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Specific heat of SrTiO3 near the structural transition
Volume 35A, number 6
SPECIFIC
PHYSICS LETTERS
HEAT
OF
SrTiO 3 NEAR
THE
12 July 1971
STRUCTURAL
TRANSITION
*
P. R. GARNIER Department of P h y s i c s and Materials R e s e a r c h Laboratory, University of Illinois, Urbana, Illinois 61801, USA
Received 9 June 1971 The specific heat of SrTiO 3 near Ta(Ta ~ 106K) has been measured using an ac technique. It is found that at Ta the specific heat discontinuity ACp/Cp ~ - 1%
The s t r u c t u r a l phase t r a n s i t i o n SrTiO 3 has been the subject of many r e c e n t i n v e s t i g a t i o n s [1-3]. T h e r e is, however, v e r y little detailed i n f o r m a t i o n on the behavior of the specific heat of SrTiO 3 in the t r a n s i t i o n r e g i o n [4]. The s p e cific heat was m e a s u r e d u s i n g an ac c a l o r i m e t r i c technique and a p p a r a t u s p r e v i o u s l y d e s c r i b e d [5]. Our s a m p l e was a chip of the "(Iii)" single c r y s tal u s e d r e c e n t l y by Golding to study the t h e r m a l expansivity and u l t r a s o n i c propagation in the s a m e t e m p e r a t u r e region [1]. The specific heat m e a s u r e m e n t s were made on 3 different s a m p l e s (S1, $2 and $3) cut f r o m the s a m e s m a l l chip. All 3 s a m p l e s were thinned by polishing on # 600 s i l i c o n c a r b i d e paper to a t h i c k n e s s of about 0 . 1 2 r a m . After a f i r s t m e a s u r e m e n t of its specific heat in this state, s a m ple S1 was then a n n e a l e d in a i r at 1250°C for 3 h o u r s , cooled (30 K p e r hour) and r e m o u n t e d . Rs specific heat was then m e a s u r e d again. Samples $2 and $3 were u s e d m a i n l y to check the r e s u l t s on s a m p l e S1. Sample $2 was not annealed; s a m ple $3 was a n n e a l e d at l l 0 0 ° C for 2 hours. The e x p e r i m e n t s on s a m p l e s $2 and $3 gave the s a m e r e s u l t s as the r e s u l t s obtained on s a m p l e S1 in its u n a n n e a l e d and a n n e a l e d s t a t e s r e s p e c t i v e l y . The specific heat v e r s u s t e m p e r a t u r e c u r v e of s a m p l e $1 for both the u n a n n e a l e d and a n n e a l e d s t a t e s i s shown in fig. 1 and 2. No t e m p e r a t u r e h y s t e r e s i s was found. As the ac t e c h nique u s e d gives only r e l a t i v e specific heats, the c u r v e s w e r e n o r m a l i z e d at 114.75 K u s i n g Todd and L o r e n s o n ' s data [6]. The 2 other points obtained by Todd and L o r e n s o n in this t e m p e r a t u r e r a n g e a r e also indicated on fig. 1. We can see
15
I0 ....
t ....
9O
95
, . , , , J , , , , t , , . . i ....
~00
105
ll0
I
115
I~
T(K)
Fig. 1. Specific heat of $1 in its unannealed state. The unnormalized Cp curve was multiplied by an appropriate factor to cause it to pass through the 114.75 K data point of Todd and Lorenson. 12.0
ACp = 0.10 c
o
l
x
~
/
~
. ////''~ 11.5
A% = O.tO
t
cot/mole
x K
II.O
,02
i
,;4
i
,&
'
~--"
,Io
'
T(K)
Fig. 2. Comparison of the specific heats of $1 in its unannealed and annealed states near Ta. The latter curve has been displaced by 0.10 cal/mole K for clarity. t h a t for the u n a n n e a l e d s t a t e : (1) T a , d e t e r m i n e d
* This work was supported In part by the Advanced Research Projects Agency under Contract HC 15-67-C-9221.
a s the t e m p e r a t u r e where dCp/d T i s equal to the average slope outside the t r a n s i t i o n r e g i o n , i s 106.30~0.2 K. (2) zlCp = 0 . 1 0 ~ : 0 . 0 1 c a l / m o l e K,
413
Volume 35A. number 6
PHYSICS LETTERS
w h e r e ACp r e f e r s to the difference between the o b s e r v e d specific heat at Ta and the value obt a i n e d by extrapolation to T a of the high t e m p e r a t u r e data outside the t r a n s i t i o n region. (3) The t r a n s i t i o n r e g i o n extends over about 2 K. The 0.4 K t e m p e r a t u r e difference between the T a we find and the T a found by Golding for the s a m e c r y s t a l p r e s u m a b l y in the s a m e state is b e l i e v e d to s t e m f r o m a t e m p e r a t u r e c a l i b r a t i o n e r r o r in e i t h e r our a p p a r a t u s or Golding's. Our value for the specific heat discontinuity a g r e e s well with both the value calculated by the mean field theory ((114± 0.04 c a l / m o l e K) [2] and the value obtained f r o m the E h r e n f e s t relation: ACp = V T A~ v (dp/dTa) = 0.13+ 0.02 c a l / m o l e K where ~v =- (1/V)(dV/dT) and the n u m e r i c a l v a l u e s of dp/dT a and A~ v have been taken f r o m ref. [1]. P i p p a r d ' s f i r s t r e l a t i o n (expected to be valid n e a r a c r i t i c a l point [7]:
Cp : Y T ~ v ( d P / d T ) + g ,
(1)
w h e r e K i s a constant, p r e d i c t s that the e x c e s s specific heat and oev should r e m a i n p r o p o r t i o n a l throughout the t r a n s i t i o n . W h e r e a s our Cp m e a s u r e m e n t s i n d i c a t e that Cp v a r i e s continuously within the 2 K wide t r a n s i t i o n region, Golding's t h e r m a l expansivity m e a s u r e m e n t s indicated a step d i s c o n t i b u i t y in oev at Ta, which d i s a g r e e s with eq. (1). A n n e a l i n g the s a m p l e has 2 effects: f i r s t , Ta i s l o w e r e d by 1 K, which, a c c o r d i n g to J o n e s and Hulm [8], c o r r e s p o n d s to a lowering of the
414
12 July 1971
oxygen c o n c e n t r a t i o n by 0.05%; second, the t r a n sition is somewhat s m e a r e d , which might be due to the oxygen v a c a n c i e s and the subsequent lower quality of the sample. But, within the u n c e r tainty limit, ACp r e m a i n s unchanged. C o n s i d e r i n g the a d v e r s e effects of the oxygen v a c a n c i e s on both T a and the t r a n s i t i o n region width [3], it may be that a v e r y pure and defectf r e e sample exhibits a much s h a r p e r t r a n s i t i o n . F u r t h e r e x p e r i m e n t s on such s a m p l e s a r e encouraged. The a u t h o r s wishes to thank P r o f e s s o r M. B. Salamon and Dr. B. Golding for valuable c o m m e n t s and suggestions.
References [1] B. Golding, Phys. Rev. Letters 25 (1970) 1439. We wish to thank Dr. Golding for giving us a piece of his crystal. [2] J. C. Slonczewski and H. Tomas, Phys. Rev. B1 (1970) 3599. [3] B. Berre, K. Fossheim and K. A. Muller Phys. Rev. Letters 23 (1969) 589. [4] D. J. Taylor and W. D. Seward, Bull. Am. Phys. Soc. 15 (1970) 1624. [5] M. B. Salamon, Phys. Rev. B2 (1970) 214. [6] S. S. Todd and R. E. Lorenson, J. Am. Chem. Soc. 74 (1952) 2043. [7] A. B. Pippard, Elements of classical thermodynamics (Cambridge University Press, 1957) p.143. [8] C. K. Jones and J. K. Hulm, Phys. Letters 26A (1968) 182; D. W. Deis et al., Bull. Am. Phys. Soc. 15 (1970) 102.
SPECIFIC
PHYSICS LETTERS
HEAT
OF
SrTiO 3 NEAR
THE
12 July 1971
STRUCTURAL
TRANSITION
*
P. R. GARNIER Department of P h y s i c s and Materials R e s e a r c h Laboratory, University of Illinois, Urbana, Illinois 61801, USA
Received 9 June 1971 The specific heat of SrTiO 3 near Ta(Ta ~ 106K) has been measured using an ac technique. It is found that at Ta the specific heat discontinuity ACp/Cp ~ - 1%
The s t r u c t u r a l phase t r a n s i t i o n SrTiO 3 has been the subject of many r e c e n t i n v e s t i g a t i o n s [1-3]. T h e r e is, however, v e r y little detailed i n f o r m a t i o n on the behavior of the specific heat of SrTiO 3 in the t r a n s i t i o n r e g i o n [4]. The s p e cific heat was m e a s u r e d u s i n g an ac c a l o r i m e t r i c technique and a p p a r a t u s p r e v i o u s l y d e s c r i b e d [5]. Our s a m p l e was a chip of the "(Iii)" single c r y s tal u s e d r e c e n t l y by Golding to study the t h e r m a l expansivity and u l t r a s o n i c propagation in the s a m e t e m p e r a t u r e region [1]. The specific heat m e a s u r e m e n t s were made on 3 different s a m p l e s (S1, $2 and $3) cut f r o m the s a m e s m a l l chip. All 3 s a m p l e s were thinned by polishing on # 600 s i l i c o n c a r b i d e paper to a t h i c k n e s s of about 0 . 1 2 r a m . After a f i r s t m e a s u r e m e n t of its specific heat in this state, s a m ple S1 was then a n n e a l e d in a i r at 1250°C for 3 h o u r s , cooled (30 K p e r hour) and r e m o u n t e d . Rs specific heat was then m e a s u r e d again. Samples $2 and $3 were u s e d m a i n l y to check the r e s u l t s on s a m p l e S1. Sample $2 was not annealed; s a m ple $3 was a n n e a l e d at l l 0 0 ° C for 2 hours. The e x p e r i m e n t s on s a m p l e s $2 and $3 gave the s a m e r e s u l t s as the r e s u l t s obtained on s a m p l e S1 in its u n a n n e a l e d and a n n e a l e d s t a t e s r e s p e c t i v e l y . The specific heat v e r s u s t e m p e r a t u r e c u r v e of s a m p l e $1 for both the u n a n n e a l e d and a n n e a l e d s t a t e s i s shown in fig. 1 and 2. No t e m p e r a t u r e h y s t e r e s i s was found. As the ac t e c h nique u s e d gives only r e l a t i v e specific heats, the c u r v e s w e r e n o r m a l i z e d at 114.75 K u s i n g Todd and L o r e n s o n ' s data [6]. The 2 other points obtained by Todd and L o r e n s o n in this t e m p e r a t u r e r a n g e a r e also indicated on fig. 1. We can see
15
I0 ....
t ....
9O
95
, . , , , J , , , , t , , . . i ....
~00
105
ll0
I
115
I~
T(K)
Fig. 1. Specific heat of $1 in its unannealed state. The unnormalized Cp curve was multiplied by an appropriate factor to cause it to pass through the 114.75 K data point of Todd and Lorenson. 12.0
ACp = 0.10 c
o
l
x
~
/
~
. ////''~ 11.5
A% = O.tO
t
cot/mole
x K
II.O
,02
i
,;4
i
,&
'
~--"
,Io
'
T(K)
Fig. 2. Comparison of the specific heats of $1 in its unannealed and annealed states near Ta. The latter curve has been displaced by 0.10 cal/mole K for clarity. t h a t for the u n a n n e a l e d s t a t e : (1) T a , d e t e r m i n e d
* This work was supported In part by the Advanced Research Projects Agency under Contract HC 15-67-C-9221.
a s the t e m p e r a t u r e where dCp/d T i s equal to the average slope outside the t r a n s i t i o n r e g i o n , i s 106.30~0.2 K. (2) zlCp = 0 . 1 0 ~ : 0 . 0 1 c a l / m o l e K,
413
Volume 35A. number 6
PHYSICS LETTERS
w h e r e ACp r e f e r s to the difference between the o b s e r v e d specific heat at Ta and the value obt a i n e d by extrapolation to T a of the high t e m p e r a t u r e data outside the t r a n s i t i o n region. (3) The t r a n s i t i o n r e g i o n extends over about 2 K. The 0.4 K t e m p e r a t u r e difference between the T a we find and the T a found by Golding for the s a m e c r y s t a l p r e s u m a b l y in the s a m e state is b e l i e v e d to s t e m f r o m a t e m p e r a t u r e c a l i b r a t i o n e r r o r in e i t h e r our a p p a r a t u s or Golding's. Our value for the specific heat discontinuity a g r e e s well with both the value calculated by the mean field theory ((114± 0.04 c a l / m o l e K) [2] and the value obtained f r o m the E h r e n f e s t relation: ACp = V T A~ v (dp/dTa) = 0.13+ 0.02 c a l / m o l e K where ~v =- (1/V)(dV/dT) and the n u m e r i c a l v a l u e s of dp/dT a and A~ v have been taken f r o m ref. [1]. P i p p a r d ' s f i r s t r e l a t i o n (expected to be valid n e a r a c r i t i c a l point [7]:
Cp : Y T ~ v ( d P / d T ) + g ,
(1)
w h e r e K i s a constant, p r e d i c t s that the e x c e s s specific heat and oev should r e m a i n p r o p o r t i o n a l throughout the t r a n s i t i o n . W h e r e a s our Cp m e a s u r e m e n t s i n d i c a t e that Cp v a r i e s continuously within the 2 K wide t r a n s i t i o n region, Golding's t h e r m a l expansivity m e a s u r e m e n t s indicated a step d i s c o n t i b u i t y in oev at Ta, which d i s a g r e e s with eq. (1). A n n e a l i n g the s a m p l e has 2 effects: f i r s t , Ta i s l o w e r e d by 1 K, which, a c c o r d i n g to J o n e s and Hulm [8], c o r r e s p o n d s to a lowering of the
414
12 July 1971
oxygen c o n c e n t r a t i o n by 0.05%; second, the t r a n sition is somewhat s m e a r e d , which might be due to the oxygen v a c a n c i e s and the subsequent lower quality of the sample. But, within the u n c e r tainty limit, ACp r e m a i n s unchanged. C o n s i d e r i n g the a d v e r s e effects of the oxygen v a c a n c i e s on both T a and the t r a n s i t i o n region width [3], it may be that a v e r y pure and defectf r e e sample exhibits a much s h a r p e r t r a n s i t i o n . F u r t h e r e x p e r i m e n t s on such s a m p l e s a r e encouraged. The a u t h o r s wishes to thank P r o f e s s o r M. B. Salamon and Dr. B. Golding for valuable c o m m e n t s and suggestions.
References [1] B. Golding, Phys. Rev. Letters 25 (1970) 1439. We wish to thank Dr. Golding for giving us a piece of his crystal. [2] J. C. Slonczewski and H. Tomas, Phys. Rev. B1 (1970) 3599. [3] B. Berre, K. Fossheim and K. A. Muller Phys. Rev. Letters 23 (1969) 589. [4] D. J. Taylor and W. D. Seward, Bull. Am. Phys. Soc. 15 (1970) 1624. [5] M. B. Salamon, Phys. Rev. B2 (1970) 214. [6] S. S. Todd and R. E. Lorenson, J. Am. Chem. Soc. 74 (1952) 2043. [7] A. B. Pippard, Elements of classical thermodynamics (Cambridge University Press, 1957) p.143. [8] C. K. Jones and J. K. Hulm, Phys. Letters 26A (1968) 182; D. W. Deis et al., Bull. Am. Phys. Soc. 15 (1970) 102.