TECHNICAL UNIVERSITY OF LIBEREC
FACULTY OF SCIENCES, HUMANITIES AND EDUCATION
DEPARTMENT of PHYSICS
PhD Thesis
Piezoelectric and Dielectric Studies of Ferroelectric Phase Transitions in Sn
2P
2(Se
xS
1-x)
6Crystals
______________________________________
Piezoelektrická a Dielektrická Studia Feroelektrických Fázových Přechodů v Krystalech Sn
2P
2(Se
xS
1-x)
6_______________________________________
Пьезоэлектрические и Диэлектрические Исследования Сегнетоэлектрических Фазовых Переходов в Кристаллах
Sn
2P
2(Se
xS
1-x)
6Author: Mgr. Iryna TYAGUR
Supervisor: Doc. RNDr. Antonín KOPAL, CSc.
Pages words figures tables references
129 23724 94 4 95
Liberec 2012
Prohlášení
Byla jsem seznámena s tím, že na mou disertační práci se plně vztahuje zákon č. 121/2000 Sb. o právu autorském, zejména § 60 – školní dílo.
Beru na vědomí, že Technická univerzita v Liberci (TUL) nezasahuje do mých autorských práv užitím mé diplomové práce pro vnitřní potřebu TUL.
Užiji-li disertační práci nebo poskytnu-li licenci k jejímu využití, jsem si vědoma povinnosti informovat o této skutečnosti TUL; v tomto případě má TUL právo ode mne požadovat úhradu nákladů, které vynaložila na vytvoření díla, až do jejich skutečné výše.
Disertační práci jsem vypracovala samostatně, s použitím uvedené literatury a na základě konzultací s vedoucím práce a konzultantem.
Datum
Podpis
ACKNOWLEDGEMENTS
My profound thanks to the Department of Physics, Technical University of Liberec, and all it’s team for given support and help during my study and research there.
I am thankful to the Institute of Physics and Chemistry of Uzhgorod National University for provided samples for my research work.
I would like to thank to S.S. Saxena and all the Quantum Group of Cavendish Laboratory, University of Cambridge, for given opportunity to realize my project, and for their help and support during the period of my research visits in Cambridge.
My profound gratitude is to my family, especially to my father for fruitful discussion and useful comments in various stages of my study.
I would like to thank to my supervisor, Antonin Kopal, for help and support during the period of my study at TUL, especially for supervising my research work.
Also I would like to say thank you to Jiri Erhart, for provided support, useful comments and notes to finalize my thesis.
Abstract
This thesis is devoted to a piezoelectric and dielectric studies of ferroelectric semiconductors of Sn2P2(SexS1-x)6 crystal family and their phase transitions due to an interesting physical properties and strong piezoelectric and pyroelectric effect. For further measurements crystals with different concentration of selenium were used. A special study is devoted to a frequency, temperature and pressure investigations of the dielectric and piezoelectric properties, also the electrical resistance measurements and their behavior in the vicinity of the phase transition point.
Keywords: piezoelectric, dielectric, Sn2P2S6, electrical resistance, phase transitions
Anotace
Tato disertační práce je věnována studiu piezoelektrických a dielektrických vlastností ferroelektrických polovodičových krystalů Sn2P2(SexS1-x)6 a jejich fázových přechodů z důvodu zajímavých fyzikálních vlastností a výrazného piezoelektrického a pyroelektrického jevu. Pro výzkum byly zvoleny krystaly s různou koncentrací selenu.
Zvláštní pozornost je věnována studiu elektrického odporu; frekvenčním, teplotním a tlakovým měřením dielektrických a piezoelektrických vlastností a jejich chování v okolí fázového přechodu.
Klíčová slova: piezoelektrický, dielektrický, Sn2P2S6, elektrický odpor, fázové přechody
Аннотация
Эта работа посвящена исследованию пьезоэлектрических и диэлектрических свойств сегнетоэлектрических полупроводников Sn2P2(SexS1-x)6 и их фaзовых переходов в связи с интересными физическими свойствами и хорошо выраженным пьезоэлектрическим и пироэлектрическим эффектом. Для исследования были использованы кристаллы с различными концентрациями селена. Особое внимание уделено частотным и температурным исследованиям диэлектрических и пьезоэлектрических свойств, а также измерениям электрического сопротивления и их поведению вблизи точки фазового перехода.
Ключевые слова: пьезоэлектрический, диэлектрический, Sn2P2S6, электрическое сопротивление, фазовые переходы
CONTENT
Outline ... 15
Chapter 1 ... 17
1. A BRIEF INTRODUCTION TO THE LANDAU THEORY OF PHASE TRANSITIONS ... 17
1.1. Second Order Phase Transitions ... 19
1.2. First Order Phase Transitions ... 21
1.3. Dielectric permittivity in paraelectric phase ... 24
1.4. Dielectric permittivity in ferroelectric phase ... 25
1.4.1. A second order phase transition ... 25
1.4.2. A first order phase transition ... 26
1.5. Incommensurate Phase and Lifshitz Point ... 26
Chapter 2 ... 30
2. INVESTIGATED SAMPLES AND THEIR PROPERTIES ... 30
2.1. Investigated Samples ... 30
2.1.1. Sn2P2S6 sample ... 30
2.1.2. Sn2P2Se6 sample ... 31
2.1.3. Ag0.10Cu0.90InP2S6 sample ... 31
2.2. Crystal Growth ... 32
2.3. Crystal Structure ... 32
2.4. x-T, p-T, E-T Phase Diagrams of Sn2P2(SexS1-x)6 ... 34
2.5. Anomalies of Macroscopic Parameters at Phase Transition ... 38
2.5.1. Spontaneous Polarization ... 38
2.5.2. Heat Capacity ... 40
2.5.3. Dielectric Permittivity ... 42
2.5.4. Dielectric Properties of Thin Films ... 44
2.5.5. Piezoelectric Properties of Ceramics and Composites ... 45
2.5.6. Ultrasonic and Piezoelectric Properties ... 48
Chapter 3 ... 50
3. MEASUREMENT METHODS AND TECHNIQUES ... 50
3.1. Sample Preparation ... 50
3.2. Measurements of Frequency Dependence ... 50
3.3. Piezoelectric Investigations ... 52
3.4. Dielectric Investigations ... 54
3.4.1. Temperature Chamber ... 54
3.4.2. Pumped Helium-3 Cryogenic System ... 55
3.5. Investigations of Electrical Resistance ... 61
3.5.1. Pressure Cell for Resistivity Measurements ... 61
Chapter 4 ... 64
4. RESULTS AND DISCUSSION ... 64
4.1. Results of Frequency Dependent Measurements ... 64
4.1.1. Sn2P2(Se0.05S0.95)6 crystal ... 64
4.1.2. Sn2P2(Se0.10S0.90)6 crystal ... 65
4.1.3. Sn2P2(Se0.25S0.75)6 crystal ... 67
4.1.4. Sn2P2S6 crystal ... 68
4.2. Piezoelectric Properties ... 69
4.3. Dielectric Properties ... 70
4.3.1. Dielectric Behavior Below Room Temperature ... 70
4.3.1.1. Sn2P2S6 Crystal ... 71
4.3.1.2. Sn2P2(Se0.05S0.95)6 Crystal ... 75
4.3.1.3. Sn2P2Se6 Crystal ... 79
4.3.2. Dielectric Behavior Above the Room Temperature ... 84
4.3.2.1. Sn2P2(Se0.05S0.95)6 Crystal ... 84
4.3.2.2. Sn2P2(Se0.10S0.90)6 Crystal ... 89
4.3.2.3. Sn2P2(Se0.25S0.75)6 Crystal ... 91
4.3.2.4. Ag0.10Cu0.90InP2S6 Crystal ... 95
4.3.3. Model of the Low Temperature Sensor on the Basis of investigated Sn2P2S6 Crystal ... 100
4.4. Electrical Resistance ... 105
4.4.1. Behavior of Electrical Resistance Below the Room Temperature ... 105
4.4.2. Electrical Resistance in the Vicinity of the Phase Transition ... 109
4.4.3. Investigations of Electrical Resistance of Sn2P2S6 under Pressure ... 115
4.4.3.1. Electrical Resistance up to 8 GPa ... 115
4.4.3.2. Electrical Resistance up to 25 GPa ... 117
References ... 124
List of Figures
Chapter 1
FIG.1.1.FREE ENERGY AS A FUNCTION OF POLARIZATION. ... 19
FIG.1.2.SECOND ORDER PHASE TRANSITION. ... 20
FIG.1.3.FIRST ORDER PHASE TRANSITION. ... 22
FIG.1.4.TEMPERATURE DEPENDENCE OF DIELECTRIC PERMITTIVITY OF RB2ZNCL4AT COOLING AND HEATING MODES IN THE VICINITY OF PHASE TRANSITION FROM INCOMMENSURATE TO COMMENSURATE POLAR PHASE ... 23
FIG.1.5.SCHEMATIC VARIATION OF POLARIZATION TOWARDS THE CURIE POINT ... 24
FIG.1.6. MODEL OF THE CRYSTAL WITH STRUCTURAL SAMPLE AB ... 27
FIG.1.7.MODEL OF THE PHASE SEQUENCE AS A FUNCTION OF TEMPERATURE ... 27
FIG.1.8.SCHEMATIC OPTICAL SOFT MODE AND A PHASE DIAGRAM FOR COMPOUNDS UNDERGOING PHASE TRANSITION TO THE INCOMMENSURATE PHASE IN THE VICINITY OF THE LP ... 28
Chapter 2 FIG.2.1. SAMPLE OF INVESTIGATED SN2P2S6 CRYSTAL AND FRAGMENT OF THE CRYSTAL STRUCTURE OF SN2P2S6 ... 33
FIG.2.2.PHASE DIAGRAM OF SN(PB)2P2S(SE)6 FERROELECTRICS ... 34
FIG.2.3. XT PHASE DIAGRAM OF SN2P2S(SE)6 ... 35
FIG.2.4. PT PHASE DIAGRAM OF SN2P2S6 ... 35
FIG.2.5. PT PHASE DIAGRAM OF SN2P2SE6 ... 36
FIG.2.6.ET PHASE DIAGRAMS OF THE SN2P2S6AT DIFFERENT VALUES OF THE HYDROSTATIC PRESSURE . 37 FIG.2.7. PET PHASE DIAGRAM OF THE SN2P2S6 ... 37
FIG.2.8.TEMPERATURE DEPENDENCE OF THE SPONTANEOUS POLARIZATION OF SN2P2S6 ... 39
FIG.2.9.DOMAIN STRUCTURE VISUALIZATION IN THE FERROELECTRIC PHASE OF SN2P2S6, USING NEMATIC LIQUID CRYSTALS ... 39
FIG.2.10.PHASE BOUNDARY BETWEEN THE INCOMMENSURATE (DARK AREA) AND COMMENSURATE FERROELECTRIC (LIGHT AREA) PHASES FOR SN2P2SE6 CRYSTAL ... 40
FIG.2.11.HEAT CAPACITY AND TRANSITION ENTROPY OF SN2P2S6 ... 40
FIG.2.12.HEAT CAPACITY AND TRANSITION ENTROPY OF SN2P2SE6 ... 41
FIG.2.13.TEMPERATURE DEPENDENCE OF DIELECTRIC PERMITTIVITY AND DIELECTRIC LOSSOF THE SN2P2S6 SINGLE CRYSTAL AT 1 KHZ,10 KHZ AND 100 KHZ ... 42
FIG.2.14.TEMPERATURE DEPENDENCE OF THE RECIPROCAL DIELECTRIC PERMITTIVITY OF THE SN2P2S6 AT FREQUENCY 100 KHZ ... 43
FIG.2.15.TEMPERATURE DEPENDENCES OF THE REAL AND IMAGINARY PARTS OF THE COMPLEX CAPACITY OF SN2P2S6 ... 44
FIG.2.16.FREQUENCY DEPENDENCES OF THE REAL AND IMAGINARY COMPONENTS OF THE COMPLEX CAPACITY AND COLE-COLE DIAGRAM FOR SN2P2S6AT TEMPERATURE 153K ... 44
FIG.2.17.FREQUENCY DEPENDENCES OF THE REAL AND IMAGINARY COMPONENTS OF THE COMPLEX CAPACITY AND COLE-COLE PLOTS AT TEMPERATURE 340K ... 45
FIG.2.18.TEMPERATURE DEPENDENCES OF THE DIELECTRIC PERMITTIVITY FOR PRESSED POWDERS OF SN2P2S6ANNEALED AT 500◦C FOR VARIOUS TIME ... 46
FIG.2.19.TEMPERATURE DEPENDENCES OF THE ULTRASONIC VELOCITY ALONG ZAXIS IN THE POLARIZED SN2P2S6SAMPLE. ... 49
Chapter 3 FIG.3.1.THE MODEL OF INVESTIGATED SAMPLE ... 50
FIG.3.2.SCHEME OF THE FREQUENCY DEPENDENCE MEASUREMENTS ... 51
FIG.3.3.DETAIL OF THE CHAMBER WITH CRYSTAL INSIDE ... 51
FIG.3.4.SCHEME OF THE MEASUREMENTS ... 53
FIG.3.5.SCHEME OF THE TEMPERATURE DEPENDENCE MEASUREMENTS ... 55
FIG.3.6.SCHEMATIC DIAGRAM OF THE TYPICAL SAMPLE BOARD: GOLD-PLATED COPPER PLATFORM ... 56
FIG.3.7.PHOTO OF THE MOUNTED AND CONNECTED SAMPLE ON THE BOARD ... 57
FIG.3.8.PHOTO A) SAMPLE BOARD WITH MOUNTED CRYSTAL CONNECTED TO THE MEASURING SYSTEM; B) SAMPLE CLOSED IN THE VACUUM TUBE FOR FURTHER MEASUREMENTS... 58
FIG.3.9. THE MAIN PARTS OF THE HELIOX SYSTEM ... 59
FIG.3.10.PHOTO OF THE HELIOX SYSTEM IN THE PROCESS OF MEASUREMENTS ... 60
FIG.3.11.PHOTO OF A PLASTIC SAMPLE BOARD FOR PRESSURE CELL WITH MOUNTED SAMPLES ... 62
FIG.3.12.PHOTO OF A PISTON CYLINDER PARTS ... 62
Chapter 4 FIG.4.1.FREQUENCY DEPENDENCES OF A) CAPACITY, B) DISSIPATION FACTOR OF SN2P2(SE0.05S0.95)6 IN AIR AND SILICONE OIL MEDIUM ... 64
FIG.4.2.FREQUENCY DEPENDENCES OF A) CAPACITY, B) DISSIPATION FACTOR OF SN2P2(SE0.10S0.90)6 IN AIR AND SILICONE OIL MEDIUM ... 66
FIG.4.3.FREQUENCY DEPENDENCES OF A) CAPACITY, B) DISSIPATION FACTOR OF SN2P2(SE0.25S0.75)6 IN AIR AND SILICONE OIL MEDIUM ... 67
FIG.4.4.FREQUENCY DEPENDENCES OF THE CAPACITY OF SN2P2S6 AT VARIOUS TEMPERATURES IN A) FERROELECTRIC AND B) PARAELECTRIC PHASE ... 68
FIG.4.5.PRESSURE DEPENDENCES OF THE HYDROSTATIC DYNAMIC PIEZOELECTRIC COEFFICIENT DH,D OF SN2P2S6SAMPLE AT VARIOUS TEMPERATURES: ... 69
FIG.4.6.PRESSURE DEPENDENCES OF THE COEFFICIENT GH(P,T) FOR SN2P2S6 SINGLE CRYSTAL AT VARIOUS TEMPERATURES ... 70
FIG.4.7.TEMPERATURE DEPENDENCES OF THE IMPEDANCE AT DIFFERENT FREQUENCIES FOR SN2P2S6 SAMPLE ... 71
FIG.4.8.TEMPERATURE DEPENDENCES OF THE PHASE ANGLE AT DIFFERENT FREQUENCIES FOR SN2P2S6 SAMPLE ... 72
FIG.4.9.TEMPERATURE DEPENDENCES OF THE SPECIFIC IMPEDANCE OF SN2P2S6AT DIFFERENT FREQUENCIES ... 72
FIG.4.10. TEMPERATURE DEPENDENCES OF THE REAL PART OF DIELECTRIC PERMITTIVITY AT DIFFERENT FREQUENCIES FOR SN2P2S6 ... 73
FIG.4.11.TEMPERATURE DEPENDENCES OF THE IMAGINARY PART OF DIELECTRIC PERMITTIVITY AT DIFFERENT FREQUENCIES FOR SN2P2S6 ... 73
FIG.4.12.TEMPERATURE DEPENDENCES OF THE REAL | AND IMAGINARY PART| OF DIELECTRIC PERMITTIVITY AT TEMPERATURE 7 – 140 K A), B) AND 140 240 K C), D) FOR SN2P2S6CRYSTAL AT DIFFERENT FREQUENCIES ... 74
FIG.4.13.TEMPERATURE DEPENDENCE OF THE RECIPROCAL DIELECTRIC PERMITTIVITY OF SN2P2S6 ... 75
FIG.4.14.TEMPERATURE DEPENDENCE OF IMPEDANCE AT DIFFERENT FREQUENCIES FOR SN2P2(SE0.05S0.95)6 CRYSTAL ... 76
FIG.4.15.TEMPERATURE DEPENDENCE OF PHASE ANGLE AT DIFFERENT FREQUENCIES FOR SN2P2(SE0.05S0.95)6CRYSTAL ... 76
FIG.4.16.TEMPERATURE DEPENDENCES OF THE SPECIFIC IMPEDANCE OF SN2P2(SE0.05S0.95)6 CRYSTAL AT DIFFERENT FREQUENCIES ... 77
FIG.4.17.TEMPERATURE DEPENDENCE OF THE REAL PART OF THE DIELECTRIC PERMITTIVITY FOR SN2P2(SE0.05S0.95)6CRYSTAL ... 78
FIG.4.18.TEMPERATURE DEPENDENCE OF IMAGINARY PART OF THE DIELECTRIC PERMITTIVITY FOR SN2P2(SE0.05S0.95)6CRYSTAL ... 78
FIG.4.19. TEMPERATURE DEPENDENCE OF THE RECIPROCAL DIELECTRIC PERMITTIVITY OF SN2P2(SE0.05S0.95)6CRYSTAL ... 79
FIG.4.20.TEMPERATURE DEPENDENCE OF IMPEDANCE AT DIFFERENT FREQUENCIES FOR SN2P2SE6SAMPLE ... 79
FIG.4.21.TEMPERATURE DEPENDENCE OF PHASE ANGLE A AT DIFFERENT FREQUENCIES FOR SN2P2SE6 SAMPLE ... 80
FIG.4.22.DEPENDENCE OF THE SPECIFIC IMPEDANCE OF SN2P2SE6AT DIFFERENT FREQUENCIES ... 81
FIG.4.23. TEMPERATURE DEPENDENCE OF THE REAL PART OF DIELECTRIC PERMITTIVITY OF SN2P2SE6 MEASURED AT DIFFERENT FREQUENCIES ... 81
FIG.4.24.TEMPERATURE DEPENDENCE OF THE IMAGINARY PART OF DIELECTRIC PERMITTIVITY OF SN2P2SE6 MEASURED AT DIFFERENT FREQUENCIES ... 82
FIG.4.25. TEMPERATURE DEPENDENCE OF THE RECIPROCAL DIELECTRIC PERMITTIVITY OF SN2P2SE6 AT ... 82
FIG.4.28. TEMPERATURE DEPENDENCES OF THE CONDUCTIVITY FOR SN2P2(SE0.05S0.95)6 CRYSTAL AT FREQUENCIES 1 KHZ,5 KHZ AND 10 KHZ ... 86 FIG.4.29. TEMPERATURE DEPENDENCES OF THE RECIPROCAL DIELECTRIC PERMITTIVITY OF
SN2P2(SE0.05S0.95)6IN HEATING AND COOLING MODES AT FREQUENCY 1 KHZ. ... 86 FIG.4.30. TEMPERATURE DEPENDENCE OF THE RECIPROCAL DIELECTRIC PERMITTIVITY FOR
SN2P2(SE0.05S0.95)6IN COOLING MODE AT FREQUENCY 1 KHZ ... 87 FIG.4.31.TEMPERATURE DEPENDENCE OF THE RECIPROCAL DIELECTRIC PERMITTIVITY FOR
SN2P2(SE0.05S0.95)6IN THE VICINITY OF THE PHASE TRANSITION TEMPERATURE IN COOLING MODE AT FREQUENCY 1 KHZ ... 88 FIG.4.32.TEMPERATURE DEPENDENCES OF THE A) REAL AND B)IMAGINARY PART OF THE DIELECTRIC
PERMITTIVITY FOR SN2P2(SE0.10S0.90)6CRYSTALIN HEATING AND COOLING MODES AT FREQUENCY
1 KHZ ... 90 FIG.4.33.TEMPERATURE DEPENDENCES OF THE A) REAL AND B) IMAGINARY PART OF THE DIELECTRIC
PERMITTIVITY FOR SN2P2(SE0.25S0.75)6CRYSTALIN HEATING AND COOLING MODES AT FREQUENCY
1 KHZ ... 92 FIG.4.34. TEMPERATURE DEPENDENCE OF THE RECIPROCAL DIELECTRIC PERMITTIVITY OF
SN2P2(SE0.25S0.75)6 IN HEATING AND COOLING MODES AT FREQUENCY 1KHZ ... 93 FIG.4.35. TEMPERATURE DEPENDENCE OF THE RECIPROCAL DIELECTRIC PERMITTIVITY OF
SN2P2(SE0.25S0.75)6 IN COOLING MODE AT FREQUENCY 1KHZ ... 94 FIG.4.36.FREQUENCY SPECTRUM OF THE CAPACITY AND DISSIPATION FACTOR OF AG0.10CU0.90INP2S6 ... 96 FIG.4.37.FREQUENCY DEPENDENCES OF THE DIELECTRIC PERMITTIVITY AND DIELECTRIC LOSS OF
LAMELLAR AG0.10CU0.90INP2S6 ... 96 FIG.4.38.TEMPERATURE DEPENDENCE OF THE REAL AND IMAGINARY PART OF DIELECTRIC PERMITTIVITY
OF AG0.10CU0.90INP2S6CRYSTAL AT FREQUENCIES 1 KHZ,5 KHZ AND 10 KHZ ... 97 FIG.4.39.TEMPERATURE DEPENDENCE OF THE DIELECTRIC DISSIPATION FACTOR OF AG0.10CU0.90INP2S6
CRYSTAL AT FREQUENCIES 1 KHZ,5 KHZ AND 10 KHZ ... 97 FIG.4.40. TEMPERATURE DEPENDENCE OF THE RECIPROCAL DIELECTRIC PERMITTIVITY OF
AG0.10CU0.90INP2S6AT FREQUENCIES 1 KHZ,5 KHZ AND 10 KHZ ... 98 FIG.4.41. TEMPERATURE DEPENDENCE OF THE RECIPROCAL DIELECTRIC PERMITTIVITY OF
AG0.10CU0.90INP2S6AT FREQUENCY 1 KHZ ... 99 FIG.4.42.TEMPERATURE DEPENDENCES OF THE SPECIFIC IMPEDANCE FOR SN2P2S6,SN2P2(SE0.05S0.95)6, AND
SN2P2SE6 CRYSTALS AT FREQUENCY 10 KHZ ... 101 FIG.4.43.(A)TEMPERATURE DEPENDENCES OF ALTERNATING CURRENT I(T);(B) THE DERIVATIVE OF
ALTERNATING CURRENT DI(T)/DT;(C) THE RELATIVE TEMPERATURE COEFFICIENT OF ALTERNATING CURRENT IN FERROELECTRIC PHASE FOR SN2P2S6,SN2P2(SE0.05S0.95)6, AND SN2P2SE6SAMPLES ... 104 FIG.4.44.TEMPERATURE DEPENDENCES OF THE RESISTANCE OF SN2P2S6AT FREQUENCIES 10,25 AND
50KHZ ... 106 FIG.4.45.TEMPERATURE DEPENDENCES OF THE REACTANCE OF SN2P2S6AT FREQUENCIES 10,25 AND
50KHZ ... 106 FIG.4.46.TEMPERATURE DEPENDENCE OF THE RESISTANCE SN2P2(SE0.05S0.95)6AT FREQUENCIES 10,25 AND
50KHZ ... 107 FIG.4.47.TEMPERATURE DEPENDENCE OF THE REACTANCE OF SN2P2(SE0.05S0.95)6AT FREQUENCIES 10,25
AND 50 KHZ ... 108 FIG.4.48.TEMPERATURE DEPENDENCE OF THE RESISTANCE OF SN2P2SE6AT FREQUENCIES 10,25 AND
50KHZ ... 108 FIG.4.49.TEMPERATURE DEPENDENCE OF THE REACTANCE OF FOR SN2P2SE6AT FREQUENCIES 10,25 AND
50KHZ ... 109 FIG.4.50.PRESSURE DEPENDENCES OF THE ELECTRICAL RESISTANCE FOR Sn2P2S6 CRYSTALS:(A) ( p),
SAMPLE NO.1, UNIPOLAR,Т = 292.0 K;(B) R( p), SAMPLE NO.2, UNIPOLAR,Т=284.2 K;(C) R( p),
SAMPLE NO.2, MONODOMAIN,Т = 286.5 K ... 112 FIG.4.51.DEPENDENCES OF THE RELATIVE PRESSURE COEFFICIENT OF ELECTRICAL RESISTANCE VERSUS
PRESSURE FOR SAMPLES: ... 114 FIG.4.52.DEPENDENCE R(P) FOR SN2P2S6 CRYSTAL AT DIFFERENT TEMPERATURES.CURVES 1DI,2DI,3DI –
PRESSURE INCREASE;1RE,2RE,3RE – PRESSURE DECREASE AT DIFFERENT TEMPERATURES ... 116 FIG.4.53.PRESSURE DEPENDENCE OF THE BAND GAP ENERGY OF SN2P2S6 AT FIXED TEMPERATUR……..117 FIG.4.54.THE PRESSURE DEPENDENCES OF THE ELECTRICAL RESISTANCE OF SN2P2S6 AT ROOM
TEMPERATURE THE LABELS #1 AND #2 MARK DIFFERENT SAMPLES.THE INSET SHOWS A PRESSURE VARIATION OF THE ENERGY GAP.91 ... 118
FIG.4.55.OPTICAL ABSORBANCE SPECTRA OF THE ORIGINAL AND RECOVERED FROM HIGH-PRESSURE
SAMPLES OF SN2P2S6.THE ORIGINAL SAMPLE HAS AN ABRUPT ABSORPTION EDGE NEAR 2.3 EV,
WHILE THE RECOVERED ONE SHOWS ITS SMOOTHING DOWN TO 1.5 EV. ... 119
List of Tables
TABLE I.DIELECTRIC AND ELECTROMECHANICAL PROPERTIES OF SN2P2S6 CERAMICS AND SN2P2S6+EPOXY COMPOSITE (WITH 84.7 VOL% OF SN2P2S6) AT THE ROOM TEMPERATURE IN COMPARISON WITH THE PROPERTIES OF THE POROUS PZT ... 47 TABLE II.AN OVERVIEW OF PHYSICAL PROPERTIES OF SN2P2S678,79,92 ... 48 TABLE III. APPROXIMATION COEFFICIENTS OF log(z0(T)) DEPENDENCES BY FOURTH-ORDER
POLYNOMIAL IN FERROELECTRIC PHASE FOR SAMPLES SN2P2S6,SN2P2(SE0.05S0.95)6, AND SN2P2SE6 AT
10 KHZ,FIG.4.42 ... 102 TABLE IV.PHYSICAL PARAMETERS OF APPROXIMATION FOR DEPENDENCER( p) ... 113
Outline
Since 1880 when Jacques and Pierre Curie originally discovered a piezoelectric effect, the commercial success of piezoelectric elements attracted the attention of industry and spurred a new effort to develop successful products. Development of electronics and discovery of ferroelectrics increased the practical use of piezoelectric materials. The ferroelectric effect was first observed by Valasek in 1921, in the Rochelle salt. The effect was not considered for some time then. Only a few decades ago ferroelectrics came into wider use. Applications as actuators and sensors for noise and vibrations control have been demonstrated extensively over the last years of the end of XXth century. During this period, several technologies were developed to use the piezoelectric and ferroelectric materials and each of these technologies has become an essential component of many types of electronic products in our daily life. In just over 100 year’s piezoelectricity moved from being a laboratory curiosity to a big business.
However, the search for a perfect material still continues. Piezoelectric and ferroelectric materials have now been in use for decades, but they are still an expanding field. Their use in computing will only increase as they are miniaturized. However, to do this, the way in which their properties vary has to be understood, so this will be a target for future research. Ferroelectrics will be used in the future, as their properties are unique.
The thesis is devoted to a family of Sn2P2(SexS1-x)6 displacive ferroelectrics and investigations of their properties as a function of frequency, temperature or pressure.
The main goals and targets of the work are:
to investigate a group of Sn2P2(SexS1-x)6 ferroelectric semiconductors with different substitution of selenium
tо investigate the dielectric and piezoelectric properties under the influence of different parameters (frequency, temperature, pressure)
to investigate the dielectric and piezoelectric behavior of crystals in the vicinity of the phase transition point
to investigate new lamellar Ag0.10Cu0.90InP2S6 samples and their dielectric behavior in the vicinity of the phase transition temperature
to study dependences of the electrical resistance of the Sn2P2(SexS1-x)6
samples under the influence of pressure
to investigate resistance’s behavior in the vicinity of the phase transition pressure
The thesis consists of four chapters. First chapter gives a brief introduction to the theory of phase transitions. A second chapter contains an introduction to investigated samples and their properties. The third chapter is devoted to the description of measurement methods and techniques. Results of investigations and their discussion are presented in the fourth chapter.
Chapter 1
1. A BRIEF INTRODUCTION TO THE LANDAU THEORY OF PHASE TRANSITIONS
In general, a phase transition or a phase change is the transformation of a thermodynamic system from one phase to another. The first attempt of classifying phase transitions was the Ehrenfest classification scheme. Under this scheme, phase transitions were labeled by the lowest derivative of the free energy that is discontinuous at the transition.
We briefly consider basic concepts of phase transitions theory. A ferroelectric material has a permanent electric dipole, and it is named in analogy to a ferromagnetic material (e.g. Fe) that has permanent magnetic dipoles. It is clear from thinking about examples that ferroelectricity is prohibited if there is a center of symmetry. If a center of symmetry is not present, the crystal classeshave one or more polar axes. Those that have a singular polar axis are ferroelectric and have a spontaneous electrical polarization. The others show the piezoelectric effect, wherein an electrical polarization is induced by application of an elastic stress; extension or compression will induce electrical polarization. Polarization is defined as dipole moment per unit volume.
Any crystal in a thermodynamic equilibrium state can be completely specified by the values of a number of variables, for example temperature, entropy, electric field, polarization, stress and strain. Usually we are in a situation where we are applying externally electric fields and elastic stresses, so we can regard the polarization and strain as dependent variables.
A fundamental postulate of thermodynamics is that the free energy can be expressed as a function of the ten variables (three components of polarization, six components of the stress tensor, and temperature). The second important thermodynamic principle is that the values of the dependent variables in thermal equilibrium are obtained at the minimum of the free energy.
The approximation in Landau-Ginzburg-Devonshire theory is just to expand the free energy in powers of the phase transition parameter with unknown coefficients (which can be fit by experiment). To be specific, let us take a simple example where we expand the free energy in terms of a single component of the polarization, and ignore
the strain field. This might be appropriate model for a uniaxial ferroelectric. We shall choose the energy for the free unpolarised unstrained crystal to be zero. For simplicity we shall restrict ourselves to the case of uniaxial ferroelectric with one component order parameter P:
P E P P
P E
T p E
T p
P
0 2 4 6
6 4
) 2 , , ( ) , , ,
(
(1.1.) where 0 is the thermodynamic potential density for paraelectric phase, P is polarization (the order parameter), E is electric field; coefficients , , are in general temperature dependent and may have any sign. The direction and magnitude of polarization vector corresponds to the minimum of the thermodynamic potential at fixed temperature in ferroelectric phase and determines its symmetry. Thus, in the ferroelectric crystals, the order parameter of phase transition has a specific physical meaning; it coincides with one of the internal parameters of the crystal as a thermodynamic system the spontaneous polarization PS.
For simplicity, in Landau theory, only coefficient is considered to be temperature dependent. For reasons of stability coefficient has to be positive in either case. Therefore, order of the transition is determined by the sign of the coefficient .
Temperature dependent coefficient can be expressed as the first order term of a Taylor’s series in (TT0):
)
( 0
0 TT
(1.2.) where 0 > 0. Therefore, coefficient is negative ( < 0) for ferroelectric phase. At the same time value of polarization has positive and negative values PPS, reflecting the presence of two domains in the ferroelectric phase. For paraelectric phase, value of coefficient is positive ( > 0); value of polarization equals to zero at the minimum of free energy. At the point of phase transition, coefficient is equal to zero.
FIG.1.1. Free energy as a function of polarization for (a) a paraelectric material, and for (b) a ferroelectric material1 Litllewood
The equilibrium configuration is determined by finding the minima of thermodynamic potential density, where we shall have
P
=0 (1.3.) If , , are all positive, the thermodynamic potential (for E = 0) has a minimum at zero polarization (FIG.1.1, a). In this case we can ignore the higher order terms than quadratic to estimate the polarization induced by an electric field from:
0
P E
P (1.4.) Therefore we have a relationship between the polarization and the field (in linear response, for small electric field) which defines the dielectric susceptibility :
1
2
2
P (1.5.) Next two paragraphs are focused on the discussion of twp different cases of phase transitions with respect to the sign of coefficient (Eq. 1.1).
1.1. Second Order Phase Transitions
If the parameters are such that < 0, while and > 0 (Eq.1.1.), then the free energy will look like in FIG.1.1, b, which has a minimum at a finite polarization. Here, the ground state exists at the non-zero spontaneous polarization PS and thus it is ferroelectric.
5 0
3
S S S S
P P P P
P P
(1.6.)
In this case we can neglect higher order terms than cubic to estimate the spontaneous polarization:
) ( 0
) (
0
0 0
2
T T P
P P
P
S S
S
S
(1.7.)
Therefore, for a second order phase transition there is a quadratic dependence of polarization versus temperature, see FIG.1.2, b.
Below, there is an example of a second-order or continuous phase transition in FIG.1.2. The order parameter (here the spontaneous polarization) vanishes continuously at the transition temperature T0 = TC, FIG.1.2, b. Second-order phase transition has a discontinuity in a second derivative of the free energy, FIG.1.2, c.
FIG.1.2. Second order phase transition. (a) Free energy as a function of the polarization at temperature T > T0, T = T0, and T < T0; (b) Spontaneous polarization P0(T) as a function of temperature; (c) Inverse of the susceptibility, where P/E is evaluated at the equilibrium polarization P0(T)1 Litllewood
Thus, ferroelectrics loose their intrinsic polarization at temperatures above a transition temperature and become paraelectric. Above the transition temperature the electrical susceptibility of the substance follows the Curie-Weiss law:
TC
T C
(1.8.)
where C is a material-specific Curie constant, T is absolute temperature and TC is the Curie temperature. Thus, the susceptibility approaches infinity as the temperature approaches TC.
Among other things, the order of the ferroelectric transition is determined by the way in which the polarization goes from the value zero to a finite value, whether the onset of PS is continuous or discontinuous. In the case of second order transition, the polarization PS is continuous.
1.2. First Order Phase Transitions
However, we should consider the case of < 0 (while remains positive, (Eq.1.1.). This is sketched in FIG.1.3, a. The parameter remains the reciprocal susceptibility at constant stress in the non-polar phase and again the basic assumption is that it can be written in Curie-Weiss form.
Relation between polarization and electric field can be found from equation (1.1.), using conditions of minima of thermodynamic potential (1.3.).
Using this condition and condition of zero potential at T = TC we can find the value of spontaneous polarization for the first order phase transition:
6 0 1 4
1 2
1
0
6 4
2
5 3
S S
S
S S S
P P
P
P P P
(1.9.)
22 0 2 0
2 4 ( )
1 2 1
4 ) 2
(
T T
T P
(1.10.)
With the quadratic coefficient negative Eq.1.1, it should be clear that even if T > T0 (so the quadratic coefficient is positive) the free energy may have a subsidiary minimum at non-zero P. As is reduced (the temperature lowered), this minimum will drop in energy below that of the unpolarised state, and so will be the thermodynamically favored configuration. The temperature at which this happens is the Curie temperature TC (by definition), which however now exceeds T0. At any temperature between TC and T0 the unpolarised phase exists as a local extreme of the free energy. The most important feature of this phase transition is that the order parameter jumps discontinuously to zero at TC. This type of phase transition is usually called a first-order
or discontinuous transition. Other common examples of this type of transition are solid- liquid transitions.
FIG.1.3. First order phase transition. a) Free energy as a function of the polarization at T > TC, T = TC, and T = T0 < TC; (b) Spontaneous polarization P0(T) as a function of temperature; (c) Susceptibility1Litllewood
Experimentally, it is often difficult to establish whether the polarization or other quantities are discontinuous or not at the transition temperature. For this reason, it has been suggested that a better definition of a first order transition is coexistence of two equilibrium states at the transition temperature, so that a definite phase boundary if formed. This definition is also subject to experimental limitations, 2Lines. The most ferroelectric phase transitions are not of the second order, but the first order, with a discontinuity in the first derivatives of the thermodynamic potential. The discontinuous change in polarization causes a discontinuous behavior in entropy and a latent heat at temperature TC.
Materials which undergo a first order transitions undergo thermal hysteresis, such that the transition occurs at different temperatures depending on whether the material is being heated or cooled (FIG.1.4). This makes the Curie point unreliable.
FIG.1.4. Temperature dependence of dielectric permittivity of Rb2ZnCl4 at cooling (1) and heating (2) modes in the vicinity of phase transition from incommensurate to commensurate polar phase6Gridnev
For a first order phase transition, the permittivity is finite, but discontinuous at TC. Since the first order phase transition does not reflect any singularity in the thermodynamic potential, the low temperature phase can exist at temperatures above TC
as a metastable phase. In practice such metastable states do tend to persist for a first order ferroelectrics and the actual transition temperature is often found to occur at somewhat higher temperature if reached from the low rather than the high temperature side. This effect is called the thermal hysteresis (FIG.1.4).
The behavior of polarization, as the order parameter for second and the first order transition is shown below.
FIG.1.5. Schematic variation of polarization towards the Curie point4
Consequently, considering the type of the phase transition, the second order phase transition exhibits a continuous change of the polarization (order parameter) and no temperature hysteresis. As for the first order phase transition, jumps in the order parameter and the temperature hysteresis are expected together with the presence of the latent transition heat.
1.3. Dielectric permittivity in paraelectric phase
Let us consider the behavior of dielectric permittivity in paraelectric phase.
Using condition of minima of thermodynamic potential (Eq.1.7.) we can express the reciprocal value of0 as:
2 2 4
2 0
5 1 3
P P P
dP
dE
(1.11.) In paraelectric phase, where (T > T0), polarization P = 0. Then, for low electric fields, temperature dependence of dielectric permittivity in paraelectric phase, (T)pa
obeys Curie-Weiss Law (Eq.1.6.) and can be written as:
) (
) (
1 ) 1
(
0 , 0
0 0
0 T T
C T
T pa T W pa
(1.12.)
Therefore, experimental results -1(T) could be approximated by the following linear equation:
