MODELING PHYSICAL PROPERIIES OF MOLTEN FLUORIDEOXIDE MELTS
A. Redkin, Yu. Zaikov, O. Tkacheva, A.Dedyukhin
Institute of High Temperature Electrochemistry
Ekaterinburg, Russia
INTRODUCTION
Fluoride and oxide melts have some common features because they are ionic liquids
but at the same time they have differences, first of all molten oxides are glass-like
viscous liquids. Fluoride–oxide molten systems such as calcium fluoride based fluxes
and cryolite alumina melts are often used as a media for different technological
processes therefore the properties of these systems are very important. At present the
modeling methods describing properties of halide melts from one hand and oxide
melts from other hand are very different. There is a necessity to find some common
points for modeling physical properties of halide-oxide melts. Such common point
can be the periodical table of elements. Bockris et.al. (1) found that influence of
different components of molten glasses on electrical conductivity depends on the
valence of cation. All cations were divided into 3 groups. The first group is of alkali
cations: Li+, Na+, K+. The second intermediate one is formed by divalent cations:
Mg2+, Ca2+, Sr2+, Ba2+, Mn 2+ and Fe2+. Al3+ and Ti4+ belong to the third group. The
most conductive are cations of the first group and the less conductive are cations of
third group. The close regularity connecting valence and electrical conductivity was
found by Biltz and Klemm (2). They divided all molten chlorides according to the
place of cation at Periodic Table on good and bad conductors. This classification can
be explained by ionic potential (IP) of cations (3). According to this approach all
molten salts can be divided into 4 groups: 1. Ideally conducting salts; 2. Good
conductors; 3. Bad conductors; 4. Isolators. Electrical conductivity of molten salts is
determined by cation mobility which depends on electronic structure of cation. Ionic
potentials of cations which reflect their structure are presented in Table 1. In order to
compare electrical conductivity of different salts obtained at different temperatures
the electrical conductivity values were divided on temperature vales at which it was
measured. These “related” values are presented in Table 2. The certain values of ionic
Li(+)
Be(2+)
B(3+)
C(4+)
LiF
17
Na(+)
10
K(+)
8
Rb(+)
7
Cs(+)
6
64
Mg(2+)
31
Ca(2+)
20
Sr(2+)
17
Ba(2+)
15
150
Al(3+)
66
Sс(3+)
40
Y(3+)
33
La(3+)
28
250
Si(4+)
110
Ti(4+)
61
Zr(4+)
55
Hf(4+)
55
7,4
NaF
3,9
KF
3,1
RbF
2,7
CsF
2,9
BeF2
1·10-4
BF3
C(4+)
MgF2
2,3
AlF3
?
Si(4+)
CaF2
3,5
SrF2
3,2
BaF2
2,9
SсF3
0,3
YF3
0,5
LaF3
0,8
Ti(4+)
ZrF4
0,01
Hf(4+)
Table 2.“Related” electrical
conductivity (Ohm-1.cm-1·T-1·103)
Table 1. Ionic potential of cations
(IP)(nм-1)
1-57
potential correspond to the certain values of electrical conductivity. Cations with ionic
potential less than 30 nm-1 form the first group of ideally conducting salts, that is
systems with the lowest ionic potential and highest conductivity. Salts with IP more
30 nm-1 and less then 50 nm-1 form the second group of good conductors. Salts
with IP in range 50-100 nm-1 are bad conductors. Certainly, this classification is rather
relative. In order to describe the properties of salts in accordance with their structure it
is better to base on the real measured property such as molar volume which is
determined by ionic potential. Hence, the electrical conductivity can be also presented
as a function of molar volume and temperature.
ELECTRICAL CONDUCTIVITY OF MOLTEN FLUORIDES
Alkali fluorides have lowest ionic potentials and form the first group of ideally
conducting salts. Alkaline earth fluorides also possess high electrical conductivity
with exception of BeF2 and MgF2. BeF2, AlF3, ZrF4, HfF4, TaF5 and NbF5 form the
group of bad conductors.
The dependence of specific conductivity for molten alkali fluorides on molar volume
at constant temperature is presented in Fig. 1. It can be described by logarithmic
equation at constant temperature. As the conductivity is temperature depending
property it can be presented as function of temperature and molar volume by the
following equation:
  6,666 exp( 
13487
V ) exp( 9,52  276 )
T
V
V2
1052 
[1]
where V – molar volume (cm3/mol);  - specific conductivity, Ohm-1·cm-1; T temperature, K The equation [1] is valid in temperature rang from melting point to
1400 K. In Fig. 1 the extrapolated values of electrical conductivity and molar volume
of alkali earth fluorides are also shown. It is possible to apply the equation [1] to the
alkaline earth fluorides conductivity (at high temperature) excepting MgF2.
2,5
Li
2,3
lnχ , Ohm-1. cm-1
2,1
1,9
Na
1,7
CaF 2
K
1,5
1,3
Rb
Cs
1,1
SrF 2
BaF 2
MgF 2
0,9
0,7
0,5
0,01
0,02
0,03
0,04
0,05
0,06
0,07
1/V, V (cm3/mol)
Fig. 1. Electrical conductivity of molten alkali and alkali-earth fluorides at 1400 K
[4].
1-58
The equation [1] is also valid for fluoride mixtures such as LiF-NaF, NaF-KF. The
comparison of experimental [4] and calculated on equation [1] values of the NaF-LiF
and NaF-KF conductivity is given in Table 3. The electrical conductivity values agree
within 10 %.
KF,
mol.fr.
0
0,12
0,2
0,25
0,37
0,4
0,5
0,63
0,88
1
Table 3. The calculated and experimental [4] conductivity in
NaF-LiF and NaF-KF systems at 1273 K
NaF-KF
LiF-NaF
χcalc – χexp
χcalc – χexp
__________ ,
__________ ,
χcalc,
χexp.
NaF,
χcalc,
χexp.
eq. (1)
[6]
χexp.
mol.fr.
eq. (1)
[6]
χexp.
%
%
5,14
5,39
4,6
0
9,55
9,97
4,2
4,84
0,15
8,32
8,64
3,7
4,68
4,69
0,2
0,3
7,41
7,52
1,5
4,52
0,375
7,05
7,04
0,1
4,35
0,5
6,52
6,75
3,4
4,31
4,49
4,0
0,6
6,16
6,00
2,7
4,20
0,8
5,57
5,83
4,5
4,07
1
5,09
5,28
3,6
3,89
4,26
8,7
3,82
4,27
10,5
ELECTRICAL CONDUCTIVITY OF THE GLASS-LIKE FLUORIDES
There are some fluoride melts which are glass-like, such as BeF2. Their properties are
very similar to glasses: high viscosity, high temperature coefficient of electrical
conductivity and so on. The electrical conductivity change with melt composition in
system LiF-BeF2 is shown in Fig.2. The isotherm can be divided into two parts. The
mixture has high conductivity in the concentration range up to 50 mol.% of BeF2. The
properties of such mixtures are determined mainly by the lithium fluoride properties.
It is seen from dependences of conductivity (χ) and density (ρ) temperature
coefficients (5, 6) (ρ = ρo – BT and lnχ = A – B/T), see Fig 3. The temperature
coefficients of physical properties reflects structure peculiarities of any system. The
temperature coefficients in the LiF rich region don’t change essentially and are close
to the coefficients of pure lithium fluoride.
Conductivity, Ohm-1Cm-1
10
8
6
4
2
0
0
0,2
0,4
0,6
BeF2, mole fraction
0,8
1
Fig. 2. Specific conductivity of LiF-BeF2 molten system at 1273 K (5).
1-59
The absolute values of electrical conductivity also reflect the difference between ionic
and glass-like melts (beryllium fluoride rich region) in the LiF-BeF2 system (see
fig.3). Thus, the electrical conductivity of this system at concentration rang 0-50
mol.% BeF2 can be described by the equation (3):
  6,666 exp( 
13487
V ) exp( 9,52  276 ) exp( 1,65 N )
T
V
V2
1052 
[2]
where V – molar volume (cm3/mol);  - specific conductivity, Ohm-1·cm-1; T temperature, K; N - BeF2 content, mole fraction. The comparison of experimental and
calculated data is given in Table 4.
conductivity
25
0,6
0,5
20
0,4
15
0,3
10
0,2
5
0,1
0
Density temperature coefficient,
-4
10
Electrical conductivity temperature
3
coefficient, 10
density
0
0
0,2
0,4
0,6
BeF2, m.fr.
0,8
1
Fig. 3. The electrical conductivity and density temperature coefficients
in the LiF-BeF2 system.
Table 4. The calculated and experimental (5) conductivity
in the LiF-BeF2 system at 1200 K
χcalc – χexp
__________ ,
BeF2,
χcalc,
χexp.
mol.fr. eq. (2)
[6]
χexp.
%
0
0,1
0,2
0,3
0,4
8,91
6,94
5,42
4,03
3,27
8,93
6,42
4,97
4,03
3,37
0,3
7,4
8,2
0,01
3,1
ELECTRICAL CONDUCTIVITY OF THE CAF2-AL2O3 MOLTEN SYSTEM
The LiF-BeF2 system can be used as a model system for describing fluoride-oxide
melt properties. There are electrical conductivity data (14, 15) for system CaF2-
1-60
MeOx, where MeOx = CaO + MgO+Al2O3+FeO+Fe2O3+SiO2+MnO. The dependence
of electrical conductivity temperature coefficient on composition of fluxes is given in
Fig.4. The change of the temperature coefficient with oxide composition is similar the
change of the temperature coefficient with beryllium fluoride content in the LiF-BeF2
system. Thus the equation [1] with additional coefficient can be applied to describe
the electrical conductivity of CaF2-Al2O3 system:
  6,666 exp( 
13487
V ) exp( 9,52  276 ) exp( 2,5 N )
T
V
V2
1052 
[2]
where N - Al2O3 content, mole fraction. The coefficient (-2,5) was obtained for
cryolite-alumina melts (7). The comparison of experimental and calculated electrical
conductivity values is presented in Fig. 5. Data on density and electrical conductivity
were taken from (8, 9).
14
Electrical conductivity temperature
3
coefficient, 10
12
Fig. 4. Electrical
conductivity
temperature
coefficient in calcium
fluoride based flux
depending on oxide
content (14, 15)
10
8
6
4
2
0
0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
1
Content of oxides, m.fr.
-1
6
Electrical conductivity, Ohm cm
7
-1.
8
calculation
experiment
5
4
3
2
1
0
0
0,1
0,2
0,3
0,4
Al2O3, m.fr.
1-61
0,5
0,6
Fig. 5.
Comparison of
calculated [eq.2]
and experimental
(14) electrical
conductivity in
system CaF2Al2O3
ELECTRICAL CONDUCTIVITY OF CRYOLITE-ALUMINA MELTS
Cryolite-alumina melts are the basic electrolytes for industrial production of
aluminum. The effect of alumina concentration on their electrical conductivity is very
important. There are a lot of investigations into the electrical conductivity of alumina
containing cryolites (10-13). It is a matter of fact that conductivity values decrease
with alumina content. The analysis of existing information allows derivation of the
following equation:
13487
V )exp( 9,52 + 276 ).exp(-1,65N )exp(-2,5N ) [3]
1
2
T
V
V2
1052 
χ = 6,666exp(-
where N1 и N2 – AlF3 and Al2O3 concentrations, mole fraction. The comparison of
experimental and calculated data are shown in Fig. 6.
Conductivity, Ohm-1.cm-1
3
calculation
[10]
[11]
2,8
2,6
2,4
2,2
2
0
0,02
0,04
0,06
0,08
0,1
Al2O3, mole fraction
Fig. 6. The specific electrical conductivity of Na3AlF6-Al2O3 system
CONCLUSION
The preliminary knowledge of some properties of fluoride-oxide melts allows
evaluating the possibility of technological usage of new compositions. The approach
proposed in this paper makes it possible modeling physical properties of new
compositions which are perspective for industrial applications.
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