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A determination of the formation energy of vacancies in sodium chloride by quenching
Solid Sta~e C ~ c a ~ i ~ United States.
Vol. i, pp. 92-95, 1963. P e ~
Press, Inc. Printed in the
A DETERMINATION OF THE FORMATION ENERGY OF VACANCIES BY QUENCHING
IN SODIUM CHLORIDE
J. Pelsmaekers, G. Pellegrini + and S. AmelincEx Solid State Physics Department, S.C.K. - C.E.N., MOL (Belgium).
(aecelved 5 se~;e,,~r J.~3) ~he equilibrium concentration of p o i n t d e f e c t s quenched i n sodium c h l o ride crystals h a s b e e n d e t e r m i n e d by d e n s i t y m e a s u r e m e n t s . The a c t i v a t i o n energy e n s u i n g f r o m t h i s m e a s u r e m e n t s i s 1 , 9 eV. C o m p a r i n g t h e a c t i v a t i o n energy obtained by o u r d e n s i t y m e a s u r e m e n t s w i t h t h e e n e r g y d e r i v e d f r o m i o n i c c o n d u c t i v i t y by E t z o l an d Mauer we f i n d t h e b i n d i n g e n e r g y o f a ~ a c a n c y p a i r t o be V g 0 , 8 9 eV.
In latest
~ho
equilibrium
years
q u e n c h i n g h a s become a s t a n d a r d
concentration
of point
defects
in metals
energies
have been deduced from such measurements.
mination
of the
tures
close
thermal
expansion
to the melting
point,
and t h e
[3
Hitherto
[1
. Most f o r m a t i o n
,
Recently
,'
directly
2]
the simultaneous parameter
at
the equilibrium
deter-
temperaconcen-
4] .
the quenching method has not been applied to insulators in view
of their poor thermal conductivity. pare concentrations
It would nevertheless be of interest to com-
of point defects in alkali halides found by quenching with
those derived from measurements ple to determine
for determining
change in lattice
have yielded
tration of vacancies in a few metals
procedure
of the ionic conductivity.
This allows in princi-
the association energy of vacancy pairs. With this in mind the
density changes resulting from frozen-in defects in sodium chloride have been determined.
The r e l a t i v e
of vacancies
density
d~.=-3~it
change
is
related
to the
concentration
by t h e r e l a t i o n •
Wp
w ho re entropy pairs
is
the formation
associated
an d
N the
with
energy for a Schottky
the formation
number o f l a t t i c e
+Permanent address:
Euratom
pair;
A$
of a vacancy pair,
sites
(Brussels).
92
for
vacancies:
n •
is is
the
the change in
the
nmnber o f
lattice
parameter
Vol. i, No. 4
k and
A ~A'~qINATION OF THE FORMATION ERER~Y OF VACANCIES IN NaCl
T have their usual meaning.
The use of this relation,
valid for vacancies,
is justified because it is found that on quenching the density decreases, that the predominant
93
and hence
defect is a vacancy.
The specimens were small prisms of about 6-8 mm long and having a cross section of 2-3 mm all cleaved from the same single crystal. Only specimens without defects,
detectable with an optical microscope,
are used. The specimen is heated
in a platinum coil, protected from air currents by a quartz tube. The whole assembly has a very small heat capacity. (platinum-platinum-rhodium) value of the thermocouple reached,
The temperature is measured with a thermocouple
in direct contact with the specimens. voltage,
corresponding
When a p r e s e t
to the desired temperature,
is
quenching is performed by immersing suddenly the whole heating assembly
in a saturated aqueous solution of sodium chloride,
whithout switching off the
heating current. The quenched crystals are again checked for perfection under the microscope. In any case they are cleaned by etching off a surface layer in ethanol. This removes the layer wherein loss of vacancies is largest. in ethyl ether by progressively
The sample is then washed
diluting the ethanol with ether;
is removed by diluting with ethylene bromide,
finally the latter
which is the floatation liquid.
This
procedure allows to transfer the crystal into the medium used for the density measurements, important
wihtout having to ex~Dose the crystal to air. This last point is
for avoiding spurious density changes due to adsorbed gases. The density measurements
described in detail elsewhere [5] in
a column
of
liquid
(~cm)
which
are performed using an apparatus and a technique . The method consists in immersing the c r y s t a l has
about
the
same density
as
the
crystal.
In
the column an accurately known density gradient is maintained by establishing a small temperature
gradient,
( ~ 5eC). A difference
the top being somewhat hotter than the bottom part
in density between the standard,
untreated crystal, and
the quenched crystal is then measured as a difference in floating level. Allowance is made for the fact that there is a temperature difference between standard and specimen. standard
All densities are in this way reduced to the floating temperature of the crystal which is 24,4@C.
The change in lattice parameter of the quenched
crystals was found to be smaller than 10 -# ~, which means that the second term on the left hand side of (I) is neglected. The final density data are plotted on a log scale as a function of the inverse temperature
in fig. I. Each point represents the average of about ten in-
dependent measurements.
The least square straight line is plotted on the same
graph. The activation energy calculated from the slope of this line is 1,9 eV.
94
A h~'£'~rU(INATION OF THZ FORMATION EN]~GT OF VACANCIES IN NaCI
Yol. i, .No. 4
-S
A d x 10
30
A e
•
•
20
16
I
From i o n i c we f i n d in
*
800"
I
quenching
is
vacancy
ductivity
but
data
not
very
pairs
known,
The r a t i o the
great.
I
seems
,
I
,
7?0"
that
c a n be a c c o u n t e d
the
do n o t
density ener~
the
;
IO00/T"
eV. The f a c t loss
to
that
of vacancies
z o r by c o n s i d e r i n g
contribute
the
that
d.c.
asso-
ionic
con-
change. of a vacancy
from a comparison
concentration
I
to suggest
clusters
to
,
780"
a n d M a u r e r 6 f o u n d Wp m 2 . 0 7
the.bindin~
chloride
*
It
and neutral
be deduced
of the
sodium
I
energy
d~ c o n t r i b u t e
could
I
Etzel
activation
In principle well
i
790"
conductivity
a smaller
ciated
I
of associated
pair,
of both
a quantity
values
in
(m) t o d i s s o c i a t e d
the
which is following
pairs
(n)
is
way. for
structure: V-~Wp
m-- • s e - ' t " 7 - - -
(2)
n
where
V
is
the
Taking
association into
energy
account
all
~d :~.. where
Wpi i s
ments.
Using
now t h e the
value
which is
somewhat
Tosi
and by
of
[7]
data
taken
ref.
[4]
of Etzel
large
as
on d i f f e r e n t of
, and of
the the
for
the
density
change
(3)
"
energy
deduced
and Y~urer to the
and Lidiard
crystals equilibrium ionic
one.rains
~1~. ~'~{1.,.~)
compared
Tharmalingam
neous measurements in
formation
of a pair.
vacancies,
is
from ionic
conductivity
measure-
leads
V u ~ | 9 eV
(Wp;u2.0? eV} theoretical [8]
estimates
. It
is
clear
a somewhat
hazardous
concentration
using
conductivity
on t h e
to
by F u m i a n d that
a comparison
procedure.
Simulta-
the method described
same specimen
should
yield
not
Vol. i, No. 4
more reliable
A h~INATION
data.
aF THZ FORMATION ~EROY aF V ~ I E S
Such measurements
are
being
carried
out
IN NaCI
95
now.
La c o n c e n t r a t i o n d'~quilibre des d~fauts ponctuele dane lee monocristaux de c h l o r u r e de s o d i u m a ~t~ d ~ t e r m i n ~ e p a r d e s m e s u r e s de d e n s i t Y . L'6ners~ie d'activation r~sultante e s t 1 , 9 e V . En c o m p a r a n t l e e ~ n e r g i e s d'activation, obtenues d a n s n o s m e s u r e s de d e n s i t Y , avec ceux, d~duites dee mesures de conductivit~ ionique faites par Etzel et Y~uer, noue trouvons une ~nergie de liaison d'une paire de
lacunes de V = 0,89 eV.
References
1. BAUERLE, J.E. and KOEHLER, J.S., Phys. Rev. 10_~, 6 (1957) 1493. 2. MESHII, M. and KAUFFMAN, J.W., Phil. M ~ a E . ~ 55 (1960) 68?; See also DE SORBO,W. and TURNBULL, D., Acts Met. Zt (1959) 83. 3. FEDER, R. and NOWICE, A.S., Phys. Rev. 109, 6 (1958) 1959. 4. SIF~ONS, R.O. and BALLUFFI, R.W., AECU-4374, Phys. Rev. 119t 2 s (1960) 600. 5. PELSMAEKERS, J. and AMELINCKX, S., Rev. Scl. Instr. ~ ,
7--~1961) 828.
6. ETZEL, H.W. and MAURER, R.J., J. Chem. Phys. 18, (1950) 1003. 7. TOSI, M.P. and FUMI, F.G., Nuovo Cimento ~, (1958) 95. 8. THARM£LINGAM, K. and LIDIARD, A.S., Phil. MaK. 6, 69 (1961) 1157.
Vol. i, pp. 92-95, 1963. P e ~
Press, Inc. Printed in the
A DETERMINATION OF THE FORMATION ENERGY OF VACANCIES BY QUENCHING
IN SODIUM CHLORIDE
J. Pelsmaekers, G. Pellegrini + and S. AmelincEx Solid State Physics Department, S.C.K. - C.E.N., MOL (Belgium).
(aecelved 5 se~;e,,~r J.~3) ~he equilibrium concentration of p o i n t d e f e c t s quenched i n sodium c h l o ride crystals h a s b e e n d e t e r m i n e d by d e n s i t y m e a s u r e m e n t s . The a c t i v a t i o n energy e n s u i n g f r o m t h i s m e a s u r e m e n t s i s 1 , 9 eV. C o m p a r i n g t h e a c t i v a t i o n energy obtained by o u r d e n s i t y m e a s u r e m e n t s w i t h t h e e n e r g y d e r i v e d f r o m i o n i c c o n d u c t i v i t y by E t z o l an d Mauer we f i n d t h e b i n d i n g e n e r g y o f a ~ a c a n c y p a i r t o be V g 0 , 8 9 eV.
In latest
~ho
equilibrium
years
q u e n c h i n g h a s become a s t a n d a r d
concentration
of point
defects
in metals
energies
have been deduced from such measurements.
mination
of the
tures
close
thermal
expansion
to the melting
point,
and t h e
[3
Hitherto
[1
. Most f o r m a t i o n
,
Recently
,'
directly
2]
the simultaneous parameter
at
the equilibrium
deter-
temperaconcen-
4] .
the quenching method has not been applied to insulators in view
of their poor thermal conductivity. pare concentrations
It would nevertheless be of interest to com-
of point defects in alkali halides found by quenching with
those derived from measurements ple to determine
for determining
change in lattice
have yielded
tration of vacancies in a few metals
procedure
of the ionic conductivity.
This allows in princi-
the association energy of vacancy pairs. With this in mind the
density changes resulting from frozen-in defects in sodium chloride have been determined.
The r e l a t i v e
of vacancies
density
d~.=-3~it
change
is
related
to the
concentration
by t h e r e l a t i o n •
Wp
w ho re entropy pairs
is
the formation
associated
an d
N the
with
energy for a Schottky
the formation
number o f l a t t i c e
+Permanent address:
Euratom
pair;
A$
of a vacancy pair,
sites
(Brussels).
92
for
vacancies:
n •
is is
the
the change in
the
nmnber o f
lattice
parameter
Vol. i, No. 4
k and
A ~A'~qINATION OF THE FORMATION ERER~Y OF VACANCIES IN NaCl
T have their usual meaning.
The use of this relation,
valid for vacancies,
is justified because it is found that on quenching the density decreases, that the predominant
93
and hence
defect is a vacancy.
The specimens were small prisms of about 6-8 mm long and having a cross section of 2-3 mm all cleaved from the same single crystal. Only specimens without defects,
detectable with an optical microscope,
are used. The specimen is heated
in a platinum coil, protected from air currents by a quartz tube. The whole assembly has a very small heat capacity. (platinum-platinum-rhodium) value of the thermocouple reached,
The temperature is measured with a thermocouple
in direct contact with the specimens. voltage,
corresponding
When a p r e s e t
to the desired temperature,
is
quenching is performed by immersing suddenly the whole heating assembly
in a saturated aqueous solution of sodium chloride,
whithout switching off the
heating current. The quenched crystals are again checked for perfection under the microscope. In any case they are cleaned by etching off a surface layer in ethanol. This removes the layer wherein loss of vacancies is largest. in ethyl ether by progressively
The sample is then washed
diluting the ethanol with ether;
is removed by diluting with ethylene bromide,
finally the latter
which is the floatation liquid.
This
procedure allows to transfer the crystal into the medium used for the density measurements, important
wihtout having to ex~Dose the crystal to air. This last point is
for avoiding spurious density changes due to adsorbed gases. The density measurements
described in detail elsewhere [5] in
a column
of
liquid
(~cm)
which
are performed using an apparatus and a technique . The method consists in immersing the c r y s t a l has
about
the
same density
as
the
crystal.
In
the column an accurately known density gradient is maintained by establishing a small temperature
gradient,
( ~ 5eC). A difference
the top being somewhat hotter than the bottom part
in density between the standard,
untreated crystal, and
the quenched crystal is then measured as a difference in floating level. Allowance is made for the fact that there is a temperature difference between standard and specimen. standard
All densities are in this way reduced to the floating temperature of the crystal which is 24,4@C.
The change in lattice parameter of the quenched
crystals was found to be smaller than 10 -# ~, which means that the second term on the left hand side of (I) is neglected. The final density data are plotted on a log scale as a function of the inverse temperature
in fig. I. Each point represents the average of about ten in-
dependent measurements.
The least square straight line is plotted on the same
graph. The activation energy calculated from the slope of this line is 1,9 eV.
94
A h~'£'~rU(INATION OF THZ FORMATION EN]~GT OF VACANCIES IN NaCI
Yol. i, .No. 4
-S
A d x 10
30
A e
•
•
20
16
I
From i o n i c we f i n d in
*
800"
I
quenching
is
vacancy
ductivity
but
data
not
very
pairs
known,
The r a t i o the
great.
I
seems
,
I
,
7?0"
that
c a n be a c c o u n t e d
the
do n o t
density ener~
the
;
IO00/T"
eV. The f a c t loss
to
that
of vacancies
z o r by c o n s i d e r i n g
contribute
the
that
d.c.
asso-
ionic
con-
change. of a vacancy
from a comparison
concentration
I
to suggest
clusters
to
,
780"
a n d M a u r e r 6 f o u n d Wp m 2 . 0 7
the.bindin~
chloride
*
It
and neutral
be deduced
of the
sodium
I
energy
d~ c o n t r i b u t e
could
I
Etzel
activation
In principle well
i
790"
conductivity
a smaller
ciated
I
of associated
pair,
of both
a quantity
values
in
(m) t o d i s s o c i a t e d
the
which is following
pairs
(n)
is
way. for
structure: V-~Wp
m-- • s e - ' t " 7 - - -
(2)
n
where
V
is
the
Taking
association into
energy
account
all
~d :~.. where
Wpi i s
ments.
Using
now t h e the
value
which is
somewhat
Tosi
and by
of
[7]
data
taken
ref.
[4]
of Etzel
large
as
on d i f f e r e n t of
, and of
the the
for
the
density
change
(3)
"
energy
deduced
and Y~urer to the
and Lidiard
crystals equilibrium ionic
one.rains
~1~. ~'~{1.,.~)
compared
Tharmalingam
neous measurements in
formation
of a pair.
vacancies,
is
from ionic
conductivity
measure-
leads
V u ~ | 9 eV
(Wp;u2.0? eV} theoretical [8]
estimates
. It
is
clear
a somewhat
hazardous
concentration
using
conductivity
on t h e
to
by F u m i a n d that
a comparison
procedure.
Simulta-
the method described
same specimen
should
yield
not
Vol. i, No. 4
more reliable
A h~INATION
data.
aF THZ FORMATION ~EROY aF V ~ I E S
Such measurements
are
being
carried
out
IN NaCI
95
now.
La c o n c e n t r a t i o n d'~quilibre des d~fauts ponctuele dane lee monocristaux de c h l o r u r e de s o d i u m a ~t~ d ~ t e r m i n ~ e p a r d e s m e s u r e s de d e n s i t Y . L'6ners~ie d'activation r~sultante e s t 1 , 9 e V . En c o m p a r a n t l e e ~ n e r g i e s d'activation, obtenues d a n s n o s m e s u r e s de d e n s i t Y , avec ceux, d~duites dee mesures de conductivit~ ionique faites par Etzel et Y~uer, noue trouvons une ~nergie de liaison d'une paire de
lacunes de V = 0,89 eV.
References
1. BAUERLE, J.E. and KOEHLER, J.S., Phys. Rev. 10_~, 6 (1957) 1493. 2. MESHII, M. and KAUFFMAN, J.W., Phil. M ~ a E . ~ 55 (1960) 68?; See also DE SORBO,W. and TURNBULL, D., Acts Met. Zt (1959) 83. 3. FEDER, R. and NOWICE, A.S., Phys. Rev. 109, 6 (1958) 1959. 4. SIF~ONS, R.O. and BALLUFFI, R.W., AECU-4374, Phys. Rev. 119t 2 s (1960) 600. 5. PELSMAEKERS, J. and AMELINCKX, S., Rev. Scl. Instr. ~ ,
7--~1961) 828.
6. ETZEL, H.W. and MAURER, R.J., J. Chem. Phys. 18, (1950) 1003. 7. TOSI, M.P. and FUMI, F.G., Nuovo Cimento ~, (1958) 95. 8. THARM£LINGAM, K. and LIDIARD, A.S., Phil. MaK. 6, 69 (1961) 1157.