keit der Ladungsträger, homogene und isotrope Turbulenz etc.)
zu beseitigen.
Die Erweiterung
auf
Störstellenleitung und verschiedene Beweglichkeiten
führt, selbst wenn die Trägerdichten sehr verschieden sind, zu keinen prinzipiellen
Schwierigkeiten.
Sie bringt jedoch eine V e r g r ö ß e r u n g des rechnerischen Aufwandes mit sich.
Herrn V. SERGIESCU, der mich in die Problematik des
Funkelrauschens eingeführt hat, möchte ich für nützliche Ratschläge und Diskussionen meinen Dank aussprechen. Auch bin ich Herrn Dr. R. GRIGOROVICI für
das kritische Durchlesen der 3 Manuskripte und Herrn
Prof. Dr. V. NOVACU für die nützlichen Diskussionen
und das gezeigte Interesse zu besonderem Dank verpflichtet.
Plastic Flow of Solid Mixtures of Li 2 S0 4 and K2SO4
ARNOLD L U N D É N ,
BJÖRN JONSON,
and
BENGT AUGUSTSSON
Department of Physics, Chalmers Institute of Technology, Göteborg, Sweden
(Z. Naturforschg. 21 a, 5 9 3 — 5 9 4 [ 1 9 6 6 ] ; received 20 O c t o b e r 1965)
The addition of K 2 S 0 4 to L i 2 S 0 4 causes a considerable change in the rheological properties of
the cubic high temperature modification. A simple device for relative measurements of the plastic
flow of the salt consisted of a sphere of stainless steel at the end of a steel rod on top of which
weights were hung in order to obtain a suitable penetration rate through the salt. This rate depended on the composition of the mixture as well as on the thermal pretreatment of the salt. T h e
temperature dependence was strong; a crude estimation gave an "activation e n e r g y " of the order
of 2 x 1 0 s cal/mole, i. e. more than an order of magnitude higher than for electrical conductivity or
cation self-diffusion. This result is in agreement with the interpretation of the electrical conductivity as being due solely to cation transport.
In a recent investigation of electromigration
in
lithium-rich solid mixtures of alkali sulfates it was
found that the electrodes sunk d o w n into the
salt1,
while this did not occur f o r pure a - L i 2 S 0 4 . F r o m
this observation we concluded that it should be pos-
K2S04
mole
0
4.0
sible to make crude measurements o f the " v i s c o s i t y "
of the solid mixtures and compare the results with
self-diffusion and conductivity data.
8.5
12.4
The measuring device consisted of a sphere of
stainless steel (diam. 2 0 m m ) sitting at the l o w end
of a steel tube (ext. diam. 6 m m ) , which was centered through an opening in the top lid of a vertical
steel tube (inner diameter 5 8 m m )
containing the
salt. The wide tube was heated in an oven, where
the temperature gradient was negligible over a range
of several cm. The temperature was measured with
a thermocouple
( M e g o p a K type K , Honeywell Re-
gulator Company)
placed inside the steel sphere.
By loading weights on top of the 6 m m tube, the
sphere was forced to penetrate through the salt with
0.86
%
Temp.
°C
780
732
680
630
620
605
580
570
825
820
815
820
810
805
V
mm/h
<^0.1
5.9
0.1
0.01
2.1
1.4
23
0.5
51
27
1.6
2.1
0.79
0.73
Remark
h,
h
h,
h,
h
h
h
h,
h
h
h
c
e
e
e
e
c
c
T a b l e 1. Penetration of a heavy steel device through solid
L i 2 S 0 4 — K 2 S 0 4 mixtures 3 . v=constant
penetration rate. The
thermal pretreatment is indicated by h if the desired temperature was approached from above, and by c if from below,
e denotes that the sphere had penetrated only slightly into
the salt, and that the extrapolated v is only to be taken as an
approximate indication of the order of magnitude.
a rate that was measured with a cathetometer. Pure
then c o o l e d to the desired temperature. W h e n this
Li2S04
temperature became stable, the sphere was lowered
and f o u r mixtures were investigated,
see
Table 1.
until it touched the surface of the salt, and the meas-
In the experiments with 0, 4 . 0 , 8 . 5 , and 1 2 . 4 %
urement was started. The penetration rate which was
K 2 S 0 4 the salt was first heated to about 9 0 0 ° C and
highest in the beginning became constant after a
depth of the order of the radius of the sphere had
1
V . LJUBIMOV a n d A . LUNDEN, Z . N a t u r f o r s c h g . , in p r e s s .
been reached. However, in some cases the penetra-
Unauthenticated
Download Date | 6/18/17 4:29 AM
tion was too slow f o r this depth to be readied with-
sity" of the salt b y applying STORE'S law. If we thus
in some 10 hours and an assumed constant rate v
consider the total weight of the sphere, supporting
was extrapolated b y a comparison of the times at
tube and load ( 7 8 8 . 6 5 grams) as the f o r c e acting
which depths of e. g. 1 or 2 m m were reached in dif-
on a sphere of radius 1.0 mm, we obtain 17 = 1.48
ferent experiments. These estimated rates, denoted
X 10 9 u - 1 poise, if the velocity v is in m m / h as in
b y e in Table 1, are considered to, at best, indicate
Table 1. The highest rate measured by us ( 0 . 8 6 % ,
the right order of magnitude. F o r the mixtures with
825°)
0 . 8 6 % K 2 S 0 4 the sphere was placed at a fixed posi-
3 x 1 0 ' poise. The calculation is of course very sim-
tion, about 5 c m below the surface of the salt, be-
plified, since we have neglected i. a. the friction be-
will
then
correspond
to a " v i s c o s i t y "
of
f o r e the measurement started. A l s o in this case it
tween the 6 m m tube and the salt 4 . N o r have we
usually took some time before the velocity v became
made any correction f o r the influence of the con-
constant. As before, the salt was heated to about
tainer wall, as is usually done in
9 0 0 ° C between two measurements. The cooling was
Viscosity
in liquids,
viscosimetry 5 .
as well as conductivity
and
con-
self-diffusion in both liquids and solids, is often
tinued to about 6 5 0 ° C , after which the salt was
considered as a process governed b y an activation
heated slowly to the temperature at which we were
energy Q. If we assume that the measured penetra-
g o i n g to measure.
tion rate is inversely proportional to a " v i s c o s i t y " ,
either stopped at the chosen temperature or
(This latter procedure is indi-
cated b y c in Table 1, whilst h stands f o r the sim-
the usual
pler procedure.) The choice of thermal pretreatment
be transformed to v = v0 exp { — Q/ (R T) } , where
has a drastic effect on the penetration rate.
v is the penetration rate measured at the tempera-
expression
t] = 1]0 exp {Q/(R
T) }
might
Stainless steel corrodes slightly in sulfate melts,
ture T and R is the gas constant. If we restrict our
and we noticed that the salt gradually became mis-
calculations to the 0 . 8 6 % mixture, the measurements
dis-
on " c o o l e d " salt (c in Table 1) give an activation
solved in water, neither Fe 2+ nor Fe 3+ ions were de-
energy of about 1 X 1 0 5 cal/mole, while the other
tected, and the amount of insoluble impurities was
measurements c o r r e s p o n d to at least 3 X 10 5 cal/mole.
coloured.
However, when a salt sample was
small. Thus we concluded that the possible contri-
Although an estimated activation energy of the or-
bution f r o m undesired impurities to the observed
der o f 2 X 10 5 c a l / m o l e might be characteristic only
changes in plastic flow should be negligible.
f o r mixtures of approximately this composition at
A c c o r d i n g to BERGMAN et al. 2 the melting point
about 8 2 0 ° C , it can b e used f o r a comparison with
from
the activation energies of the order of 10 4 cal/mole
0 to 2 0 % K o S 0 4 . There is thus a considerable tem-
f o u n d f o r the electrical conductivity and cation self-
decreases f r o m 8 6 0 to 5 3 5 ° C when g o i n g
perature range that was not covered b y the present
diffusion of pure lithium sulfate 6 . F o r liquids the
measurements, except f o r the observation that the
activation energies of the three transport processes
device we used penetrated too fast through the solid
usually are of the same order of magnitude, which
salt to permit measurements. Of course it would
we thus find is not the case f o r the solid sulfates.
have been possible to extend the measurements to
This result is in agreement with our current model
higher temperatures by reducing the load on top of
a c c o r d i n g to which the cations have a high mobility
the tube, but f o r the present comparison we pre-
in a lattice built up b y the sulfate ions. While the
ferred to have the same weight in all measurements.
high electrical conductivity is mainly due to cation
be
mobility, plastic flow requires a deformation of the
considered as a c c u r a t e 3 , they prove that the plastic
anion lattice, which should correspond to a much
flow depends strongly on composition, temperature,
larger activation energy.
Although
the present measurements
cannot
and the pretreatment of the salt. For a comparison
with liquids it is instructive to estimate the " v i s c o 2
3
A.
G.
BERGMAN,
A.
I . KISLOVA,
and
V.
I . POSYPIAKO,
Dokl.
A k a d . Nauk U S S R 8 8 , 8 1 5 [ 1 9 5 3 ] .
T h e results for the 0 . 8 6 % mixture are to be considered as
more reliable than for the other series, since several improvements were made in the experimental techniques before the last mixture was studied. However, even the first
measurements are sufficient as a base of a qualitative discussion.
This investigation is supported by the Swedish Technical Research Council.
4
The neglected tube surface is about 7b% of the surface of
the sphere, when the penetration has gone so far that 5 cm
tube length is surrounded by salt. The gradual increase in
total surface area (sphere + tube) was of the order of 10%
for several of the measurements reported here.
3
A.
DINSDALE a n d
F.
MOORE, V i s c o s i t y
and
its
Measurement,
Chapman and Hall, London 1 9 6 2 .
6
A.
KVIST a n d
A.
LUNDEN, Z . N a t u r f o r s c h g . 2 0 a , 2 3 5
Unauthenticated
Download Date | 6/18/17 4:29 AM
[1965].