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X-ray and dielectric studies on the critical phenomena in triglycine sulfate
Volume 25A. number
PHYSICS
1
X-RAY
AND DIELECTRIC PHENOMENA IN
K. ISHIDA,
H. YAMADA,
Department
of Physics.
LETTERS
STUDIES TRIGLYCINE
17 July 1967
ON THE CRITICAL SULFATE
T. SEKIDO, Y. SHIOZAKI and T. MITSUI Faculty Sapporo.
Received
of Science. Hokkaido
linicevsity.
Japan
30 May 1967
Precise measurements have been made on the critical X-ray scattering by triglycine sulfate. Obtained results suggest that interaction between the ferroelectric dipoles is strong along the b axis. A possible behaviour of the bulk dielectric constant is demonstrated.
As is well known [I] triglycine sulfate is ferro electric below about 490C. The spontaneous polarization takes place along the b axis. Several authors studied critical phenomena associated with the ferroelectric phase transition in triglytine sulfate [2-41. In 1961 Shibuya et al. [2] discovered critical X-ray scattering by triglycine sulfate. We are doing detailed investigations of this phenomenon by means of the standard method for precise measurements of diffuse X-ray scattering [ 51. Cu Ke radiation monochromatized by a curved quartz crystal has been used and scattered X-rays have been detected by a proportional counter with the help of a pulse height analyzer. Strong critical scattering has been observed around the (0 11 1) Bragg reflection. Careful measurements have revealed that in reciprocal space the weight distribution of critical scattering extends perpendicularly to the b * axis, lattice vector. where b * stands for the reciprocal This fact proves that interaction between ferroelectric dipoles [2] is stronger along the b axis than along the a or c axis, in agreement with other preliminary observations [6,7]. Behaviour of dielectric constants near the Curie point is another interesting example of the critical phenomena and has been investigated by a few authors [3,4]. We also have made precise measurements of dielectric constants along the b axis in the same manner as described in ref. 8. Gold electrodes were evaporated on both surfaces of the b-cut crystal plate, of 0.98mm thickness. Reciprocal values of the measured E (e meas ) are shown in fig. 1. It is interesting to observe that l/e meas has a slightly lower value than the one predicted by the Curie-Weiss law at
/, -LO
-0.05
0 T-Tc
0.05
o.lo
I
0.15
l”Cl
Fig. 1. Reciprocal dielectric constants l/emeas and l/ei as functions of temperature 2’. The Curie temperature ~~ was about 49.42’C. The temperature was changed at the rate of 0.003°C/nlin.
about Tc i 0.02OC. According to Nishikawa [9] it could be a result of non-linear local fluctuations of polarization. (rhe dielectric constant at the Curie temperature T, (Emeas (Tc) ) depends upon the crystal thickness [8], and a possible explanation of this fact was given by assuming that there exists a surface layer between the electrode and the crystal [8]. Since the estimated thickness of the surface layer is so thin (160 A) as can be neglected compared with the crystal thickness, simple considerations based upon eq. (1) of ref. 8 have led to the relation; I/ei = (l/emeas) 5
Volume 25A.
number
1
PHYSICS
LETTERS
2. I.Shibuga and T.Mitsui. J.Phys. Sot. Japan 16 (1961) 479. 3. P. P. Craig. Phys. Letters 20 (1966) 140. 4. J.A.Gonzalo. Phys. Rev. 144 (1966) 662, 5. For instance. A. Guinier. X-ray diffraction (Freeman and Co.. London. 1963) P. 179. 6. I.Shibuya and T.Mitsui (unpLblished work. 1958). 7. Y.Yamada. Y.Fujii and H.Terauchi (unpublished work. 1966). 8. T.Sekido and T.Mitsui. J. Phys. Chem. Solids 28
(l/E meas CT,) ), where Ei is the bulk dielectric constant. i.e., E of the interior of the crystal. Fig. 1. shows values of l/Ei estimated using the above relation. More comprehensive studies are in progress on these critical phenomena and will be published in the near future.
1. F. Jona and G.Shirane. gamon Press.
Ferroelectric
New York.
(Per-
crystals
17 July 1967
(1967). to be published. 9. K. Nishikawa. private communication.
1962) Chap. II.
*****
PERTURBATION
THEORY
WITH
HARTREE-FOCK
STATES
*
H. P. KELLY Department
of Physics.
Univevsitp
of Virginia.
Received
The use of Hartree-Fock states for perturbation summing hole-particle interactions is given.
Charlottesville.
is discussed.
An approximate
-0
-0
n
”
K
_-
K
K
n
---
--a
-0
(4
(b)
-___ Q-O D__ H’
---
m
K
l
(d)
6
Energy
ml
o--u K
l K’
n
_____(e)
Fig. 1. Diagrams for a multiple perturbation expansion. The he&y dot represents an interaction with an external field. (a) Second order term. (b) Hole-particle diagram and its exchange (c) which are included when excited states are calculated with a potential including interactions with state n. (d) and (e) are diagrams involving one correlation interaction among electrons in states m and n. where
“d = -2& * Work supported in part by the U.S. Atomic Commission. Document ORO-2915-77.
method for
---_ --__ 0 Q_ n
The lowest solution is the usual 1s state. All other solutions are in the continuum [ 5] and correspond to triplet states for e-H scattering in the Hartree-Fock approximation [6]. Consider the Hamiltonian perturbed by a term V’ = e < cos 6 F,, due to a small external field F= FoZ. The first-order perturbation correlation to the energy vanishes, and the second-order (in F,) energy shift is given by Ad2) = -$cfdFo2,
USA
30 May 1967
calculations
Complete sets of states calculated with a Hartree-Fock potential [l] VHF may be used to carry out perturbation calculations [ 2 -41. Since the excited single-particle states of VHF are calculated in the field of the nucleus and N other electrons, for many neutral atoms all the excited states of VHF lie in the continuum [2]. This is illustrated by the especially simple example of the Hartree-Fock equation for hydrogen
Virginia,
I(ls (?- cOS@ / k) ( 2/(Els-$).
(2)
PHYSICS
1
X-RAY
AND DIELECTRIC PHENOMENA IN
K. ISHIDA,
H. YAMADA,
Department
of Physics.
LETTERS
STUDIES TRIGLYCINE
17 July 1967
ON THE CRITICAL SULFATE
T. SEKIDO, Y. SHIOZAKI and T. MITSUI Faculty Sapporo.
Received
of Science. Hokkaido
linicevsity.
Japan
30 May 1967
Precise measurements have been made on the critical X-ray scattering by triglycine sulfate. Obtained results suggest that interaction between the ferroelectric dipoles is strong along the b axis. A possible behaviour of the bulk dielectric constant is demonstrated.
As is well known [I] triglycine sulfate is ferro electric below about 490C. The spontaneous polarization takes place along the b axis. Several authors studied critical phenomena associated with the ferroelectric phase transition in triglytine sulfate [2-41. In 1961 Shibuya et al. [2] discovered critical X-ray scattering by triglycine sulfate. We are doing detailed investigations of this phenomenon by means of the standard method for precise measurements of diffuse X-ray scattering [ 51. Cu Ke radiation monochromatized by a curved quartz crystal has been used and scattered X-rays have been detected by a proportional counter with the help of a pulse height analyzer. Strong critical scattering has been observed around the (0 11 1) Bragg reflection. Careful measurements have revealed that in reciprocal space the weight distribution of critical scattering extends perpendicularly to the b * axis, lattice vector. where b * stands for the reciprocal This fact proves that interaction between ferroelectric dipoles [2] is stronger along the b axis than along the a or c axis, in agreement with other preliminary observations [6,7]. Behaviour of dielectric constants near the Curie point is another interesting example of the critical phenomena and has been investigated by a few authors [3,4]. We also have made precise measurements of dielectric constants along the b axis in the same manner as described in ref. 8. Gold electrodes were evaporated on both surfaces of the b-cut crystal plate, of 0.98mm thickness. Reciprocal values of the measured E (e meas ) are shown in fig. 1. It is interesting to observe that l/e meas has a slightly lower value than the one predicted by the Curie-Weiss law at
/, -LO
-0.05
0 T-Tc
0.05
o.lo
I
0.15
l”Cl
Fig. 1. Reciprocal dielectric constants l/emeas and l/ei as functions of temperature 2’. The Curie temperature ~~ was about 49.42’C. The temperature was changed at the rate of 0.003°C/nlin.
about Tc i 0.02OC. According to Nishikawa [9] it could be a result of non-linear local fluctuations of polarization. (rhe dielectric constant at the Curie temperature T, (Emeas (Tc) ) depends upon the crystal thickness [8], and a possible explanation of this fact was given by assuming that there exists a surface layer between the electrode and the crystal [8]. Since the estimated thickness of the surface layer is so thin (160 A) as can be neglected compared with the crystal thickness, simple considerations based upon eq. (1) of ref. 8 have led to the relation; I/ei = (l/emeas) 5
Volume 25A.
number
1
PHYSICS
LETTERS
2. I.Shibuga and T.Mitsui. J.Phys. Sot. Japan 16 (1961) 479. 3. P. P. Craig. Phys. Letters 20 (1966) 140. 4. J.A.Gonzalo. Phys. Rev. 144 (1966) 662, 5. For instance. A. Guinier. X-ray diffraction (Freeman and Co.. London. 1963) P. 179. 6. I.Shibuya and T.Mitsui (unpLblished work. 1958). 7. Y.Yamada. Y.Fujii and H.Terauchi (unpublished work. 1966). 8. T.Sekido and T.Mitsui. J. Phys. Chem. Solids 28
(l/E meas CT,) ), where Ei is the bulk dielectric constant. i.e., E of the interior of the crystal. Fig. 1. shows values of l/Ei estimated using the above relation. More comprehensive studies are in progress on these critical phenomena and will be published in the near future.
1. F. Jona and G.Shirane. gamon Press.
Ferroelectric
New York.
(Per-
crystals
17 July 1967
(1967). to be published. 9. K. Nishikawa. private communication.
1962) Chap. II.
*****
PERTURBATION
THEORY
WITH
HARTREE-FOCK
STATES
*
H. P. KELLY Department
of Physics.
Univevsitp
of Virginia.
Received
The use of Hartree-Fock states for perturbation summing hole-particle interactions is given.
Charlottesville.
is discussed.
An approximate
-0
-0
n
”
K
_-
K
K
n
---
--a
-0
(4
(b)
-___ Q-O D__ H’
---
m
K
l
(d)
6
Energy
ml
o--u K
l K’
n
_____(e)
Fig. 1. Diagrams for a multiple perturbation expansion. The he&y dot represents an interaction with an external field. (a) Second order term. (b) Hole-particle diagram and its exchange (c) which are included when excited states are calculated with a potential including interactions with state n. (d) and (e) are diagrams involving one correlation interaction among electrons in states m and n. where
“d = -2& * Work supported in part by the U.S. Atomic Commission. Document ORO-2915-77.
method for
---_ --__ 0 Q_ n
The lowest solution is the usual 1s state. All other solutions are in the continuum [ 5] and correspond to triplet states for e-H scattering in the Hartree-Fock approximation [6]. Consider the Hamiltonian perturbed by a term V’ = e < cos 6 F,, due to a small external field F= FoZ. The first-order perturbation correlation to the energy vanishes, and the second-order (in F,) energy shift is given by Ad2) = -$cfdFo2,
USA
30 May 1967
calculations
Complete sets of states calculated with a Hartree-Fock potential [l] VHF may be used to carry out perturbation calculations [ 2 -41. Since the excited single-particle states of VHF are calculated in the field of the nucleus and N other electrons, for many neutral atoms all the excited states of VHF lie in the continuum [2]. This is illustrated by the especially simple example of the Hartree-Fock equation for hydrogen
Virginia,
I(ls (?- cOS@ / k) ( 2/(Els-$).
(2)