression would be:
Table 11.
LaCIS H ~ C L Tach 29.0 ... 3 x 1 0 870 432 211 TlCb PbCI. x 10-8 2 x 1025 -15
Journal of Chemical Education
across the face of the table qualitatively separates the ionic and covalent chlorides, using the magnitude of the equivalent conductance as criterion for this classification. Useful correlations of this nature for conductance and related properties were first advanced by Biltz and Klemm (19) in 1926 to search for the trends relating structure and properties of molten salts. The electrical conductance of a molten salt and its temperature dependence yield information (16, 20, 21) regarding the nature of the conducting species, the existence of complex ions, the relative electrovalency or covalency of the system, structure and intermolecular forces in the melt, and the degree of dissociation. When correlated with other liquid transport properties (viscosity, diffusivity, thermal conductivity) additional information on problems such as the mechanisms for the transport processes in molten salts can frequently be gained. For nearly all molten electrolytes, it is found experimentally that plots of log A and log k versus 1/T are essentially linear over limited temperature ranges. Recent studies of the electrical conductance of molten salts have, therefore, considered ionic transport as a rate process, to which the simple Arrhenius expressions
10-
LiCl NaCl KC1 RbCl CsCl
Electrical Conductance of Some Simple Molten Electrolytes (22)
Melting point ("C)
Specific conduc6 ances (mho)
Equivalent conduce ances (mho)
Heat of activation* (kcal)
Entropy of activations (eu)
610 808 772 717 645
6.221 3.903 2 407 1.769 1.411
180.8 152.5 122.2 111.5 88.46
2.06 2.92 3.36 4.40 5.20
-6 1 -6 4 -6 7 -6.2 -6.2
All values refer to the properties at 100°C above the melting point of each alkali chloride respectively.
Linear plots of log A versus 1/T would then be expected only when the heats of activation of the conducting ionic species are almost equal, or when one is much smaller than the others. I t is generally found, however, that the simpler relation fitasthe observed results well for most pure molten silks and is also applicable t o salt mixtures (20,$1). The mechanism of electrical transport in simple ionic melts (spherical ions) has been envisaged as the jumping of an ionic species from one lattice site t o a neighboring vacancy (hole) in the direction of the applied field. This is superimposed on the natural Brownian motion of the species which occurs in the absence of any perturbing field. I n this treatment ($$, the enthalpy of hole formation contributes predominantly t o t,he enthalpy of activation for conductance. For more complex molten electrolytes, with polyatomic disc-like ionic species, such as the molten carbonates, a Grott,huss-type process, in which the mechanism of elect,rical transport is envisaged as a cooperative st,ep, involving a simple ion jump and rotat,ion of an ion pair species, has bcrn advanced ($4). The problem of partial ionizat,ion in molten salts, similarly, is receiving attention ($5, $6). The concept. of the reduced conductivity ($5) seems most promising for estimat,es of the extent to which "kinetically free" ions are present in molten salts. The degree of dissociation, a,for a 1: 1type molten elect,rolyteis given hy: where Xo is the average mobility of the ionic species reduced to unit viscosity (1 cp), and p and ?I are the molar conductance and viscosity respectively. In the application t o ionic melts, the conductivities should be reduced to unit viscosity by tll'm in the above relation, where m is the proportionality constant relating the energies of activation for viscosity and electrical conductance respectively. The value for a thus found for molten KBr, which is generally accepted to be completely ionized, is 1.22. The degree of dissociation for mercuric bromide, which is only poorly conducting in the molten state (cf. Table 3) has been predicted ($6) as equal to 2 X in the liquid state near its melting point.
a two dimensional array for a solid and liquid of one kind of atom only is shown in a and b, respectively, and for an ionic melt in e. The arrangement in a is one in which the atoms occupy all the available sites in a perfect lattice; in the liquid state, as in b, there is, hy contrast, no long range order, and the atoms are not localized as in t,he solid but continuously int,erchangc places; they can, in consequence, share the whole of t,he available volume. Local regions (clusters) of relatively high order are seen in the quasi-crystalline concept of the liquid state. It is apparent, as illustrated in Fig. 4c, that in an ionic melt the state is more complex than for the monatomic liquid. While long-range crystalline order is entirely absent, a residue of local order, persisting as a memory of the highly organized crystalline structure, is maintained by each ion in the distribution of neighbors in its immediate vicinity. The local arrangement of neighbors may be regarded as a blurred reproduction of the first coordination shells of neighbors in a single crystal 1att.ice. The Temkin (31) model, which may be interpreted statistically as one in which anions and cations are randomly distributed among themselves irrespective of valency, but that each anion is surrounded by cations and vice versa, has been useful in thcrmodynamic studies of simple ionic mixtures. The problem of deviations from the random mixing concept in the short-range order of anions and cations is one of current interest in studies of molten salt mixtures. In Figure 5 the arrangement is shown for clusters in (a) pure potassium chloride, (b) potassium chloride with some lithium chloride, and (c) this mixture with some lithium fluoride, all in the molten state.
1'4) Figure 5.
Id
Ib)
Miring in molten salts.
lnferoctions in Ionic Molten Solts
I t is apparent from such considerations that the quasi-crystalline concept of the liquid state is generally most appropriate for ionic melts. The most fruitful theoretical contributions (27-30) have been made by focusing attention on the point that the essential difference between a solid and a liquid is that a solid, at most temperatures, can be regarded as ordered, while a liquid, for the most part, is disordered. The problem is illustrated schematically in Figure 4 where
The Temkin model may be regarded as a prediction for the behaviour of an ideal melt. Heat of mixing and entropy of mixing may contribute to deviations from ideality. Thus for a two cation-two anion mixture such as LiCl and KF, from an inspection of the lattice energies (kcal/mol) it can be seen that the mixing process may be predicted as a partial exchange of the type: salt:
LiCl
lattice energy: 192
Figure 4.
Process of
furion.
+ KF
189
-
LiF 239
+ KC1 163
since the right-hand side represents the most stable configuration (21 kcal). From the electrostatic viewpoint, as illustrated in Figure 5, the arrangement having small anion-small cat,ion pairing would be a lower energy configuration than the purely randomly mixed assembly. While the system is still completely ionic (i.e., consists of kinetically free ionic species) the concept of "contact" ion pairs or paired ions thus enters in the descript,ion of ionic melts. A quasi-lattice model Volume 39, Number 2, February 1962
/ 65
of molten reciprocal salt systems in which such asymmetric interactions are correlated with the relative field effects of the different ionic species has been recently advanced in the discussion of thermodynamic activities in molten salt mixtures (32). Extension of t,he principles of equilibrium and reaction calorimetry (33, 34) to investigate deviations from thermodynamic ideality in mixtures of simple ionic salts will contribute data important to the fundamental question of ionic interactions and deviations from thermodynamically ideal behaviour.
and electrical conductance and Raman spectra for molten ZnCl? have been recently. interpreted (18) by the model illustrated in Figure 6. Thus the melt is a liquid with "fragments" of the original double layers, and individual Z n C k 4ions as the main species present; with increasing temperatures the "dissociation" becomes more extensive, and discrete Zn+Zions, in addition to the Z I I C ~ ~ions - ~ and "fragments" first formed at the melting point of this salt, are assumed present. Such systems are beyond the scope of the present survey; the advance of the spectroscopic techniques (36) into the field of high temperature chemistry promises significant contributions to the structural problems of these more complex molten salt systems. Acknowledgment
This work was made possible, in part, by support received from the U. S. Air Force, Office of Scientific Research, for fundamental studies on the structure and physical properties of moltco salts al Rcnqsrlaer Polytechnic Institute. Figure 6. Reprerentation of lo) cryrtolline ZnCh and lbl molten ZnCln at higher temperatures (18). The rmoll circles are Zn and t h e chlorides are in planes a b o v e and below t h e zinc species lcf. Fig. 314).
Literature Cited (1) JANZ,G . J., '%ibliography of Molten Salts," Rensselser
A theory for simple ionic melts, recently advanced (35),investigates the properties of ionic pair distributions for a model in which the shorerange ion-core forces and the ion coulomb interactions are each equally influential in determining the characteristics of the salt near its melting point. Significantly this treatment predicts that the short-range ion-core interactions drive the ions into local close packed latticelike arrangements. The configuration about any given ion is a series of concentric shells of average charge density arranged in a manner suggesting local latticelike structure. The Debye limiting law is shown to be a special case of this model for extremely high temperatures, or very low ion number densities. At temperatures near the melting point, in these ionic melts, the "diffuse" ion atmosphere around a central ion, in contrast to that for dilute aqueous electrolytes, would be equivalent to a thin skin of neutralizing charge only a few hundredths of an Angstrom unit thick. The concepts of the relaxation time effect and the electrophoretic effect, important to the interpretation of the variation of ionic mobility in aqueous electrolytes, thus are not the effective processes in melts of ionic salts. Sufficiently enhanced, such purely ionic interactions may be experimentally realized as deviations from thermodynamic ideality (e.g., cryoscopic studies), as changes in electrical conductance (enhanced covalency), and possibly spectroscopically. It is, in part, the search for more direct experimental evidence of such interactions that is stimulating the current activity in the development of high temperature techniques in ultraviolet, infrared, and Raman spectroscopy. Salts having a pronounced covalent component of bonding offer additional structural problems in the molten states. This may be illustrated by a salt such as ZnClr. The crystal structure of ZnCL is similar to that of CdClz (Fig. 3c) in which the cations are situated in octahedral "holes" between two infinite layers of chlorines, the latter being held together by van der Waals forces. The properties of viscosity 66
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Journol o f Chemical Education
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Volume 39, Number 2, February 1962
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