- Email: [email protected]
Dielectric constant of triglycine sulfate at the Curie point
J. Phys. Chsm. Solti
Pergamon Press 1967. Vol. 28, pp. 967-970.
DIELECTRIC
CONSTANT
Printed in Great Britain.
SULFATE AT
OF TRIGLYCINE
THE CURIE POINT TATSUYA SEKIDO* and TOSHIO MfisuI Department of Physics, Faculty of Science, Hokkaido University, Sapporo, Japan (Received1 Septin
1966; in revisedform 2 December1966)
Abstract-The dielectric constants of triglycine sulfate have been measured accurately along the ferroelectric b axis in the vicinity of the Curie temperature. It has been found that the dielectric constant inferred directly from a simple capacitance measurement at the Curie point is approximately proportional to the crystal thickness, if use is made of the crystals which exhibit almost perfectly square hysteresis loops. It has been suggested that the observed relation can be explained by assuming that the surface layers of thiclmess of 160 A exist. Contrary to Brophy and Webb’s results, there is no pronounced dispersion of the dielectric constant at the Curie point between 30 c/s and 1 MC/S.
1. INTRODUCTION sulfate (TGS)
has been investigated by many workers as a typical ferroelectric crystal which exhibits a second-order phase transition.“) Recently CRAIG(~) and GONZALO(~) have made very accurate measurements on the temperature dependence of dielectric constant of TGS. Their results demonstrate that dielectric constant has a finite peak value at the Curie point in agreement with the previous results of other authors.(4*s) Usually it has been speculated that the observed peak value is determined by inhomogeneities of temperature, stress distributions and partial clamping of the crystal by the electrodes,@) or saturation of polarization, etc.(‘) As has been cited by GONZAL,O,(~)we did careful measurements of the dielectric constants of TGS in the vicinity of the Curie point T, in 1964 and investigated what factors actually determine the magnitude of the dielectric constant c at T, (abbreviated as l (T,) below). Experimental procedures and results are described in the next section. TRICLYCINE
2.-ALPRocED~ANDREsuL~ Crystal plates were cut perpendicularly to the ferroelectric b axis. The surfaces were polished
with a slightly wet cloth. Gold electrodes were evaporated on the both surfaces. The crystal condensers were put in a massive copper block in a furnace, and this furnace was set in a thermostat. Temperature of the specimen could be changed as slowly as about O-OOl”C/min. The dielectric constants were measured by use of an inductive arm bridge within the accuracy of about O-1 per cent between 30 c/s and 1 MC/S. The Curie temperature of the crystal was about 49-4X. An example of the dielectric constant vs. temperature curve is shown in Fig. 1. This curve was obtained reproducibly within the experimental
I.Eu -0.01
0 T-
0.01
Tc , ‘C
FIG. 1. Dielectric constants c of TGS in the vicinity of the Curie point TO (49.42%). Temperature T was *Present address: Toyota Central Research and changed at the rate of O+03°C/min. Thickness of the Development Laboratories, Showa-ltu, Nagoya, Japan. specimen was 0.98 mm. 967
TATSUYA
968
SEKIDO
error when temperature was changed in the very vicinity of the Curie point with a rate less than about 0~003”C/min. This fact suggests that the temperature inhomogeneities in the crystal is negligible if temperature is changed slower than O~OOS°C/min. All the following measurements were made by changing temperature slower than 0~003”C/min. Sometimes the finite value of ~(7’~) was attributed to the saturation of polarization againat an applied field.(v) ~(7’~) measured with a small a.c. signal field was, however, practically independent of the a.c. amplitude as shown in Fig. 2. Therefore, it may be concluded that the saturation effect is not responsible for the finite value of c(T,). The internal stress caused by the crystal imperfections such as dislocations or the external
and TOSHIO
MITSUI
the value of l (T,) = 3 -0 x lo5 whereas a specimen which had the same thickness and exhibited a round hysteresis loop gave the value of E(T,) = 1.5 x 105. It has been observed that annealing of crystals at 60” for 15 hr increased l(T,) by 0 - 20 per cent but not more than 20 per cent even if the annealing time was increased. Also such an annealing had only little effect in improving the round hysteresis loop into the square hysteresis loop. During these experiments it was felt that in general a thick crystal shows a large value of c(T,). Therefore, we made crystal specimens of several thicknesses and spattered electrodes on their surfaces under almost the same conditions, i.e. amount and temperature of the molten gold and the distances between it and the specimens were made almost the same. Among the crystal condensers made in this manner we used those which exhibited almost perfect square hysteresis loops. The criterion for the squareness used is dP/dE >/ 2.7 x 10-a(&!/cma)/(V/cm)
1.99b
’
Afd’LiTUDE
I
I
I
,
2 OF AC Ff ELD \
I v/cm
FIG. 2. ~(2’~) as a function of amplitude of the applied a.~. fields. Thickness of the specimen was l-01 mm.
stress caused by the partial clamping by electrodes could be an origin of the finite value of c(TJ as mentioned by several authors.(3*s) It seems to be a generally accepted postulation that a square hysteresis loop is evidence that a crystal condenser is free from the internal and the external stresses.
at P = 0 with the applied field of 1 kV/cm and 50 c/s, where P is the polarization and E is the electric field. These crystals were then annealed at 60” for about 16 hr. The E(TJs of these crystals are shown as a function of thickness of the crystal in Fig. 3. BROPHYand WEBB(*) reported that the dielectric dispersion occurred around 1 kc/s (Fig. 4.). If this is true, the relaxation could be an origin of the finite value of c(T,). The dielectric constant measured by our inductive arm bridge, however,
x1$ E(Tc)
1
TGS
I
0
0
In fact we could round off the hysteresis loop by applymg external stresses to the crystal condenser which otherwise showed a square hysteresis loop. Also it has been found that the TGS crystal which shows a square hysteresis loop at room temperatures has always a higher value of e(T,) than the crystal which shows a round hysteresis loop. For example, a specimen of which thickness was 1.5 mm and which exhibited an almost perfect sauare hvsteresis 1000 at room temnerature gave
0 FIG. 3.
CRYSTAL TLIICKNESS,
2 mm
as a function of the crystal thickness.
DIELECTRIC
CONSTANT
OF TRIGLYCINE
gave no evidence of a pronounced dielectric dispersion between 30 c/s and 1 MC/S as shown in Fig. 4, though a slight decrease of a(T,) with increasing frequency was observed. Possibly our data can be connected smoothly with those of HILL and kHIKI’*’ as can be seen in Fig. 4. PRESENT
HILL
WORK
and ICHIKI
SULFATE
AT THE
CURIE
cps
FIG, 4. a(Z’,) of TGS as a function of frequency of the applied B.C. field, in comparison with BROPHY and WEBB’S result@ and HILL and fCXiIKX’a results.(*) Thickness of the specimen was l-11 mm.
3. DISCUSSION
The results shown in Fig. 3 suggest that the most predominant factor which determines magnitude of E(TJ is the crystal thickness if the crystal is free from the internal and external stresses. One possible way to explain the results of Fig. 3 is to assume existence of the surface layers as has been discussed by CHYNO~ETH.(~~)If the both surfaces of TGS have layers of which thickness is I and dielectric constant is et as shown in Fig. 5, and if the thickness of the crystal is d and +-----d------+
FIG. S. Crystal
condenser having the surface layers of thickness 1.
969
its bulk dielectric constsnt is et, simple electrostatic consideration leads to the relation,
Here Emea8 is the dielectric constant obtained from the measured capacitance of the crystal condenser on the assumption that a homogeneous dielectric medium exists between the metal electrodes. By this definition, emeasbecomes equal to E(I’,) at the Curie point. Now if Edbecomes infinite at the Curie point as Gonzalo’s experimentsf3) and the statistical theories(11*12)suggest, equation (1) becomes E(T,) = (e,/2E)d.
FREQUENCY,
POINT
(2)
That is, E(T,) is proportional to the crystal thickness d. A plausible structure of the surface layer might be that the rotatable dipoles(13) are frozen-in within the layers as would occur inside the whole crystal at very low temperatures. Measurement of the dielectric constant along the b axis was made at the liquid helium temperature and the value of 6.2 was obtained. Thickness of the specimen was 1.01 mm. The straight line in Fig. 3 was drawn by putting Ed= 6-2 and 2 = 1.6 x 10m6cm, CHYNOWETH(~~)tentatively estimated the thickness of the surface layer to be between lo-’ cm and 10e6 cm. The above value of E is consistent with his estimation. In our experiment, however, it is not certain whether the surface layer was created by overheating of the surface during spattering of the electrode or it exists even on a natural surface of the crystal. Our results shown in Fig. 4 suggest that there is no pronounced dielectric dispersion at the Curie point from 30 c/s to 1 Mcfs. BROPHYand WEBB(*) determined the dielectric constant by measuring the thermal noise in the crystal, At the present no interpretation can be given on the discrepancy between their results and ours.
dcknowledgetnents-The authors sre indebted to Dr. H. TOYODA of Nippon Telegraph and Telephone Public Corporation for supp&ing good single crystals of TGS. They would like to express their gratitude also to Dr. E. NAKAMURAfor his helpful advice during the course of this work.
TATSUYA
970
SEKIDO
and
TOSHIO
1. JONA F. and Snmhm
2. 3. 4. 5. 6. 7.
G., Ferroelectric Crystals, Chapter II. Pergamon Press, New York (1962). CRAIOP. P., Phys. L&t. 20,140 (1966). GONZALOJ. A., Phys. Reu. 14+2, 662 (1966). HOSHINOS., Mmur T., JOIUAF. and PEP~SKY R., Phys. Beu. 107,1255 (1957). TRIEBWASSBR S., IBM J. Res. Dew. 2, 212 (1958). Ref. 1. pp. 29-30. For instance, Kllmxc W., Ferroektrics and Antifctroelectrics in Solid State Physks Vol. 4, p. 14,
8. 9. 10. 11. 12. 13.
MITSUI
edited by F. SEITZand D., TURNBULL,Academic Press, New York (1957). BROPHYJ. J. and %kBB S. L. Phys. Rev. 128, 584 (1962). HILL R. M. and 1cmc1 S. K., Phys. Rev. U&1140 (1362). CHYNOWBTH A. G., Phys. Rev. 117, 1235 (1960). DOME C. and Sm M. F., J. Math. Phys. 2, 63 (1961). BARKERG. A., JR., Phyr. Reu. 124,768 (1961). SHIBUYA I. and Mmur T., J. Phys. Sot. Japan 16, 479 (1961).
Pergamon Press 1967. Vol. 28, pp. 967-970.
DIELECTRIC
CONSTANT
Printed in Great Britain.
SULFATE AT
OF TRIGLYCINE
THE CURIE POINT TATSUYA SEKIDO* and TOSHIO MfisuI Department of Physics, Faculty of Science, Hokkaido University, Sapporo, Japan (Received1 Septin
1966; in revisedform 2 December1966)
Abstract-The dielectric constants of triglycine sulfate have been measured accurately along the ferroelectric b axis in the vicinity of the Curie temperature. It has been found that the dielectric constant inferred directly from a simple capacitance measurement at the Curie point is approximately proportional to the crystal thickness, if use is made of the crystals which exhibit almost perfectly square hysteresis loops. It has been suggested that the observed relation can be explained by assuming that the surface layers of thiclmess of 160 A exist. Contrary to Brophy and Webb’s results, there is no pronounced dispersion of the dielectric constant at the Curie point between 30 c/s and 1 MC/S.
1. INTRODUCTION sulfate (TGS)
has been investigated by many workers as a typical ferroelectric crystal which exhibits a second-order phase transition.“) Recently CRAIG(~) and GONZALO(~) have made very accurate measurements on the temperature dependence of dielectric constant of TGS. Their results demonstrate that dielectric constant has a finite peak value at the Curie point in agreement with the previous results of other authors.(4*s) Usually it has been speculated that the observed peak value is determined by inhomogeneities of temperature, stress distributions and partial clamping of the crystal by the electrodes,@) or saturation of polarization, etc.(‘) As has been cited by GONZAL,O,(~)we did careful measurements of the dielectric constants of TGS in the vicinity of the Curie point T, in 1964 and investigated what factors actually determine the magnitude of the dielectric constant c at T, (abbreviated as l (T,) below). Experimental procedures and results are described in the next section. TRICLYCINE
2.-ALPRocED~ANDREsuL~ Crystal plates were cut perpendicularly to the ferroelectric b axis. The surfaces were polished
with a slightly wet cloth. Gold electrodes were evaporated on the both surfaces. The crystal condensers were put in a massive copper block in a furnace, and this furnace was set in a thermostat. Temperature of the specimen could be changed as slowly as about O-OOl”C/min. The dielectric constants were measured by use of an inductive arm bridge within the accuracy of about O-1 per cent between 30 c/s and 1 MC/S. The Curie temperature of the crystal was about 49-4X. An example of the dielectric constant vs. temperature curve is shown in Fig. 1. This curve was obtained reproducibly within the experimental
I.Eu -0.01
0 T-
0.01
Tc , ‘C
FIG. 1. Dielectric constants c of TGS in the vicinity of the Curie point TO (49.42%). Temperature T was *Present address: Toyota Central Research and changed at the rate of O+03°C/min. Thickness of the Development Laboratories, Showa-ltu, Nagoya, Japan. specimen was 0.98 mm. 967
TATSUYA
968
SEKIDO
error when temperature was changed in the very vicinity of the Curie point with a rate less than about 0~003”C/min. This fact suggests that the temperature inhomogeneities in the crystal is negligible if temperature is changed slower than O~OOS°C/min. All the following measurements were made by changing temperature slower than 0~003”C/min. Sometimes the finite value of ~(7’~) was attributed to the saturation of polarization againat an applied field.(v) ~(7’~) measured with a small a.c. signal field was, however, practically independent of the a.c. amplitude as shown in Fig. 2. Therefore, it may be concluded that the saturation effect is not responsible for the finite value of c(T,). The internal stress caused by the crystal imperfections such as dislocations or the external
and TOSHIO
MITSUI
the value of l (T,) = 3 -0 x lo5 whereas a specimen which had the same thickness and exhibited a round hysteresis loop gave the value of E(T,) = 1.5 x 105. It has been observed that annealing of crystals at 60” for 15 hr increased l(T,) by 0 - 20 per cent but not more than 20 per cent even if the annealing time was increased. Also such an annealing had only little effect in improving the round hysteresis loop into the square hysteresis loop. During these experiments it was felt that in general a thick crystal shows a large value of c(T,). Therefore, we made crystal specimens of several thicknesses and spattered electrodes on their surfaces under almost the same conditions, i.e. amount and temperature of the molten gold and the distances between it and the specimens were made almost the same. Among the crystal condensers made in this manner we used those which exhibited almost perfect square hysteresis loops. The criterion for the squareness used is dP/dE >/ 2.7 x 10-a(&!/cma)/(V/cm)
1.99b
’
Afd’LiTUDE
I
I
I
,
2 OF AC Ff ELD \
I v/cm
FIG. 2. ~(2’~) as a function of amplitude of the applied a.~. fields. Thickness of the specimen was l-01 mm.
stress caused by the partial clamping by electrodes could be an origin of the finite value of c(TJ as mentioned by several authors.(3*s) It seems to be a generally accepted postulation that a square hysteresis loop is evidence that a crystal condenser is free from the internal and the external stresses.
at P = 0 with the applied field of 1 kV/cm and 50 c/s, where P is the polarization and E is the electric field. These crystals were then annealed at 60” for about 16 hr. The E(TJs of these crystals are shown as a function of thickness of the crystal in Fig. 3. BROPHYand WEBB(*) reported that the dielectric dispersion occurred around 1 kc/s (Fig. 4.). If this is true, the relaxation could be an origin of the finite value of c(T,). The dielectric constant measured by our inductive arm bridge, however,
x1$ E(Tc)
1
TGS
I
0
0
In fact we could round off the hysteresis loop by applymg external stresses to the crystal condenser which otherwise showed a square hysteresis loop. Also it has been found that the TGS crystal which shows a square hysteresis loop at room temperatures has always a higher value of e(T,) than the crystal which shows a round hysteresis loop. For example, a specimen of which thickness was 1.5 mm and which exhibited an almost perfect sauare hvsteresis 1000 at room temnerature gave
0 FIG. 3.
CRYSTAL TLIICKNESS,
2 mm
as a function of the crystal thickness.
DIELECTRIC
CONSTANT
OF TRIGLYCINE
gave no evidence of a pronounced dielectric dispersion between 30 c/s and 1 MC/S as shown in Fig. 4, though a slight decrease of a(T,) with increasing frequency was observed. Possibly our data can be connected smoothly with those of HILL and kHIKI’*’ as can be seen in Fig. 4. PRESENT
HILL
WORK
and ICHIKI
SULFATE
AT THE
CURIE
cps
FIG, 4. a(Z’,) of TGS as a function of frequency of the applied B.C. field, in comparison with BROPHY and WEBB’S result@ and HILL and fCXiIKX’a results.(*) Thickness of the specimen was l-11 mm.
3. DISCUSSION
The results shown in Fig. 3 suggest that the most predominant factor which determines magnitude of E(TJ is the crystal thickness if the crystal is free from the internal and external stresses. One possible way to explain the results of Fig. 3 is to assume existence of the surface layers as has been discussed by CHYNO~ETH.(~~)If the both surfaces of TGS have layers of which thickness is I and dielectric constant is et as shown in Fig. 5, and if the thickness of the crystal is d and +-----d------+
FIG. S. Crystal
condenser having the surface layers of thickness 1.
969
its bulk dielectric constsnt is et, simple electrostatic consideration leads to the relation,
Here Emea8 is the dielectric constant obtained from the measured capacitance of the crystal condenser on the assumption that a homogeneous dielectric medium exists between the metal electrodes. By this definition, emeasbecomes equal to E(I’,) at the Curie point. Now if Edbecomes infinite at the Curie point as Gonzalo’s experimentsf3) and the statistical theories(11*12)suggest, equation (1) becomes E(T,) = (e,/2E)d.
FREQUENCY,
POINT
(2)
That is, E(T,) is proportional to the crystal thickness d. A plausible structure of the surface layer might be that the rotatable dipoles(13) are frozen-in within the layers as would occur inside the whole crystal at very low temperatures. Measurement of the dielectric constant along the b axis was made at the liquid helium temperature and the value of 6.2 was obtained. Thickness of the specimen was 1.01 mm. The straight line in Fig. 3 was drawn by putting Ed= 6-2 and 2 = 1.6 x 10m6cm, CHYNOWETH(~~)tentatively estimated the thickness of the surface layer to be between lo-’ cm and 10e6 cm. The above value of E is consistent with his estimation. In our experiment, however, it is not certain whether the surface layer was created by overheating of the surface during spattering of the electrode or it exists even on a natural surface of the crystal. Our results shown in Fig. 4 suggest that there is no pronounced dielectric dispersion at the Curie point from 30 c/s to 1 Mcfs. BROPHYand WEBB(*) determined the dielectric constant by measuring the thermal noise in the crystal, At the present no interpretation can be given on the discrepancy between their results and ours.
dcknowledgetnents-The authors sre indebted to Dr. H. TOYODA of Nippon Telegraph and Telephone Public Corporation for supp&ing good single crystals of TGS. They would like to express their gratitude also to Dr. E. NAKAMURAfor his helpful advice during the course of this work.
TATSUYA
970
SEKIDO
and
TOSHIO
1. JONA F. and Snmhm
2. 3. 4. 5. 6. 7.
G., Ferroelectric Crystals, Chapter II. Pergamon Press, New York (1962). CRAIOP. P., Phys. L&t. 20,140 (1966). GONZALOJ. A., Phys. Reu. 14+2, 662 (1966). HOSHINOS., Mmur T., JOIUAF. and PEP~SKY R., Phys. Beu. 107,1255 (1957). TRIEBWASSBR S., IBM J. Res. Dew. 2, 212 (1958). Ref. 1. pp. 29-30. For instance, Kllmxc W., Ferroektrics and Antifctroelectrics in Solid State Physks Vol. 4, p. 14,
8. 9. 10. 11. 12. 13.
MITSUI
edited by F. SEITZand D., TURNBULL,Academic Press, New York (1957). BROPHYJ. J. and %kBB S. L. Phys. Rev. 128, 584 (1962). HILL R. M. and 1cmc1 S. K., Phys. Rev. U&1140 (1362). CHYNOWBTH A. G., Phys. Rev. 117, 1235 (1960). DOME C. and Sm M. F., J. Math. Phys. 2, 63 (1961). BARKERG. A., JR., Phyr. Reu. 124,768 (1961). SHIBUYA I. and Mmur T., J. Phys. Sot. Japan 16, 479 (1961).