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Heat capacity and equilibration time near Tc of YBa2Cu3O7
Physiea C 153-155 (1988) 1086-1088 North-Holland, Amsterdam
H E A T C A P A C I T Y A N D EQUILIBRATION TIME N E A R T c OF YBa2CuaO 7
A. V. V O R O N E L , D. Linsky, A. Kisliuk, S. Drislikh School of Physics and Astronomy, Sackler Faculty of Exact Sciences, Tel Aviv University, R a m a t Aviv, Tel Aviv 69978, Israel and B. Fisher, A. Kessel, Physics Department, Technion, Haifa, Israel.
In our careful heat capacity measurements around T¢ of YBa2Cu30 ~ bulk sample we have found long equilibration times diverging at the very critical point. These times are one order of magnitude longer than those times out of the critical region (hours instead of tens of minutes). Cp anomaly which we obtain taking into account these times is m u c h stronger than the anomalies reported before. (1) But our Cp values out of the critical region are in agreement with other investigators. The dimensionless parameter according to our measurements / / = A C e / T e l ~ 3 which we can calculate following the usual definitions is a few times larger than it is accepted now. (1) But the usual definition of a j u m p for a diverging heat capacity might be fully inadequate. (2)
The recent publications on the heat capacity anomaly near T¢ of YBa(2)Cu(3)0(7-6) reviewed in (1) are in agreement in their estimations of this anomaly as a j u m p close to what can be expected from the mean field theory consideration. The size of this j u m p was rather definitely determined as A C p / T c - 0.04-0.07 m J / g r . K z. All these publications had a common feature. They assumed their results related to the equilibrated systems without a real check of equilibrium time's longitude. Since our adiabatic calorimeter (2,3) allowed such a check we made a try and really found a non-trivial relaxation behaviour in the vicinity fo T¢ of our sample. (4) Usually the relaxation can be approximated by an exponential formula T m - T , = A - e x p ( - t / r ) expressing the deviation of the measured temperature T m from its value in the stationary regime T s. Here r is the relaxation time which is enough for the measured temperature "I'm to approach in e times to its equilibrium value T s. This formula and corresponding values r (about 500-700 sec. for our sample) are rather valid in the whole intgerval of measurements (see Fig. 1), but in the very vicinity of T e.
-4t 3
4 5 TIME, x 1000 sec.
6
FIGURE I E x p o n e n t i a l r e l a x a t i o n of temperature:
't
a)
T < TC
(T = 84.6K)
b)
T > T
(r = 89.7K) C
a
-81
"-,°1 t
.
10
.
.
.
.
.
.
.
.
12 TIME, =1000 sec.
14
0921-4534/88/$03.50 ©Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
In this vicinity the relaxation depends on time differently. In Fig. 2, one can see this more complicated relaxation process for one of the points in semilogarithmic scale.
A.V. Voronel et aL
/ Heat capacity and equifibration time
Fig. 3 presents two runs of our measurements on the same sample divided by a break followed by overheating of the sample. Both runs exhibit a kind of singular behaviour near T e. The sample, after overheating, has probably deteriorated and the singular behaviour in t h e second run looks m u c h less pronounced than in the first run. But in both cases, one can see that the mean field approach is hardly applicable. Nevertheless, if one has to use the commonly used concept of the heat capacity j u m p , one obtains two to six times higher values A C p / T c ~ 0.1 - 0 . 4 m J / g r . K 2 from our data (the highest points of the first r u n are not included in Fig. 3). First of all, it means that the dimensionless ratio p = A C p / T c 7 characterizing a degree o f a strong coupling for our sample has to be at least more than /~ $ 3 which makes it close to the corresponding value for La(l.85)Sr(0.15)CuO(4). (1) This is a very plausible and hopefully meaningful agreement.
-4
t-
!
time constant
12
-
2800
-
14
"lr~"
16
1087
18
TIME, .lO00sec.
FIGURE 2 Two relaxation times in the critical region (T = 85.7K) In this picture one can see some additional time which complicates the simple exponential formula and can be interpreted as the presence of the second exponent with m u c h longer relaxation time (about a few thousand seconds). More probably it means just a nonexponential relaxational behaviour of a superconductor of this kind. We are working on this now. Thus, it is obvious that the heat capacity data measured, taking into consideration the full time of relaxation, can be different from the data. (1) This difference is not a matter of accuracy of the measurements, but a function of an adequacy in our estimation of the relaxation times. It makes our measurements extremely difficult and time consuming.
Then, one could have noticed that an indirect evidence of a long relaxation near T c has already been obtained by Junod et al. (5)
106
,
108
,
• sample W338
104
,,~
II I ~'~;
•
106
~.~,:, z
"/ ""
mJ
,r.--P
, Y BozCu307
"
:
CT-• 2~
,
8o
" ° X ~,l& i ~ 1 ~
.+:o,+w?o, , 90
~oo
~o
1
1104
TN
~2o
TIKI
I FIGURE +
•
•
as a function of temperature from the paper (5). T The vertical scale is in 51.25 times smaller units than in Fig. 3.
+
2.1!
+
o**O . ÷.+
82
+ °
*+'¢* ° .
•
86
FIGURE 3 C--P-as a function of temperatures; T ÷
First run;
o °
TEMPERATURE, I(
~ Second run. L-J
4
90
1088
A.V. Voronel et al. / Heat capacity and equilibration time
In Fig. 4, one can see their data for two samples as functions of temperature. The authors have remarked that the scattering of data reaches its maximum at the temperature of about 100K and there is no technical reason for that. Taking into account that their calorimeter changes its temperature with time about 10-15 K/hour, one can see the temperature axis simultaneously as a time scale. Thus the authors have observed the scattering of the heat capacity data after about 20-30 minutes after passing the critical point, which agrees roughly with the expectation based on our own data.
REFERENCES (1) M. Newitt et al., Phys. Rev. Vol. B36 (1987) 2398. (2) A. Voronel in "Phase Transitions and Critical Phenomena", Vol. 5B, ed. by C. Domb and M. Green, Academic Press, London, 0976) 343-393. (3) U. Steinberg, T. Sverbilova, A. Voronel, J. Phys. Chem. Sol. Vol. 42, (1981) 24. (4) A. Voronel et al., Invited talk at the France-Israel Symposium, Paris, October 7, 1987. (5) A. Janod et al., Europhys. Letts., Vol. 4 0987) 247.
H E A T C A P A C I T Y A N D EQUILIBRATION TIME N E A R T c OF YBa2CuaO 7
A. V. V O R O N E L , D. Linsky, A. Kisliuk, S. Drislikh School of Physics and Astronomy, Sackler Faculty of Exact Sciences, Tel Aviv University, R a m a t Aviv, Tel Aviv 69978, Israel and B. Fisher, A. Kessel, Physics Department, Technion, Haifa, Israel.
In our careful heat capacity measurements around T¢ of YBa2Cu30 ~ bulk sample we have found long equilibration times diverging at the very critical point. These times are one order of magnitude longer than those times out of the critical region (hours instead of tens of minutes). Cp anomaly which we obtain taking into account these times is m u c h stronger than the anomalies reported before. (1) But our Cp values out of the critical region are in agreement with other investigators. The dimensionless parameter according to our measurements / / = A C e / T e l ~ 3 which we can calculate following the usual definitions is a few times larger than it is accepted now. (1) But the usual definition of a j u m p for a diverging heat capacity might be fully inadequate. (2)
The recent publications on the heat capacity anomaly near T¢ of YBa(2)Cu(3)0(7-6) reviewed in (1) are in agreement in their estimations of this anomaly as a j u m p close to what can be expected from the mean field theory consideration. The size of this j u m p was rather definitely determined as A C p / T c - 0.04-0.07 m J / g r . K z. All these publications had a common feature. They assumed their results related to the equilibrated systems without a real check of equilibrium time's longitude. Since our adiabatic calorimeter (2,3) allowed such a check we made a try and really found a non-trivial relaxation behaviour in the vicinity fo T¢ of our sample. (4) Usually the relaxation can be approximated by an exponential formula T m - T , = A - e x p ( - t / r ) expressing the deviation of the measured temperature T m from its value in the stationary regime T s. Here r is the relaxation time which is enough for the measured temperature "I'm to approach in e times to its equilibrium value T s. This formula and corresponding values r (about 500-700 sec. for our sample) are rather valid in the whole intgerval of measurements (see Fig. 1), but in the very vicinity of T e.
-4t 3
4 5 TIME, x 1000 sec.
6
FIGURE I E x p o n e n t i a l r e l a x a t i o n of temperature:
't
a)
T < TC
(T = 84.6K)
b)
T > T
(r = 89.7K) C
a
-81
"-,°1 t
.
10
.
.
.
.
.
.
.
.
12 TIME, =1000 sec.
14
0921-4534/88/$03.50 ©Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
In this vicinity the relaxation depends on time differently. In Fig. 2, one can see this more complicated relaxation process for one of the points in semilogarithmic scale.
A.V. Voronel et aL
/ Heat capacity and equifibration time
Fig. 3 presents two runs of our measurements on the same sample divided by a break followed by overheating of the sample. Both runs exhibit a kind of singular behaviour near T e. The sample, after overheating, has probably deteriorated and the singular behaviour in t h e second run looks m u c h less pronounced than in the first run. But in both cases, one can see that the mean field approach is hardly applicable. Nevertheless, if one has to use the commonly used concept of the heat capacity j u m p , one obtains two to six times higher values A C p / T c ~ 0.1 - 0 . 4 m J / g r . K 2 from our data (the highest points of the first r u n are not included in Fig. 3). First of all, it means that the dimensionless ratio p = A C p / T c 7 characterizing a degree o f a strong coupling for our sample has to be at least more than /~ $ 3 which makes it close to the corresponding value for La(l.85)Sr(0.15)CuO(4). (1) This is a very plausible and hopefully meaningful agreement.
-4
t-
!
time constant
12
-
2800
-
14
"lr~"
16
1087
18
TIME, .lO00sec.
FIGURE 2 Two relaxation times in the critical region (T = 85.7K) In this picture one can see some additional time which complicates the simple exponential formula and can be interpreted as the presence of the second exponent with m u c h longer relaxation time (about a few thousand seconds). More probably it means just a nonexponential relaxational behaviour of a superconductor of this kind. We are working on this now. Thus, it is obvious that the heat capacity data measured, taking into consideration the full time of relaxation, can be different from the data. (1) This difference is not a matter of accuracy of the measurements, but a function of an adequacy in our estimation of the relaxation times. It makes our measurements extremely difficult and time consuming.
Then, one could have noticed that an indirect evidence of a long relaxation near T c has already been obtained by Junod et al. (5)
106
,
108
,
• sample W338
104
,,~
II I ~'~;
•
106
~.~,:, z
"/ ""
mJ
,r.--P
, Y BozCu307
"
:
CT-• 2~
,
8o
" ° X ~,l& i ~ 1 ~
.+:o,+w?o, , 90
~oo
~o
1
1104
TN
~2o
TIKI
I FIGURE +
•
•
as a function of temperature from the paper (5). T The vertical scale is in 51.25 times smaller units than in Fig. 3.
+
2.1!
+
o**O . ÷.+
82
+ °
*+'¢* ° .
•
86
FIGURE 3 C--P-as a function of temperatures; T ÷
First run;
o °
TEMPERATURE, I(
~ Second run. L-J
4
90
1088
A.V. Voronel et al. / Heat capacity and equilibration time
In Fig. 4, one can see their data for two samples as functions of temperature. The authors have remarked that the scattering of data reaches its maximum at the temperature of about 100K and there is no technical reason for that. Taking into account that their calorimeter changes its temperature with time about 10-15 K/hour, one can see the temperature axis simultaneously as a time scale. Thus the authors have observed the scattering of the heat capacity data after about 20-30 minutes after passing the critical point, which agrees roughly with the expectation based on our own data.
REFERENCES (1) M. Newitt et al., Phys. Rev. Vol. B36 (1987) 2398. (2) A. Voronel in "Phase Transitions and Critical Phenomena", Vol. 5B, ed. by C. Domb and M. Green, Academic Press, London, 0976) 343-393. (3) U. Steinberg, T. Sverbilova, A. Voronel, J. Phys. Chem. Sol. Vol. 42, (1981) 24. (4) A. Voronel et al., Invited talk at the France-Israel Symposium, Paris, October 7, 1987. (5) A. Janod et al., Europhys. Letts., Vol. 4 0987) 247.