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Equilibrium and Transport Properties of Low-Melting Salts.

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[9S] 0. L. Ciiupmuii and C. L. Mi.Ifitosh,Chem. Comniun lY71. 770
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and W Hzihd, Tetrahcdi-on Lett. fY6I. 637.
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Y6. 279 ( 1 974).
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Chem internat. Edit. I?. 162 (1973).
[99] W Schiifrr. A. Sdiiveiq. G . Mrritv. 7: Surruc. and J . K . Crutitluii. Tetrahedron Lett. lY74, 1213.
[I001 M J . S. D e i u r and N . Z-ifiujsrid Thcor. Chim. Acta 17, 235 (1970).
[ 1011 H.-C. Wrytier.. Angew Chem 85. 920 (1973). Angew. Chem. internat.
Edit. l 2 . X4X (1973).
[I023 G. Sryholii, L:. Jc,rr-rrk, and R. Corirpprr. Angew. Chem. 83. 91X (1973);
Angew Chem. internat. Edit. 12.847 (1973). Review of hetcrocyclobutadienes:
R. Gompper and G. S q h o l d , Topics in Nonbenzenoid Aromatic Chemistry,
in press: for a henzo derivative, cf.: B M. Adger, M. Kearing. C . PI! R w s .
and R. C. Srorr. .I. C . S. Chem. <'omm. 11/73. 19
[103] W Sreglich, E. Buschmann, and 0.Hollirzer, Angew. Chem , in press.
[ 1041 G. Murer and U . SdiBfer-. unpublished; L'. SchiiJrr. Diplomarbeit, Universitiit Marburg 1974.
[IOS] R. B. Wiodirurd and R. Ho/ftmrmi, Accounts Chem. Res. 1. 17 (1968).
[lob] a) R. J . Bwiiher and S. ff Peyerim/ioff, J . Amer. Chem. Soc Y l ,
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105. 2290 (1972): b) L. 7: Scort and M . Jonrs. Chem. Rev. 72. I81 (1972).
'on, R. T K . Baker. and R. L. Wdf+i:yiiny. Tetrahedron
Lett. 1Y6Y. 4749.
[I101 P. B. Shei~iiiiand A . P Wdf. J Amer. Chem. Soc. 97. 406, 5291
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G. Miriw. unpublished.
[ 1 181 R. Gofiipprr. F. Hoishotv'. W Schnridi, and G. Sc,rholr/. J. Amer. Chem.
Soc. YS, 8479 (1973)
[ 1 191 Regarding energetic considerations. cf.: S. H i i n i ~and H . Pirrrw, Angew.
Chem. XS. 143 (1973): Angew. Chem internat. Edit. 12, 149 (1973).
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[124] Together with H.-G. Harron: we are indebted to Dr. B. Mnnn. Fachbereich Physikalische Chemie, Universitat Marburg, for his asastatice in the
construction of the equipment for low-temperature spectroscopy.
Equilibrium and Transport Properties of Low-Melting Salts
By Joachim Richter[*]
An understanding of the physical and chemical phenomena and the structure of salt melts
calls not only for kinetic and spectroscopic data but also for systematic studies on the equilibrium
and transport properties of individual systems. The present article deals with the activity
coefficients, transport numbers, and self-diffusion and interdiffusion coefficients of salt melts,
and the results of consistent measurements of these quantities are reported.
1. Introduction
The term salt melts (or more generally electrolyte melts) is
applied to inorganic salts (or electrolytes) that dissociate into
their ionic constituents in the molten state. A distinction is
made between pure molten salts that consist of only one
component, e.g. NaN03, and salt melts that consist of two
or more components, r.g. N a N 0 3 +Ca(N03)2.
Nitrate melts are among the most thoroughly investigated
low-melting salt melts. The general discussions below are
illustrated by results for the systems N a N 0 3 + A g N 0 3 and
LiN03+AgN03.
Interest in salt melts has increased rapidly in recent years
for two reasons:
I'[
Prof. Dr. J. Richter
Lehrstuhl fur Physikalische Chemie 11 der Technischen Hochschule
5 I Aachen, Templergrdhen 59 (Germany)
438
The first reason is the increasingly rapid development of a
wide range of practical applications for salt melts, e.g. in
reactor construction, in the remelting of electrolyte slags and
other applications in metallurgy, and as effective, very fluid
heat exchangers at high temperatures, in the electrolytic isolation of metals or in fuel cells; moreover, increasing numbers
of chemical reactions can be carried out with high rates and
in high yields in salt melts, and so on.
The second reason for the growing interests in salt melts
is the great importance that they haveattained in fundamental
research. The study of the thermodynamic, kinetic, and spectroscopic properties of these liquids is improving our understanding of the physical and chemical phenomena and of
the structure of melts. Though the matter is still under discussion, there is good reason to hope that the structure of salt
melts will be easier to understand than that of systems such
as N a N 0 3 in water, i. e. systems with a neutral solvent, which
Angew.
Chem. intrrmf. Edit.
1 Vol. 13 ( 1 9 7 4 ) No. 7
have much more complicated structures. Fundamental
research is being carried out at present in an effort to clarify
the structure of salt melts; this necessitates systematic studies
on the equilibrium properties and transport phenomena of
individual systems.
The modern literature on salt melts dates back to about
1960 (see e.g. the monographs[' - 5 . *I, the book of tablesc6],
and the data c~llection['~).
The latest findings and results
are presented in the series "Advances in Molten Salt Chemistry", the first volumei"lofwhichappeared in 1971, the second"'
in 1973. The transport properties of salt melts in particular
have formed the subject of recent reviews"". "I. The literature
is rounded off by a number of general surveys['2-ts1.
300
1 250
200
2. Activity Coefficients
For the thermodynamic description of salt melts, one requires
a clear definition of the activity coefficients of all the components present in a system. Proposals have been made by
7iinzkidt"', F o r/ nnd ' 'I, and F/or!~"'l, but these are not very
suitable for a general description because of the models on
which they are based. H u ~ s e I " . ~ "introduced
~
the general
concept of an "ideal electrolyte melt", and defined suitable
activity coefficients in binarj. electrolyte melts by means of
the Equation
150
,
24 0
260
280
1, L O C I
1161j
,
300
Fig. 1. Emf (0)
a s a function of the tempcrature 7, for the system
N a N O 3 + A g N O j with the mole fraction . Y of
~ silver nitrate as thc parameter
(numbers by the straight lines).
The activity coefficient 1; of the component j is dimensionless,
and depends, as usual, on the temperature T, the pressure
P, and the composition.
is an abbreviation for
+,
350
pj is the chemical potential of the component j in the mixture,
poj is the chemical potential of the pure liquid component
j, and R is the gas constant. Jl,!" is the corresponding expression
for the standardized ideal melt. The standardized ideal mixture
is defined by the condition that the melt is completely dissociated, contains no complex ions, and the expression J l i = In xi
( x i : true mole fraction of the ionic species i) is valid for
every ionic species i. The reference melt can thus be described
by measurable quantities such as the stoichiometric mole
fractions.
These new activity coefficients have the advantage that they
allow the description of the thermodynamic behavior even
of complicated melts, i. e. melts in which the constituents
have different valencies. The logarithms of these activity coefficients can be represented by power series in the mole fraction
with whole-number exponents, which satisfy the general principles of thermodynamics. The limiting laws for the freezing
point depression and for the vapor pressure of salt melts
can thus be given in a simple formlztl.Moreover, for a large
number of binary systems, the activity coefficients for the
two components of these systems (the parameters of their
series expansion) can be calculated from the known analytical
expression for the additional molar free enthalpy GE[**l.The
additional functions of the molar free enthalpy, the molar
entropy, and the molar enthalpy can also be derived from
these series.
Angrw. Chum. intrrnot. Edit.
1 Vol. 13 ( 1 9 7 4 ) No. 7
300
-t
-" 250
w
D
8
200
150
260
-
280
260
Tc
"TI
300
Fig. 2 Emf (0)
as a functlon of the tcrnpernturc E. for the system
L i N O 3 + A g N O . ? with !he mole fraction .x2 of silver nitrate as the parameter
(numbers by the straight lines).
439
Keteluur and l’b~[’~’
have compared the four definitions of
the ideal mixture given by Trrnkin, Forlund, Flory, and ha as^.,
and pointed out the differences in the models.
Sehrn[24fhas recently determined the activity coefficients for
the systems NaN03 + A g N 0 3 and L i N 0 3 + A g N 0 3 in the
temperature range 240 to 310’C over the entire concentration
range, as far as the phasediagram allows, by emf measurements
on a chemical cell. A nitrate electrode of a form similar to
that developed by Ketelaar and Dummers-duKlerk[25. was
used. The measured emf (@) is shown as a function of temperature, with the mole fraction of silver nitrate as the parameter,
in Figure 1 for the system N a N 0 3 + A g N 0 3 and in Figure
2 for the system L i N 0 3 +AgN03. Figure 3 shows the activity
coefficients calculated from these results for the two systems
at fixed temperatures. The interdiffusion coefficients were
determined at these temperatures (see Section 5.2 and Fig.
7).
Because of the linear dependence of the emf on the temperature,
six constants that are characteristic of the salt melts investigated, and that d o not depend either on the composition
or on the temperature, can be determined from the analytic
presentation of the activity coefficients[271.
The function $jd can now be determined in succession for
the individual systems (two components with or without a
common ion, e.g. N a N 0 3 + A g N 0 3 or NaCl+ KBr, three
components with one or two common ions or without a commonion,e.g.NaNO, +KNO, +Ca(NO,),,NaCl+KCI+KBr,
or AgCl +TINO’ + KBr, rtc.), and the following rather more
complicated expression[”] is found for the general formulation:
(3)
v, is the sum of the dissociation numbers for the component
j, x, is the mole fraction, vJT is the dissociation number of
the ion r in the component j,and 1 indicates the components
that have an ion in common with the component j. The
product in eq. (3) is accordingly taken over the ions of the
component j, the summation in I over all p components that
have an ion in common with j, and the summation in i
over all n components present.
This complicated expression (3) becomes very simple for most
of the systems investigated, and together with eq. (2).it allows
the determination of activity coefficients from emf measurements for any salt melt, regardless of its composition.
For very simple systems (in which all the components have
the same dissociation number and contain a common ion,
P. y. K N 0 3 + A g N 0 3
this agrees with the usual
literature definition, which was taken over from solutions
of low molecular weight non-electrolytes:
+
lnuj =In xj + ln yj
0.9
‘
1.0
lb63]
In this expression, a, is the activity and y, is the activity
coefficient of the component j. The definitions differ in all
other cases. The new definition [eqs. (1+(3)] has the advantage that the logarithm of the activity coefficient for al/ systems
can be expanded in series, which are of fundamental importance to all the limiting laws of the salt melts considered.
I
0.8
0.6
0.4
0.2
X?
Fig. 3. Activity coefficients f 2 as a function of the molc fraction .x2 of silver
nitrateforthesystem N a N 0 ~ + A g U d , a t290 C [ o - - o ) a n d forthesystem
L i N O J + A g N O , a t 260 C ( 0 0 ) .
On the basis of the definition ( l ) , it is possible to derive
an expression that enables the activity coefficients of any
salt melt, regardless of its composition, to be given explicitly.
The emf(@)of a chemical (isothermally-isobarically reversible)
cell obeys the following relation:
F is the Faraday constant and @DO
is the emf of the cell
with the pure component k, for whose ions the electrodes
of the cell are reversible. q is the factor that precedes the
chemical potential of the component k in the expression for
the affinity of the heterogeneous reaction corresponding to
k.
440
3. Transport Numbers
The transport numbers are generally determined by three
methods, i. e. the Hittorf method, the moving boundary
method, and emf measurements on concentration cells with
transport. The Hittorf method was used for salts melts e.g.
by Kuwarnirru and Ukada~”’,who, like Duke er U / . [ ~ ~ used
I,
the formula of Aziz and Wetrn~re[”~
for the evaluation. The
question of the external and internal transport numbers (reference systems) and their relation to one another has not yet
been clarified here; this problem is being examined at present
by H ~ u s e The
~ ~ moving
~ ~ . boundary method is applied to
salt melts only in isolated cases[331,since it is extremely difficult
to investigate systems of this type by optical methods. We
determined the transport numbers of the systems
N a N 0 3 + A g N 0 3 and LiN03+AgN03 with the aid of a
concentration
The concentration cell with transport can be represented for
such a system by the following scheme:
Angrw. Chem. inrernar. Edit.
Vol. 13 ( 1 9 7 4 ) / No. 7
The terminals of the cell, which connect the silver electrodes
(Ag) to the measuring instruments, consists of copper. The
double line symbolizes the direct liquid contact between the
two melts with different concentrations ( X I = mole fraction
of silver nitrate in the left half-cell, XII =mole fraction of silver
nitrate in the right half-cell). From the emf measured as a
function of temperature and composition, the internal transport numbers r N h . and t A g . (thoj is zero, since the common
nitrate ions are reference particles in the sense of the Hittorf
reference system) are determined from the following formulal3S1.
(ps51
(4)
x 2 is the mole fraction and ,fi is the activity coefficient of
silver nitrate: r . , = f K a or fl.,.; t;,+t.Zq = I . Eq. (4) is evaluated
graphically with the aid of the activity coefficients determined
by Se/trul”l (for further details see[-’(’I).The concentration
range in which measurements are possible is O . ~ < U Z < 1.0
at 240 C to 0.1 < x 2 < l . 0 at 300’C for the system
N a N 0 3 + A g N 0 3 , and 0.1 < x 2 < 1.0 in the same temperature
range for the system L i N 0 3 +AgNO,. The transport numbers
ofthesystems N a N 0 3 + A g N 0 3 (Fig. 4) and LiN03+AgN03
(Fig. 5 ) are shown as examples at the same temperatures
as for the activity coefficients (Fig. 3).
O u r values are compared in Figure 4 with data found by
D i k e et ul.13”1 with a Hittorf apparatus. The temperature
control was improved in the emf measurements; an analysis
u$er the experiment is unnecessary, and the emf apparatus,
unlike the Hittorf apparatus used by Duke et ul., contains
no membrane. The deviation of the transport numbers from
the previously found linearity with respect to the mole fraction
thus seems to be verified.
x2
-
of the silver ions 21s a fiiiiction of thL‘
Fig. 5. Transport numbers !,<,
mole fraction y 2 of silver nitrate for the system L i N 0 3 + A g N 0 . $ . ( x
x ):
a t 300 C (after [29]): ( 0 0 ) : at 260 C.
From these transport numbers, together with the known
densities and electric conductivities of the systems, it is possible
to calculate the ion mobilities, equivalent conductivity, and
ionic conductivities, as well as their limiting values and values
for the ideal melt, as suggested in the papers by Timmerniunn
and
and by A m k r e ~ i f z [and
~ ~ ~calculated for the
systems discussed here.
4. Self-Diffusion
4.1. General and Definitions
Investigations on salt melts have so far been confined to
the phenomenon of self-diffusion, apart from the few exceptions
of interdiffusion (see Section 5). The starting assumption is
that the simplest relations between the mobilities and radii
of the ions and the structure of the melt are to be expected
in self-diffusion, i. e. “in the limiting case in which the difference
between two diffusing substances in a binary mixture disap-~
pears[381”(the exact definition of self-diffusion is given below),
since the measurements are carried out in very simple systems
(usually one-component systems) with few assumptions. Moreover, self-diffusion experiments are easier and much faster
to carry out than interdiffusion experiments (see Section 5).
The term diffusion is used in general for any mass transport
in a mixture that is caused by a concentration gradient. The
collective term self-diffusion in particular, which we shall have
to differentiate below, is applied to the transport of a labeled
ionic species in relation to the same unlabeled ionic species
in a salt or in a salt mixture at a concentration gradient
close to zero for the labeled particles.
[16Ll
1/
oj2
04
xz
-
0.6
d.8
o;
Fig. 4. Transport numbers f,q
of the silver ions as a function of the mole
fraction I? of s~lver nitrate for the system NaNO3+AgNO3. (-- -): at
305+5 C (after [30]):( 0 . 0 ) :at 2 9 0 i 1 C .
Figure 5 shows a comparison of the transport numbers for
thesystem LiNO, +AgNO, withtheresultsofHittorfmeasurements by Kawamura and Okada‘291,for which the above
remark is valid.
Angew. Chum. inturnat. Edit.
/ Vol. 13 ( 1 9 7 4 ) / No. 7
For the definition of self-diffusion, it is necessary to clarify
three terms that have been adopted in the literature, i.e.
tracer diffusion, intradiffusion, and self-diffusion.
Let us first consider a melt that consists of one component,
i.e. of two ionic constituents, e.g. molten sodium chloride
with the component NaCl and the two ionic constituents
Na and C1. If we replace some of the Na’ ions by labeled
N a + * ions (experimentally by addition of a radioactive isotope), we have a system for which all three phenomena can
be defined.
The diffusion flow density, i. e. the quantity of substance passing through a reference surface per unit area and per unit
441
time, can be defined in any desired reference system. For
experimental purposes, we observe the transport of the labeled
constituent in relation to the unlabeled constituent. The movements are therefore coupled by the experimental conditions.
However, we determine the mean velocity of the ionic constituent with respect to the chosen reference velocity. For simplicity, we consider the one-dimensional case of diffusion (position coordinate z) in the Fick reference system.
In trcicer dijfiision, the reference velocity for the diffusion flow
density w j T of the labeled ionic component j* (with molarity
cf) in the Fick reference system, i. e. the mean volume velocity
G, is given by:
Pf is the mean velocity of the labeled ionic constituent j*.
Experience shows that each independent diffusion flow is a
homogeneous linear function of all the independent concentration gradients if extremely high gradients are ruled
For the salt melt considered here, it follows that the diffusion
flow density defined in eq. ( 5 ) is:
value of the tracer diffusion coefficient for a vanishingly small
concentration of the labeled ionic constituent j*:
(7)
This is found experimentally by measurement of 07 as a
function of cf and extrapolation to cf+O. This is the same
as saying that the difference in the chemical and physical
properties disappears.
We can see that self-diffusion does nor become identical with
intradiffusion, since intradiffusion allows differences in the
physical properties, i.e. in particular in the masses of the
isotopes. Analogous isotope effects in the mobilities were carefully investigated by Luntl~hand Ljubinior.["I for the system
Li,S04+ KzS04. These authors defined a mass effect (relative
difference in mobility divided by the difference between the
masses of the isotopes) and determined its dependence on
the composition. It was found that the isotope effects cannot
be disregarded.
In the remainder of this discussion, therefore, we shall consider
only tracer diffusion and self-diffusion as its limiting value
in the sense defined above.
Tracer diffusion and self-diffusion are defined in the same
way in aqueous electrolyte solutions and in non-electrolyte
solutions[43! In non-electrolyte solutions, the self-diffusion
of the solute at infinite dilution must be physically identical
with the interdiffusion (see Section 5). Bearrnun["l showed
that for simple systems of binary non-electrolyte solutions,
the interdiffusion coefficient becomes equal to the self-diffusion
coefficient at infinite dilution. We were able to show the
same result for simple binary salt melts[441.
The tracer diffusion coefficient Df is defined by eq. (6). The
operator ?/& meansdifferentiation with respect to the position
coordinate z for a fixed time. The temperature and pressure
are the same for all positions (other transport phenomena,
such as thermal diffusion, would otherwise occur). Tracer
diffusion is thus the diffusion of the labeled ionic constituents
in relation to the Fick (or any other chosen) reference system.
The tracer diffusion is measured with radioactive isotopes
that differ in their physical and chemical behavior from the
unlabeled ionic constituents.
4.2. Experimental Methods for the Measurement of Self-Diffusion
If one stipulates that the differences between the chemical
properties of the labeled and the unlabeled ionic constituents
are negligible, the tracer diffusion will be identical with the
intrcidiffsion postulated by Albright and
These
authors introduced the concept of intradiffusion because of
the difference between and the ambiguity of the terms tracer
diffusion and self-diffusion. However, since intradiffusion
cannot be brought about experimentally in the strict sense
of its definition, the additional concept of intradiffusion, in
my opinion, leads to further confusion. The intradiffusion
coefficient is numerically equal to the tracer diffusion coefficient if the differences between the chemical properties of
the labeled and of the unlabeled ions disappear.
In tracer diffusion, the concentration of the labeled ions is
very low. The labeled ions do not interact directly with one
another, or, as formulated by B e ~ r r n a n ' ~the
~ ~labeled
,
ions
move in an essentially homogeneous environment. The tracer
diffusion coefficient nevertheless depends on the concentration
of the labeled ions. The hypothetical intradiffusion coefficient,
because of the chemical identity of the two ionic species,
is independent of the ratio between the concentrations of
the labeled and the unlabeled ions, and depends only on
the total concentration of the ionic constituent observed.
The se[f-diffirsion coefficient D,, of the ionic component i (the
same as j, but unlabeled) will be taken here as the limiting
The most suitable method for the determination of self-diffusion in salt melts is the capillary method, which is the method
most commonly used in the investigations. The capillary
method exists in two variants. In one case (method I),
a capillary
closed at one end and filled with labeled ions is introduced
into a bath containing unlabeled salt; in the second variant
(method 2), the capillary contains the unlabeled salt, while
the bath contains the labeled ions. Method 1 (diffusion out
of a capillary) was introduced by D w w k i n i'f ~ 1 . f ' ~for
~ salt
melts; method 2 (diffusion into a capillary) was devised by
Bockris and H ~ o p e r ~ ~ ~ ] .
Instead of the capillary, a sintered plate with fine pores may
be impregnated with labeled ions and introduced into a bath
containing unlabeled salt (method 3). This method (porous
frit technique) was devised by Djordjrcic and ~Yilfs["'~for
salt melts, and developed further by Sj6b/0rn[~*~.
There have been a number of experiments in which a layer
of labeled salt was applied over unlabeled salt in a capillary;
unlike in methods 1 and 2, therefore, the boundary is situated
inside the capillary (method 4). This method, which was introduced by Aiiyrll and Bockris[4y1and further developed by
W ~ / l i n [is~ now'fi'o
~],
longer used.
Finally, Ketrlaarand Honig'". 521developedthe paper electrophoresis method (method 5), in which glass-fiber paper is
442
Angew. Chrm. internat. Edit.
1 Vol. 13
(1974) 1 N o . 7
Tnble I . Self-diffusion coefficients /A,, in NaNO., (molten) at 3.50 C. For
methods I. 2. 3. and 5 see text.
D,, 10"
Method
Ref
'1
[m-'s
2.33 i0 04
2.27 i0.07
2.27 20.07
1.102 0.09
2.13 2 0 0 5
2.44 & 0. I
2.49 0. I
*
impregnated with the salt melt and supported on a glass
plate. The tracer diffusion coefficients are then calculated from
the Gaussian distribution obtained after a certain time as
a result of the diffusion of the radioactive isotopes. In an
improvement of this method introduced by Krfdncrr and
K i . ~ c r k [ ~in
" l 1967, the glass fiber paper is replaced by quartz
glass fibers, and an A1,0, substrate is used as the support.
This avoids the exchange of the Na- ions in the N a N 0 3
melt under investigation with the ions in the glass.
As a comparison of the five methods, Table I shows the
self-diffusion coefficients of Na' in NaNO, at 350°C as found
by seven groups of
Method 4 is unsuitable for
nitrate melts, and does not therefore appear in Table I . As
has also been observed in measurements on other systems,
method 2 gives slightly lower values, and methods 3 and
5 slightly higher values, than method I. We shall not consider
the errors of the individual methods in detail, but merely
note that the capillary method has been found to be the
best for salt melts.
Another suitable method for the experimental study of self-diffusion is NMR spectroscopy, whose application to salt melts
is still in its early stages because of experimental difficulties.
The first investigation on self-diffusion in salt melts was published by Klenini and Berue15'1 in 1953. The authors used
the capillary method to investigate the diffusion of radioactive
thallium ions in thallium chloride. Very many investigations
of self-diffusion in salt melts and above all in metals and
metal alloys have now been carried out. (See in particular
Refs. 145. 53. 5 6 . 6 0 - 641, which are concerned with the nitrate
melts discussed here or with their components.)
tinguish it from self-diffusion. Whereas self-diffusion is investigated mainly in one-component systems, interdiffusion can
only occur in systems containing two or more components.
Self-diffusion in salt melts has been extensively studied both
theoretically and experimentally; on the other hand, the development of experimental methods for the investigation of interdiffusion is still in its early stages.
The theoretical treatment of interdiffusion is particularly
simple for salt melts in which two ionic constituents migrate
independently of each other in relation to a third. In the
following discussion we shall again consider the systems
N a N 0 3 + A g N 0 3 and LiN0, +AgNO,, which consist of
three ionic constituents or of two components in the sense
of the Gibbs phase rule with a common anion. In both systems,
the cations of the component 1 (Na' or L i + )and the cations
of the component 2 (Ag-) move in relation to the common
anion (NO;). This situation is illustrated schematically in
Figure 6.
lass]
Fis 6 Schcinatic representation i,1 .I s i l t mclt ci>n\t.;tinsof two compoiiciits
with a common anion. z = position coordinate @denotes the cationic constitthe common anionic
uent of component 1 . 0 that of component 2. and
constituent.
8
In the measurements, the movement of one cation is observed
in relation to that of the other. The movements of the two
types of cation are thus coupled by the experimental conditions; in this sense, they are not independent of each other.
For this reason there is only one interdiffusion coefficient
for each system.
This interdiffusion coefficient D can be defined by a generalization of the Fick law[661:
J =
0
The most reliable values for the self-diffusion coefficient D,,,
of Na' in NaNO, appear to be those given by Bockris and
Nuytrrrrjtrrii"51, which are shown in Table 2 as a function
of the temperature Tc.
Table 2. Self-diffusion coefficicnts Dh., of Na ' in N a N O J as a function
of the temperature F [65].
.
~~
~~~
~~
~
r, [ C]
-- . . . . .
DNr . 10' [m' s ~~~
~~
.
~
350
3 70
2.14
2.38
390
420
2.61
3.04
. .. .
'1
.
~~~~
...-
.
5. Interdiffusion
5.1. Fundamental Principles
The transport process referred to in normal scientific usage
as diffusion will be referred to here as interdiffusion, to disAnguw. Chrm. intrrnat. Edit.
Vol. 13 11974)
No. 7
2-
-
I,
D
_-- -w,
1
grad x,,
V(1 -X,J
( n = 1,2)
,,,j,
i s the diffusion flow density of the component n
in an
arbitrary reference system with the reference velocity 0, w,,
are the corresponding weight factors, and
is the molar
volume of the melt. D is retained in this type of definition
in every reference system. As we showed earlier[h71,this is
possible only for salt melts with three ionic constituents. [With
this choice of definition, we no longer have the difficulty
of converting Dv into D M (D":diffusion coefficient in the
Fick reference system, D M: diffusion coefficient in the barycentric system) ere., which is usually found in the literature.]
v
The only reference systems of any appreciable importance
for diffusion in salt melts are the Fick system and the Hittorf
system.
Fick's law[81in the Fick reference system (index w) has the
form:
,j2 =
-
V, rad x 2
D=-VZg
(9)
443
Vt is the partial molar volume of component 1. The corresponding equation in the Hittorf reference system (index -),
with the mean velocity of the common anionic constituent
as the reference velocity, is[671:
v l - and v2- are the dissociation numbers of the anionic
constituents of components I and 2.
Fick's second law or a relation corresponding to Fick's second
law and following from Fick's first law in the form (9) or
(10) is used in the majority of diffusion experiments.
5.2. Experimental Methods for the Measurement of Interdiffusion
Four methods have so far been developed for the investigation
of interdiffusion in salt melts. However, all these methods
embrace only a very small concentration range, so that they
are only suitable for the investigation of the limiting values
of the diffusion coefficients for x,+O. S ' O h l ~ m ' developed
~~~~~~
a gravimetric method, GustaJwon rt N / . [ ' ~ 701 an optical
method, Laity and Miller[711
a method that involves the use
of a diaphragm cell, and Thalmnyer et af.1721
a chronopotentio[ ~ ~now
] improved the gravimemetric technique. S j i i b / ~ m has
tric method so that measurements are possible over the entire
concentration range.
We have modified the method involving the diaphragm cell
in such a way that the interdiffusion coefficients of low-melting
salt mixtures can be determined relatively accurately over
the entire concentration range with the aid of a new evaluation
procedure[74! The results for the system N a N 0 3 + AgN03
at 290°C and for the system L i N 0 3 + A g N 0 3 at 260'C are
shown in Figure I .
above all kinetic data are necessary in addition to knowledge
of the thermodynamic properties. We confine ourselves here
to the thermodynamic data, which include not only those
discussed already but also e. y. the transport coefficients of
the melts in centrifugal and gravity cells[75-7 h 1 and in thermop i l e ~ [ ~ ' . ~ The
' ! latter are being determined at present in
our laboratory for the systems examined here.
A possibility for the unified presentation of the data discussed
here is offered by the formalism of the coefficients of friction,
as formulated e.y. by Klrmm[7H1.This allows one first to
calculate the interfriction coefficients, which are a measure
of the interactions between different ionic constituents. From
these interfriction coefficients, with a very simple assumption
about the relationship between self-diffusion and interdiffusion[791 , It is possible to calculate the self-friction coefficients,
'
which are a measure of the interactions between similar ionic
constituents.
For the binary nitrate melts examined here, therefore, we
obtain a total of six friction coefficients for each system.
The transport processes investigated are largely determined
by the structure of the salt melt. There are several models
for the structure of simple salt melts, which proceed from
the experimentally based requirement that a salt melt must
contain cavities. The various approaches differ in the interpretation of the size, mode of formation, and distribution of
these cavities in the melt, and lead to the quasi-lattice model,
to the hole model, to the crystallite or polyhedral hole model,
and to the free volume model as described by Sundheimi3'
for salt melts. These models are rarely discussed nowadays,
since they are not very specific and they give a sufficiently
good description of the transport properties only with simplifying assumptions.
The models of Temkin['61, Forland" 71, and F/ory[181and
Hasse's definition[". 201 are based on purely thermodynamic
considerations, and formulate the reference melt idealized in
some form (ideal behavior of the melt). By themselves, these
do not provide evidence of the true structure of a salt melt.
An entirely new development is appearing at present as a
result of model calculations using the computer simulation
technique, which are yielding the first good results (cf. e.g.
Ref.'*"').
1.0
0
0.2
1657]
0.4
xz
-
1
0.6
0.8
10
Fig. 7. Interdiffusion coefficients D as a function of the mole fraction xz
of silver nitrate for the system NaNOJ+AgNO., at 290-C ( 0 - 0 ) and
).
for the system LiNO, f A g N 0 3 at 260 C ( 0
~~
Though the measuring accuracy is relatively good in these
investigations, optical methods will probably prove, after
further development, to be the best methods for the investigation ofdiffusion in salt melts, owing to the greater fundamental
accuracy of measurement.
6. Closing Remarks
For a deeper understanding of the physical and chemical
phenomena and the structure of salt melts, spectroscopic and
444
Optical measurements are necessary in addition to transport
and friction coefficients, since the existence of compounds
or complexes in the melt cannot be conclusively demonstrated
by thermodynamic measurements alone. When the investigations on the transport coefficients of thermal diffusion have
been completed, we may obtain a more accurate picture of
the structure of low-melting salts.
I am grateful t o Prof: Dr. R . Haase for his generous encottragement of my own work in this field. Part of this work was
supported by the Deritsche Forschungsgemeinschaf, t o which
we are also gruteful.
Received: May 7, 1973 [A 6 IE]
German verslon. Angew Chem. X6. 467 (1974)
Translated by Express Translation Service. London
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