A Collection of Articles on Physics and Others

By Jin Tong Wang Ph. D

This book is about Dr. Jin Tong Wang’s collected research works included: 1) Brillouin “Small Angle, Right Angle and Backscattering”. There were achieved three significances, a) smallest angle scattering in the world at that time. It was a world record; b) discovered from small angle, right angle and backscattering results, the sound velocity was not a constant with the same phonon mode. It actually depends on the phone frequencies. At that time, no one in this field didn’t know how to interpret it. Based on the results in the study, published a paper in Physical Review B in 1986; 2) By the support of Office of Naval Research, we created quite a few navel Ferro-piezoelectric materials. We have done experiments on ferroelectricity, piezoelectricity and pyroelectricity measurements. Based on the experiment we have some intriguing findings; 3) We also work on theories on several topics. First of all, we proposed a displacive- order-disorder (DOD) ferroelectric transition model for para-ferroelectric phase transition mechanism. The paper was published in the well-known European journal “Ferroelectrics”. The DOD phase transition mechanism clarified the long-time dispute whether the para-ferroelectric phase transition was displacive or order-disorder one; 4) Derived an Accurate Formulation of Faraday, Magnetic Circular Dichroism (MCD) and Kerr Effect of Light in Ferro-electromagnet.; 5) published several papers in the frontier of quantum mechanics including: the red shift of photon frequency in gravitational potential; the mechanism of electron photo emission; the unification of classical mechanics and quantum mechanics; the origin of quantum particle entanglement and quantum wave packet tunneling. Some papers have caught attentions by physics communities; 5) two patents created by author. One is microwave-plasma and plasma torch gasifier. Another one is plasma torch directly refine metal titanium; 6) Also published some papers in Chinese. Some were appeared well-known Chinese News Paper. In some paper, the advantages and disadvantages in two social systems were analyzed in physical point of view. All these published papers are edited in this collection.

• Language: English
• Publisher: Xlibris US
• Release date: Aug 14, 2022
• ISBN: 9781669813644

Jin Tong Wang Ph. D

In 1981, I came to The United States of America to study as a graduate student at Montana State University. It would be my new live in the rest of my live in USA, I believed. In the early of eighties of last contrary, China opened the country’s door to the world. Chinese government stars to send scholars to the west countries. USA was the first choice. Scholars from Chinese universities and institutes were admired to have the opportunity to go to the west countries to study and pursue higher degrees. After passed all exams. and courses, I started to undertake the experiment and thesis writing for my Ph. D degree citation. My thesis project was “Anomalies of Hypersound Velocity and Attenuation in Ferroelectric Tri-Sarcosine Calcium Chloride (TSCC) for Brillouin Small Angle, Right Angle and Backscattering”. In this study, I achieved three significances: 1) I achieved a smallest angle scattering in the world at that time. It was a world record; 2) I discovered from my small angle, right angle and backscattering results that the sound velocity was not a constant with the same phonon mode. It actually depends on the frequencies. At that time, no one in this field didn’t know how to interpret it; 3) Based on the results in my study, I published a paper in Physical Review B, the highest physical journal, in 1986. In the fall of 1986, I received Ph. D in physics from Montana State University. Later, in the year of 1995 I was a research visiting professor at the Tax Center for High Tc Superconductivity to do research for a couple of months. In the fall of that year I was offered an assistant professor at Southern University and A&M College in Louisiana State. By the support of a Federal Agency, I established an Electronic Material Research Laboratory at Southern University. By the grants several post-doctoral were nurtured and going on their carrier. Several graduates obtained degrees from Southern University. Many undergraduates were doing research in this lab. We created quite a few navel ferro-piezoelectric materials. We have done experiments on ferroelectricity, piezoelectricity and pyroelectricity measurements. Based on the experiment we have some intriguing findings. We also work on theories on several topics. First of all, I proposed a displacive- order disorder(DOD) ferroelectric transition model for para-ferroelectric phase transition mechanism. The paper was published in the well-known European journal “Ferroelectric”. Before my paper there was unsolved dispute whether the para-ferroelectric phase transition was displacive or order-disorder one. My DOD model solved this dispute. I also derived an Accurate Formulation of Faraday, Magnetic Circular Dichroism (MCD) and Kerr Effect of Light in Ferro-electromagnet. I also created two patents. One is microwave-plasma and plasma torch gasifier. Another one is plasma torch directly refine metal titanium. I retired from Southern University in 2017. I keep an active research activity. I wrote and published several papers in the frontier of quantum mechanics. My studies focused on the frontier topics of quantum mechanics. Some of my research results have caught attentions from physics communities. I also published some papers in Chinese. I analyzed the advantages and disadvantages in two social systems in physical point of view. All these published papers were edited in this collection. I would like to leave these paper for our decedents. That will be my greatest pleasure.

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Rev. date: 08/12/2022

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CONTENTS

Preface

PART I: SCIENTIFIC ARTICLES

Anisotropy in Anomalies of Hypersound Velocity and Attenuation in Ferroelectric TSCC

Anomalies Of Hypersound Velocity And Attenuation In Ferroelectric Tris-Sarcosine Calcium Chloride (TSCC) For Small-Angle And Right-Angle Brillouin Scattering And Brillouin Backscattering

Displacive to Order-Disorder Two-Step Phase Transition Model for Para-Ferroelectric Transition

Nuclear Instruments and Methods in Physics Research A 410 (1998) P 304-308

Nuclear Instruments and Methods in Physics Research A 387 (1997) 315-18

The Origin Of The Spooky Behavior Of Quantum Particles: Time Reversal

Energy Structure of Two-Dimensional Graphene-Semiconductor Quantum Dot

Graphene-Semiconductor Quantum Well with Asymmetric Energy Gaps

Photoemission Process — Relation With Quantum Entanglement

Whether Or Not The Maxwell Theory Works On The Atomic Level

Accurate Formulation of Faraday, Magnetic Circular Dichroism (MCD) and Kerr Effect of Light in Ferroelectromagnet

Magneto-Electric (ME) Effects in BiFeO3 Ferroelectromagnet

Direct Theoretical Method For The Determination Of Peak Laser Intensities From Freeman Resonances In Above-Threshold Ionization

High-Precision Quasienergies For A Driven Two-Level Atom At The Two-Photon Preresonance

How Can An Atom Or Ion Remember Its Initial State?

Quantum States In A Nanotube Quantum Dot

Spin-Dependence Of The Electron Scattering Cross Section By A Magnetic Layer System And The Magneto-Resistance

Changes Of X-Ray Diffraction Pattern In Ferroelectrics Due To The Field-Induced Phase Transition

Crystal Symmetry Dependence Of The Polarization Of Brillouin Scattered Light

Depth-Dependence Of Electromechanical Properties In A Thick 0.7Pb(Mg1/3(Nb0.9Ta0.1)2/3)O3-0.3PbTiO3 Ceramic Disk

Optical Properties Of The Half-Metallic La3/4Ca1/4MnO3

Sample Processing Pressure-Dependence of Weak Links in Polycrystalline Yba2Cu3O7

Dielectric Characteristics Of A Relaxor 0.9PMN-0.1PT Synthesized With Hot And Cold Pressing

Synthesis And Characterization Of (1-x)(Na0.5Bi0.5)TiO3-xA16Bi2O12

Magnetic Field Effect On Dielectric Properties Of Pb(Fe1/2Nb1/2)O3 Single Crystal

Dielectric Properties Of 0.65Pbmg1/3(Nb(1-X)Tax)2/3O3-0.35Pbtio3

Dielectric Characteristics Of A Relaxor 0.9PMN-0.1PT Synthesized With Hot And Cold Pressing

Study Of PMN-PT Thick Films Fabricated By Spin-Coating

Effect of Ta-doping on dielectric properties of yPbMg1/3(Nb(1–x)Tax)2/3º3–(1 – y)PbTiO3

Effect Of Pb Volatilization Of Dielectric Properties Of 0.77PbMg1/3(Nb0.9Ta0.1)2/3O3-0.23PbTiO3

Magnetic Field Effect on Dielectric Properties of Pb(Fe0.5Nb0.5)O3 (PFN)

Growth And Properties Of PMN-PT Single Crystals

Ferroelectric/Piezoelectric Materials And Their Applications In Advanced Sciences And Technologies

Effects of changes of parameters on gap of high-Tc cuprates

Time-Dependence Of The Magnetization In Ba2Sr2CaCu2Ox Single Crystal Under Zero Field Cooled Condition

Electro-Mechanical Coupling Characteristics Of PZT For Sensor And Actuator Application

X-Ray Radiation Effects On The Dielectric Properties Of PZT Ceramics

Influence Of Several Irreversible Losses On The Performance Of A Ferroelectric Stirling Refrigeration-Cycle

Polaronic Effect In Materials With Ferroelectric Phase Transitions

Fabrication and transport studies on PrBa2(Cu1–xMx)3O7: M = Ga, Zn, and Co

Electron energy loss studies on V, Nb, Ta and VN, NbN and TaN

Red Shift Of Photon Frequency In Gravitational Potential

Unification Of Quantum Mechanics And Classical Mechanics

Time To Take For A Quantum Wave Packet Tunneling Through A Square Barrier

PART II: PATENTS

Declaration (37 Cfr 1.63) For Utility Or Design Application Using An Application Data Sheet (37 Cfr 1.76) And Assignment

Gasifier

PART III: ARTICLES IN CHINESE

PREFACE

When an airplane of Chinese landed on San Francisco International airport in August 1981, It would be my new live in the rest of my live, I believed. In the early of eighties last contrary, China open the country’s door to the world. Chinese government stars to send scholars to the west countries. The United States of America is the first choice. Scholars from universities and institutes are admired to have the opportunity to go to the west countries to do research and pursued higher degrees.

After I made a lot efforts, I finally approved to be a visiting scholar to Montana State University, United States. However, at the University I was accepted as a graduate student. Because by Chinese rules only a person of 35 years old or younger can be approved to be study abroad as a student. At that time, I was 39 years old.

I love physics. I studied very hard. In the second year at Montana State University, I passed the qualifying examination with number one in score at that year. Then in the third year I passed the Ph. D comprehensive examination with a pretty good score. I also finished the course credit in the third year. I was start to undertake the experiment and thesis writing for my Ph. D degree citation. My thesis project is Anomalies of Hypersound Velocity and Attenuation in Ferroelectric Tri-Sarcosine Calcium Chloride (TSCC) for Brillouin Small Angle, Right Angle and Backscattering. In this study, I achieved three significances: 1) I achieved a smallest angle scattering in the world at that time. It is a world record. 2) I discovered from my small angle, right angle and backscattering results that the sound velocity is not a constant with the same phonon mode. It actually depends on the frequencies. At that time, no one in this field didn’t know how to interpret it. 3) Based on the results in my study, I published a paper in Physical Review B in 1986. It is rear that a graduate student can published a paper in this physics highest journal.

In the fall of 1986, I received Ph. D in physics. Surprisingly I was not exited as I thought. I somehow, depressed. I thought that is it. Later I may face some more challenges, I was not so sure of my future and how I would take care of my family.

In this year, there was a quite exciting event in physics. That is the discovery of high transition temperature superconductors in oxides with transition temperature Tc above nitrogen boiling point (77K). Even the transition temperature is still much lower than room temperature. However, comparing the transition temperature of traditional lower Tc superconductors. It was considered a great leap. Many scientists in physics and chemistry rash in trying to find new superconductor. I was one of them. I cooperate with a well-known professor at Temple University in the quest of new superconductors. I fortunately, obtained a research grant from a federal agency to conduct the superconductivity research. In this effort, I although, did not find new superconductor. I did find some new phenomenon of superconductivity. I studied magnetic flax dynamics in high Tc superconductor and I found the magnetic flax in a superconductor has two categories: intrinsic and extrinsic and I with a professor at Temple University experimentally first time discovered that in a temperature region below Tc, the superconductor YBCO exhibits paramagnetic property. In 1986, A group of researchers, at Houston University invented a high Tc superconductor YBa2Cu3O6+∂ which’s superconductivity transition temperature as high as 94K well above the liquid nitrogen boiling temperature. His creation evoked an excitement in physics community. He then becomes famous. The Texas state provide him a big grant to build a Research Center for High Tc Superconductivity at Houston University. In the year of 1995 I was lucky to excepted as a research visiting professor to this center to do superconductivity research for a couple of months. In the fall of that year I was offered an assistant professor at Southern University and A&M College in Louisiana State. I worked there until I retired from there.

While I was a professor at Southern University in Louisiana, I obtained grants from the federal agency to conduct Ferro-Piezoelectric materials research. By the support of ONR, I established an Electronic Material Research Laboratory at Southern University. By the grants several post-doctoral were nurtured and going on their carrier. Several graduates obtained degrees from Southern University. Many undergraduates were doing research in this lab.

By the support of that federal agency, we created quite a few navel Ferro-piezoelectric materials. We have done experiments on ferroelectricity, piezoelectricity and pyroelectricity measurements. Based on the experiment we have some intriguing findings. We also work on theories on several topics. First of all, I proposed a displacive- order disorder ferroelectric transition model for para-ferroelectric phase transition mechanism. The paper is published in the well-known European journal Ferroelectric. Before my paper there is unsolved dispute whether the para-ferroelectric phase transition is displacive or order-disorder one. I also derived an Accurate Formulation of Faraday, Magnetic Circular Dichroism (MCD) and Kerr Effect of Light in Ferro-electromagnet. I also created two patents. One is microwave-plasma and plasma torch gasifier. Another one is plasma torch directly refine metal titanium.

At Southern University, I was promoted finally to tenured full professor. I retired from Southern University in 2017. Even after I retired, I keep an active research activity writing and published several papers in the frontier of quantum mechanics. My studies focused on the mechanism of electron photo emission; the unification of classical mechanics and quantum mechanics; the origin of quantum particle entanglement and quantum wave packet tunneling.

I also published some papers in Chinese. Some are appeared well-known Chinese paper. All these published papers are edited in this collection. I would like to leave these paper for our decedents. That will be my greatest pleasure.

Jin Tong Wang, Ph. D

87960.png87967.png87976.png87984.png

PART I

Scientific Articles

(in English)

Doctoral Dissertation Tittle etc.

"ANOMALIES OF HYPERSOUND VELOCITY AND ATTENUATION IN

FERROELECTRIC TRIS-SARCOSINE CALCIUM CHLORIDE

(TSCC) FOR BRILLOUIN SMALL ANGLE, RIGHT

ANGLE AND BACKSCATTERING"

by

Jin Tong Wang

A thesis submitted in partial fulfillment

of the requirements for the degree

of

Doctor of Philosophy

in

Physics

MONTANA STATE UNIVERSITY

Bozeman, Montana

July, 1986

Proceedings of the Sixth International Meeting on Ferroelectricity, Kobe 1985

Japanese Journal of Applied Physics, Vol. 24 (1985) Supplement 24-2, pp. 494-496

Anisotropy in Anomalies of Hypersound Velocity

and Attenuation in Ferroelectric TSCC

T. HIKITA, J. T. WANG, P. T. SCHNACKENBERG and V. H. SCHMIDT

Physics Department, Montana State University,

Bozeman, Montana 59717 USA

From Brillouin shift and linewidth of longitudinal phonons propagating along the [100] and [001] directions of TSCC, the polarization relaxation time was calculated to be r = 3.1 x 10–12/(Tc – T) see below the transition temperature Tc. The anomalies in the longitudinal phonons of the [010] propagation were carefully examined using an annealed crystal of excellent quality. No essential difference was observed between the velocities of a normal and high quality crystals. The relaxation time was deduced as a function of temperature from the observed anomalies in the velocity and linewidth. Spectra are observed for nearly forward scattering from the q//[010] phonons.

Introduction

Tris-sarcosine calcium chloride (TSCC), (CH3NHCH2COOH)3·CaCl2 is a uniaxial ferroelectric¹) whose space group is 91536.png (Pnam) in the paraelectric phase (PE) phase²) and 52310.png (Pn21a) in the ferroelectric (FE) phase,³) Courtens et al.⁴) reported that the dielectric constant εb for TSCC exhibits a logarithmic correction to Curie-Weiss behavior, because of the dipole-dipole interaction which is important in the critical region, ⁵) Raman scattering studies⁶, ⁷) show the unusual characteristic that the transverse optic (TO) and longitudinal optic (LO) modes soften in the same way below Tc and have nearly equal frequencies. This indicates that the dipole-dipole interaction is weak,⁸) so short-range interactions must be responsible for the itrides of transition even though dipole-dipole interaction may be responsible for the reported logarithmic correction.

Brillouin scattering in this crystal is interesting, because we can deduce dynamical behavior of the phase transition in the gigahertz region. Previous Brillouin scattering results have been reported in several paperse. ⁶, ⁹, ¹⁰) The Brillouin shifts and the linewidth of the q//[100] and [001] longitudinal phonons showed large anomalies at the transition temperature. These phonon modes couple piezoelectrically with polarization fluctuations in the FE phase.⁹) From the temperature where the damping constant attains maximum value, the dipolar relaxation time of dipoles can be evaluated.⁹) However, the situation is quite different for the [010] longitudinal phonons. These phonons induces longitudinal polarization waves along the [010] direction. The fluctuations of these polarization waves are suppressed because of the appearance of a depolarization field in the plane waves.¹¹) Thus the [010] longitudinal phonons are presumed to show no anomalies relevant to the polarization fluctuations through piezoelectric coupling.

However, in refs. 9 and 10, relatively large anomalies were observed in the velocity and the dampling constant of the q//[010] phonons. Such anomalies are not deduced from the phenomenological theory. So, we should be very careful to assert such anomalies in ferroelectric crystals. For instance, the anomaly of longitudinal sound velocity of the [001] propagation in TGS in the PE phase was formerly believed to occur from electrostrictive coupling¹²) (fluctuation¹²)). However, it was demonstrated that this anomaly is almost completely eliminated by measuring the sound velocity in a very small region of a crystal of very good quality.¹³) Therefore, in this paper, we have grown very good crystals and the sample was annealed to improvement the quality.⁴) The Brillouin spectra of the q//[010] phonons were carefully analyzed by a high resolution triple-pass Fabry-Perot interferometer. The temperature dependence of the Brillouin shift and the linewidth was compared with that of the former experiment. To determined the temperature correspondence between this experiment and the former experiment, the dielectric constant εb was measured simultaneously on the same sample.

To investigate the dispersion of this phonon mode, a small angle scattering¹⁴) (θ=7.6°) has been performed. This experiment also helps to understand the broadening of Brillouin spectra for right angle scattering. The relaxation time was calculated as a function of temperature from the velocity dispersion and the damping constant. The origin of this relaxation time is discussed.

Experimental Procedure

Single crystals of TSCC were grown from aqueous solutions of sarcosine and calcium chloride by slow cooling. The solution for the sample of precise q//83101 phonon measurement was prepared from chemicals of special quality and was filtered by a 0.2 μm pore size membrane filter. This sample was shaped into a form of rectangular parallelepiped and carefully polished. Aluminum was evapolated as electrodes for measurement of the dielectric constant εb.

This sample was annealed at 140°C for 24 hours in a vacuum glass tube to improve the quality of the crystal as described in ref. 4. No extra mechanical or heat treatment was added to the sample after removal from the vacuum environment. The dielectric constant was measured simultaneously with Brillouin scattering at 10 kHz by the use of a ratio transformer.

For the sample of a small angle scattering, a papallelepiped which is 8 mm long along the c-axis was prepared. This sample was not heat treated.

The Brillouin scattering equipment and the cryostat are the same as those already described in ref. 9. However, we have used a triplepass Fabry-Perot interferometer, smaller collection angles ~0.5° and higher resolution (1.3 GHz – 2 GHz Free Spectral Range) in this paper. Therefore, these conditions made us easier to obtain Brillouin shifts and linewidth of much higher accuracy.

Results and Discussion

Figure 1 shows temperature dependence of Brillouin shift and linewidth of longitudinal [100] phonons. The transition temperature is 130 K. A similar result has been obtained for the q//[001] phonons,⁹) The large anomalies in the Brillouin shift and the linewidth arise from the linear coupling of strain and polarization (piezoelectric coupling) in the FE phase. We can evaluate the relaxation time of the electric polarization by comparing the temperature where the linewidth attains a maximum value with the transition temperature.⁹) The transition temperature can be determined either by the εb measurement or by a knee point in the velocity. The relaxation time was obtained to be τ = 3.1 ´ 10–12/(Tc – T) sec.

The polarization relaxation time measured by the dielectric dispersion measurement¹⁵) gave τ = (5.7 to 11) g 10–12/(Tc – T) sec. This value is in relatively good agreement with our result. E. Nakamura et al.³,¹⁵) claim that the TSCC transition has an order-disorder character from the dielectric measurement and X-ray structure analysis. However, even in a displacive ferroelectric, if the soft mode is over-damped, the system shows a character which is quite similar to that of order-disorder transition. In this case, the effective relaxation time is given by 58926.png . Here w0 is soft mode frequency and g is damping constant. Recently, very precise Raman spectroscopy⁷) has been done on this crystal by M. Sugo et al., placing special emphasis on the measurement of the

1.jpg

Fig 1. Temperature dependence of Brillouin shift ( 91681.png ) and linewidth ( 91683.png ) (FWHM) of longitudinal phonons in TSCC propagating along the [100] direction. The scattering geometry is x + y(zz) – x + y.

TO and LO soft modes. Their result of temperature dependence of the effective relaxation time gave 3.1 x 10–12/(Tc – T) sec which is identical with our value. The above results suggest that the dielectric relaxation is strongly related to the over-damped TO soft mode.

Slight anomalies in the shift and the linewidth in the PE phase are attributed to quadratic coupling of polarization and strain 59205.png . This type of anomaly is referred to as fluctuation damping.¹²) However, as we already mentioned in §1, we should be very careful about assert that this kind of anomaly is really of intrinsic character. Therefore, we measured Brillouin shift and linewidth in an excellent sample. The scattering geometry is x + y(zz) x – y and the dielectric constant εb was also measured during the Brillouin scattering measurement.

The high contrast of the triple-pass Fabry-Perot interferometer enabled us to determine the linewidth much more accurately than before. The temperature dependence of Brillouin shift of the q//[010] phonons is illustrated in Fig. 2. A comparison of this data with the former result of the shift of the q//[010] phonons leads us to the conclusion that there is no essential difference between these two results. Therefore, we can assert with high probability that this anomaly is intrinsic to the FE phase transition in TSCC.

2.jpg

Fig. 2. Temperature dependence of velocities of the q//[010] phonuns measured by right angle Brillouin scattering ( 91686.png ) and by small angle (θ = 7.6°) scattering ( 91688.png ).

3.jpg

Fig. 3. Temperature dependence of Brillouin linewidths of the q//[010] phonons of TSCC at ~ 21 GHz ( 91708.png ) and at ~ 2 GHz ( 91710.png ).

Figure 3 shows the temperature dependence of the linewidth (FWHM) which is expressed as a damping constant (I) devided by π in a simple exponential decay process.⁹) The linewidth increases with decreasing temperature and takes a maximum value at 126.5 K which is 3.5 K below the transition temperature.

The temperature dependence of the Brillouin shift and the damping constant is not so simple as that of piezoelectric coupling. For this we calculate the relaxation time at each temperature from the above data. According to the theory of sound attenuation and dispersion,¹⁶) the elastic stiffness c(ω) and damping constant (I) can be expressed as follows using complex elastic stiffness c*(ω),

4.jpg

where Δc is the difference between the high frequency limit elastic stiffness and the low frequency limit elastic stiffness. The other symbols have their usual meanings. From eqs. (2) and (3), the relaxation time is expressed by

5.jpg

Using extrapolated value of the stiffness around 140 K as c͚, the relaxation time was calculated as a function temperature. The result is shown in Fig. 4. The relaxation time shows rather unusual behavior which cannot be expressed in a simple power low of |Tc = T|.

The phonon velocity and the damping constant of the small angle scattering are also shown in Figs. 2 and 3. Although, the phonon frequency is one order of magnitude smaller that of right angle scattering, only small dispersion is observed. A large dip-like anomaly is reported in the ultrasonic velocity at 20 MHz.¹⁷) The damping constant at 2 GHz does not show a large anomaly as

6.jpg

Fig. 4. Temperature dependence of relaxation time deduced from the velocity and the damping constant of TSCC propagating in the [010] direction.

At 21 GHz. The anomaly is less than 10 MHz, if it exists. This range is consistent with the calculated 96744.jpg at 2 GHz from the velocity at 2 GHz and the relaxation time.

Determination of linewidth around 10 MHz is very difficult, because the accuracy of the measurement is limited not only by the resolution of the Brillouin spectrometer but also by the broadening of the incident laser light. Though we could not determine meaningful temperature dependence of the linewidth in the small angle scattering, the very narrow linewidth might suggest that the line broading from right angle scattering is not of static origin such as caused by itride variation of the refractive index, etc.

Considering the complicated feature of the temperature dependence of the relaxation time, the anomaly might not caused by a single origin such as energy fluctuations which arise from the 59403.png coupling term.¹²) Since the dipole-dipole interaction is very small in TSCC, a crossover behavior where the origin of the anomaly changes from dipole-dipole interaction dominant to short-range interaction dominant might be expected. For further investigation, Brillouin scattering of other than these two scattering angles together with precise ultrasonic measurements are strongly recommended.

Acknowledgement

The authors would like to express their gratitude to Prof. T. Ikeda for his useful suggestions and comments on this paper.

References

¹) Y. Makita; J. Phys. Soc. Jpn. 20 (1965) 2073.

²) T. Ashida, S. Bando and M. Kakudo: Acta Cryst. B 28 (1972) 1560.

³) N. Mishima, K. Itoh and E. Nakamura: Acta Cryst. C 40 (1984) 1824.

⁴) E. Sandvold and E. Courtens: Phys. Rev. B 27 (1983) 5660.

⁵) A. I. Larkin and D. E. Khmel’nitskii: Zh. Eksp. Teor. Fiz. 56 (1969) 2087 (Sov. Phys. -JETP 29 (1969) 1123).

⁶) S. D. Prokhorova, G. A. Smolensky, I. G. Siny, E. G. Kuzminov, V. D. Mikvabia and H. Arndt: Ferroelectrics 25 (1980) 629.

⁷) M. Sugo, M. Kasahara, M. Tokunaga and I. Tatsuzaki: J. Phys. Soc. Jpn. 53 (1984) 3234.

⁸) G. V. Kozlov, A. A. Volkov, J. F. Scott, G. E. Feldkamp and J. Petzelt: Phys. Rev. B 28 (1983) 255.

⁹) T. Hikita, P. T. Schnackenberg and V. H. Schmidt: Phys. Rev. B 31 (1985) 299.

¹⁰) G. A. Smolensky, I. G. Siny, A. T. Tagantsev, S. D. Prokhorova, V. D. Mikvabia and W. Windsch: Pis’ma v Zh. Eksp. Teor. Viz. 39 (1984) 307 and paper presented at The Third Soviet-Japanese Symposium on Ferroelectricity which was held in Novosibirsk, Sept. 9–14, 1984 (to be pubulished in Ferroelectrics, Vol. 63-64).

¹¹) M. A. Krivoglaz: Fiz. Tverd. Tela 5 (1963) 3439.

¹²) W. Rehwald: Adv. Phys. 22 (1973) 721.

¹³) B. A. Strukov, S. A. Taraskin, V. A. Fedorikin and K. A. Minaeva: Proceedings of The Second Japanese-Soviet Symposium on Ferroelectricity (J. Phys. Soc. Jpn. 49 (1980) Suppl. B) p. 7.

¹⁴) T. Hikita: J. Phys. Soc. Jpn. 53 (1984) 1513.

¹⁵) K. Deguchi, N. Aramaki, E. Nakamura and K. Tanaka: J. Phys. Soc. Jpn. 52 (1983) 1897.

¹⁶) For instance, K. F. Herzfeld and T. A. Litovitz: Absorption and Dispersion of Ultrasonic Waves (Academic, New York, 1959).

¹⁷) G. Sorge and U. Straube: Ferroelectrics 21 (1978) 533.

Physical Review B volume 34, number 1 1 JULY 1986

Anomalies Of Hypersound Velocity And Attenuation

In Ferroelectric Tris-Sarcosine Calcium Chloride

(TSCC) For Small-Angle And Right-Angle

Brillouin Scattering And Brillouin Backscattering

Jin Tong Wang and V. Hugo Schmidt

Department of Physics, Montana State University, Bozeman, Montana 59717

(Received 13 December 1985)

The Brillouin spectra of ferroelectric tris-sarcosine calcium chloride have been observed using small-angle and right-angle scattering and also backscattering. For different-frequency phonons along the same direction, analogous anomalies in the sound velocity and the attenuation are seen. The smallest angle we have achieved is 7.48°. The temperature and frequency dependences of the sound velocity are discussed. The fact that the linewidth maximum for [001] phonons occurs somewhat below Tc seems to indicate that the anomalies are due to piezoelectric coupling induced by spontaneous polarization below Tc. For [010] phonons the elementary relaxation times which relate to the energy are estimated as 59506.png see above Tc and 59515.png sec below Tc. The phonon attenuations are also estimated and compared with the observed ones. For the [001] phonons the elementary relaxation time is estimated as τ0 = 5.25 ´ 10–14 sec, in good agreement with the value obtained from right-angle Brillouin scattering.

Introduction

Tris-sarcosine calcium chloride (TSCC), formula (CH3NHCH2COOH)3CaCl2, was found to exhibit a ferroelectric (FE) phase transition at the Curie point, 130 K.¹(a) At that time it was claimed that the Curie point for this crystal was 127 K.¹(b) The crystal structure of TSCC is significant for both dielectric and the ultrasonic velocity anomalies. The TSCC crystal is orthorhombic with lattice constants a = 9.156±0.01, b = 17.460±0.045, and c = 10.265±0.005 Å, and with Z=4 formula units in the unit cell. The space group is Pnma 59529.png in the paraelectric (PE) phase and 59524.png in the FE phase.² According to the structural analysis by Ashida et al., the crystal structure of TSCC is pseudohexagonal when viewed down the a axis.³ There are 12 sarcosine zwitterion molecules in the unit cell. They are of two types. One comprises the four molecules in the mirror plane. The other eight molecules in general positions (type 2) are slightly bent. There are three kinds of N—H ‧ ‧ ‧ Cl hydrogen bonds present in TSCC, one with a total bond length of 3.18 Å and two with 3.22 Å, but with different N—H distances.⁴

Since the crystal at room temperature belongs to the orthorhombic system, it is optically biaxial. The acute bisectrix is the a axis, the optical plane is perpendicular to the c axis, and the crystal is optically positive.⁵

When the crystal undergoes the PE-FE transition, the reflection planes perpendicular to the FE b axis are suppressed.⁶ The sarcosine molecules in the crystal have the form

91800.png

which may have permanent dipole moments because of the NH2+ and COO– groups.⁵

The FE transition is a structural phase transition. Such transitions are generally divided into two categories, displacive and order-disorder. Particularly with TSCC there have been strong arguments about which category the FE transition falls into. However, a well-defined limit between these categories does not exist, and we consider that TSCC shows features of both transition types.

Chen and Schaack⁴ are the latest proponents of an order-disorder transition for TSCC. They interpret their infrared and Raman results in terms of a softening of an optical phonon caused by its interaction with an unspecified entity which relaxes rapidly due to thermally activated hopping across a double-minimum well barrier. The protons in hydrogen bonds presumably are ordered in the N––H ‧ ‧ ‧ Cl configuration at all temperatures because the anions are dissimilar. However, there may be ordering of the mirror-plane sarcosine molecules associated with motion of their methyl or carboxyl groups.⁵ The observation by Sandvold and Courtens⁶ of logarithmic behavior of dielectric susceptibility and spontaneous polarization over a temperature range as wide as 50 K indicates that there are dipole-dipole interactions in TSCC, in agreement with a report on the specific heat.⁷ It might thus turn out that TSCC is the best current example of uniaxial dipolar behavior in a ferroelectric. The spontaneous polarization is very small whereas Tc is large, so the ratio of dipolar energy to thermal energy (calculated by Lajzerowicz and Legrand⁸ for some other ferroelectrics) is quite small, of order 0.01. Another interesting property of this crystal is that the TO and LO phonons are underdamped and soften at the same temperature,⁹ which was interpreted as indicating that the transition is entirely displacive. These results also indicate that the short-range force and Coulomb force participate in the phase transition almost equally.¹⁰ Since there are such different indications of the strength of the dipole-dipole interaction, studies which may confirm the role of interactions are of particular interest.

One can expect two large anomalies in a Brillouin scattering study of TSCC. First, we can expect large anomalies in the velocity and attenuation of longitudinal phonons propagating along directions perpendicular to the polar axis.¹¹ These anomalies are caused by piezoelectric coupling in the FE phase. Because TSCC in the PE phase is centrosymmetric and hence not piezoelectric, this coupling is not intrinsic but rather is induced by the spontaneous polarization. From these anomalies we can evaluate the relaxation time of the polarization of the electric dipole system.¹² Second, Sorge and Straube¹¹ observed that at 20 MHz the longitudinal ultrasonic wave propagating along the polar axis b also shows large anomalies of attenuation and velocity near Tc. Because of the depolarization effect, in a system with electron-dipole––dipole interactions such as the dipole-dipole interaction along the b axis in TSCC, these anomalies are expected to occur not from piezoelectric coupling but from electrostrictive coupling.

We have performed small-angle and right-angle Brillouin scattering and Brillouin backscattering and have measured the dielectric constant simultaneously when performing the right-angle scattering. The frequency range in which we were working is about 2 GHz (for small-angle scattering) to 30 GHz (backscattering). The smallest angle we used is 7.48°. As far as we know, it is the smallest Brillouin scattering angle ever achieved. As usual, we evaluate the elementary relaxation times for phonons propagating along and perpendicular to the polar axis by investigating anomalies in their velocity and attenuation from Brillouin scattering. A remarkable feature of our experiment is the large frequency range (2–30 GHz) in which the sound velocity is apparently larger in backscattering than in small-angle and right-angle scattering.

Experimental Procedure

Single crystals of TSCC were grown from an aqueous solution of sarcosine and calcium chloride by slow cooling. The solution was prepared from chemicals of special quality and was filtered by a 0.2-mm-pore-size membrane filter. The sample is a carefully polished rectangular parallelepiped. Aluminum was evaporated onto two surfaces of the right-angle-scattering sample as electrodes for measurement of the dielectric constant ε0. This sample was annealed at 140°C for 20 h in an evacuated glass tube to improve the quality of the crystal.

The sample for the small-angle scattering and backscattering is also a parallelepiped which is 8 mm long along the a axis. This sample was not heat-treated.

Each sample was placed in an optical cell described previously.¹³ The optical cell is surrounded by two copper radiation shields with the outer shield connected directly to the liquid-nitrogen reservoir. The temperature in the inner shield was controlled at about 10 K lower than that of the optical cell. In this way, the temperature in the optical cell could be controlled within 3 mK during the measurement using a Lake Shore Cryotronics model CSC-400 temperature controller.

A Lexel model 95-2 argon-ion laser operating in a single mode at a wavelength of 5145 Å and a power level of 300 mW was used as a light source. In order to keep the difference of temperature between the sample and the temperature sensor constant, we kept the power level of the laser constant. The scattered light was collected in a cone of 0.4° and analyzed by a piezoelectrically scanned Burleigh model 140 Fabry-Perot interferometer. Finesse optimization and drift control were achieved by a homemade control system using an AIM-65 microcomputer and interface. The period of a single scan of the Fabry-Perot was about 10 s. The signal was stored in the microcomputer and displayed in a multichannel analyzer. The finesse of the spectrometer was typically 42–46. The laser line broadening due to the jittering was claimed by the manufacturer to be about 10 MHz FWHM (full width at half maximum). The angle of the incident light cone was about 0.458°.

For reducing the natural-phonon linewidth, the natural-phonon spectrum and the instrumental function were assumed to have Lorentzian distributions, and the broadening due to collection optics was assumed to have rectangular distribution. In this case, the natural-phonon linewidth (Wph) is given by¹²

59534.png

where Wobs, Winst, and Wang, represents the observed, instrumental, and collection optics linewidths, respectively. In our experiments, Winst =