SYNTHESIS AND CHARACTERIZATION OF
BaTiO3 FERROELECTRIC MATERIAL
By KOLTHOUM ISMAIL OSMAN
A Thesis Submitted to the Faculty of Engineering, Cairo University In Partial Fulfillment of the Requirements for the Degree of DOCTOR OF PHILOSOPHY
In METALLURGICAL ENGINEERING
FACULTY OF ENGINEERING, CAIRO UNIVERSITY GIZA, EGYPT 2011 SYNTHESIS AND CHARACTERIZATION OF
BaTiO3 FERROELECTRIC MATERIAL
By KOLTHOUM ISMAIL OSMAN
A Thesis Submitted to the Faculty of Engineering, Cairo University In Partial Fulfillment of the Requirements for the Degree of DOCTOR OF PHILOSOPHY
In METALLURGICAL ENGINEERING
Under The Supervision of
Prof. Dr. F. A. ELREFAIE Metallurgy Dept., Cairo Univ. Prof. Dr. M. El-SAYED ALI Metallurgy Dept., Atomic E. A. Prof. Dr. R. ABDEL-KARIM Metallurgy Dept., Cairo Univ.
FACULTY OF ENGINEERING, CAIRO UNIVERSITY GIZA, EGYPT 2011 SYNTHESIS AND CHARACTERIZATION OF
BaTiO3 FERROELECTRIC MATERIAL
By KOLTHOUM ISMAIL OSMAN
A Thesis Submitted to the Faculty of Engineering, Cairo University In Partial Fulfillment of the Requirements for the Degree of DOCTOR OF PHILOSOPHY
In METALLURGICAL ENGINEERING
Approved by the Examining Committee Prof. Dr. F. A. ELREFAIE Metallurgy Dept., Cairo Univ. Prof. Dr. M. El- SAYED ALI Metallurgy Dept., Atomic E. A. Prof. Dr. S. M. EL-RAGHY Metallurgy Dept., Cairo Univ. Prof. Dr. WAFA I. ABDEL-FATTAH National Research Center.
FACULTY OF ENGINEERING, CAIRO UNIVERSITY GIZA, EGYPT 2011
Contents List of Figures ………………………………………………………….... IV List of Tables ……………………………………………………………. VII List of Acronyms, Abbreviations...………………………………………. VIII List of Symbols and Definitions …………………………………………. IX Acknowledgment ………………………………………………………... X Abstract ………………………………………………………………….. XI CHAPTER (1) Introduction………………………………...………………………….. 1 CHAPTER (2)
Literature Review
Part-I: Ferroelectric Properties 3 2.1. Electrical Ceramics………………………………………………… 3 2.1.1. Dielectric Materials……………………………………………… 4 2.1.1.1 Dielectric Constant…………………………………………..... 7 2.1.1.2. Dielectric Loss………………………………………………... 9 2.1.1.3. Dielectric Strength ……………..…………………………….. 9 2.1.2. Piezoelectricity…………………………………………………... 10 2.1.3. Pyroelectricity ...………………………………………………… 11 2.1.4. Ferroelectricity ………………………………………………….. 12 2.2. Ferroelectric Materials …………………………………………… 16
2.2.1. Lead Titanate (PbTiO3, PT) ……………………………………... 16
2.2.2. Lead Zirconate Titanate {Pb(ZrxTi1-x)O3,PZT} ………………… 16 2.2.3. Lead Lanthanum Zirconate Titanate (PLZT) …………………… 17 2.2.4. Lead Magnesium Niobate (PMN) ………………………………. 18
2.2.5. Barium Titanate (BaTiO3) ………………………………………. 19
2.2.5.1. Methods of Preparation of BaTiO3 …………………………... 22 I- Solid-state reaction method …………………………………. 22 II- Chemistry-based methods..………………………………….. 24 III- Other methods ………………………………………………. 26
I 2.2.5.2. Effect of Dopants or Additives on BaTiO3 Properties ………. 28 2.3. Applications of Ferroelectric Ceramics ………………………….. 29 2.3.1. Ceramic Capacitors ……………………………………………… 30 2.3.2. Types of Ceramic Capacitors ……………………………………. 32 2.3.3. Functions of The Capacitors ……………………………………. 33
2.4. Part-II: Kinetics and Thermodynamic Studies on Barium
Titanate Formation …………………………………..………………… 34 2.4.1. Types of Chemical Reactions …………………………………… 34 2.4.2. Reaction Kinetics …………………………………..…………… 35 2.4.2.1. Theory …………………………………..……………………. 35 2.4.2.1.1. Generalized Kinetic Equation ……………………………... 35 2.4.2.1.2. Reaction Kinetic Techniques ……………………………… 37 2.4.2.1.2.1. Isothermal Reaction Kinetics …………………………. 37 I- Model equation …………………………………..……… 37 II- Model free equation …………………………………..… 37 2.4.2.1.2.2. Non-Isothermal Reaction Kinetics …………………… 37 I. Constant reaction rate technique ………………………… 37 II. Constant heating rate technique …………………………. 38 a- Kinetic model determination …………………………. 38 b- Model free kinetics …………………………………... 39 2.5. Thermodynamics of the Chemical Reactions …………………. 39 2.6. Experimental Techniques …………………………………..…..… 41 CHAPTER (3) Experimental Work…………………………………………………… 43
3.1. Materials for The Preparation of BaTiO3 Powder ……………… 43 3.1.1. Titanium Dioxide Powders………………………………………. 43
3.1.1.1. Preparation of TiO2-c fine powder from TiCl4 ……………… 43 3.2. Instruments …………………………………..……………………. 44
3.3. Methods of Preparation of The BaTiO3 Powder………………. 46
II 3.3.1. BaCO3/TiO2-c Powder Mixture (High-energy ball milling process) ………………………………. 46
3.3.2. Ba(NO3)2/TiO2-c Powder Mixture……………………………..... 47 3.4. Materials Characterization ………………………………………. 48
3.4.1. BaTiO3 Powder Characterization ……………………………….. 48 3.4.1.1. Thermal analyses……………………………………………... 48 3.4.1.2. Phase analyses and the crystallite size ………………………. 48 3.4.1.3. Specific surface area (BET) …………………………………. 49 3.4.2. Reaction Kinetics …………………………………..…………… 49 3.4.3. Pressing and Sintering …………………………………..………. 49 3.4.4. Density Measurement …………………………………..……….. 49 3.4.5. Dilatometric Study …………………………………..……….…. 50 3.4.6. Microstructure …………………………………..………………. 50 3.4.7. Dielectric Properties …………………………………..………… 50 CHAPTER (4) Results……….…………………….…………………..………………… 52 4.1. Powder Characterization ………………………….………..…… 52
4.1.1. BaCO3-TiO2 Powder Mixture …………………………………... 52
4.1.1.1. BaCO3-TiO2 starting powders ……………………………….. 52 4.1.1.1.1. Thermal analysis (DTA &TGA) ………………………… 52 4.1.1.1.2. SEM of the starting powders …………………………..… 53
4.1.1.2. BaCO3/TiO2-c milled powder mixtures ……………………... 54 4.1.1.2.1. Thermal analysis (DTA &TGA)…………………………. 54
4.1.1.2.2. SEM of the BaCO3/TiO2-c milled mixture………………. 55 4.1.1.2.3. Dilatometric study (TMA)……………………………….. 56
4.1.1.2.4. X-Ray Diffraction of the BaCO3/TiO2-c milled mixture… 58
4.1.1.3. Characterization of the BaCO3/TiO2-c calcined mixtures…… 59
4.1.1.3.1. SEM of BaTiO3 powders ……………………………….... 59 4.1.1.3.2. The crystallite size and the specific surface area...... 59
4.1.1.3.3. BaTiO3 formation- important variables……………………. 61
III a) Effect of milling time ……………………………………………... 61 b) Effect of calcination temperature …………………………………. 63 c) Effect of calcination time …………………………………..……... 65
4.1.2. Ba(NO3)2/TiO2-c Powder Mixture ……………………………… 67 4.1.2.1 Thermal analysis (DTA &TGA) ……………………………... 67 4.1.2.2. Powder morphology…………………….………...... 68 4.1.2.3. The crystallite size and the specific surface area ……..…….. 68 4.1.2.4. X-Ray Diffraction …………………………………………… 69 4.2. Reaction Kinetics ………………………………………………….. 70
4.2.1. BaCO3/TiO2-c reaction………………………………………….. 70 4.2.1.1. X-Ray Diffraction method…………………………………… 70 4.2.1.1.1. Isothermal reaction kinetics ……………………………... 71 I) Model free reaction kinetics ………………………………. 71 II) Determination of reaction kinetics models ………………... 74
4.2.2. Ba(NO3)2/TiO2-c Reaction ……………………………………… 76 4.2.2.1. Non isothermal reaction kinetics…………………………….. 76 4.2.2.1.1. Model free reaction kinetics……………………………… 76 I) Thermo-gravimetric reaction analysis …………………….. 76 II) Differential thermal analysis DTA ………………………... 79 4.2.2.1.2. Kinetic model determination ……………………………. 82 4.3. Thermodynamic approach …………………………………..…… 86
4.3.1. BaCO3/TiO2-c Reaction ………………………………………… 86
4.3.2. Ba(NO3)2/TiO2-c Reaction …………………………………..…. 88
4.4. Characterization of the BaTiO3 sintered compacts …………… 89
4.4.1. BaTiO3 Prepared From BaCO3/TiO2-c Mixture ………………. 89
4.4.1.1. Compacting and sintering behavior of BaTiO3 powder ……... 89
4.4.1.2. Microstructure of the sintered BaTiO3 ………………………. 90
4.4.1.3. Phase analysis of the BaTiO3 ceramics ……………………… 92
4.4.2. BaTiO3 Prepared From Ba(NO3)2/TiO2-c Mixture ……………... 94
4.4.2.1. Compacting and sintering behavior of BaTiO3 powder …...... 94
4.4.2.2. Microstructure of the sintered BaTiO3 ………………………. 94
IV 4.5. Electrical properties of BaTiO3 ………………………………….. 95
4.5.1. BaTiO3 Prepared From BaCO3/TiO2-c Mixture ………………. 95
4.5.2. BaTiO3 Prepared From Ba(NO3)2/TiO2-c Mixture …………… 98 CHAPTER (5) Discussion …………………………………..……………….…………. 100 5.1. Thermal analysis………………………………………………….. 100
5.1.1. BaCO3/TiO2-c System………………………………………….. 100
5.1.1.1. BaTiO3 and Ba2TiO4 as reaction products…………………. 102
5.1.2. Ba(NO3)2/TiO2-c System….……………………………………. 103 5.2. Reaction kinetics………………….…………………………….… 104
5.2.1. BaCO3/TiO2-c Reaction…………………………………...…… 104
5.2.2. Ba(NO3)2/TiO2-c Reaction …………………………………...... 105 5.3. Reaction mechanism …………………………………………….. 106
5.3.1. BaCO3/TiO2-c System………………………………………….. 106 5.3.1.1. Realistic approach to the reaction mechanism …………….… 112
5.3.2. BaTiO3 Prepared From The Ba(NO3)2/TiO2-c Mixture………... 115
5.4. Characterization of The BaTiO3 Sintered Material…………… 116 5.4.1. Densification and Microstructure………………………………. 116
5.5. Electrical Properties of BaTiO3………………………………..… 116 CHAPTER (6) Conclusions ………….…………………………………………………. 120 References………………………………………………………………. 122 Appendices……………………………………………………………… 134
V List of Figures
Figure (2.1): Shift in the distribution of charge in a ceramic insulator when it is placed in an electric field between two electrically conductive electrodes………………………… 4 Figure (2.2): Types of polarization mechanisms……………………….. 5 Figure (2.3): Polar and non-polar molecules
a) CO2 does not have a permanent dipole moment
b) H2O does have a permanent dipole moment...... 7 Figure (2.4): Schematic illustration of the definition of the relative dielectric constant k΄……………………………………… 8 Figure (2.5): Hysteresis loops resulting from plots of polarization vs. applied voltage……………………………………………. 14
Figure (2.6): Change in the hysteresis loop shape for BaTiO3 at various temperatures……………………………………………… 14
Figure (2.7): Schematic of the perovskite structure of BaTiO3………… 19 Figure (2.8): Reversal in the direction of spontaneous polarization in
BaTiO3 by reversal of the direction of the applied field…. 21 Figure (2.9): Schematic diagram showing single-layer ceramic capacitor………………………………………………….. 30 Figure (2.10): Schematic diagram showing a multilayer ceramic capacitor………………………………………………….. 32
Figure (3.1): Schematic diagram of the preparation steps of the BaTiO3 powders by high energy ball milling method…………….. 47
Figure (4.1): DTA-TG of barium carbonate (BaCO3) …………………. 52
Figure (4.2): DTA-TG of titanium dioxide (TiO2-c) …………………... 53
Figure (4.3): SEM of dispersed powder of; (a) BaCO3 (b) TiO2-c …… 53
Figure (4.4): DTA-TG for BaCO3/TiO2-c milled powder mixture…….. 54
VI Figure (4.5): DTG curve of the BaCO3/TiO2-c milled powder mixtures 55
Figure (4.6): SEM of dispersed powder of the BaCO3/TiO2-c milled mixture …………………………………………………... 55
Figure (4.7): Relative linear shrinkage of the as milled BaCO3/TiO2-c mixtures..…………………………………………………. 57 Figure (4.8): Shrinkage rate versus temperature and time for the as
milled BaCO3/TiO2-c mixtures..…………………………. 57
Figure (4.9): XRD pattern of BaCO3/TiO2-c powder mixture milled for 12.5h ……………………………...……………………… 58
Figure (4.10): XRD patterns of BaCO3/TiO2-c and BaCO3/TiO2-BDH powder mixtures, milled for 7.5h and calcined at 900/1h...……………………………………..……………. 59
Figure (4.11): SEM micrographs for the BaTiO3 powders prepared from
the BaCO3/TiO2-c powder mixture and milled for: a) 7.5hs, b) 10h, c) 12.5h …………………………………… 60
Figure (4.12): Effect of milling time on the formation of BaTiO3, from
BaCO3/TiO2-c milled powder mixtures calcined at 800°C/3h …………………………………………………. 62
Figure (4.13): XRD patterns of BaCO3-TiO2-c powder mixtures milled for 7.5h and calcined at different temperatures………….. 63
Figure (4.14): XRD patterns of BaCO3/TiO2-c powder mixtures milled for 10h and calcined at different temperatures....………… 64
Figure (4.15): XRD patterns of BaCO3/TiO2-c powder mixtures milled for 12.5h and calcined at different temperatures.……...... 64
Figure (4.16): Effect of Calcination time on the formation of BaTiO3,
from BaCO3/TiO2-c powder mixture milled for 7.5h and calcined at 700°C ……………………………………….... 65
Figure (4.17): Effect of Calcination time on the formation of BaTiO3,
from BaCO3/TiO2-c powder mixture milled for 7.5h and
VII calcined at 750°C ………………………………………… 66
Figure (4.18): Effect of Calcination time on the formation of BaTiO3,
from BaCO3/TiO2-c powder mixtures milled for 7.5h and calcined at 775°C…………………………………………. 66
Figure (4.19): Effect of Calcination time on the formation of BaTiO3,
from BaCO3/TiO2-c powder mixture milled for 7.5h and calcined at 800°C……………………………………….… 67
Figure (4.20): DTA-TG curve for the Ba(NO3)2/TiO2-c powder mixture 68
Figure (4.21): SEM micrographs of the BaTiO3 powders prepared from
Ba(NO3)2/TiO2-c powder mixture, calcined at 600°C for 6h ………………………...... 69
Figure (4.22): XRD patterns of the Ba(NO3)2/TiO2-c powder mixtures, calcined at 600°C …………………………………….…... 70 Figure (4.23): Calibration curve for calculating fraction reacted α from the raw value α* …………………………………………. 72 Figure(4.24): The fraction reacted (α) versus time (t) curves obtained
from the XRD analysis for reaction of BaCO3/TiO2-c powder mixtures (milled for 7.5h and calcined at different temperatures) …………………………………...... 73
Figure(4.25): Arrhenius plot of ln(t) versus 1/T for reaction of BaCO3
and TiO2-c powder mixture milled for 7.5h, at constant conversion ratios…………………………………………. 73 Figure (4.26): g(α) versus the reaction time for different reaction kinetic models…………………………………………………….. 74 Figure (4.27): g(α) versus time for the reaction model "R3" (three dimensional movement of the grain boundary).………….. 75 Figure (4.28): Arrhenius plot of ln k(T) versus 104/T ………………….. 75 Figure (4.29): TG curves obtained at heating rates 5, 10, and 15°C/min... 77 Figure (4.30): OZAWA kinetic analysis carried out in the temperature
VIII range 530-560°C..………………………………………… 78 Figure (4.31): OZAWA kinetic analysis carried out in the temperature range 560-580°C..………………………………………… 78 Figure (4.32): OZAWA kinetic analysis carried out in the temperature range 590-740°C..………………………………………… 79
Figure (4.33): DTA curve of the Ba(NO3)2/TiO2-c mixture at a heating rate of 1 °C/min…………………………………………... 80
Figure (4.34): DTA curve of the Ba(NO3)2/TiO2-c mixture at a heating rate of 0.6 °C/min…………………………………..……. 80
2 Figure (4.35) Arrhenius plot of ln(β/T m) versus 1/Tm………….………. 81 Figure (4.36): TG analysis made at constant heating rates of 5, 10, 15°C/min…………………………………………………. 82 Figure (4.37): f (α) reaction model data fitting..…………………………. 84 Figure (4.38): Fraction reacted (α) from TG curve, obtained for
Ba(NO3)2/TiO2-c, when heating at a rate 5°C/min……….. 84 Figure (4.39): Arrhenius plot of ln [β (dα/dT)/f(α)] versus 103/T.……… 85 Figure (4.40): Effect of compacting pressure on the green and sintered (at 1300/3h) density for powders milled for 7.5h and calcined at 800°C/3h …………………………………….. 89
Figure (4.41): SEM micrographs of the BaTiO3 compacts sintered at
1300/3h and prepared from BaCO3/TiO2-c mixture: A) the as milled powder B) the as milled powder, calcined at 800/3h prior to sintering ……………………... 91
Figure (4.42): SEM micrograph of surface of BaTiO3 compact made
from BaCO3/TiO2-c mixture, calcined at 800°C/3h, sintered at 1350°C/3h in air………………………………. 92
Figure (4.43): XRD patterns of the BaTiO3 ceramic, prepared from
BaCO3/TiO2-c mixture and sintered at different temperatures for 3h..…………………………………….. 93
IX Figure (4.44): Tetragonality of BaTiO3 prepared from BaCO3/TiO2-c mixture as a function of the sintering temperature.……… 93
Figure (4.45): SEM micrograph of surface of BaTiO3 compact made
from Ba(NO3)2/TiO2-c mixture, calcined at 600°C/6h, sintered at 1300°C/3h.……………………………………. 94 Figure (4.46): Dielectric properties as a function of temperature and
frequency for the BaTiO3 prepared from BaCO3/TiO2-c powder mixture, milled for 7.5h, calcined at 800/3h, and sintered at 1300/3h...……………………………………... 96 Figure (4.47): Dielectric properties as a function in temperature and
frequency for the BaTiO3 prepared from BaCO3-TiO2-c powder mixture; milled for 7.5h, calcined at 800°C/3h, and sintered at 1350°C/3h………………….…………….. 96 Figure (4.48): Reciprocal of relative permittivity versus temperature at
T>Tc, for the BaTiO3 prepared from BaCO3/TiO2-c powder mixture, sintered at 1300°C for 3h.……………… 97 Figure (4.49): Reciprocal of relative permittivity versus temperature at
T>Tc, for the BaTiO3 prepared from BaCO3/TiO2-c powder mixture, sintered at 1350°C for 3h………………. 97 Figure (4.50): Dielectric properties as a function of temperature and
frequency for the BaTiO3 sample, prepared from
Ba(NO3)2 -TiO2 powder mixture, sintered at 1300°C/3h… 98 Figure (4.51): Reciprocal of relative permittivity versus temperature at
T>Tc for the BaTiO3 sample, prepared from Ba(NO3)2/
TiO2-c powder mixture, sintered at 1300°C/3h………...... 99 Figure (5.1): The energy changes during the course of the reaction
between BaCO3 and TiO2………………………………… 105 Figure (5.2): Schematic diagram of the mechanism of formation of
BaTiO3 phase from BaCO3/TiO2-c powder mixture 109
X Figure (5.3): The change in Gibbs free energy (∆G) versus temperature for the different possible reactions that could take place
during the calcination of BaCO3 and TiO2……………….. 110 Figure (5.4): Schematic diagram for the realistic approach describing
the reaction mechanism of formation of BaTiO3 from
BaCO3/TiO2-c powder mixture………………………….. 114 Figure (5.5): Schematic diagram of the mechanism of formation of
BaTiO3 phase from Ba(NO3)2/TiO2-c powder mixture…... 115 Figure (5.6): A comparison between the calculated results of the relative permittivities according to Maxwell-Garnet formula, the present study results obtained for the samples sintered at different temperatures, and some of the previously published results……………………………… 119
Figure (6.1) XRD patterns for the TiO2 powder calcined at: (A) 300°C, (B) at 500°C…………………………………. 134
Figure (6.2) XRD patterns for the BaCO3 powder: (A) as received, (B) calcined at 1000°C…………………. 134
Figure (6.3) Effect of calcination time for the BaCO3/TiO2-c mixture powders milled for 10h, at different calcination temperatures……………………………………………… 135
Figure (6.4) Effect of calcination time for the BaCO3/TiO2-c mixture powders milled for 12h, at different calcination temperatures……………………………………………… 136 Figure (6.5) The fraction reacted (α) versus time (t) curves obtained
from the XRD analysis for reaction of BaCO3/TiO2-c powder mixtures (milled for 10h and calcined at different temperatures)…………………………………… 137
Figure (6.6) Arrhenius plot of ln(t) versus 1/T for reaction of BaCO3
and TiO2-c powder mixture milled for 10 h and calcined
XI at different temperatures…………………………………. 137 Figure (6.7) The fraction reacted (α) versus time (t) curves obtained
from the XRD analysis for reaction of BaCO3/TiO2-c powder mixtures (milled for 12.5h and calcined at different temperatures)…………………………………… 138
Figure (6.8) Arrhenius plot of ln(t) versus 1/T for reaction of BaCO3
and TiO2-c powder mixture milled for 12.5h and calcined at different temperatures…………………………………. 138 Figure (6.9) Dielectric properties as a function of temperature and
frequency for the BaTiO3 prepared from BaCO3/TiO2-c powder mixture, milled for 10 h, calcined at 800°C/3h, and sintered at 1300°C/3h...... 143 Figure (6.10) Reciprocal of relative permittivity versus temperature at
T>Tc, for the sintered BaTiO3 prepared from BaCO3/
TiO2-c powder mixture, milled for 10h...... 143 Figure (6.11) Dielectric properties as a function of temperature and
frequency for the BaTiO3 prepared from BaCO3/TiO2-c powder mixture, milled for 12.5h, calcined at 800°C/3h, and sintered at 1300°C/3h………………….. 143 Figure (6.12) Reciprocal of relative permittivity versus temperature at
T>Tc, for the sintered BaTiO3 prepared from BaCO3/
TiO2-c powder mixture, milled for 12.5 h……………… 144
XII List of Tables Table-2.1: Examples of electro-ceramics, physical properties, and applications………………………………………………….. 3
Table-2.2: Kinetic model functions for treating the conversion (α, fraction reacted) versus time data for solid state reactions….. 36
Table-3.1: List of the materials used for the preparation of the BaTiO3 powder……………………………………………………….. 43
Table-3.2: Equipment and devices that were used in the preparation of the BaTiO3material…………………………………………... 45
Table-4.1: The crystallite size, BET surface area, and equivalent sphere
diameter for the BaTiO3 powders, prepared from the
BaCO3/TiO2-c milled mixture and calcined at 800°C for 3h.... 61
Table-4.2: The fraction reacted of BaCO3/TiO2-c mixture, milled for different times, calcined at different temperatures and times... 62 Table-4.3: The crystallite size, BET surface area, and equivalent sphere diameter for the BaTiO3 powders prepared from the Ba(NO3)2/TiO2-c reaction….………………………………... 69
Table-4.4: The activation energies of the reaction of BaCO3 and TiO2-c 72 Table-4.5: Enthalpies, entropies, and free energy change of different possible reactions that may occur during the formation of
BaTiO3 from BaCO3/TiO2-c powder mixture………………... 87 Table-4.6: Enthalpies, entropies, and free energy change of different possible reactions that may occur to form BaTiO3 from Ba(NO3)2-TiO2-c powder mixture…………………………… 88
Table-4.7: The relative densities of samples prepared from the milled
and calcined BaCO3/TiO2-c powder mixture………………… 90 Table-4.8: The relative densities of the sintered samples prepared from
the Ba(NO3)2/TiO2-c mixture………………………………… 94
Table-5.1: Activation energies (in kJ/mole) obtained for BaTiO3 powders using: a) Model-free and b) Reaction kinetic model equations…………………………………………………… 106
Table-6.1: The standard thermodynamic data for ∆Ho, ∆So, and cp…… 139 Table-6.2: The enthalpies & entropies calculated for different substances 140
XIII Acronyms, Abbreviations and Definitions i. Acronyms and Abbreviations
PVA Polyvinyl Alcohol PZT Lead Zirconate Titanate PLZT lead lanthanum zirconate titanate PMN Lead Magnesium Niobate AGG Abnormal Grain Growth PTCR Positive Temperature Coefficient Resistors MLCCs Multilayer Ceramic Capacitors TG Thermogravimetry DTA Differential Thermal Analysis DSC Differential Scanning Calorimetry XRD X-Ray Diffraction EGA Gas Chromatography whenever Gas Analysis reactions involving gas evolutions TMA Thermo-Mechanical Analyzer CRH Constant Heating Rate Technique BET Specific Surface Area
XIV ii. Definitions & Symbols in Equations Definitions Piezoelectricity The ability of certain crystalline materials to develop an electrical charge proportional to a mechanical stress Pyroelectricity Crystals contain within their crystal structure a preexisting spontaneous polarization along at least one crystallographic direction, heating of the crystal results in mechanical deformation Ferroelectricity Crystals exhibiting spontaneous polarization; they retain a dipole even after an applied voltage has been removed Ferroelectric Ferroelectric crystals possess regions with uniform domains polarization, all the electric dipoles are aligned in the same direction Domain switching The reversal of the polarization in the domain Coercive field A very strong field at which the domain switch their direction until the domains in one direction balance the
domains in the opposite direction, results in zero net polarization Poling Maximum alignment of domains that can be achieved by
cooling the BaTiO3 crystal through the Curie temperature) while an electric field is applied Dielectric materials Ceramic materials that are good electrical insulators Relative permittivity The degree of polarizability or charge storage or Dielectric constant capability of a material Dielectric loss The flow of electric charge through the dielectric material Dielectric strength The capability of the material to withstand an electric field without breaking down and allowing electrical current to pass, volts per mil (thousandth of an inch) or volts per centimeter
XV Symbols in Equations P The polarization
Pr Remanent polarization
Ps The spontaneous polarization ά The polarizability of the molecule
χe The dielectric susceptibility -14 εo The permittivity of the free space (8.85 x 10 farads/cm)
εr The relative permittivity E The applied electric field
Ec Coercive field δ The angle of lag, it is the measure of the dielectric loss tanδ Loss tangent or the dissipation factor
εrtanδ Loss factor Q The amount of charge that can be stored within a dielectric material, in coulomb C The capacitance T Temperature R The gas constant
tc The crystallite size λ The wave length Ķ The shape coefficient
ρ The theoretical density of BaTiO3 α The fraction reacted ß The full-width at half-maximum β The heating rate A The pre-exponential factor of the Arrhenius equation
Ea The activation energy of the reaction
К The temperature dependant rate constant = Aexp (Ea/RT) ∆G Gibbs free energy ∆H, ∆S The enthalpy and entropy, respectively
XVI ACKNOWLEDGMENTS
I would like to express my great thanks to all those who helped me during this work. First, I am very grateful to all my supervisors for their continuous support, guidance and advice to me:
Deep thanks to, Prof. Dr. M. M. El-SAYED (Metallurgy Department/Egyptian Atomic Energy Authority) for his great and effective help during this study.
Many thanks to Prof. Dr. F. A. ElREFAIE (Metallurgy Department/Cairo University).
Many thanks to Prof Dr. R. ABDEL-KARIM (Metallurgy Department/Cairo University)
Many thanks to Dr. A. A. ABDEL-SALAM (Metallurgy Department /Egyptian Atomic Energy Authority)
I would like to express my great and deep thanks to: Prof. Dr. S. M. El-RAGHY (Metallurgy Department/Cairo University) for his help and support during this study.
Prof. Dr. S. M. El-HOUTE (Metallurgy Department/Egyptian Atomic Energy Authority) for her effective help and support during this study.
Many thanks and heartfelt gratitude for all laboratory staff in the metallurgy department/Egyptian Atomic Energy Authority for their great help to complete this work.
Finally, I would like to express my great thanks to my family for their continuous support and assistance.
XVII ABSTRACT
BaTiO3 powder was prepared at low temperatures using the solid-state reaction, starting with two different precursors; the BaCO3/TiO2 and the Ba(NO3)2/TiO2-c powder mixtures. It was found that, a single phase BaTiO3 was formed after calcination at 750°C for 10h and at 600°C for 6h for the first and second mixtures, respectively. Thermal and XRD analyses were used to study the formation kinetics of BaTiO3. Contracting volume reaction model was found to control both reactions. The SEM of the as milled powder, TMA, TG and thermodynamics analysis have been used to propose a realistic approach describing the reaction mechanism of BaTiO3. Characterization and the dielectric properties of the sintered BaTiO3 were investigated. The relative permittivity and the dielectric loss measured at room temperature and at 1kHz were 2028.5 and 0.043 for BaTiO3 prepared from BaCO3/TiO2, while they were
1805.33 and 0.41 for BaTiO3 prepared from Ba(NO3)2/TiO2.
XVIII
CHAPTER (1) Introduction
Introduction Ferroelectric ceramics or ferroelectrics refer to the group of dielectrics having the property of spontaneous polarization (i.e., they retain a dipole even after an applied voltage has been removed). The key characteristics of a ferroelectric crystal are that the direction of the polarization can be reversed by application of an electric field and that a hysteresis loop results. Ferroelectrics mainly have two characteristics, asymmetry and high dielectric constant or high permittivity [D. W. Richerson, 1992; N. Nikulin, 1988]. Several ceramic materials with ferroelectric properties have been developed and utilized for a variety of applications such as; ferroelectric thin films for non volatile memories, piezoelectric materials for medical ultrasound imaging and actuators, and electro-optic materials for data storage and displays. The biggest applications of ferroelectric ceramics have been in the areas of dielectric ceramics for capacitor applications, especially with the development of ceramic processing and thin film technology. The perovskite family having a structure of the type
ABO3 is the most popular type of ferroelectrics. Many ferroelectric materials such as; barium titanate (BaTiO3), lead titanate (PbTiO3), lead zirconate titanate (PZT), lead lanthanum zirconate titanate (PLZT), and relaxor ferroelectrics like lead magnesium niobate (PMN) have this perovskite type structure [S. Ahmed et al., 2006].
Barium titanate is one of the most widely used ferroelectric materials due to its high dielectric constant and low loss characteristics. As advanced miniaturization requires smaller circuit area, the multilayer ceramic capacitors (MLCCs) with higher efficiency were developed. The MLCCs films (thick or thin) usually require a sub-micron grain size of the ceramic. Conventionally,
BaTiO3 powders are manufactured at high temperatures, by solid-state reaction or from chemically derived precursors. These methods produce large, non- uniform, and agglomerated particles that have to be milled and heat treated again to obtain the required particle size (0.5-1.5μm) to fabricate reliable MLCCs (B. D. Stojanovic et al., 2002). Another possibility to obtain the
- 1 - required grain size could be by mechanical activation of raw materials during powder preparation process. The mechanical activation using high energy milling process is one of the most effective methods for obtaining highly dispersed powders. It results in a decrease of particle size that leads to the initiation of solid state reaction between the starting components at lower temperatures (L. B. Kong et al., 2002; E. Brzozwski et al., 2003; V. Berbenni et al., 2001).
The aim of this work is to prepare BaTiO3 fine powders at a lower temperature through solid state reaction, starting with two different precursors; the BaCO3-
TiO2 and the Ba(NO3)2-TiO2 mixtures. Studying the different aspects (such as; milling time, calcination time and temperature) for the preparation of barium titanate from BaCO3 and TiO2 using high energy planetary milling is the second step. Thermodynamics and kinetic analysis will be performed to study the mechanism of BaTiO3 formation through solid state reaction in both mixtures. And the final step will be studying the sintering behavior and the dielectric properties of the prepared BaTiO3 powders.
This thesis consists of five chapters; Chapter (1), an introduction, giving the general characteristics of the ferroelectric materials, its applications, and a brief perspective on the BaTiO3 ferroelectric materials. Chapter (2) consists of two parts; part-I contains the literature survey that provides an overview of the electrical ceramics, dielectric materials, ferroelectric materials. Since the main purpose of this work is the preparation of BaTiO3 ferroelectric materials, the last section of the literature survey focuses on the BaTiO3 ferroelectric materials: the general characteristics of the BaTiO3, methods of preparation, and its applications. Part-II includes Kinetics and thermodynamic study of chemical reactions accompanying the formation of BaTiO3. Chapter (3) focuses on the experimental work including; materials and methods of preparation used for the BaTiO3 preparation. Chapter (4) includes experimental results, while chapter (5) is devoted to a thorough discussion of these results. At the end of this thesis there are the conclusions in chapter (6).
- 2 -
CHAPTER (2) Part-I: Literature Review
2. LITERATURE REVIEW 2.1. Electrical Ceramic Ceramic materials have a wide range of electrical properties. Some of them do not allow passage of an electric current even in a very strong electric field and thus are excellent insulators. Others allow passage of an electric current and have application as electrical conductors. The third type allows an electric current to pass only under certain conditions or when an energy threshold has been reached and thus are useful semiconductors. However, some ceramics do not conduct electricity but undergo internal charge polarization that allows the material to be used for storage of an electrical charge in capacitors [D. W. Richerson, 1992]. Examples of electro-ceramics include Zinc oxide for varistors, lead zirconium titanate (PZT) for piezoelectrics, barium titanate for capacitors, tin oxide as gas sensors, lead lanthanum zirconium titanate (PLZT) and lithium niobate for electro-optic devices. Table-2.1 summarizes the physical properties of some electro-ceramics required for these applications (D. Segal, 1989).
Table-2.1: Examples of electro-ceramics, physical properties, and applications Material properties Applications
Al2O3, Low permittivity; high thermal Packaging, substrates AIN, BeO conductivity BaTiO3 high permittivity; high breakdown voltage Capacitors PZT, High piezoelectric coefficients Piezoelectric BaTiO3, transducers, saw LiNbO3 devices BaTiO3 Change of resistance with temperature Thermistors (PTC) ZnO Change of resistivity with applied field Varistors PLZT Change of birefringence with field Electro-optics
ZrO2 Ionic conductivity Gas sensors
SnO2 Surface-controlled conductivity Gas sensors Ferrites Permeability, coercive field Magnets PZT Change of polarization with temperature Pyroelectrics
- 3 - 2.1.1. Dielectric Materials Ceramic materials that are good electrical insulators are referred to as dielectric materials. Although these materials do not conduct electrical current when an electric field is applied, they are not inert to the electric field (E). The field causes a slight shift in the balance of charge within the material as shown in Figure (2.1), so that the system acquires an electrical dipole moment (P) [D. W. Richerson, 1992]. The dipole moment per unit volume is called polarization. This moment is proportional to the electric field, E [H. M. Rosenberg, 1988].
+ electrode - electrode
______+ + + + + + + + + + + + + _ _ + _ _ _ + _ _ _ + _ + _ + _ + – _ _ + _--+ + + + +_ _ + + _ + + _ + + + + + _ _ + _ _ _ + _ _ _ + _ _ _ +_ _ _ + + + + + + + + + + + + + + ______
- electrode + electrode (a) (b) Figure (2.1): Shift in the distribution of charge in a ceramic insulator when it is placed in an electric field between two electrically conductive electrodes
The polarization is always proportional to the applied field; thus
P = εoχeE….(2.1)
Where: χe is the dielectric susceptibility, a unitless constant that describes the dielectric’s ability to form dipoles [M. Allison, 2007]. Since the dielectric susceptibility χe is equal to (εr-1), where εr is the relative permittivity, the polarization will be [R. M. Rose et al., 1971]:
P = εoE (εr-1) ….(2.2)
The field that a molecule in the interior of a dielectric situated between the plates of a charged condenser actually experiences is known to be larger than the applied field. This is related to the polarization which occurs within and on the surfaces of the dielectric. The actual field acting on the molecule is
- 4 - therefore called the local field (Eloc). The dipole moment induced in a molecule by the local field is given by [R. M. Rose et al., 1971]:
Pmol = ά Eloc ….(2.3)
Where: Pmol represents its moment and ά is called the polarizability of the molecule. For dielectrics containing N molecules per unit volume, the total dipole moment or polarization is:
P = N ά Eloc …. (2.4) Substituting Equation (2.4) in Equation (2.2) gives:
(εr-1) = P/ εo Eloc = N ά Eloc / εo E ….(2.5)
There are several polarization mechanisms: Electronic polarization; orientation (dipolar) polarization; space charge polarization; and atomic or ionic polarization. These are illustrated in Figure (2.2).
No Applied Electric Electric
Field Field
+ - + + - + E + - - + - +
Electronic polarization Orientation polarization
+ - + - + + + - - - + - + + - + - + - + - + - + + - - + - + - - - + - + + - + - + + + + - - - + - + - + + - - - + - + + - +
Space charge polarization Atomic or ionic polarization
Figure (2.2): Types of polarization mechanisms [D.W. Richerson, 1992; R. M. Rose et al., 1971]
a) Electronic polarization Electronic polarization occurs in all dielectric materials. When an electric field, E, acts on an individual atom, the electrons surrounding each nucleus are shifted very slightly in the direction of the positive electrode and the nucleus is
- 5 - very slightly shifted in the direction of the negative electrode and the atom acquires a dipole moment P, so that: P = ά E, where ά is the polarizability of the atom. As soon as the electric field is removed, the electrons and the nuclei return to their original distributions and polarization disappears. The displacement of charge is very small for electronic polarization, so the total amount of polarization is small compared to the other mechanisms of polarization [D.W. Richerson, 1992; H. M. Rosenberg, 1988].
b) Orientation polarization If the system is composed of heteronuclear (nonsymmetrical) molecules then the disposition of the individual atoms within the molecule may be such that the molecule itself has a permanent dipole moment. Examples are H2O, HCl,
CH3Br, Hf, and C2H5(NO2) [H. M. Rosenberg, 1988]. For the H2O, the covalent bonds between hydrogen and oxygen atoms are directional such that the two hydrogen atoms that have a net positive charge are on one side of the oxygen that has a net negative charge. Under an electric field, the molecule will align with the positive side facing the negative electrode and the negative side facing the positive electrode [D. W. Richerson, 1992]. A molecule which is composed of different atoms is not necessarily polar, e.g. CO2 is non-polar because the carbon and oxygen atoms are arranged in a straight line with the carbon in the middle as shown in Figure (2.3-a). H2O is polar because the ions are arranged in a triangle (Figure 2.3-b) [H. M. Rosenberg, 1988].
Orientation polarization results in a much higher degree of polarization than electronic polarization, because larger charge displacement is possible in the relatively large molecules compared to the spacing between electrons and nucleus in individual atoms [D. W. Richerson, 1992]. In solids, however, the molecules are usually too tightly bound for the orientation polarization to occur. It is much more important in liquids and gases. Due to the randomizing effect of the thermal vibrations this type of polarization is more effective as the temperature is decreased and it gives rise to a dielectric constant, which is temperature dependent [H. M. Rosenberg, 1988].
- 6 - Non-polar Polar
O O C O H H
(a) (b)
Figure (2.3): a) CO2 does not have a permanent dipole moment
b) H2O does have a permanent dipole moment c) Space charge polarization Space charges are random charges caused by cosmic radiation, thermal deterioration, or are trapped in the material during the fabrication process [D. W. Richerson, 1992].
d) Atomic or ionic polarization Atomic polarization involves displacement of atoms or ions within a crystal structure when an electric field is applied, the field will tend to stretch the bonds between the ions and this will change the moment of the molecule. A wide range of polariztion effects is possible through this mechanism, depending on the crystal structure, the presence of solid solution, and other factors [D. W. Richerson, 1992, H. M. Rosenberg, 1988].
2.1.1.1 Dielectric Constant The degree of polarizability or charge storage capability of a material is identified by the term dielectric constant or as relative permittivity. The concept of the relative dielectric constant is illustrated in Figure (2.4). When an electric field is applied to two flat plates of a metal, one plate becomes positive and the other negative. The electric field causes polarization in the material in the space between the conductive plates. The relative dielectric constant (k΄) compares the polarizability of the material with that of the vacuum between the plates [D. W. Richerson, 1992]:
- 7 -
k΄ = k material / k vacuum .... (2.6)
In other references; the relative permittivity is quoted as εr, while ε0 is defined as the permittivity of the free space (8.85 x 10-14 farads/cm), and ε is the permittivity of the dielectric material. In this thesis the permittivity terms (εr,
ε0, ε) will be used according to Equation (2.7).
εr= ε/ ε0 ....(2.7)
------
Dielectric
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + K + - k` = material Kvacuum ------
Vacuum
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+ - Figure (2.4): Schematic illustration of the definition of the relative dielectric constant k΄
Materials with low dielectric constant are used for electrical insulator applications. Materials with high dielectric constant are used in capacitors for charge storage and other functions. The dielectric constant is affected by temperature. The nature of the effect depends on the source of polarization. Electronic polarization is relatively insensitive to temperature, so temperature has little effect on the dielectric constant. Molecular orientation polarization is opposed by thermal agitation, so the dielectric constant goes down as the temperature increases. Atomic/ionic polarization tends to increase with temperature due to an increase in charge carriers and ion mobility. The dielectric constant is also affected by the frequency of the applied electric field or the frequency of other electromagnetic fields impinging on the material. The polarization requires time to respond to an applied field. Electronic polarization occurs very rapidly and is present even at high frequencies. For example, visible light is of relatively high frequency (1015 cycles per second)
- 8 - and has an electric interaction with the electronic polarization of a dielectric. Molecular orientation polarization is only affected by low frequencies. In high- frequency field, the molecules do not have time to realign with each cycle [D. W. Richerson, 1992].
2.1.1.2. Dielectric Loss An ideal dielectric would allow no flow of electric charge, only a displacement of charge via polarization. Hence the current leads the voltage by 90°C; or out of phase by a quarter-cycle. Real materials always have some loss. The phase angle between the current and voltage is not exactly 90°C; the current leads the voltage by 90- δ, where δ is defined as the angle of lag. The angle of lag, δ, is the measure of the dielectric power loss. 2 Power loss = πƒVo εrtanδ ….(2.8)
The product "εrtanδ" is called the loss factor and "tanδ" is referred to as the loss tangent or the dissipation factor. The loss factor consequently characterizes the usefulness of a material as a dielectric or as insulator; in both cases a low loss tangent is desirable [R. M. Rose et al., 1971].
The dielectric loss results from several mechanisms: (1) ion migration; (2) ion vibration and deformation; (3) electronic polarization. The most important mechanism to most ceramics is ion migration. Ion migration is strongly affected by temperature and frequency. The losses due to ion migration increase at low frequencies and as the temperature increases [D. W. Richerson, 1992]. Another undesirable energy loss in dielectrics arises from overheating or cyclic heating, which leads to the degradation of the dielectric and breakdown [R. M. Rose et al., 1971]. Most dielectrics are, therefore, rated by three factors: (1) Relative permittivity, (2) tangent of lag angle, and (3) dielectric strength.
2.1.1.3. Dielectric Strength Dielectric strength is the capability of the material to withstand an electric field without breaking down and allowing electrical current to pass. It has units of volts per unit of thickness of the dielectric material, volts per mil (thousandth
- 9 - of an inch) or volts per centimeter are often used [D. W. Richerson, 1992]. If the applied field exceeds certain critical value, the dielectric material breaks down and conducts electricity and this limits the operating conditions for dielectrics which are used in insulators or in capacitors [H. M. Rosenberg, 1988].
Dielectric breakdown begins with the appearance of a number of electrons in the conduction band; these electrons are accelerated rapidly by the high field in the dielectric, and attain high kinetic energies. Some of the kinetic energy is transferred (by collisions) to valance electrons, which are thereby elevated to the conduction band. If a large enough number of electrons is initiated in this process, it multiplies itself, and an avalanche of electrons is loosed in the conduction band. The current through the dielectric increases rapidly; and the dielectric is apt to locally melt, burn, or vaporize.
Conduction of electrons is required to initiate the process. These may originate in a number of ways. A common origin is the arcing between a high potential lead and the contaminated surface of an insulator. Impurity atoms can also donate electrons to the conduction band. Interconnecting pores in dielectrics sometimes provide direct breakdown channels as a result of electrical gas discharge. Where a dielectric is subject to high field over a long period, breakdown is generally preceded by local melting. In old capacitors breakdown can occur at relatively low field strengths if the dielectric has suffered chemical and mechanical abuse [R. M. Rose et al., 1971].
A brief account of other properties existing in dielectric materials, such as; piezoelectricity, pyroelectricity and ferroelectricity, is given in the following sections.
2.1.2. Piezoelectricity Piezoelectricity is the ability of certain crystalline materials to develop an electrical charge proportional to a mechanical stress [D. Segal, 1991]. Polarization occurs in single crystals of some materials when a stress is
- 10 - applied, one side of the crystal derives a net positive charge and the opposite side derives a net negative charge. Only crystals that are anisotropic with no center of symmetry are piezoelectric (there are 32 crystal classes, 20 of them are piezoelectric). Even these are not piezoelectric in all directions. The piezoelectric effect is reversible in that, piezoelectric crystals when subjected to an externally applied voltage, they change shape by a small amount [D. W. Richerson, 1992].
The piezoelectric effect was discovered by Pierre and Jacques curie and first reported in 1880. Piezoelectricity was identified by the Curies in a number of naturally occurring and laboratory grown single crystals. Examples included quartz, zinc blende (sphalerite), boracite, tourmaline, topaz, sugar, and
Rochelle salt (sodium-potassium tartrate tetrahydrate (NaKC4H4O6.4H2O). The piezoelectric phenomenon has led to the widespread use of piezoelectric ceramics as transducers in ultrasonic devices, microphones, phonograph pickups, accelerometers, and sonar devices [D. W. Richerson, 1992].
2.1.3. Pyroelectricity Pyroelectric crystals are a special class of piezoelectric crystals. They contain within their crystal structure a preexisting spontaneous polarization along at least one crystallographic direction, heating of the crystal results in mechanical deformation due to thermal expansion, which causes a change in the extent of polarization. Of the piezoelectric crystal classes, 10 are pyroelectric. Examples of pyroelectric crystals include würtzite, tourmaline, Rochelle salt, triglycine sulfate, BaTiO3. Most pyroelectric materials lose their pyroelectric behavior as the temperature is increased to a few hundred degrees except the
LiTaO3 material, which retains its pyroelectric behavior up to 609°C. As a result, LiTaO3 has been developed into a scanning microcalorimeter capable of sensitivity in the sub-microcalorie range. It has also been used as a high- sensitivity microenthalpimeter for monitoring catalytic processes [D. W. Richerson, 1992].
- 11 - 2.1.4. Ferroelectricity Ferroelectricity is a phenomena discovered in 1921, it is analogous to the ferromagnetic phenomena of iron. Ferroelectric materials do not show any connection with iron at all. The term was devised to explain a spontaneous polarization upon cooling below a curie temperature as well as a display of ferroelectric domains and ferroelectric hysteresis loop. Ferroelectrics (ferroelectric materials) are a subclass of pyroelectric crystals, exhibiting spontaneous polarization; they retain a dipole even after an applied voltage has been removed. Ferroelectric behavior is dependent on the crystal structure. The crystal must be noncentric and contain alternate atom positions or molecular orientations to permit the reversal of dipole and the retention of polarization after the voltage is removed [D. W. Richerson, 1992]. Ferroelectric ceramics do not absorb moisture, nor do they dissolve in water, being able to perform over a wide range of operating temperatures. However, every ferroelectric has a temperature point above which the material becomes substantially non-electric, i.e. dielectric, known as its Curie temperature [N. Nikulin, 1988].
Ferroelectric crystals possess regions with uniform polarization called ferroelectric domains. Within a domain, all the electric dipoles are aligned in the same direction. There are many domains in a crystal separated by interfaces called domain walls. A ferroelectric single crystal, when grown, has multiple ferroelectric domains. A single domain can be obtained by domain wall motion made possible by the application of an electric field. A very strong field could lead to the reversal of the polarization in the domain, known as domain switching [S. Ahmed et al., 2006]. The key characteristic of a ferroelectric crystal is that the direction of the polarization can be reversed by application of an electric field and that hysteresis loops result. Figure (2.5) describes what happens in a ferroelectric crystal such as tetragonal BaTiO3 when an electric field is applied. The ferroelectric domains are randomly oriented prior to application of the electric field, that is at E = 0 and the net
- 12 - polarization is zero (Pnet= 0). As an electric field is applied, and upon increasing this electric field the domains begin to move in the BaTiO3 and align parallel to the applied field. This results in increase in net polarization along line OA. The polarization reaches a saturation value (B) when all the domains are aligned in the direction of the field. If the electric field is reduced to zero, many of the domains will remain aligned such that a remanent polarization (Pr) exists. Interpolation of the line BC until it intersects the polarization axis gives a value Ps, which refers to the spontaneous polarization [D. W. Richerson, 1992; A. J. Dekker, 1971].
If the electric field is reversed, the domain will switch direction. When enough domains switch, the domains in one direction balance the domains in the opposite direction and result in zero net polarization. This occurs for an electric field called the coercive field (–Ec). Continued increase in the negative electric field causes net polarization in the opposite direction, reaching the point B where all the available domains are aligned [D. W. Richerson, 1992; A. J. Dekker, 1971]. Maximum alignment of domains can be achieved by cooling the BaTiO3 crystal through the 120°C (cubic-to-tetragonal transition or Curie temperature) while an electric field is applied (this is referred to as poling). Poling forces a maximum number of domains to form in one direction and results in maximum polarization [D. W. Richerson, 1992].
The shape of the hysteresis loop varies for different temperatures below the Curie temperature as shown in Figure (2.6). It gets thinner as the temperature increases and becomes single line above the Curie temperature when the material is no longer ferroelectric. Ferroelectric behavior is dependent on the crystal structure. The crystal must be noncentric and must contain alternate atom positions or molecular orientations to permit the reversal of the dipole and the retention of polarization after the voltage is removed [D. W. Richerson, 1992].
- 13 - P
B C
Ps
Pr
A
-Ec E O Ec
-Pr
-B
Figure (2.5): Hysteresis loops resulting from plots of polarization vs. applied voltage [D. W. Richerson, 1992; A. J. Dekker, 1971]
30°C 90°C 120°C 125°C 85°F (195°F) (250°F) (255°F)
Figure (2.6): Change in the hysteresis loop shape for BaTiO3 at various temperatures [D. W. Richerson, 1992]
Ferroelectrics have been categorized in the literature in different ways. One approach classifies them as soft or hard. Soft ferroelectrics are water soluble, mechanically soft, and have low melting or decomposition temperature. Examples of these materials are; Rochelle salt, some other tartarates, some
- 14 - sulfates, nitrates and nitrites. Most of these involve hydrogen bonding above Curie temperature, the "H" ions and bonds are distributed randomly in a non ordered fashion. At the Curie temperature the crystals transform from a disordered paraelectric structure to an ordered ferroelectric structure. The ordered structure has specific pairs of positions the hydrogen ions can fit into, to form the reversible dipoles. Other common sources of dipoles in soft 3+ ferroelectric crystals are tetrahedral groups such as PO4 .
Hard ferroelectrics include the oxides formed at high temperature. They are mechanically hard, and are not water-soluble. Examples include BaTiO3,
KNbO3, CdNb2O6, PbNb2O6, PbTa2O6, PbBi2Nb2O9, and many others. Many of the hard ferroelectrics contain a small, highly charged cation (Ti4+, Zr4+, Nb5+, Ta5+) in an oxygen octahedron and have a similar ferroelectric mechanism to BaTiO3. Others contain asymmetrical ions with a "lone-pair" electron configuration; examples are Pb2+, Bi3+, Sn2+, Te4+, I5+. Each of these has two electrons outside a closed d shell. These form a lone-pair orbital on one side of the ion and promote a directional bonding. The resulting structure has dipoles that result in spontaneous polarization when the dipoles do not cancel each other [D. W. Richerson, 1992].
Another classification of ferroelectrics is based on the magnitude of atomic displacements and the resulting spontaneous polarization. Some crystals have atomic displacement along a single axis (one-dimensional). Since the complete displacement in these crystals is concentrated in a single direction, the 2 spontaneous polarization is high (25µC/cm ). Examples include; BaTiO3,
PbTiO3, LiNbO3, SbSI, and Bi2WO6. Atomic displacements in some crystals are along planes (two-dimensional). The spontaneous polarization is only 2 5µC/cm . Examples include BaCoF4, HCl, NaNO2, and thiourea. Ferroelectrics with tetrahedral groups or hydrogen bonding have complex structures with three-dimensional effects on polarization. Spontaneous polarization is less than 3µC/cm2) [D. W. Richerson, 1992].
- 15 - 2.2. Ferroelectric Materials Several ceramic materials with ferroelectric properties have been developed and utilized for a variety of applications. Among these ferroelectric materials, the perovskite family having a structure of the type ABO3 is the most popular type. Many ferroelectric ceramics such as; barium titanate (BaTiO3), lead titanate (PbTiO3), lead zirconate titanate (PZT), lead lanthanum zirconate titanate (PLZT), and relaxor ferroelectrics like lead magnesium niobate (PMN) have a perovskite type structure [S. Ahmed et al., 2006]. A brief account of some of these materials is given in the following sections.
2.2.1. Lead Titanate (PbTiO3, PT)
Lead titanate is a ferroelectric material having a structure similar to BaTiO3 with a high Curie point (450°C). On decreasing the temperature through the Curie point a phase transition from the paraelectric cubic phase to the ferroelectric tetragonal phase takes place. Lead titanate ceramics are difficult to fabricate in the bulk form as they undergo a large volume change on cooling below the Curie point, as a result of a phase transformation from cubic to tetragonal in PbTiO3, leading to a strain of >6%. Hence, pure PbTiO3 crack and fracture during fabrication. The spontaneous strain developed during cooling can be reduced by modifying the lead titanate with various dopants such as; Ca, Sr, Ba, Sn, and W to obtain a crack free ceramic [S. Ahmed et al., 2006].
2.2.2. Lead Zirconate Titanate {Pb(ZrxTi1-x)O3,PZT}
Lead zirconate titanate (PZT) is a binary solid solution of PbZrO3 an antiferroelectric (orthorhombic) and PbTiO3 a ferroelectric (tetragonal perovskite structure). PZT has a perovskite type structure with the Ti4+ and Zr4+ ions occupying the B site at random. At high temperature PZT has the cubic perovskite structure, which is paraelectric. On cooling below the Curie point line, the structure undergoes a phase transition to form a ferroelectric tetragonal or rhombohedral phase. In order to suit some specific requirements
- 16 - for certain applications, PZT can be modified by doping it with ions having a valance different from the ions in the lattice. PZT can be doped with ions to form "hard" and "soft" PZT's. Hard PZT's are doped with acceptor ions such as k+, Na+ (for A site), Fe3+, Al3+, Mn3+ (for B site), creating oxygen vacancies in the lattice. Hard PZT's usually have lower permittivity, smaller electrical losses and lower piezoelectric coefficients. These are more difficult to pole and depole, which makes them ideal for rugged applications. On the other hand, doping soft PZT's with donor ions such as La3+ (for A site) and Nb5+, Sb5+ (for B site) lead to the creation of A site vacancies in the lattice. The soft PZT's have higher permittivity, larger losses, higher piezoelectric coefficients, and are easy to pole and depole. They can be used for applications requiring very high piezoelectric properties [S. Ahmed et al., 2006].
2.2.3. Lead Lanthanum Zirconate Titanate (PLZT) PLZT is a transparent ferroelectric ceramic formed by doping La3+ ions on the A sites of lead zirconate titanate (PZT). The PLZT ceramics have the same perovskite structure as BaTiO3 and PZT. The transparent nature of PLZT has led to its use in electro-optic applications. The two factors that are responsible for getting a transparent PLZT ceramic are: the reduction in the anisotropy of the PZT crystal structure by the substitution of La3+ and the ability to get a pore free ceramic by either hot pressing or liquid phase sintering .
B The general formula for PLZT is given by (Pb1-xLax)(Zr1-yTiy)1-x/4O3V 0.25xO3 A 3+ and (Pb1-xLax)1-0.5x(Zr1-yTiy)V 0.5xO3. The first formula assumes that La ions go to the A site and vacancies (VB) are created on the B site to maintain charge balance. The second formula assumes that vacancies are created on the A site. The actual structure may be a combination of A and B site vacancies. At room temperature the PLZT have a tetragonal ferroelectric phase (FT), rhombohedral ferroelectric phase (FR), cubic relaxor ferroelectric phase (FC), orthorhombic antiferroelectric phase (A0), and a cubic paraelectric phase (PC) [S. Ahmed et al., 2006].
- 17 - The electro-optic applications of PLZT ceramics depend on their composition.
PLZT ceramic compositions in the tetragonal ferroelectric phase (FT) region have a hysteresis loop with a very high coercive field (EC). Materials with this composition exhibit linear electro-optic behavior for E PLZT ceramic compositions with the relaxor ferroelectric behavior are characterized by a slim hysteresis loop. They show large quadratic electro- optic effects which are used for making flash protection goggles to shield from intense radiation. This is one of the biggest applications of the electro-optic effect shown by transparent PLZT ceramics. The PLZT ceramics in the antiferroelectric region show a hysteresis loop expected from an antiferroelectric material. These components are used for memory applications [S. Ahmed et al., 2006]. 2.2.4. Lead Magnesium Niobate (PMN) Relaxor ferroelectrics are a class of lead based perovskite type compounds with the general formula Pb(B1,B2)O3 where B1 is the lower valency cation (like 2+ 2+ 2+ 3+ 5+ 5+ Mg , Zn , Ni , Fe ) and B2 is the higher valency cation (like Nb , Ta , W5+). Pure lead magnesium niobate is a representative of this class of materials with a Curie point at -10ºC. Relaxor ferroelectrics like PMN can be distinguished from normal ferroelectrics such as BaTiO3 and PZT, by the presence of a broad diffused and dispersive phase transition on cooling below the Curie point. At room temperature relaxor ferroelectrics have high dielectric constant and low temperature dependence. The relaxors also show a very strong frequency dependence of the dielectric constant. The Curie point shifts to higher temperatures with increasing frequency [S. Ahmed et al., 2006]. - 18 - 2.2.5. Barium Titanate (BaTiO3) Barium titanate (BaTiO3 or BTO) was synthesized to become the first and the most widely studied ceramic material, due to its excellent dielectric, ferroelectric and piezoelectric properties [N. Nikulin, 1988]. The high dielectric constant of BaTiO3 ceramics results from its crystal structure. BaTiO3 has the perovskite structure as shown in Figure (2.7). (A) Ti O Ba (B) Figure (2.7): Schematic of the perovskite structure of BaTiO3 A) Cubic lattice (above Curie temperature, 120°C) B) Tetragonal lattice (below Curie temperature, 120°C) [D. W. Richerson, 1992] - 19 - In Figure (2.7), each barium ion is surrounded by 12 oxygen ions. The oxygen ions plus the barium ions form a face-centered cubic lattice. The titanium atoms reside in octahedral interstitial positions surrounded by six oxygen ions. Because of the large size of the Ba ions, the octahedral interstitial position in BaTiO3 is quite large compared to the size of the Ti ions. The Ti ions are too small to be stable in this octahedral position. There are minimum-energy positions off-center in the direction of each of the six oxygen ions surrounding the Ti ion. Since each Ti ion has a +4 charge, the degree of polarization is very high. When an electric field is applied, the Ti ions can shift from random to aligned positions and result in high bulk polarization and high dielectric constant [D. W. Richerson, 1992]. Barium titanate has three crystalline forms: cubic, tetragonal, and hexagonal. The tetragonal polymorph is the most widely used because of its excellent ferroelectric, piezoelectric, and thermoelectric properties [S. Luo et al., 2003]. Temperature has a strong effect on the crystal structure and polarization characteristics of BaTiO3. Above 120°C (and up to 1400°C), BaTiO3 is cubic and the BaTiO3 have a spontaneous random polarization as described above. In this temperature range the Ti4+ ion lies in the center of an octahedron of oxygen ions (as shown in Figure-2.7-A). The thermal vibration is high enough to result in the random orientation of the titanium ions in its octahedral interstitial 4+ position in BaTiO3. The Ti ion does shift position, resulting polarization when electric field is applied, but it returns to its stable central position as soon as the field is removed. Thus, there is no retained polarization, no hysteresis loop, and no ferroelectric behavior. As the temperature of BaTiO3 is lowered slightly below 120°C (Curie temperature), a displacive transformation occurs in which the structure of the BaTiO3 changes from cubic to tetragonal (Figure- 2.7-B). One crystallographic axis increases in length (unit cell goes from 4.010 to 4.022 Å) and the other two decrease in length (from 4.010 to 4.004 Å). The Ti4+ ion moves off-center toward one of the two oxygen ions of the long axis, resulting in a spontaneous increase in positive charge in this direction. This is - 20 - illustrated in Figure (2.8-a). Application of an electric field opposite to the polarity of this original dipole will cause the Ti4+ ion to move through the center of the octahedral site and to an equivalent off-center position. This is shown in Figure (2.8-b). This results in a reversal polarization, hysteresis in the E versus P curve, and ferroelectricity [D. W. Richerson, 1992]. Ba2+ Ba2+ + + + + + + Ti4+ + + + + + O2- O2- + Ti4+ E E + + + + + + (a) (b) Figure (2.8): Reversal in the direction of spontaneous polarization in BaTiO3 by reversal of the direction of the applied field The dielectric properties of BaTiO3 were found to be dependent on the grain size and temperature. At the Curie point, large grained BaTiO3 (≥10 μm) has a high dielectric constant because of the formation of multiple domains in a single grain, the motion of whose walls increases the dielectric constant at Curie point. For a BaTiO3 with fine-grains (~1μm), a single domain forms inside each grain. The movement of domain walls is restricted by the grain boundaries, thus leading to a low dielectric constant at the Curie point compared to coarse-grained BaTiO3. At room temperature, the dielectric constant of coarse-grained BaTiO3 ceramics was found to be in the range of 1500-2000. On the other hand, fine-grained BaTiO3 exhibits a room temperature dielectric constant between 3500-6000. This is because the internal stresses in fine grained BaTiO3 are greater than in the coarse grained material, which leads to a higher permittivity at room temperature [S. Ahmed et al., 2006]. - 21 - 2.2.5.1. Methods of Preparation of BaTiO3 I- Solid-state reaction method During the last decade a wide number of synthetic methods have been developed for the preparation of barium titanate powders, but large scale production is frequently based on solid-state reactions of mixed powders BaCO3 and TiO2 at high temperatures (1100-1400°C). Despite the multiple advantages of the solid-state method for preparing BaTiO3, being a single process and a low cost technique, there are some problems with it to be solved. In fact, the high calcination temperature required by the solid-state reaction process leads to many disadvantages of the BaTiO3 powder such as; large particle size, wide size distribution and high degree of particle agglomeration, which generally limits the ability to fabricate reliable electronic components out of it [L. Wu et al., 2009]. So it is desirable to lower preparation temperature in order to obtain BaTiO3 powder with fine and homogenous structure, and to enable the use of cheap metal electrodes; i.e., replacing 70Pd/30Ag by 30Pd/70Ag and Ni electrodes, for the aim of reducing the cost of multilayer capacitors [D. Prakash et al., 2000; D. Zhang et al., 2004]. One approach used to influence initial powder microstructure and sintering properties of the material is to mechanically activate the powder using a high- energy ball milling process (also known as mechanochemical process) [L. B. Kong et al., 2002; V. P. Pavlović et al., 2007; M. V. Nicolić et al., 2006; E. Brzozwski et al., 2003; V. Berbenni et al, 2001]. This method is superior to both the conventional solid-state reaction and the wet-chemistry-based processing routes for ceramic powder preparation, since it allows the use of low-cost and widely available oxides as starting materials and skips the calcination step at intermediate temperatures, leading to a simplified process. Furthermore, the mechanically activated powders possess a much higher sinterability than those powders synthesized by conventional solid-state reaction and the wet-chemistry-based processing routes [V. P. Pavlović et al., 2007]. - 22 - L. B. Kong et al., 2002, have applied high-energy ball milling process to a mixture of BaCO3 and TiO2 powders, and obtained BaTiO3 at 800°C. This temperature is lower than that required in the conventional solid-state reaction process and comparable with those required by most of the chemical-based processing routes. M. V. Nicolić et al., 2006 studied the sintering mechanisms of mechanically activated BaTiO3 powder (for 60 and 120 min.) and compared it with the non-activated BaTiO3 powder. They found that, the sintering of the mechanically activated BaTiO3 took place in three stages with one sintering mechanism (grain boundary diffusion) compared to the non-activated BaTiO3 where there was only one stage with a volume diffusion mechanism. Also they found that, the apparent activation energies were lower for the activated powder compared to the non-activated one and are similar for the two activation times. V. P. Pavlović et al., 2007 studied the effects of mechanical activation of BaTiO3 on the evolution of the microstructure during non-isothermal sintering and the influence of mechanical activation on the electrical properties of activated BaTiO3. They showed that, mechanical activation and sintering regime had a significant influence on the dielectric properties of the specimens. The relative permittivity of the activated samples was larger than that of the non-activated samples. They suggested that, the small values of dielectric permittivity for non-activated samples could be attributed to the low densification and the high porosity of these samples. L. Wu et al., 2009 studied the dielectric properties of BaTiO3 ceramics fabricated by solid-state reaction from nano-size fine activated powders, and compared the results with those obtained for the material fabricated from micro-size coarse powders (prepared by ball milling). They found that, the crystal structure and the dielectric properties of BaTiO3 ceramic depend on the grain size of the raw material. They found that, when the particle size of the raw material becomes finer, the crystal structure changes from tetragonal to pseudo-cubic. The dielectric constant increases with decreasing grain size (for - 23 - pure nano-powders the room temperature dielectric constant is about 5000, and that of coarse powders is about 2200). The ferroelectric phase transition temperature decreases with decreasing the grain size. The sintering temperature of the ceramic using nano-powders as a raw material is 150°C lower than that using pure coarse powder. II- Chemistry-based methods Various chemistry-based methods have been proposed to produce high purity BaTiO3 fine powders at low temperatures. These include hydrothermal method, sol-gel processing, Spray pyrolysis, the oxalate route, microwave heating, a micro-emulsion process, and a polymeric precursor method…etc. The reaction mechanisms and thermodynamic modeling for powder formation during most of these methods have been studied. Hydrothermal method Hydrothermal method has been used for the low-temperature fabrication of BaTiO3 either as powders or thin films. This technique produces highly reactive powders toward sintering and also produces crystalline powders with controlled particle size and stoichiometry, and in some cases controlled shape. Extensive studies focused on the powder phase compositions and particle size and their effect on the dielectric properties of the barium titanate. H. Xu et al., 2004 reported that high purity BaTiO3 fine powders with high sintering density and high dielectric constant (6200) have been synthesized hydrothermally under moderate conditions, the tetragonal content and particle size of the as- prepared powder being optimized. S.-K. Lee et al., 2003 prepared nano-crystallite BaTiO3 powders using acylated titanium and barium acetate with hydrothermal method. They studied the effect of molar ratio of the starting material on the formation of BaTiO3 powders and they found that, the particle size differed with synthesizing conditions. Some researchers have investigated the reaction kinetics of BaTiO3 nucleation and growth from precursors in the hydrothermal method of preparation. A solid- - 24 - state kinetic analysis, supported by micro structural evidence proposed by J. Moon et al., 2003 indicated that the formation mechanism of BaTiO3 is dissolution and precipitation. J. Lisoni et al., 2002 have investigated the growth kinetics of BaTiO3 thin film deposits on the surface of TiO2 rutile single crystals under hydrothermal conditions. They found that impurities strongly affect the morphology of the hydrothermal BaTiO3 film grown on TiO2 (001) substrates. The high purity hydroxide allowed the formation of deposits with a pronounced crystal habit with octahedral grains. A less pure reagent with higher strontium content led to layered films of fine sized cubic BaTiO3 in contact with the TiO2 substrate, and large tetragonal grains on the top of the cubic layer (covering approximately 25% of the films). Sol-gel processing Sol-gel processing route was extensively studied, because it is very effective in producing ceramic powders of high purity, small size, and good uniformity at relatively low temperatures. The sol-gel method implies a stable colloidal (sol) solution, which gels into film when dried. The solution preparation is traditionally based on dissolved organometallic molecular precursors (usually alkoxides). Hydrolysis and poly-condensation occur and thus macromolecular oxide network is formed (O. Harizanov et al., 2004). W. Li et al., 2009 used the sol-gel process for the synthesis of BaTiO3 nano powders with pure perovskite structure at low temperature (700°C). They studied the effect of the initial particle sizes of BaTiO3 powder on the phase structure, microstructure and dielectric properties of the ceramics produced. The sol-gel technique is advantageous for the coating process since it allows the control of composition, surface morphology engineering and low temperature processing (which permits the use of thermally fragile substrate). Accordingly, several investigators used this technique for the formation of thin films (A. Dixit et al, 2002; O. Harizanov et al., 2004; M. M. Silvàn et al., 2002; P. Vitanov et al., 2003; R. Xu et al., 2002; D.H. Yoon et al., 2003, K. Yao et al., 2002). - 25 - Spray pyrolysis Spray pyrolysis is another technique used for synthesizing nanoparticles BaTiO3 with tetragonal phase by combustion of metal nitrates used as the oxidizer and carbohydrazide used as the fuel source with 1:1 molar ratio [S. Lee et al., 2004]. Fang T. and Lin H., 1987 showed that a high-purity barium titanate of nearly perfect stoichiometry can be prepared by precipitating barium titanyl oxalate {BaTiO.(C2O4)2. 4H2O.} and subsequently converting this material to the titanate by pyrolysis. C. Torres et al., 2003 used Barium and titanium stearate as precursor to obtain pure BaTiO3 at low temperature. III) Other methods Z. Peng et al., 2003 proposed a novel approach to prepare nano-powders of BaTiO3 by a solution reaction. A solution including titanate group was formed by using H2TiO3, H2O2, and NH3 in mole ratio of 1:8:2 together with Ba(NO)3 and by controlling the reaction conditions, dispersed and uniform nano- powders of BaTiO3 (average size of 15 nm) were obtained from the solution. Y. Yuan et al., 2004 prepared high performance X7R dielectric materials, with a high dielectric constant of 5200 and dielectric loss lower than 1.0%, by nanometer oxides doping method. They doped BaTiO3 powder with nanometer Nb2O5 and Co3O4. Recently, C. N. George et al., 2009 reported a modified combustion process for the preparation of a single phase BaTiO3. In This method they replaced the polyvinyl alcohol, used before, by citric acid and urea by ammonia. This change enabled the production of single phase BaTiO3 nanoparticles in a single step combustion process. J. Moon et al., 2002 prepared barium titanate from chemically modified titanium oxide precursor. Coprecipitated gels were obtained from titanium isopropoxide precursor modified with acetylacetone and barium acetate, by the addition to a KOH solution. Many other methods were used for the synthesis of BaTiO3 nano powders such as; Oxalate Coprecipitation (L. S-Seveyrat et al., 2007; X. Wang et al., 2004), - 26 - The thermal decomposition of (Ba, Ti)-citrate polyester resins (P. Duran et al., 2002), Surface-coated nano-powders (M.-B. Park* et al., 2002; M.-B. Park** et al , 2002), Gelcasting (S. Gong et al., 2003), Modified SiO2-exaggerated grain growth (J. M. Saldaña et al., 2002), Spark-plasma-sintering (B. Li et al., 2004), Attrition milling for undoped-BaTiO3 (O. P. Thakur et al., 2007). Other researches for preparing barium titanate films include; Anodic oxidation- based electrochemical on Ti metal (F.-H. Lu et al., 2002), Barium titanate screen-printed thick films (B. D. Stojanovic et al., 2002; B. D. Stojanovic et al., 2004), Mist plasma evaporation (H. Huang* et al., 2004; H. Huang** et al., 2004), Pulsed laser deposition (H. Kakimoto et al., 2001) Drawbacks of low temperature fabrication methods of BaTiO3: Most of the synthesis methods of BaTiO3 at low temperatures, especially wet chemical methods have some disadvantages or limitation for the synthesis of ultrafine BaTiO3 powders. For example: Hydrothermal BaTiO3 powders are usually of a paraelectric cubic phase, which needs additional heating to transform it to the tetragonal phase required to obtain ferroelectric properties. Due to the additional heating, the ultra-fine BaTiO3 powders get aggregated. The sol-gel method, in general, is faced with such difficulties as expensive precursors, the low production rate, and uncontrollable process. In the co-precipitation method, the requisite pH conditions and initial concentrations of metal cations are critical issues. True co-precipitation can not be achieved in a number of systems because of the large solubility differences among the solutes. Spray pyrolysis sometimes produces a small amount of a second phase and hollow particles. The second phase is known to be the result of a chemical segregation during precipitation (S. lee et al., 2004). - 27 - 2.2.5.2. Effect of dopants or additives on BaTiO3 properties Pure barium titanate, exhibits a great change in dielectric constant near the transition temperature. Generally, BaTiO3 is doped with small amounts of impurities to modify its properties and to widen the number of potential applications (Y. Park et al., 1997; M. T. Benlahrache et al., 2004). The polarization characteristics of BaTiO3 can be modified by crystal chemical alterations of the crystal structure. Barium (Ba) ion is very large and results in a large octahedral site in which the titanium ions can readily move. Substitution of smaller ions for Ba reduces the size of octahedral site and restricts the motion of the Ti ion. Addition of CaZrO3 or MgZrO3 to BaTiO3 results in a decrease in sensitivity to temperature by broadening the temperature versus dielectric constant curve. Addition of PbTiO3 to BaTiO3 increases the temperature at which the transformation occurs (Curie temperature) where the dielectric constant is a maximum, while the additions of SrTiO3, SrSnO3, CaSnO3, or BaSnO3 reduces the Curie temperature [D. W.Richerson, 1992]. Y. Park et al., 1997 reported that adding CeO2: 1.5 TiO2 to BaTiO3 decreased the ferroelectric transition temperature for cubic/tetragonal transformation and increased the transition temperature of tetragonal/orthorhombic and orthorhombic/rhomobohedral. They reported that, excess titanium dioxide increased the solubility limit of cerium dioxide in barium titanate. However, X. Wang* et al., 2003 found that the addition of CeO2 in a certain amount (0.4wt %) improves the piezoelectric and dielectric of the BNBT [(Bi0.5Na0.5)0.94Ba0.06TiO3] material. They found that CeO2 addition below 0.2wt% enhances the grain growth, while CeO2 addition over 0.2wt% decreases the grain size. B. D. Stojanvic et al, 2003 reported that the niobium had a prominent influence on the dielectric properties. They found that barium titanate doped with a concentration of 0.6mole% of Nb as donor dopant and 0.1mole% Mn, as acceptor dopant showed higher dielectric constant than undoped BaTiO3. M. T. Benlahrache et al., 2004 found that the addition of - 28 - NaNbO3 to BaTiO3 causes a considerable change in the microstructure of the sample (i.e. grain growth inhibition) and increase in density, dielectric constant, and dielectric strength. In addition, they found that, this kind of additives makes the dielectric constant flat in a wide temperature range and of good stability with frequency. J. Fisher et al., 2005 studied the effect of Al2O3 dopant on the abnormal grain growth (AGG) in BaTiO3 at various temperatures. They found that, for samples sintered at temperature ≤1250°C, the addition of up to 0.1mole% Al2O3 promotes the AGG, while further additions of Al2O3 inhibits it. They attributed the promotion of AGG to the dissolution of Al2O3 in the BaTiO3 lattice and the release of TiO2. While the inhibition occurs by Al2O3 reacting with excess TiO2 and BaTiO3 to form Ba4Al2Ti10O27. When sintering at temperature ≥1250°C, a thick liquid film is formed at the grain boundaries. As the Al2O3 content increases, the volume of the liquid film increases, retarding grain growth. The effects of other additives on the dielectric properties of BaTiO3 were studied by several researchers. These included; Y2O3/MgO co-doping (W.-C. Yang et al., 2004), Ru-doped BaTiO3 (C. H. Lin et al.,2003), Mn-doped BaTiO3 (X. Wang** et al., 2003; J. Tangsritrakual et al., 2010), Rhodium- doped BaTiO3 (S. Madeswaran et al, 2004), Neodymium-doped BaTiO3 (Y. Li et al., 2004), Copper-doped BaTiO3 (H. T. Langhammer et al., 2003), and single dopants such as: Sm2O3, Ho2O3 , Bi2O3, La2O3, CeO3, and Ta2O5 (Z. Li C. et al., 2005). 2.3. Applications of Ferroelectric Ceramics Piezoelectric and ferroelectric ceramics are extremely important and widely used in many technologies. Applications include phonograph pickups, band- pass filters, and control of oscillator frequencies in communication equipment, sonic delay lines, sonar, high-voltage step-up transformers, ultrasonic cleaning, medical ultrasound uses, industrial nondestructive inspection, watches, and - 29 - accelerometers (D. W. Richerson, 1992). With the development of ceramic processing and thin film technology, many new applications have emerged. These include; multilayer ceramic capacitors (MLCCs), piezoelectric actuators, and positive temperature coefficient resistors (PTCR), ferroelectric thin films for non volatile memories, electro-optic devices [S. Ahmed et al., 2006], and for humidity sensors based on composite material of nano-BaTiO3 and polymer RMX [J. Wang et al., 2002]. Recently, Y.-H. Chen et al, 2011 reported that synthetic nano-BTO and nano-STO can be used for removing Cu2+ from aqueous solutions and hence can be exploited in environment remedies. However, the biggest use of ferroelectric ceramics has been in the area of dielectric ceramics for ceramic capacitors. As the energy topic has become of increasing importance, the preparation of dielectric materials with high dielectric constant is highly demanded for the energy storage in the form of ceramic capacitors. This will be discussed in more details in the following section. 2.3.1. Ceramic Capacitors A capacitor is a dielectric material placed between two electrically conductive electrodes as shown in Figure (2.9). ______ Dielectric material + + + + + + + + + + + + + + + + + + + + + + + + + + + + + _ + Figure (2.9): Schematic diagram showing single-layer ceramic capacitor [D. W.Richerson, 1992] When the capacitor is placed in electric circuit, it is able to store electrical charge. The higher the degree of polarizability of the dielectric material, the - 30 - higher the relative dielectric constant and consequently the more the charge that can be stored. The amount of charge (Q) (in coulombs) that can be stored is equal to the applied voltage (V) (in volt) times the capacitance (C) (in farads). Q = VC …. (2.9) When a dielectric of relative permittivity (εr) is inserted into a parallel-plate capacitor the capacity which is: Co = εo A/d ….(2.10) Will increase to: C = Co εr = εo εr A/d ….(2.11) Where: A is the total area of the electrodes, εo is the permittivity of vacuum (8.85 x 10-12 farads/m), d is the spacing between the two electrodes or plates (i.e. thickness of the dielectric material). That is, the dielectric has increased the capacity by a factor of εr [R. M. Rose et al., 1971]. Then the capacitance is dependent on the relative dielectric constant (εr) and the geometry of the capacitor. The capacitance increases as the area and relative dielectric constant increase and as the thickness of the dielectric material decreases. Most capacitors have capacitance of much lower level in the range of microfarads (10-6 F), or nanofarad (10-9 F), or picofarad (10-12) [D. W. Richerson, 1992]. From the definition of capacity and current, we can write [R. M. Rose et al., 1971]: V = Q/C = ∫ I dt/C …. (2.12) And differentiating this relation, we get: I = C dV/dt …. (2.13) for the current through the capacitor. If the voltage used is sinusoidal, that is, it varies as: V = Vo sinωt …. (2.14) Vo is the maximum value of the voltage and ω = 2πf, where f is the frequency, and t is the time. Then: I = C Vo ω cosωt … (2.15) - 31 - 2.3.2. Types of Ceramic Capacitors The ceramic capacitors comprise two types: single layer and multilayer. The single-layer ceramic capacitor (the parallel plate capacitor) as mentioned above consists of dielectric material sandwiched between two parallel plates (see Figure-2.9). It has a relatively low capacitance capability because of the relatively small thickness of the monolithic dielectric layer [Richerson D. W., 1992]. The decrease in size of discrete components produces a decrease in the overall size of the capacitors. Since the physical size of the capacitor plays a huge role in the capacitance value, a solution was found in the form of stacking many layers of dielectrics on top of alternating conductors to form a so called multilayer ceramic capacitor (MLCC) [M. Allison, 2007] as schematically shown in Figure (2.10). Area A Dielectric slabs Thin metal electrods Figure (2.10): Schematic diagram showing a multilayer ceramic capacitor A multilayer ceramic capacitor has a higher capacitance, than the single-layer ceramic capacitor, because thinner and many dielectric layers can be fabricated [D. W. Richerson, 1992]. The capacitance of the multilayer ceramic capacitor (MLCC) is increased by a factor of (n-1) where n is the number of layers in the capacitor. The capacitance of the MLCC can be expressed as; C = εo εr (n-1)A/d .... (2.16) - 32 - Until 1995, the internal electrodes of most MLCCs were made of expensive noble metals such as alloys of silver and palladium. These have been replaced by base metals such as nickel or copper, which reduced the cost considerably [M. Allison, 2007]. 2.3.3 Functions of The Capacitors Capacitors are important elements in any electric circuit and can be used for a variety of different functions: energy storage, blocking, coupling, decoupling, bypassing, filtering, transient voltage suppression, and arc suppression. Energy storage involves building up a large charge in the capacitor for release at a later time. A couple of common applications are welding and photoflash bulbs. Blocking involves the interaction of the capacitor with dc versus ac currents. Direct current results in polarization in the capacitor and blocks the flow of current. Alternating current results in charge and discharge of the capacitor in opposite directions during each ac cycle, which has the effect of allowing ac current to pass. This characteristic is used to "couple" one circuit to another. Decoupling involves the use of a capacitor to isolate specific voltages to different areas of the circuit. Bypass involves the simultaneous use of blocking and coupling to separate the dc and ac components of a mixed signal. Bypass is achieved by placing the capacitor in parallel with the circuit device. The ac signal passes through the capacitor and the dc signal passes through the device. Filtering involves the use of a capacitor to separate ac signals of different frequencies. The higher the capacitance, the higher the current at any given frequency. Conversely, the higher the frequency at a fixed capacitance, the higher the level of current passing through. Thus filtering provides a means of tuning or frequency discrimination [D. W. Richerson, 1992] - 33 - Part-II: Kinetics and Thermodynamic Approach 2.4. Kinetics and Thermodynamic Studies on Barium Titanate Formation In the previous part (section-2.2.5), the different preparation methods to produce BaTiO3, from different titanium and barium precursors, have been reviewed. The BaTiO3 formation takes place through a chemical reaction between chemical precursors that could be in solid, liquid, vapor, or gaseous states. Studying the kinetic and the thermodynamics of these reactions is of fundamental importance to understand the mechanism by which this important material is formed. Since the method used for the BaTiO3 formation in the present work is the reaction in solid state between BaCO3 and TiO2; then the following paragraphs will concentrate on the solid state reactions. 2.4.1. Types of Chemical Reactions A chemical reaction in general is a process characterized by chemical changes in the reactants to give the products. a- Homogeneous reactions: The homogeneous reaction is the case when the reactants are in the same phase b- Heterogeneous reactions: Heterogeneous reactions deal with reactants in two or more different phases. In this case the phase interfaces play an important role in the reaction; where material transport across them takes place during the course of the reaction. c- Displacement reactions: Single displacement, A+BC→AC+B Double displacement, AB+CD→AD+CB d- Synthesis reactions: A + B → AB e- Decomposition reactions: AB→A+B f- Redox reactions: These are reactions where oxidation or reduction takes place; combustion is an oxidation reaction. g- Exothermic reactions: These are chemical reactions in which energy is released - 34 - h- Endothermic reactions: These are chemical reactions in which energy required for the reaction to occur is absorbed from the surrounding. Although in solid state chemical reactions material transport takes place in crystalline phases producing new phases, this does not mean that gases or liquids do not take a part in solid state reactions. 2.4.2. Reaction Kinetics Reaction kinetics are studies of the various aspects of the chemical reaction such as; the determination of its velocity as a function in temperature as well as its activation energy. In addition, it can give information about the reaction mechanism. 2.4.2.1 Theory 2.4.2.1.1. Generalized Kinetic Equation The rate of solid state reaction can generally be expressed by: d E Aexp( a ). f ….(2.17) dt RT Where: α is the reacted fraction at time t, f(α) is the function representing the reaction model as shown on Table (2.2), A is the pre-exponential factor of the Arrhenius equation, R is the gas constant, T is the absolute temperature, and Ea is the activation energy of the reaction. Equation (2.17) can be put in the integral form as follows: α d T E A exp( a ). dt 0 f 0 RT α d Putting g() 0 f T E Then; g() A exp( a ). dt ….(2.18) 0 RT The different expressions for g(α) are given in Table (2.2). - 35 - Table-2.2: Kinetic model functions for treating the conversion (α, fraction reacted) versus time data for solid state reactions. After E. K. Reza et al., (2007) and A. Khawan et al., (2006) Model Differential form Integral form f(α) = 1/k dα/dt g(α) = kt Nucleation models Power low (P2) (2α)1/2 (α)1/2 Power low (P3) (3α)2/3 (α)1/3 Power low (P4) (4α)3/4 (α)3/4 Avarami-Erofeyev (A2) 2(1- α)[-ln(1- α)]1/2 [-ln(1- α)]1/2 Avarami-Erofeyev (A3) 3(1- α)[-ln(1- α)]2/3 [-ln(1- α)]1/3 Avarami-Erofeyev (A4) 4(1- α)[-ln(1- α)]3/4 [-ln(1- α)]1/4 Prout-Tompkins (B1) α (1- α) ln(α /1- α)]+ cb Geometrical contraction models Contracting area (R2) 2(1- α)1/2 [1-(1- α)1/2] Contracting volume (R3) 3(1- α)2/3 [1-(1- α)1/3] Diffusion models 1-D Diffusion (D1) 1/(2α) (α)2 2-D Diffusion (D2) [-ln(1- α)]-1 [(1- α)ln(1- α)]+ α 3-D Diffusion-Jander (D3) [3(1-α)2/3]/[2(1-(1- α)1/3)] [1-(1- α)1/3]2 Ginstling-Brounshtein (D4) 3/[2((1- α)-1/3-1)] 1-(2 α/3)-(1- α)2/3] Reaction-order models Zero-order (F0/R1) 1 α First-order (F1) (1- α) -ln(1- α) Second-order (F2) (1- α)2 (1- α)-1-1 Third-order (F3) (1- α)3 0.5(1- α)-2-1 a In some references f(α) and g(α) have opposite designations. b Constant of integration. - 36 - 2.4.2.1.2. Reaction Kinetic Techniques 2.4.2.1.2.1. Isothermal Reaction Kinetics I- Model equation The reaction in this technique will take place in isothermal condition, that is at constant temperature then Equation (2.18) becomes: g(α) = К . t ….(2.19) Where: К is the temperature dependant rate constant which is equal to Aexp (Ea/RT). This integral equation could be used with the different model equations given in Table (2.2), to determine the reaction model and from the slope k; the activation energy could be calculated. II- Model free equation Rewriting Equation (2.19) as follows: E ln g(α) = ln A- a + ln t ....(2.20) RT Data of α versus time were obtained from at least three experiments done at three different temperatures. From these data the time values for constant conversion α at different temperatures were obtained. An Arrhenius plot of ln t and 1/T could be obtained at a constant value of α i.e. constant g(α). Then the activation energy of the reaction could be calculated without a need of the reaction model equation. 2.4.2.1.2.2. Non-Isothermal Reaction Kinetics In this technique the reaction proceeds upon heating the reactants at a constant heating rate; or heating in such a way that the reaction proceeds at a constant reaction rate. However, the constant reaction rate needs special programmed heating arrangement that is not normally available in commercial scientific equipment. I. Constant reaction rate technique The reaction will be expressed by Equation (2.17) - 37 - d E Aexp( a ). f = constant dt RT Then taking the logarithms, the following equation will be obtaind: E ln f(α) = constant-ln A+ a ....(2.21) RT Having the constant reaction rate data of α versus T, the kinetic parameters could be determined according to Equation (2.21). II. Constant heating rate technique a- kinetic model determination As the reactants have been heated at a constant heating rate β where: dT dt Then Equation (2.17) can be rewritten as: d . = k(T). f(α) ….(2.22) dT From the data of α and T obtained upon heating the reactants at different heating rates, values of dα/dT could be calculated at a constant temperature. Then plotting the values of β.dα/dT versus f (α) according to Equation (2.22) for different reaction models (from Table-2.2), straight lines will be obtained for the model equation f (α), which describes the reaction kinetics. Then for the determination of the activation energy, Equation (2.18) A T Eα g() exp( ).dT 0 RT Can be solved by introducing the function: ex P(x) x2 and by using Doyle approximation P(x) =-5.331-1.052x Coats A. W. and Redfern T., 1964 have derived the following equation: g() AE E ln ln a a ….(2.23) T 2 R RT - 38 - The predetermined f(α) which describes the reaction according to Equation (2.22), corresponds to a g(α) equation from Table (2.2). Then using this g(α) in Equation (2.23), Arrhenius plot could be obtained by plotting ln g(α)/T2 versus 1/T, and the activation energy Ea could be calculated. b- Model free kinetics In these techniques the kinetic parameters of the reaction could be obtained without knowing neither f(α) nor g(α). Based on the approximation made on E T a the integration of e RT . dT as mentioned in the previous section-a. 0 The reaction kinetics could be determined according to the following equation: AR Ea.R ln 2 ln ….(2.24) Tm Ea Tm This equation has been derived by Kissinger H. E., 1957 from the analysis of differential thermal analysis (DTA) data obtained by heating the reactants at different heating rates; Tm is the temperature at which a DTA peak occurs. Ozawa T., 1965 derived another equation for the analysis of thermogravimetric data obtained also at different constant heating rates β. The activation energy could be obtained from the slope of the Arrhenius plot of lnβ versus 1/T according to the following equation: ln β +0.4567Ea/RT= constant ….(2.25) 2.5. Thermodynamics of the chemical reactions While the reaction kinetics deal with the changes in concentration of the reactants and/or the products during the course of the reaction, thermodynamics deal with the energy balance between the products and reactants. It can tell which process can principally occur and whether it consumes or releases energy to the surroundings i.e., endothermic or exothermic. From the thermodynamic point of view, the sign of the Gibbs free energy change (∆G) of the reaction governs the feasibility of the reaction. Thus if ∆G is negative, the - 39 - reaction might proceed. At low temperature one observes many examples for which ∆G is negative but for which no significant reaction occurs because of sluggish kinetics. At high temperature however, the kinetic terms are less restrictive and consequently thermodynamic considerations become very important. The Gibbs free energy change of a reaction is, of course, composed of an enthalpy term (∆H) and an entropy term (∆S): ∆G = ∆H - T∆S ….(2.26) At low temperature T∆S is often small and the sign of ∆G is dominated by the sign of ∆H; at high temperature the T∆S term becomes of increasing importance (Swalin R. A., 1972). Thus, in general one can state that a chemical reaction can occur when the Gibbs free energy of the system decreases; that is when ∆G is negative or less than zero, which stands for the equilibrium. Calculations of the thermodynamic parameters in Equation (2.26) as a function of temperature are very important for studying the different aspects of the chemical reaction. This can be done through the following equations: First the enthalpy change for the different chemical precursors taking part in the reaction is: T HT H298 CPdT ….(2.27) 298 Where: = ∆H˚298 is the standard heat of formation and CP is the heat capacity [Kubaschewski O. et al., 1979] given by: -3 5 2 CP = a+b*10 T– c*10 /T ….(2.28) Where: a, b, and c are constants (the heat capacities of different compounds that were used in these calculations are presented in Table (6.1) in the appendix (Kubaschewski O. et al., 1979). The high temperature values of the second term in Equation (2.26) that is ∆S is given by the following equation: T CP ST S298 dT ….(2.29) 298 T - 40 - The thermodynamic data for the standard values ∆H298, ∆S298 for the chemical precursors used in the present work, was obtained from O. Kubaschewski et al., 1979 and M. Kh. Karapetyants, 1978 reference books. Applying these calculations for the precursors that could be used for the formation of BaTiO3 by solid state reactions. The following formulas could be used to calculate ∆S, ∆H, and ∆G for any proposed reaction that could possibly occur. The enthalpy change for the reaction is given by: ∆HR =∑∆HProduct -∑∆HReactant ….(2.30) and for the entropy change ∆SR =∑∆SProduct -∑∆SReactant ….(2.31) Where: ∆HProduct, ∆SProduct and HReactant, SReactant are the values calculated from Equations 2.27, 2.29 individually for each product and reactant precursor. Finally the Gibbs free energy change of the reaction at any temperature is calculated from the following equation: ∆GR =∆HR -T∆SR ….(2.32) The results of the thermodynamic analysis together with kinetic and XRD analyses might be useful for better understanding the reaction mechanism of BaTiO3 formation through solid state reaction. 2.6. Experimental techniques In order to follow up the chemical and/or the physical changes that occur during the course of a reaction, a wide variety of techniques have been developed. Among these, there are the group of thermal analysis equipment, evolved gas analysis, and x-ray diffraction. In the reactions where the weight of the reactants changes during the course of the reaction, thermogravimetry (TG) is an important tool in this respect. While, in the reactions where heat changes occur, which is normal in almost all reactions, differential thermal analysis (DTA) and differential scanning - 41 - calorimetry (DSC) are very useful. Differential thermal analysis can be used to study reactions accompanied by weight changes, melting, solidification, and phase changes as well. Usually both TG and DTA are used in reaction kinetic investigations. In any reaction the reactants undergo changes and give products of different chemical composition or phases. So, the x-ray diffraction (XRD) is helpful in this respect. It could be used also in reaction kinetic determination. In the later case, a calibration curve should be prepared for accurate quantitative phase analysis. Another technique used in reaction kinetic studies is gas chromatography whenever gas analysis (EGA) is required for reactions involving gas evolutions. Objectives The present work deals with the formation of barium titanate from different precursors through solid state reactions. Objectives of this work are: 1. Studying the different aspects of preparing barium titanate from BaCO3 and TiO2 using high energy planetary milling, such as: Milling time Calcination temperature Calcination time 2. Studying the preparation of BaTiO3 from Ba(NO3)2 and TiO2. 3. Studying the phase formation using XRD analysis. 4. Performing thermodynamic and kinetic analyses to study the mechanism of BaTiO3 formation through solid state reaction in the following systems. a- BaCO3-TiO2 system b- Ba(NO3)2-TiO2 system 5. Studying the sintering behavior of the prepared BaTiO3 powders. 6. Studying, the microstructure and dielectric properties of the sintered BaTiO3 prepared in this work through the solid state reactions. - 42 - CHAPTER (3) Experimental Work EXPERIMENTAL WORK 3.1. Materials for the preparation of BaTiO3 powder Table (3.1) gives a list of the materials that were used for the preparation of the BaTiO3 powder in this study. These starting materials were BaCO3, Ba(NO3)2, TiO2-c derived from TiCL4 and TiO2-BDH powders. All starting powders were of high purity to avoid uncontrolled chemical reactions during preparation and the consequent bad effect on the final properties of the BaTiO3 ferroelectric material Table-3.1: List of the materials used for the preparation of the BaTiO3 powder. Starting Materials Sources Purity - BaCO3 - Aldrich Chemical Company, USA 99% - Ba(NO3)2 - Fisher ChemAlert® Guide, USA 99.6% - TiO2-BDH - BDH Chemicals Ltd. Poole, England 98% - TiCl4 - Aldrich Chemical Co. Ltd., Gillingham- Dorset-England 3.1.1. Titanium dioxide powders In this study, two types of titanium dioxide were used; the first was TiO2-BDH powder. The second one denoted as TiO2-c, which is a very fine powder, prepared from TiCl4. 3.1.1.1. Preparation of TiO2-c fine powder from TiCl4 TiCl4 was added to ice cold distilled water to form an intermediate compound (which might be, hydrated titanium tetrachloride, titanium hydroxy chloride, or titanium oxychloride) as suggested by M. M. Archuleta et al., 1993 and S. R. Dhage et al., 2004. Few drops of ammonium hydroxide have been added to precipitate some TiO2 which will act as a seed for the nucleation of TiO2 fine powder upon, during overnight aging with continuous stirring. - 43 - Equation of seed formation is: TiCl4 + 4NH4OH → TiO2 + 4NH4Cl + 2H2O ....(3.1) While the hydrolysis reaction with water is: TiCl4 + 2H2O → TiO2 + 4HCl ...(3.2) The last reaction is thermodynamically favorable with ∆G = -54.29 kJ/mole, at 25°C, in agreement with L. G. Hua et al., 2005. The precipitate was then filtered, washed several times by distilled water and oven dried at 100°C overnight. Following that, the dried TiO2 powder was ground in agate mortar and sieved with 112μm screen. The obtained TiO2 had a surface area of 86m2/g. However, the TGA analysis showed that the dried TiO2 powder still contained ~17.3wt% of moisture. So, this was taken in consideration while making the mixture of BaCO3 and TiO2-c in a molar ratio of 1:1. 3.2. Instruments To prepare and characterize the barium titanate ferroelectric material (BaTiO3), different types of equipment and devices have been used. The functions and models of these equipment and devices are given in Table (3.2). - 44 - Table-3.2: Equipment and devices used in the preparation of the BaTiO3material Equipment Model Function 1. Agate Mortar 1. Fritsch 1. Crushing 2. Planetary Mill 2. Retsch PM400-type 2. Mechanical Milling Hydraulic Press Perkin-Elmer, Pressing (Max. load is 25 ton) Sintering Furnaces 1. Carbolite Furnace GPC 1300, Sintering UK 2. Carbolite Furnaces, RHF 17/3E (Max. Temperature 1700C), UK Drying Furnace NEY Furnace, M-525 Drying Scanning Electron JEOL, JSM 5400 Examination of Microscope (SEM) Microstructure X-Ray Diffractometer XRD-3A Shimadzu, Japan Phase Analysis (XRD) Thermo-Gravimetric TGA-50 Shimadzu, Japan Thermal Analysis Analyzer (TGA) Thermo-Mechanical TMA-50 Shimadzu, Japan Thermal Analysis Analyzer (TMA) Differential Thermal DTA-50 Shimadzu, Japan Thermal Analysis Analyzer (DTA) Surface Area (Flowsorb 2300, Micromeritics Surface Area Analyzer (BET) Instrument, Norcross, GA) Grinder-Polisher METKON ® Polishing GRIPO ® 1 RCL meter Philips, PM6304 Dielectric Measurements - 45 - 3.3. Methods of preparation of the BaTiO3 powder In this study, the solid-state reaction method was used for obtaining BaTiO3 powders starting with two different powder mixtures: the BaCO3-TiO2 mixture and the Ba(NO3)2-TiO2 mixture. The BaCO3-TiO2 powder mixture was pre- activated prior to the solid-state reaction using the high energy ball mill. While for the Ba(NO3)2-TiO2 powder mixture, it was ground in agate mortar followed by sieving. 3.3.1. BaCO3/TiO2-c powder mixture (High-energy ball milling process) The BaCO3 powder together with TiO2 were used as the starting materials with a nominal composition of BaTiO3. Two types of the titanium dioxide powder were used as mentioned before, the commercial TiO2-BDH and TiO2-c. The milling operation was carried out using planetary ball mill. Two 250 ml plastic polyamide bowls and 32 agate balls (for each bowl), each ball has a diameter of 15mm and weight of 5.6 gm. The milling speed was set at 200rpm. The milling was stopped for 5 min for every 30 min to cool down the system. The powders were mixed with Ethyl Alcohol to form slurry, and then milled in the planetary mill for different milling times: 2.5, 5, 7.5, 10, and 12.5 hours. The slurry was dried at 90C in the drying furnace and then crushed in agate mortar to eliminate agglomerates. After that, the powder was passed through a sieve of size 112 µm. The sieved powder was calcined at different temperatures (600-900°C) and for different calcination times, using a heating rate of 10°C/min and then furnace cooled. The preparation steps of the BaTiO3 powder, using high-energy ball milling process are schematically shown in Figure (3.1). - 46 - BaCO3 Titanium Alcohol dioxide Planatery-ball mill ( 2.5- 12.5h, milling times) Drying, at 90°C Crushing Sieving, 112μm Calcination (600-900°C) Characterization Figure (3.1): Flow chart of the preparation steps of the BaTiO3 powders by high energy ball milling method 3.3.2. Ba(NO3)2 /TiO2-c powder mixture The Ba(NO3)2 together with TiO2-c starting powders were mixed and crushed in agate mortar for 2h, then passed through a sieve of size 112μm. The mixture was calcined at 600°C for 1h and six hours. - 47 - 3.4. Materials Characterization For both methods of preparation Standard characterization techniques were applied on the; starting powders, the as prepared BaTiO3 powder, and the sintered specimens. 3.4.1. BaTiO3 Powder Characterization 3.4.1.1. Thermal analyses The thermal behaviors of the starting and the prepared powders were studied, using differential thermal analyzer (DTA) and the thermo-gravimetric analyzer (TGA) at a heating rate of 5°C/min. 3.4.1.2. Phase analysis and the crystallite size X-ray diffractometer (XRD) was used to determine the different phases present in the starting and the calcined powders, as well as the sintered specimens. The diffraction patterns were recorded over the angular range 2θ from 20 to 80°. The crystallite sizes (tc) of different samples were estimated from the (110) peaks of XRD patterns, using Scherrer’s formula: tc= Ķ λ/ßcosθ…..(3.2) Where, Ķ is the shape coefficient (value between 0.9 and 1.0), λ the wave length, ß is the full-width at half-maximum, and θ the diffraction angle. The full-width at half-maximum (ß) that is used for the calculation of crystallite size must be corrected. For this purpose, we chose the single peak at 2θ of 31.5° within the XRD pattern and a standard sample (sintered at high temperature) with narrow peak width, bo, of 0.17°, assuming coefficient Ķ=0.9. The ß parameter was corrected using the following equation (X. Li et al., 1997): 2 2 2 B = ß +b0 …(3.3) Where: B is the measured full-width at half-maximum (FWHM) of each phase - 48 - 3.4.1.3. Specific surface area (BET) Specific surface area of the BaTiO3 powders was measured using BET area meter. Then the equivalent sphere diameter was calculated from the expression: D= 6/ρS …(3.4) Where: D is the average diameter of spherical particles, S is the surface area of 3 the powder, and ρ is the theoretical density of BaTiO3 (6.02 kg/cm ). 3.4.2. Reaction Kinetics XRD, DTA and TG were used for the determination of the reaction kinetics of the formation of BaTiO3 powder from BaCO3/TiO2-c and Ba(NO3)2/TiO2-c mixtures. 3.4.3. Pressing and Sintering The as prepared powders were die-pressed into discs of 12 mm diameter and approximately 2mm thickness. The samples were pressed at different pressures (381, 609, 762, and 1066 MPa) to optimize the highest green density. Finally, the compact samples were sintered at 1300C for 3h. The sintering process was done as follows; first, the compacted discs were pre- heated at 600 for 3h in order to eliminate the binder and other organic materials, then the temperature was raised to 1300C at a heating rate of 2°C/min where the samples were soaked for 3h followed by cooling at a rate of 2°C/min. 3.4.4. Density measurement The green density (ρ) of the compacts was estimated from the mass and volume measurements in air. The apparent density of the sintered ceramics was determined both geometrically and by the Archimedes method of immersion in water, according to following equation: - 49 - ρ = [mo /m1-(m2-mw)] x ρwater …(3.5) Where: ρ = ceramic density mo = dry weight m1 = wet weight in air m2 = wet weight suspended in water mw = weight of wire (used to suspend the sample in water) suspended in water ρwater = density of water 3.4.5. Dilatometeric Study To study the shrinkage behavior of the compact made from the as milled powder, dilatometric investigations were carried out using Thermo-Mechanical Analyzer (TMA). The compacts were heated to 1300°C at a heating rate of 5°C/min. 3.4.6. Microstructure The characteristics of the prepared and calcined powders including particle morphology, agglomerations and grain size were examined using a Scanning electron microscope (SEM). The as-fired surfaces of the sintered bodies were also examined by SEM. 3.4.7. Dielectric Properties The dielectric behaviors were investigated with RCL meter. For electrical properties characterization, the sintered samples were surface ground using silicon carbide grit 2400 to obtain parallel and flat faces. Thickness and diameter of the samples were measured by a micrometer. Silver electrodes were painted onto both main sides of the samples and then these samples were heat-treated at 550°C for 30 min to ensure the contact between the electrodes and the ceramic surface. After that, the samples were placed between two platinum thin plates in a tube furnace and connected to RCL meter by platinum wire. - 50 - The capacitance of the sintered samples was measured as functions in both temperature and frequency. The dielectric properties were determined over the temperature range from room temperature to 200°C in the frequency range from 500Hz to 100 kHz. Before each heating run, the samples were first heated up to the selected temperature and held there for 30 min. The dielectric constant or the relative permittivity (εr) was calculated from the measured capacitance (C) according to the following equation: εr =Cd/ εoA …(3.6) Where: d is the thickness of the dielectric, A is the total area of electrodes and -12 εo is the dielectric permittivity of vacuum (8.854x10 Farad/meter). - 51 - CHAPTER (4) Results 4. RESULTS 4.1. Powder Characterization 4.1.1. BaCO3-TiO2 powder mixture 4.1.1.1. BaCO3-TiO2 starting powders 4.1.1.1.1. Thermal analysis (DTA &TGA) Figure (4.1) shows the DTA and the TG results obtained for the barium carbonate starting powder (BaCO3). The DTA curve shows three endothermic peaks at 838.3°C, 991, 1260°C. The endothermic behaviour is accompanied with a total weight loss of the powder of approximately 22.39 % as shown on the TG curve. Figure (4.2) shows the DTA and the TG results obtained for the titanium dioxide starting powder (TiO2-c). The DTA shows only small endothermic peak at 79.17°C and upon increasing the temperature to 1000°C, the DTA curve shows no endothermic or exothermic behaviors. Meanwhile, the TG curve shows a total weight loss of the powder of approximately 18 %. 0 300 600 900 1200 1500 5 50 0 0 TG,% -5 DTA,uV -50 -10 22.39 % -100 -15 838.3°C 991°C -150 DTA, uV DTA, Weight loss, % loss, Weight -20 -200 1312°C -25 1260°C -250 -30 -300 0 200 400 600 800 1000 1200 1400 1600 Tempearature,°C Figure (4.1): DTA-TG of barium carbonate (BaCO3) - 52 - 2 10 0 0 -2 79.17°C DTA, uV -10 -4 -20 -6 -30 -8 -40 -10 -50 uV DTA, -12 Weight loss, % Weight -14 TGA, % 18,137 % -60 -16 -70 -18 -80 -20 -90 0 200 400 600 800 1000 1200 Temperature,°C Figure (4.2): DTA-TG of titanium dioxide (TiO2-c) 4.1.1.1.2. SEM of the starting powders Figure (4.3) shows the SEM micrographs of the BaCO3 and TiO2-c starting powders. The morphology of BaCO3 powder shows rods or needlelike shapes (Figure 4.3-a), while that for the TiO2 powder, shows agglomerates of spherical shape (Figure 4.3-b). (a) (b) Figure (4.3): SEM of dispersed powder of; (a) BaCO3 (b) TiO2-c - 53 - 4.1.1.2. BaCO3-TiO2-c milled powder mixtures 4.1.1.2.1. Thermal analysis (DTA &TGA) Figure (4.4) shows the DTA-TG curves for the BaCO3-TiO2-c milled powder mixtures. It can be seen from the figure that, the DTA curve does not show any endothermic or exothermic peaks during heating up till a temperature of about 1000°C, while the thermo-gravimetric (TG) curve shows a weight loss of 18.5% upon heating up to the same temperature. In order to obtain detailed results from the TG curve shown in Figure (4.4), a differential curve DTG was reproduced, and it is shown in Figure (4.5) together with the TG curve. A DTG peak at 40°C corresponds to a weight loss of 2.47 % on the TG curve from the room temperature to 220°C. A second DTG peak at 293°C corresponds to a weight loss of 2% taking place between 220 and 430°C. Then in the temperature range from 430 to 1000°C, the TG curve shows 15.8 % weight loss taking place in three consecutive stages; characterized by three DTG peaks at 612, 729, and 915°C. The maximum rate of weight loss occurred at 915°C. 5 20 0 0 -20 -5 -40 -10 -60 DTA,uV weight loss, % loss, weight -80 -15 -100 -20 -120 0 200 400 600 800 1000 1200 Temperature,°C Figure (4.4): DTA-TG for BaCO3/TiO2-c milled powder mixture - 54 - 5 0 Dr TG -0.0005 0 292.6°C -2.47% 728.8°C -2% -0.001 40°C TGA, % 611.8°C -5 -0.0015 -10 -15.8% -0.002 TG Dr Weight loss, % Weight -0.0025 -15 -0.003 914.7°C -20 -0.0035 0 100 200 300 400 500 600 700 800 900 1000 1100 Temperature,°C Figure (4.5): DTG curve of the BaCO3/TiO2-c milled powder mixtures 4.1.1.2.2. SEM of the BaCO3-TiO2-c milled mixture Figure (4.6) shows the SEM micrographs of the as milled BaCO3/TiO2-c powder mixtures. It can be seen from the figure that, the morphology of the milled powder still preserved some of the starting powder shape (Figure 4.3-a, 5000x magn.). Fine particles less than 200 nm in size and large agglomerates of 3μm or greater could be observed. Higher magnification (15000x), Figure (4.6-b), shows that large agglomerates are composed of small particles. (a) (b) Figure (4.6): SEM of dispersed powder of the BaCO3/TiO2-c milled mixture - 55 - 4.1.1.2.3. Dilatometeric Study (TMA) Thermo-Mechanical Analyzer (TMA) was used to study the shrinkage behavior of the compacts made from the as milled BaCO3/TiO2-c powder mixture, milled for different milling times. The dilatometeric curves were obtained using the constant heating rate technique, CRH, at 5°C/min as a heating rate. Figure (4.7) shows the relative linear shrinkage of the different compacts. From the figure it can be seen that, irrespective of the milling time, the shrinkage took place in two stages: the first one started at ~654°C and ended at 895°C, this stage may contain two or three consecutive steps. Then upon further heating, no shrinkage could be observed until the second stage of shrinkage started at ~1135°C and continued with an increasing rate during the heating up to ~1320°C. In this later stage it can be seen that, the shrinkage of the powder compact increased with the increase in the milling time. The shrinkages values were: 16, 21.4, 23.4% for 7.5, 10, 12.5h milling time, respectively. Figure (4.8) shows the linear shrinkage rate versus temperature and time. From the figure it can be seen that, in the first stage the maximum in the shrinkage rate decreased with the increase of milling time, while in the second stage, the maximum in the shrinkage rate increased with the increase of the milling time. Irrespective of the milling time, the maxima in the shrinkage rates occurred nearly at the same temperature of ~714°C for the first stage and at ~1292°C for the second stage. In addition, in the first stage of shrinkage the figure shows that, for the 12.5h milling time there were two clearly observed maxima; the first one at 714°C and the second at 836°C. On the other hand, for the 7.5 and 10 h milling times a maximum was observed also at 714°C, while the second one was less significant (it broadened from ~775°C to ~915°C). - 56 - 0.05 1400 Temperature,°C 0 654°C 1200 895°C 1135°C 1000 -0.05 800 -0.1 1308°C 600 -0.15 7.5h-16% 400 Temperature,°C Relative linear shrinkage linear Relative 10h- 21.4% -0.2 200 12.5h- 23.4% -0.25 0 0 1000 2000 3000 4000 5000 6000 7000 8000 Time, sec Figure (4.7): Relative linear shrinkage of the as milled BaCO3/TiO2-c mixtures 0.05 1400 614°C 0 915°C 775°C 1200 -0.05 836°C -0.1 1000 -0.15 714.2°C 800 -0.2 DrTMA-7.5 600 (ΔL/L.sec) -0.25 Temperature,°C -0.3 400 DrTMA-10 Relative linear shrinkage rate rate shrinkage linear Relative -0.35 DrTMA-12.5 200 -0.4 1292°C -0.45 0 0 1000 2000 3000 4000 5000 6000 7000 8000 Time, sec Figure (4.8): Shrinkage rate versus temperature and time for the as milled BaCO3/TiO2-c mixtures - 57 - 4.1.1.2.4. X-Ray Diffraction of the BaCO3-TiO2-c milled mixture Figure (4.9) shows the XRD pattern for the as milled BaCO3 and TiO2-c powder mixture milled for 12.5h. It can be seen that, all the diffraction peaks correspond to either BaCO3 or TiO2 phases. This implies that no reaction took place between the BaCO3 and TiO2-c powder mixtures during the mechanical milling. Figure (4.10) shows the XRD patterns for two equimolar mixtures of BaCO3 and titanium dioxide. In the first mixture the TiO2-BDH powder was used, while in the second the TiO2-c obtained from the titanium tetra chloride was used. The two mixtures were milled for 7.5h and calcined at 900/1h. It can be seen from the figure that, the XRD pattern of the BaCO3/TiO2-BDH powder mixture contained peaks corresponding to unreacted BaCO3 and TiO2. As for the BaCO3/TiO2-c powder mixture, the XRD pattern showed only BaTiO3 phase. This might be due to the relatively higher reactivity of the fine TiO2-c powder. Accordingly, it was decided to use the TiO2-c powder in the present work for the BaTiO3 preparation. 45 BaCO -γ 40 3 TiO2 35 30 25 I, a. u. a. I, 20 15 10 5 0 20 30 40 50 60 70 80 2^Theta Figure (4.9): XRD pattern of BaCO3/TiO2-c powder mixture milled for 12.5h - 58 - 60 ) BaTiO 110 50 ( BaCO3-γ TiO ) 2 ) ) 40 211 ( ) 111 ) ( ) ) 002 ( ) 200 ) ( 202 001 310 ( ) ( 30 ( 210 212 ( ( I, a. u. a. I, TiO2-c 311 ( 20 TiO2-BDH 10 0 20 30 40 50 60 70 80 2^theta Figure (4.10): XRD patterns of BaCO3/TiO2-c and BaCO3/TiO2-BDH powder mixtures milled for 7.5h and calcined at 900/1h. 4.1.1.3. Characterization of the BaCO3-TiO2-c calcined mixtures 4.1.1.3.1. SEM of BaTiO3 powders Figure (4.11) shows the morphology of the BaTiO3 powders prepared from the BaCO3/TiO2-c milled mixtures, and calcined at 800°C for 3h. It can be seen from the figure that the powders are in the form of spherical agglomerates. The size of agglomerates ranged from; 150nm to 2.2μm, 150nm to 2.5 μm, and 150nm to 3μm for the powders milled for 7.5, 10, and 12.5h, respectively. 4.1.1.3.2. The crystallite size and the specific surface area Table (4.1) gives the crystallite size, BET surface area, and the equivalent sphere diameter for the BaTiO3 powders prepared from the BaCO3-TiO2-c milled mixture. Values in Table (4.1) show that, this method of preparation produces a fine powder. The crystallite size of the mechanically milled powders decreases with the increase of milling time. As for, the specific surface area; it increases with the increase of milling time. - 59 - (a) (b) (c) Figure (4.11): SEM micrographs for the BaTiO3 powders prepared from the BaCO3/TiO2-c powder mixture and milled for: a) 7.5h, b) 10h, c) 12.5h - 60 - Table-4.1: The crystallite size, BET surface area, and equivalent sphere diameter for the BaTiO3 powders, prepared from the BaCO3/TiO2-c milled mixture and calcined at 800°C for 3h. Milling time 7.5h 10h 12.5h Crystallite size from XRD, nm 27.25 25.9 23.585 Specific surface area (BET), m2/gm 1.0445 2.087 2.3249 Equivalent sphere diameter from BET, nm 954 477.6 422.8 4.1.1.3.3. BaTiO3 formation- important variables Different parameters such as; the milling time, the calcination temperature, and the calcination time affect the formation of barium titanate (BaTiO3) from the BaCO3/TiO2-c powder mixtures, these parameters will be discussed in the following paragraphs: a) Effect of milling time: Figure (4.12) shows the XRD patterns for BaCO3/TiO2-c powder mixtures milled for 2.5, 5, 7.5, 10 and 12.5h, followed by calcination at 800°C for 3h. It can be seen that, milling time up to 5hours is not enough for the complete conversion of BaCO3 and TiO2-c to BaTiO3. Milling time of 7.5h showed a complete formation of BaTiO3 phase. The XRD patterns of the powders milled for 10 and 12.5h were identical to the pattern of the powder mixture milled for 7.5h. The fractions reacted, that is the amounts of BaTiO3 formed as a result of the reaction between BaCO3 and TiO2-c, are given in Table (4.2) as function of milling time for the powders calcined at different temperatures for different times. The fractions reacted were calculated from the integrated peak area of the XRD lines (011) for BaTiO3, (111) for BaCO3, and (200) for TiO2-c. It can be seen that, the reacting fraction increases with the milling time up to a milling time of 10 hours. On the other hand, the mixed powder milled for 12.5h showed a slight decrease in the fraction reacted relative to that for the powders milled for 10h. - 61 - ) BaCO3-γ 110 BaTiO3 ( TiO2 BaTiO3 ) BaCO3- ) ) 211 ( ) β ) 111 ) 002 ) ( ( ) ) 200 202 ) ( ( 310 001 ( ( 210 311 ( 212 ( ( I, a. u. a. I, 12.5h 10h 7.5h 5h 2.5h 20 30 40 50 60 70 80 2^Theta Figure (4.12): Effect of milling time on the formation of BaTiO3, from BaCO3/TiO2-c milled powder mixtures calcined at 800°C/3h Table-4.2: the fraction reacted of BaCO3/TiO2-c mixture, milled for different times and calcined at different temperatures and times Percentage fraction reacted Calcination Milling Milling Milling Milling Milling temperature time 2.5h time 5h time 7.5h time 10h time 12.5h 700/1h 16.5 28.2 48.72 50.5 50.11 750/5h 33.2 54.73 77.3 82.1 80.94 800/1h - 43.3 68.9 70 69.8 800/3h 100 100 100 - 62 - b) Effect of calcination temperature: The XRD patterns of powder mixtures milled for 7.5, 10, and 12.5h and calcined at different temperatures from 600 to 900°C for one hour are shown in Figures (4.13-4.15). Figures (4.13) and (4.14) show that for the powder mixtures milled for 7.5 and 10h, the formation of BaTiO3 starts at 600°C (peak of BaTiO3 phase appears at 2θ: 31.5°). On the other hand, the XRD patterns for powder mixture milled for 12.5h (Figure 4.15) show that the BaTiO3 phase could be detected at 700°C. XRD patterns for the calcined powders at 800°C, irrespective of the milling time, showed very small amounts of an orthotitanate intermediate phase (Ba2TiO4) at 2θ: 28.6°, which coexisted with BaTiO3, BaCO3 and TiO2-c phases. Further, upon increasing the calcination temperature to 900°C only a single phase BaTiO3 was formed. In all of the above XRD patterns, BaO phase was not observed even in small quantities. BaCO3-γ TiO2 BaTiO3 BaCO3-β Ba2TiO4 900°C/1h I, a. u. a. I, 800°C/1h 700°C/1h 600°C/1h RT 20 30 40 50 60 70 80 2^Theta Figure (4.13): XRD patterns of BaCO3/TiO2-c powder mixtures milled for 7.5h and calcined at different temperatures - 63 - BaCO3-γ TiO2 BaTiO3 BaCO3-β Ba2TiO4 900°C/1h I, a. u. a. I, 800°C/1h 700°C/1h 600°C/1h RT 20 30 40 50 60 70 80 2^Theta Figure (4.14): XRD patterns of BaCO3/TiO2-c powder mixtures milled for 10h and calcined at different temperatures BaCO3-γ TiO2 BaTiO3 BaCO3-β Ba2TiO 4 900°C/1h I, a. u. a. I, 800°C/1h - 700°C/1h 600°C/1h RT 20 30 40 50 60 70 80 2^Theta Figure (4.15): XRD patterns of BaCO3/TiO2-c powder mixtures milled for 12.5h and calcined at different temperatures - 64 - c) Effect of calcination time: Figures (4.16-4.19) show the effect of the calcination time on the amount of BaTiO3 phase formed after calcination of the BaCO3/TiO2-c powder mixtures, milled for 7.5h, at different calcination temperatures. It can be seen from the figures that, irrespective of the calcination temperature, the formation of BaTiO3 phase increases with the increase of calcination time. Similar figures for the powder mixtures milled for 10 and 12.5h are given in the appendix (Figures 6.3 and 6.4). The XRD peak corresponding to the Ba2TiO4 intermediate phase (in trace amount) appears only on the XRD patterns obtained for the milled powder calcined at 750°C for 2h and at 800°C for 1h. Upon increasing the calcination time to 5h at 750°C and to 3h at 800°C; this intermediate phase disappeared and only a single phase BaTiO3 existed. BaTiO3 BaCO3-γ TiO2 15h I, I, a. u. 10h 7h 1h 20 30 40 50 60 70 80 2^Theta Figure (4.16): Effect of Calcination time on the formation of BaTiO3, from BaCO3/TiO2-c powder mixture milled for 7.5h and calcined at 700°C - 65 - 250 BaCO3-γ TiO2 200 BaTiO3 Ba2TiO4 150 10h I, a. u. a. I, 100 8h 7h 50 5h 2h 0 20 30 40 50 60 70 80 2^Theta Figure (4.17): Effect of Calcination time on the formation of BaTiO3, from BaCO3/TiO2-c powder mixture milled for 7.5h and calcined at 750°C 160 BaCO3-γ 140 TiO2 120 BaTiO3 Ba TiO 100 2 4 80 4h I, a. u. a. I, 60 3h 40 2h 20 1h 0 20 30 40 50 60 70 80 2^Theta Figure (4.18): Effect of Calcination time on the formation of BaTiO3, from BaCO3/TiO2-c powder mixtures milled for 7.5h and calcined at 775°C - 66 - BaCO3-γ TiO2 BaTiO3 Ba2TiO4 I, a. u. a. I, 5h 3h 2h 1h 20 30 40 50 60 70 80 2^Theta Figure (4.19): Effect of Calcination time on the formation of BaTiO3, from BaCO3/TiO2-c powder mixture milled for 7.5h and calcined at 800°C 4.1.2. Ba(NO3)2/TiO2-c powder mixture 4.1.2.1. Thermal analysis (DTA &TGA) Figure (4.20) shows the DTA-TG curve obtained upon heating equimolar Ba(NO3)2 and TiO2-c powder mixture. Three endothermic peaks at 605, 633.7 and 675.2°C are observed on the DTA curve. These were accompanied with a total weight loss of the powder of approximately 34.2% as shown on the TG curve. The first part of the weight loss of 3.15% lies in the temperature range from 25 to 400°C, and corresponds to the elimination of the adsorbed water on the surface of TiO2-c powder. The second part of 31.05% weight loss lies between 600 and 700°C, which is due to the reaction between Ba(NO3)2 and TiO2-c. - 67 - 5 20 TGA, % 0 -3.15% 0 -5 DTA, uV -20 -10 -31.05% -15 -40 -20 -60 DTA,uV Weight loss,% Weight -25 675.2°C -80 -30 605°C -100 -35 633.7°C -40 -120 0 200 400 600 800 Temperature,°C Figure (4.20): DTA-TG curve for the Ba(NO3)2/TiO2-c powder mixture 4.1.2.2. Powder morphology The SEM, Figure (4.21), shows the morphology of the BaTiO3 powders prepared from the reaction of Ba(NO3)2/TiO2-c powder mixture at 600°C for 6h. It can be seen from the figure that, the powder contains fine and coarse agglomerates. The size of the agglomerates which are mostly spherical is in the range from 0.3μm to 3μm. 4.1.2.3. The crystallite size and the specific surface area Table (4.3) gives the crystallite size, BET surface area, and equivalent sphere diameter for the BaTiO3 powder prepared from Ba(NO3)2 and TiO2-c, reacted at 600°C for 6h. It can be seen that, the equivalent sphere diameter calculated from the specific surface area is nearly 11 times greater than the crystallite size obtained from the XRD line broadening, indicating that each agglomerate on the average consists of eleven crystals. - 68 - Figure (4.21): SEM micrograph of the BaTiO3 powder prepared from the Ba(NO3)2/TiO2-c powder mixture, calcined at 600C for 6h. Table-4.3: The crystallite size, BET surface area, and equivalent sphere diameter for the BaTiO3 powder prepared from the Ba(NO3)2/TiO2-c reaction. Crystallite size from XRD, nm 23.8 Specific surface area (BET), m2/gm 3.8519 Equivalent sphere diameter from BET, nm 258.7 4.1.2.4. X-Ray Diffraction Figure (4.22) shows the XRD patterns of two Ba(NO3)2 and TiO2-c powder mixtures, calcined at 600°C for one hour for the first and six hours for the second. From the figure it can be seen that, after calcination of the mixture for one hour, TiO2-c and Ba(NO3)2 phases still existed, indicating that a calcination time of one hour was not enough for complete formation of BaTiO3. When the powder mixture was calcined at this temperature for additional five hours, i.e. 6h in total, a single phase perovskite BaTiO3 was then obtained. No peaks for BaO or any other intermediate phases appeared in the XRD patterns. - 69 - ) BaTiO3 110 ( Ba(NO3)2 TiO2 ) ) ) ) ) 211 111 002 ) ( ( ( ) I, I, a. u. ) ) ) 200 202 ( ( 310 001 ( 210 311 ( 212 ( ( ( 6h 1h 20 30 40 50 60 70 80 2^Theta Figure (4.22): XRD patterns of the Ba(NO3)2/TiO2-c powder mixtures calcined at 600°C 4.2. Reaction Kinetics 4.2.1. BaCO3/TiO2-c reaction 4.2.1.1. X-Ray Diffraction method X-Ray diffraction method for the reaction kinetics determination is a quantitative x-ray analysis, where the formation of BaTiO3 from the reaction between BaCO3 and TiO2 during isothermal heat treatment has been followed up. A raw value of the fraction reacted (α*) after isothermal treatment at a temperature (T) for time interval (t) h of the as milled BaCO3-TiO2 mixture was calculated from peak heights of x-ray diffraction lines (011) for BaTiO3, (111) for BaCO3, and (200) for TiO2 and is given by the following equation: I(011) [BaTiO ] α* = 3 ….(4.1) I(011) [BaTiO3 ] I(111) [BaCO3 ] I(200) [TiO2 ] To calculate the real values of the fraction reacted (α) that will be used in the reaction kinetic studies, powder mixtures having different compositions of - 70 - BaCO3, TiO2-c, and BaTiO3 powders of known α values were prepared and their x-ray diffraction patterns were analyzed according to Equation (4.1). The values of α* were plotted against the real α values to yield a calibration curve as shown in Figure (4.23). This has been made to overcome instrumentation errors and the effect of the absorption of x-ray. 4.2.1.1.1. Isothermal reaction kinetics The reaction between BaCO3 and TiO2 has been studied by using isothermal reaction kinetics technique. I) Model free reaction kinetics: The reaction between BaCO3 and TiO2 proceeds according to the general reaction kinetics formula: 1 d E Aexp( a ) .…(4.2) f () dt RT Where: A is the pre-exponential factor, Ea is the activation energy, R is the universal gas constant, and T is the absolute temperature in degrees Kelvin. For an isothermal condition Equation (4.2) can be integrated to give: E g(α) = Aexp( α ). t ....(4.3) RT α 1 Where: g(α) = d 0 f () The logarithmic form of Equation (4.3) becomes: ln g(α) = ln A+ ln(t) -Ea/RT ….(4.4) XRD patterns obtained for milled and heat treated BaCO3/TiO2-c mixtures at different temperatures in isothermal conditions, for different time intervals have been analyzed to determine the fraction reacted α as described in details in the previous section. Figure (4.24) shows the fraction reacted (α) values versus calcination time (t), calculated from the XRD patterns (given in Figures 4.16- - 71 - 4.19) of the powder mixtures; milled for 7.5h and calcined under isothermal conditions in the temperature range 700-800°C for different calcination times. Similar curves for powder mixtures milled for 10, 12.5h are given in the appendix (Figures 6.5 to 6.8). Taking a constant fraction reacted, i.e. constant α value, at different isothermal temperature and applying Equation (4.4), Arrhenius plot of ln (t) versus (1/T) could be obtained and is shown in Figure (4.25). It reveals a straight line relationship, from the slope of which the activation energies could be calculated. Table (4.4) shows the calculated values of the activation energies determined by this method for the powder mixtures milled at different milling times. Table-4.4: The activation energies of the reaction of BaCO3 and TiO2-c mixture Milling time, h 7.5 10 12.5 Activation energy, kJ/mole 190±7 202±20 196±9 1 0.8 0.6 α* 0.4 0.2 0 0.2 0.3 0.4 0.5 0.6 0.7 0.8 α Figure (4.23): calibration curve for calculating fraction reacted α from the raw value α* - 72 - 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 700°C Fraction reacted (α) reacted Fraction 750°C 0.2 775°C 0.1 800°C 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Calcination time, h Figure (4.24): The fraction reacted (α) versus time (t) curves obtained from the XRD analysis for reaction of BaCO3/TiO2-c powder mixtures (milled for 7.5h and calcined at different temperatures) 11 α=70 10.5 α=64 10 α=56 9.5 9 ln t ln 8.5 8 y 56%= 2.1941x - 12.624 E56% = 183.43 kJ/mole y = 2.2799x - 13.11 E = 190.6 kJ/mole 7.5 64% 64% y70% = 2.3599x - 13.656 E70% = 197.288 kJ/mole 7 9.2 9.4 9.6 9.8 10 10.2 10.4 104/T Figure (4.25): Arrhenius plot of ln(t) versus 1/T for reaction of BaCO3 and TiO2-c powder mixture milled for 7.5h, at constant conversion ratios - 73 - II) Determination of reaction kinetics models: The corrected fraction reacted (α) and the time (t) data have been used to calculate the different g(α) values given in Table (2.2), chapter-2, for different reaction kinetic models. These values were then plotted versus the reaction time according to Equation (4.3), as shown in Figure (4.26). From the figure, it can be seen that the best fitting of the data was for the three dimensional movement of the phase boundary in spherical symmetry according to the following reaction kinetic formula [V. Satava et al. (1971); W. W. Wendlandt et al, (1974)]: 1/3 E g(α) = 1-(1- α) = Aexp( a ). t = k(T).t ....(4.5) RT For isothermal condition, g (α) versus time will obey a straight line relationship as shown in Figure (4.27). Plotting the slopes of these lines (obtained at different temperatures) versus 1/T we get an Arrhenius plot Figure (4.28). The activation energy calculated from the slope of the Arrhenius plot is 206.6 KJ/mole which agrees quite well with the value obtained previously for the model free reaction kinetic analysis. 5 F0/R1, zero order 4.5 D1, 1-D diffusion 4 D4 F1, first orderl 3.5 D3, Jander A2, Avarami 3 A4, Avarami 2.5 R3, Ph Bd g(α) 2 1.5 R2 = 0.9847 1 R2 = 0.9949 0.5 R2 = 0.9722 0 0 0.5 1 1.5 2 2.5 3 3.5 time, h Figure (4.26): g(α) versus the reaction time for different reaction kinetic models - 74 - 4 700°C y = 0.2375x + 0.0312 3.5 750°C 775°C 3 800°C 2.5 y = 0.1445x + 0.0618 2 g g (α) 1.5 y = 0.065x + 0.0659 1 y = 0.0231x + 0.0618 0.5 0 0 5 10 15 20 time, h Figure (4.27): g (α) versus time for the reaction model "R3" (three dimensional movement of the grain boundary) 0 -0.5 -1 -1.5 -2 -2.5 ln k(T) ln -3 -3.5 -4 y = -24.647x + 21.509 -4.5 0.92 0.94 0.96 0.98 1 1.02 1.04 103/T Figure (4.28): Arrhenius plot of ln k (T) versus 104/T - 75 - 4.2.2. Ba(NO3)2/TiO2-c Reaction 4.2.2.1. Non isothermal reaction kinetics While an isothermal reaction technique was used in studying the kinetics of the reaction of BaCO3 and TiO2, non-isothermal reaction kinetics at a constant rate of heating was used in studying the reaction of Ba(NO3)2 and TiO2. In the former, XRD data were used while in the later DTA and TG were used. 4.2.2.1.1. Model free reaction kinetics: I) Thermo-gravimetric reaction analysis The Thermo-gravimetric data obtained from different investigations carried out at different heating rates have been employed to determine the activation energy of the reaction. The reaction extent (α) was determined from the weight loss using the following formula: W - W i T Wi - We Where: Wi is the initial weight of the powder mixture before the beginning of the reaction, WT is its weight at temperature T, and We is the weight at the end of the reaction. For a constant rate of heating dT/dt = β, Equation (4.2) could be represented as: d E (A/ )exp( a ) f dT RT α d T E g() (A/ ) exp( a ).dT 0 f 0 RT T E i.e. g() (A/ ) exp( a ).dT ….(4.6) 0 RT The integral at right hand side of Equation (4.6) was approximated by OZAWA, introducing P function as: E E E Log P ( a ) = exp( a )/( a )2 RT RT RT Then reducing Equation (4.6) for a constant fraction reacted α, consequently constant g(α) , the following equation could be obtained: - 76 - E Log β + 0.4567 a = constant .…(4.7) RT From the Arrhenius plot of Equation (4.7) the activation energy of the reaction could be determined irrespective of the reaction model. Thermogravimetric curves obtained at heating rates 5, 10, and 15C/min are shown in Figure (4.29) which shows that the reaction started at a relatively slow rate in the temperature range 530-560°C, then it proceeds faster in the temperature range 560-580°C. In the temperature range 590-740°C the reaction rate showed great decrease and then after increased till the end of the reaction. The OZAWA kinetic analysis carried out for these three temperature ranges are shown in Figures (4.30 to 4.32), from which activation energies of 210.44 ± 29.7, 232.62 ± 25.9, and 181.83 ± 15.63 KJ/mole were obtained respectively. It should be noted here that A in Figures 4.29 to 4.32 stands for the heating rate β, as imbedded in the software of the TG-50- Shimadzu-Japan. Figure (4.29): TG curves obtained at heating rates 5, 10, and 15°C/min - 77 - Figure (4.30): OZAWA kinetic analysis carried out in the temperature range 530-560°C Figure (4.31): OZAWA kinetic analysis carried out in the temperature range 560-580°C - 78 - Figure (4.32): OZAWA kinetic analysis carried out in the temperature range 590-740°C II) Differential thermal analysis DTA The differential thermal analysis (DTA) curves obtained upon heating the reactants at different heating rates are shown in Figures (4.33, 4.34). The results have been analysed according to Kissinger equation as follows: AR Ea.R ln 2 ln ….(4.8) Tm Ea Tm Where: β is the heating rate, Tm is the DTA peak temperature in degrees Kelvin, R is the universal gas constant. The figures show three endothermic peaks for the DTA curves obtained when applying relatively small heating rates. At higher heating rates; two peaks were obtained and sometimes one because of overlapping. The values of DTA peak temperatures obtained at 2 different heating rates were used to plot ln(β/T m) versus 1/Tm according to Equation (4.8). This gives Arrhenius plots shown on Figure (4.35) and activation energies of; 209.45 ± 20 kJ/mole for the first peak, 226.33 ± 22 kJ/mole for the second peak, and 180 kJ/mole for the third peak, which are in good agreement with those obtained from TGA data (using OZAWA kinetics). - 79 - Figure (4.33): DTA curve of the Ba(NO3)2/TiO2-c mixture at a heating rate of 1 °C/min Figure (4.34): DTA curve of the Ba(NO3)2/TiO2-c mixture at a heating rate of 0.6 °C/min - 80 - -10 -10.5 [530-560°C] -11 ) -11.5 m 2 -12 T / y = -25.054x + 16.254 β ( -12.5 ln -13 2 R = 0.9956 -13.5 -14 -14.5 1.05 1.1 1.15 1.2 1.25 103/Tm ,k-1 (a) -10 -10.5 [560-580°C] -11 ) -11.5 m 2 y = -27.073x + 16.49 T / -12 β 2 ( R = 0.9967 ln -12.5 -13 -13.5 -14 1 1.02 1.04 1.06 1.08 1.1 103/Tm ,k-1 (b) -11.5 590-740°C -12 ) -12.5 m 2 y = -21.623x + 10.592 T / -13 β ( 2 ln -13.5 R = 0.9966 -14 -14.5 1.04 1.06 1.08 1.1 1.12 1.14 1.16 103/Tm ,k-1 (c) 2 Figure (4.35): Arrhenius plot of ln(β/T m) versus 1/Tm - 81 - 4.2.2.1.2. Kinetic model determination The results of the thermogravimetric analysis made at constant heating rates of 5, 10, 15°C/min are shown in Figure (4.36). These data could be analysed according to the general rate equation: d A eEa/RT. f () ….(4.9) dt For the constant heating rate technique dT dt Where: " " is the heating rate. Then Equation (4.9) becomes d . (A eEa/RT). f () ….(4.10) dT 120 100 80 60 α% , 40 TG-5°C/min 20 TG-10°C/min TG-15°C/min 0 500 550 600 650 700 750 800 Temperature,°C Figure (4.36): TG analysis made at constant heating rates of 5, 10, 15°C/min From Figure (4.36) different values of dα/dT could be obtained at a constant temperature but at different heating rates. These values when multiplied by the corresponding heating rate and plotted against f(α) according to Equation - 82 - (4.10); might show a straight line relationship. This could not be accomplished except for the f(α) describing the reaction. Plotting "β.dα/dT" versus f(α) for different kinetic models (from Table (2.2)- Chapter-2) as shown in Figure (4.37) helps in the kinetic model determination. It can be seen from the figure that, contracting volume (shrinking core or three dimensional phase boundary movement) is the reaction model which shows the best straight line fit. The calculated fraction reacted α from the TG curve obtained at a heating rate of 5°C/min is shown on Figure (4.38). These data were analyzed according to the following equation obtained from Equation (4.10): d Ea ln / f () = ln A - ….(4.11) dT RT Where: f(α) = 3(1- α)2/3 for the contracting volume The analysis was done by dividing the curve into three consecutive sections; The first at the beginning of the reaction in the temperature range from 530- 560°C, the second in the temperature range from 560 to 620°C where most of the reaction takes place, and the third in the temperature range from 620 to 680°C at the end of the reaction. It can be seen that, these three sections are characterized by different reaction rates. The results of these analyses are shown as Arrhenius plots on Figure (4.39-a, b, c). The slope of the straight lines shown is Ea/R from which activation energies for the reaction could be calculated. The activation energy values were; 208.6±23, 248.1±27.3, and 177.1±18 kJ/mole for the data obtained in the temperature ranges from 530- 560°C, 560 to 620°C, and 620 to 680°C respectively. These results are in close agreement with those given in the previous sections by using the model free methods DTA-Kissinger and TG-OZAWA. - 83 - 3.5 R3 Contraction vol. y = 9.6864x + 1.8835 3 D4 2 A3, Avarami R = 0.9999 Power low (P2), α1/2 2.5 2 (α) f 1.5 y = -7.785x + 1.4448 R2 = 0.9975 1 0.5 y = -3.6125x + 0.3806 R2 = 0.9987 0 0 0.02 0.04 0.06 0.08 0.1 β (dα/dT) Figure (4.37): f(α) reaction model data fitting 1.2 1 0.8 0.6 0.4 Fraction reacted (α) reacted Fraction 0.2 0 500 520 540 560 580 600 620 640 660 680 700 Temperature, °C Figure (4.38): Fraction reacted (α) from TG curve, obtained for Ba(NO3)2/TiO2, when heating at a rate 5°C/min - 84 - -6.8 -7 -7.2 y = -24.947x + 23.384 -7.4 R2 = 0.9439 ln [β (dα/dT)/f(α)] [β ln -7.6 -7.8 1.21 1.22 1.23 1.24 1.25 103/T, K-1 (a) 530-560C -2 -2.5 -3 -3.5 -4 y = -29.684x + 29.008 -4.5 R2 = 0.9897 -5 -5.5 ln [β (dα/dT)/f(α)] [β ln -6 -6.5 1.06 1.08 1.1 1.12 1.14 1.16 1.18 1.2 103/T, K-1 (b) 560-580°C -2.4 -2.8 y = -21.189x + 19.699 -3.2 R2 = 0.9809 -3.6 ln [β (dα/dT)/f(α)] [β ln -4 1.05 1.06 1.07 1.08 1.09 1.1 1.11 103/T, K-1 (c) 590-740°C Figure (4.39): Arrhenius plot of ln [β (dα/dT)/f(α)] versus 103/T - 85 - 4.3. Thermodynamic approach In the previous sections the formation of BaTiO3 by solid-state reaction has been investigated by using x-ray diffraction technique through phase analysis from the starting precursors to the end product. It has been also studied by both isothermal and non-isothermal reaction kinetics using different experimental techniques such as XRD, DTA, and TG. In fact, the transformation of the reactant to the final product (BaTiO3), could take place by using different paths; i.e. different reaction formulas. The thermodynamic approach here could be useful in examining whether a certain reaction could take place under certain conditions, while another could not. This could be done through the calculation of the change in the Gibbs free energy (∆G) of the reaction at different temperatures. The standard thermodynamic data for ∆H, ∆S, and cp- from O. Kubaschewski et al., 1979 and M. Kh. Karapetyants et al., 1978 reference books- were used together with Equation (2.32) in Section (2.5)-Chapter (2); to calculate ∆H, ∆S, and ∆G at different temperatures. 4.3.1. BaCO3/TiO2-c reaction The results of the thermodynamic data calculated at different temperatures for the different possible reactions between BaCO3 and TiO2 and the decomposition reaction of BaCO3 are given in Table (4.5). It can be seen that negative ∆G values were obtained for both the direct reaction between BaCO3 and TiO2 giving BaTiO3 at a temperature ≥ 600°C (Reaction-1), and for the formation of the intermediate phase (Ba2TiO4) at temperature ≥ 800°C for reactions 3 and 6. - 86 - Table-4.5: enthalpies, entropies, and free energy changes of different possible reactions that may occur during the formation of BaTiO3 from BaCO3/TiO2-c powder mixture. Reaction (1) Reaction (2) BaCO3+TiO2→BaTiO3+CO2 BaCO3→BaO+CO2 T ∆ST ∆HT ∆GT T ∆ST ∆HT ∆GT 298 0.15909 108.935 61.5259 298 0.17171 271.453 220.282 873 0.10512 78.1032 -13.666 873 0.15875 263.66 125.074 973 0.0983 71.6415 -24.001 973 0.1562 261.312 109.326 1073 0.09183 64.8672 -33.672 1073 0.15362 258.67 93.8341 1173 0.08567 57.7814 -42.712 1173 0.15101 255.735 78.6024 1273 0.07976 50.3851 -51.149 1273 0.14837 252.507 63.6333 1373 0.17807 248.984 4.49774 1373 0.10642 42.679 -103.44 Reaction (3) Reaction (4) BaTiO3+BaCO3→Ba2TiO4+CO2 Ba2TiO4+TiO2→2BaTiO3 T ∆S ∆HT ∆G T ∆ST ∆HT ∆GT 298 0.19015 241.692 185.028 298 -0.0311 -132.76 -123.5 873 0.21872 256.119 65.1798 873 -0.1136 -155.92 -56.746 973 0.22019 257.475 43.2298 973 -0.1219 -163.69 -45.087 1073 0.22115 258.455 21.1588 1073 -0.1293 -171.43 -32.675 1173 0.22169 259.054 -0.9865 1173 -0.136 -179.13 -19.579 1273 0.22187 259.271 -23.167 1273 -0.1421 -186.76 -5.8563 1373 0.2541 259.103 -89.782 1373 -0.1477 -194.33 8.43987 Reaction (5) Reaction (6) BaO+TiO2→BaTiO3 2BaCO3+TiO2→Ba2TiO4+2CO2 T ∆ST ∆HT ∆GT T ∆S ∆HT ∆G 298 -0.0126 -162.52 -158.76 298 0.34924 350.627 246.554 873 -0.0536 -185.56 -138.74 873 0.32384 334.222 51.5139 973 -0.0579 -189.67 -133.33 973 0.31849 329.117 19.2292 1073 -0.0618 -193.8 -127.51 1073 0.31299 323.322 -12.513 1173 -0.0653 -197.95 -121.31 1173 0.30736 316.835 -43.698 1273 -0.0686 -202.12 -114.78 1273 0.30163 309.656 -74.316 1373 0.36052 301.782 -193.22 1373 -0.0716 -206.31 -107.93 Where: ∆GT= Gibbs free energy change, kJ/mole ∆ST = Entropy change, kJ/mole.K ∆HT= Enthalpy change, kJ/mole T = Temperature, °K - 87 - 4.3.2. Ba(NO3)2/TiO2-c reaction Table (4.6) shows the thermodynamic data calculated at different temperatures for direct reaction between barium nitrate and titanium dioxide to form barium titanate (Reaction-7) as well as for the decomposition reaction of barium nitrate (Reaction-8). It can be seen that, ∆G becomes negative at about 600°C for the direct reaction between Ba(NO3)2 and TiO2, while it becomes negative for the decomposition of the nitrate at 1000°C. Table-4.6: enthalpies, entropies, and free energy changes of different possible reactions that may occur to form BaTiO3 from Ba(NO3)2/TiO2-c powder mixture. Reaction (7) Reaction (8) Ba(NO3)2+TiO2→BaTiO3+2NO2+1/2 O2 Ba(NO3)2→BaO+2NO2+1/2 O2 T ∆S ∆HT ∆G T ∆S ∆HT ∆G 298 0.42632 341.84 214.798 298 0.43894 504.359 373.554 473 0.39156 328.224 143.018 473 0.42142 497.579 298.245 573 0.37356 318.653 104.604 573 0.41078 492.008 256.633 673 0.3564 307.803 67.9445 673 0.39985 485.198 216.099 773 0.33986 295.684 32.9684 773 0.38872 477.148 176.669 873 0.3238 282.299 -0.37857 873 0.37743 467.856 138.361 973 0.30811 267.652 -32.1385 973 0.36602 457.322 101.188 1073 0.29272 251.743 -62.3448 1073 0.35451 445.546 65.1609 1173 0.27758 234.573 -91.0249 1173 0.34291 432.527 30.2893 1273 0.33125 418.266 -3.41957 1273 0.26264 216.144 -118.202 Where: ∆GT= Gibbs free energy change, kJ/mole ∆ST = Entropy change, kJ/mole.K ∆HT= Enthalpy change, kJ/mole T = Temperature, °K - 88 - 4.4. Characterization of the BaTiO3 sintered compacts 4.4.1. BaTiO3 prepared from BaCO3/TiO2-c mixture 4.4.1.1. Compacting and sintering behavior of BaTiO3 powder Figure (4.40) shows the effect of compacting pressure on the green and sintered densities for powders milled for 7.5h and calcined at 800°C for 3h, then sintered at 1300 for 3h. From the figure it can be seen that, the green and the sintered densities of samples increased with the increase of compacting pressure. Table (4.7) gives the relative densities in percent of the theoretical 3 density of BaTiO3 (6.02kg/cm ) for the samples sintered at 1300 for 3h, and made from powders milled for 7.5, 10 and 12.5 h. The samples were prepared from: the as milled powder (Sas milled), the milled and calcined powder (S800°C), and the calcined powder mixed with 2 wt% polyvinyl alcohol (S800°C + PVA). 7 6 sinterd 3 5 cm / green 4 3 Density, gm Density, 2 1 0 300 500 700 900 1100 1300 compacting pressure, MPa Figure (4.40): Effect of compacting pressure on the green and sintered (at 1300/3h) densities for powders milled for 7.5h and calcined at 800°C/3h. - 89 - Table-4.7: The relative densities of BaTiO3 sintered samples (at 1300°C for 3h) prepared from the milled and calcined BaCO3/TiO2-c powder mixture. Relative density Sample name Milling time Milling time Milling time 7.5h 10h 12.5h Sas milled 82 86 88.9 S800°C 87.9 84.1 83.6 S800°C + PVA 95 94.3 90 4.4.1.2. Microstructure of the sintered BaTiO3 Figure (4.41) shows two sets of SEM micrographs of the sintered surface of BaTiO3 compact made from powder; prepared from BaCO3/TiO2-c mixture, milled for different milling times (7.5, 10, and 12.5 hours), and sintered at 1300°C in air for three hours. The first set, Figure (4.41-a), is for compacts made from as milled powders. While the second set, Figure (4.41-b), is for compacts made from the as milled powder mixture after calcination at 800/3h prior to the sintering process. It can be seen from the SEM micrographs that, there is a significant difference in the microstructure between the two sets. The specimens of the second set show less porosity and remarkable grain growth in comparison with the first one. In addition, the SEM micrographs of the first set show voids resulting from the release of CO2 during the chemical reaction between BaCO3 and TiO2-c. The grain size measured from the SEM micrographs for specimens of the second set was higher than that for the first one. The grain sizes are 1-5μm, 1-3μm, and 1-2μm for 7.5, 10, and 12.5h milling times, respectively, for the first set. While the corresponding values for the second set are 1-7μm, 1-5μm, and 1-4μm. It was concluded that, the grain size is inversely proportional to the milling time. Figure (4.42) shows the SEM micrographs of the surface of sample sintered at higher temperature of 1350°C for 3h. It can be seen that, the sample showed a microstructure of very coarse grains of size ranging from 30-50 μm. - 90 - Milled for 7.5h Milled for 7.5h & calcined. Milled for 10h Milled for 10h & calcined. Milled for 12.5h Milled for 12.5h & calcined. (A) (B) Figure (4.41): SEM micrographs of the BaTiO3 compacts sintered at 1300°C for 3h and prepared from BaCO3/TiO2 mixture: A) the as milled mixture B) the as milled mixture, calcined at 800°C/3h prior to sintering - 91 - Figure (4.42): SEM micrograph of surface of BaTiO3 compact made from BaCO3/TiO2-c mixture, calcined at 800°C/3h, sintered at 1350°C/3h in air 4.4.1.3. Phase analysis of the BaTiO3 ceramics BaTiO3 powder prepared from BaCO3/TiO2-c powder mixture milled for 7.5h and calcined at 800°C/3h, was pressed at 381 MPa and sintered for 3h in the temperature range from 900-1300°C. Figure (4.43) shows the XRD patterns made on the sintered sample surface. It can be seen that the peaks at 2θ 45.5° for the sample sintered at 900°C corresponds to the (200) line of BaTiO3 cubic structure. As the sintering temperature increased to 1000°C, the diffraction peak at 2θ 45.5° slightly widened and started to split. This implies that tetragonal phase of BaTiO3 is dominating in the ceramics sintered at 1000°C. However, it was difficult to distinguish between the two planes (002) and (200) due to their overlapping. Upon increasing the sintering temperature to 1100°C, the splitting of the (002) and (200) peaks became more and more observable, which indicates that the tetragonality of BaTiO3 ceramics increases with the sintering temperature. This can be clearly observed from Figure (4.44), where the tetragonality as expressed by the ratio of c/a is plotted versus the sintering temperature. - 92 - ) ) 200 002 ( ( ) ) 002 200 1300°C ( ( 1250°C I, a. u. a. I, 1100°C 1000°C 900°C 25 30 35 40 45 50 55 60 65 70 75 80 44 45 46 2^theta Figure (4.43): XRD patterns of the BaTiO3 compacts, prepared from BaCO3/TiO2-c mixture and sintered at different temperatures for 3h 1.014 1.012 1.01 1.008 1.006 1.004 Tetragonality, c/a Tetragonality, 1.002 1 0.998 800 900 1000 1100 1200 1300 1400 Temperature, °C Figure (4.44): Tetragonality of BaTiO3 prepared from BaCO3/TiO2-c mixture as a function of the sintering temperature - 93 - 4.4.2. BaTiO3 prepared from Ba(NO3)2/TiO2-c mixture 4.4.2.1. Compacting and sintering behavior of BaTiO3 powder Samples prepared from the BaTiO3 powder derived from the Ba(NO3)2/TiO2-c mixture, were pressed at 381 MPa and sintered at 1300°C for 3h in air. Table (4.8) gives the sintered densities of three different samples prepared from: powder calcined at 1200°C for 3h (SN-1200P), as milled powder pressed and calcined at 1200°C for 3h then crushed and re-pressed again (SN-1200C), and the powder calcined 1200°C/3h and mixed with 2 wt% polyvinyl alcohols (SN-PVA). Table-4.8: The relative densities of the BaTiO3 sintered samples prepared from the Ba(NO3)2/TiO2-c mixture. Relative density SN-1200-P 75 SN-1200-C 79.2 SN-PVA 83 4.4.2.2. Microstructure of the sintered BaTiO3 Figure (4.45) shows the SEM micrograph of the surface of BaTiO3 compact, sintered at 1300°C in air for three hours. The figure apparently shows a bimodal grain size distribution, where relatively small grains having a size less than 1μm, coexist with relatively large grains up to 5μm in size. Figure (4.45) SEM micrograph of surface of BaTiO3 compact made from Ba(NO3)2/TiO2-c mixture, calcined at 600°C/6h, sintered at 1300°C/3h - 94 - 4.5. Electrical properties of BaTiO3 4.5.1. BaTiO3 Prepared from BaCO3/TiO2-c mixture. Figure (4.46) shows a plot of the relative permittivity, εr and dielectric loss tanδ as functions of temperature and frequency for the sample made from the as prepared BaTiO3 powder and sintered at 1300°C for three hours, this sample has a sintered density of 87% of the theoretical density (Similar curves for powders milled for 10, 12.5h are shown in Figures 6.9 and 6.11, in the appendix). From the figure it can be seen that, the dielectric properties changed significantly with temperature. The maximum values of the relative permittivity were obtained as expected at the Curie temperature at 120°C. Upon increasing the temperature above the Curie temperature εr decreased to its values at the room temperature. While the dielectric losses tanδ showed minimum values at the Curie temperature and then increased to its values at the room temperature upon increasing the temperature. The dielectric constant and dielectric losses slightly decrease upon increasing the frequency. The sample sintered at higher temperature of 1350°C/3h which is characterized by coarse grained microstructure and high sintered density of 98 % T.D., showed higher relative permittivity approaching 10000 as shown on Figure (4.47). Figures (4.48 and 4.49) show the changes in the reciprocal permittivity with temperature above the Curie temperature for samples sintered at 1300 and 1350°C for 3h respectively, where the dielectric behavior can be characterized by Curie-Weiss law. C ε ε T Tc Where, C is the Curie constant, Tc is the Curie temperature, εo is the permittivity of the free space. The figures showed a straight line relationship from the slope of which Curie constants of 1x 105 C and 1.67 x 105 C for samples sintered at 1300 and 1350°C for 3h, respectively, were calculated. (Similar figures for powders milled for 10, 12.5h are shown in Figures 6.10 and 6.12, in the appendix) - 95 - 10000 0.5 9000 εr at 500Hz 0.45 r 8000 7280.908775 εr at 1 KHz 0.4 7000 εr at 10kHz 0.35 6000 εr at 20kHz 0.3 5000 εr at 100kHz 0.25 4000 0.2 3000 2028.543041 0.15 tanδ loss, Dielectric 2000 0.1 Relative permittivity, ε permittivity, Relative tanδ=0.066 1000 tanδ=0.043 tanδ=0.016 0.05 tanδ=0.019 0 tanδ=0.01050 0 50 100 150 200 250 Temperature, °C Figure (4.46): Dielectric properties as a function in temperature and frequency for the BaTiO3 prepared from BaCO3/TiO2-c powder mixture, milled for 7.5h, calcined at 800°C/3h, and sintered at 1300°C/3h 12000 1 500Hz 9812 0.9 r 10000 1kHz 0.8 10kHz 8000 0.7 20kHz 0.6 6000 100kHz 0.5 0.4 4000 0.3 1771 0.2 tanδ loss, dielectric Relative permittivity, ε permittivity, Relative 2000 0.0594 0.1 0 0.0157 0 0 50 100 150 200 250 Temperature,°C Figure (4.47): Dielectric properties as a function in temperature and frequency for the BaTiO3 prepared from BaCO3/TiO2-c powder mixture, milled for 7.5h, calcined at 800°C/3h, and sintered at 1350°C/3h - 96 - 0.0016 y = 1E-05x - 0.001 0.0014 R2 = 0.9963 0.0012 0.001 0.0008 0.0006 0.0004 Reciprocal permittivity Reciprocal 0.0002 0 120 130 140 150 160 170 180 190 200 210 Temperature,°C Figure (4.48): Reciprocal of relative permittivity versus temperature at T>Tc, for the BaTiO3 prepared from BaCO3/TiO2-c powder mixture, sintered at 1300°C for 3h 0.0008 0.0007 y = 6E-06x - 0.0005 R2 = 0.9856 0.0006 0.0005 0.0004 0.0003 0.0002 Reciprocal permittivity Reciprocal 0.0001 0 100 120 140 160 180 200 220 Temperature, °C Figure (4.49): Reciprocal of relative permittivity versus temperature at T>Tc, for the BaTiO3 prepared from BaCO3/TiO2-c powder mixture, sintered at 1350°C for 3h - 97 - 4.5.2. BaTiO3 Prepared from Ba(NO3)2/TiO2-c mixture. The dielectric properties of the BaTiO3 material prepared from the Ba(NO3)2/TiO2-c mixture showed similar behavior to that prepared from BaCO3/TiO2-c mixture as can be seen from Figure (4.50). The dielectric properties changed significantly with temperature, while slightly decreased with increasing the frequency. The maximum values of the relative permittivity were obtained at the Curie temperature (130°C) which is 10°C higher than that for BaTiO3 prepared from BaCO3/TiO2-c powder mixture. However, the BaTiO3 prepared from the Ba(NO3)2/TiO2-c mixture showed lower relative permittivities and higher dielectric losses than that for BaTiO3 prepared from 5 BaCO3-TiO2. Curie constant of 1.43 x 10 C was obtained from the slope of the straight line relationship between the reciprocal of the permittivity with temperature above the Curie temperature, Figure (4.51). This value is in good agreement with the values reported recently for BaTiO3 prepared from the BaCO3-TiO2 mixture and with that obtained by S. Babkair et al., 2005 and Y. J. Kim et al., 2009. 3500 1.98 2931.9 500Hz r r 3000 1kHZ 10kHz 2500 20kHz 1.48 100KHZ 2000 1805.334 0.98 1500 1000 0.41013 0.48 tanδ loss, dielectric Relative permittivity, ε permittivity, Relative 500 0.128 0.0175 0.00175 0.00175 0 -0.02 0 50 100 150 200 250 Temperature,°C Figure (4.50): Dielectric properties as a function of temperature and frequency for the BaTiO3 sample, prepared from Ba(NO3)2/TiO2-c powder mixture, sintered at 1300°C/3h - 98 - 0.0014 y = 7E-06x - 0.0003 0.0012 R2 = 0.9049 0.001 0.0008 0.0006 Reciprocal permittivity Reciprocal 0.0004 0.0002 0 125 135 145 155 165 175 185 195 205 Temperature, °C Figure (4.51) Reciprocal of relative permittivity versus temperature at T>Tc for the BaTiO3 sample, prepared from Ba(NO3)2/TiO2-c powder mixture, sintered at 1300°C/3h - 99 - CHAPTER (5) Discussion 5- DISCUSSION 5.1. Thermal analysis 5.1.1. BaCO3/TiO2-c system DTA and TG curves show the heat and weight changes due to the reaction and as well the effects due to any phase changes that might occur during the course of heating for the reactants and the products. This depends on different variables such as; the degree of finesse of the starting powder which differs according to the manufacturer, the degree of mixing of the reactants i.e. homogeneity, the milling method and the milling parameters, in addition to the thermal analysis parameters such as the heating rate and the gas flow. In the present work, the DTA of the milled BaCO3/TiO2-c mixture did not show any pronounced exothermic or endothermic peaks as shown in Figure (4.4), the heating rate used in this experiment was 5°C/min. The TG curve showed a weight loss of 15.8% which occurred between 600-1000°C, corresponding to the formation of one mole BaTiO3 as a result of the reaction of one mole BaCO3 and one mole TiO2. This value is equivalent to the release of one mole CO2, in agreement with the results of L. S-Seveyrat et al., 2007, V. Berbenni et al., 2001, E. Brzozowski et al., 2003 and S. N. Basahel et al., 1992. On the other hand, L. B. Kong et al., 2002 using planetary milled BaCO3-TiO2 powder mixture from Aldrich Chemicals, showed relatively lower value of weight loss of 12.1%, which might be due to deficiency in the carbonate proportion in their powder mixture. E. Brzozwski et al., 2003, in agreement with the present DTA results, stated that the BaCO3 phase transition peaks could be less significant due to its fast decomposition. Their starting powders were from Mallinckrodt for BaCO3 and from Degussa for TiO2. On the other hand S. N. Basahel et al., 1992, used BaCO3 from BDH and TiO2 from Hering Kahlfaun AG of particle sizes less than 125μm which were mixed with mortar and pestle. Their DTA results - 100 - obtained at a heating rate of 20°C/min showed small endothermic peaks corresponding to the BaCO3 phase transition. L. S-Seveyrat et al., 2007, using Merck powders ball milled for 2h detected a sharp DTA peak for BaCO3 phase transition upon heating up at a rate of 10°C/min in air flow. The derivative thermogravimetry Figure (4.5) showed that three stages of weight loss took place during the formation of BaTiO3; the first one was at the beginning of the reaction in the temperature range 550-670°C and corresponds to DTG peak at 611.8C. The second stage proceeded at a slower rate than the first one, in the temperature range 670-820°C and corresponds to a small DTG peak at 728.8 °C. The third stage took place in the temperature range 820- 950°C. It is characterized by a very large DTG peak at 914.7°C. The thermomechanical analysis (TMA), Figure (4.6), for the relative linear shrinkage and Figure (4.7) for the relative linear shrinkage rate reflect the DTG results mentioned above, but lag behind by about 100°C. This comes from the difference in nature between weight loss and dimension changes in the compact during the course of the reaction where CO2 gas will be evolved or released. This could result in competition between swelling (expansion) and contraction due to particle rearrangement at the beginning. Then upon increasing the temperature and the continuous release of CO2 from the sample, contraction in the compacts showed two linear shrinkage peaks at 714.2°C and 836°C (for the powder milled for 12.5h). In the powder milled for shorter times (7.5, 10 h) an overlap between those two peaks occurred, which could be related to the difference in powders activities. The slowing down in rate of weight change (DTG-Figure 4.5) during the second stage of the reaction might be a result of an increase in CO2 pressure released in large quantities at the first stage in the vicinity of the reactants. The presence of CO2 gas thermodynamically suppresses the reaction until paths for CO2 release are created through microcracks formation caused by CO2 build up. The forced removal of CO2 gas from the reaction field might accelerate the formation of barium titanate as end product. - 101 - 5.1.1.1. BaTiO3 and Ba2TiO4 as reaction products X-ray phase analysis made on the product of the solid state reaction in air between BaCO3 and TiO2 showed that BaTiO3 is the dominating phase. The small peak indicating the appearance of the intermediate phase Ba2TiO4 shown on the XRD pattern for powder calcined at 800°C might be questionable; First, because it could not be confirmed by the appearance of other peaks corresponding to this intermediate phase. Second, the peak height is very small and very close to the base line. Third, the position of this peak could be overlapped with one of BaCO3 lines. This trace amount of Ba2TiO4 does not appear on the XRD patterns made for the powders calcined at 600, 700, 900 and 1000°C. L. S-Seveyrat et al., 2007 found nearly similar results i.e. BaTiO3 formation at 780°C and very small amount of Ba2TiO4 at 800-1050°C for the reaction of BaCO3 with TiO2. As for their calcined powders made from coprecipitated oxalate of barium and titanium, the XRD showed only BaTiO3 and no Ba2TiO4 was detected. V. Berbeni et al., 2001 showed that a relatively small amount of Ba2TiO4 was formed upon heating powder mixture milled for 159h and calcined for 12h in flowing nitrogen atmosphere, in the temperature range of 650 to 720°C. At 635°C they found that the reaction proceeded forming Ba2TiO4, and upon calcination between 750 to 810°C no Ba2TiO4 was detected. E. Brzozowski et al., 2003 detected a similar behavior, where a very small amount of intermediate phase was preceded by BaTiO3 formation. In addition, they found that the temperature at which this trace amount of Ba2TiO4 was formed and the temperature at which this phase retransformed to BaTiO3 depends on the reactivity of TiO2 powder and on the milling time. On the other hand, L. B. Kong et al., 2002 came up with a conclusion, telling that the intermediate phase Ba2TiO4 was formed before the formation of BaTiO3 at 700°C. This is not only contradicting with the above results but it contradicts also with their own XRD pattern, which shows that BaTiO3 starts to form at 600°C. This rules out the statement saying that the formation of - 102 - BaTiO3 should be preceded by the formation of Ba2TiO4 intermediate phase. A. Lotnyk et al., 2006 found that an as prepared sample (in high vacuum) containing orthotitanate Ba2TiO4 and metatitanate BaTiO3 phases, when stored in air for two weeks transformed totally to the metatitanate BaTiO3 phase. In the present work using planetary milling a single phase BaTiO3 was obtained after calcination at 750°C for 10h, in agreement with the results obtained by V. Berbeni et al., 2001 and E. Brzozowski et al., 2003. The present results agree as well with those reported for the wet chemical methods, in which a calcination step at 700°C is necessary to obtain a single phase BaTiO3 [X-H. Wang et al., 2003; J. Zhen et al., 2006; W. Li et al., 2009; M. Cernea et al., 2005]. L. S-Seveyrat et al., 2007 using ball milling, could not obtain a single phase BaTiO3 from BaCO3-TiO2 mixture if the calcination temperature was lower than 1100°C. 5.1.2. Ba(NO3)2/TiO2-c system DTA and TG analyses showed that the reaction between Ba(NO3)2 and TiO2-c proceeds during heating up in three consecutive stages. These stages are characterized by three endothermic peaks which are accompanied by loss in the weight of the reactants. This will be discussed later in the part of the reaction kinetics. XRD pattern, Figure 4.22, showed that a single phase BaTiO3 was obtained after calcination at 600°C for 6h of Ba(NO3)2 and TiO2-c mixture. This result shows a lower formation temperature of BaTiO3 compared to that for the BaCO3/TiO2-c system. J. M. Mchale et al., 1995 showed a complete formation of a single phase BaTiO3 after calcination of Ba(NO3)2 and TiO(NO3)2 mixture at 600°C for 10 min in O2, which is in agreement with the above mentioned result. - 103 - 5.2. Reaction kinetics 5.2.1. BaCO3/TiO2-c reaction The results obtained from the data, of fraction reacted (α) versus the time (t) under isothermal conditions, were analyzed according to the model free method and as well the model controlled method. The model free kinetics showed that the activation energy for the reaction between BaCO3 and TiO2-c milled powders is independent of the milling time. Activation energies of 190±7, 202±20 and 196±9 kJ/mole were obtained for the reactions of the powders milled for 7.5, 10, 12.5h respectively. Activation energies of 170 kJ/mole obtained by Rout S. K. et al., 2006 and of 196±14 KJ/mole obtained by S. N. Basahel et al., 1992 are in good agreement with the corresponding values obtained in the present work. As for the determination of the reaction models the α/t data fitting for a number of selected models are listed in Table (2.2), Chapter(2)-Part-II. These models that have been selected for the fitting were chosen aiming to find out the model that can best fit the data which describe the reaction between BaCO3/TiO2-c. The results showed that the product growth during the reaction was controlled by phase boundary reaction model in spherical symmetry (contracting volume), in agreement with the conclusion reached by S. N. Basahel et al., 1992. Figure (5.1) shows the energy changes during the course of the reaction between BaCO3 and TiO2. It can be seen that the reactants must be activated by heating up. Activation energy of about 200kJ/mole was calculated from the reaction kinetics for the formation of BaTiO3 through an endothermic reaction. - 104 - Energy Activation energy Products Heat absorbed from the surrounding Reactants ΔH = 64.87, kJ/mole Course of reaction At 800°C: BaCO3 +TiO2 → BaTiO3 +CO2 , ΔG = -33.67 kJ/mole Figure (5.1): The energy changes during the course of the reaction between BaCO3 and TiO2 5.2.2. Ba(NO3)2/TiO2-c reaction This reaction has been studied using non-isothermal reaction kinetics, i.e. constant heating rate method. As mentioned earlier the reaction took place in three consecutive stages and the values of the activation energies obtained for each stage have been tabulated in Table (5.1). The data were analyzed according to the model free method using TG data/ T. Ozawa, 1965 (Equation- 4.7) and DTA data/ H. E. Kissinger, 1957 (Equation-4.8). The TG data when fitted according to chosen and selected models from Table (2.2), showed that the phase boundary mechanism controlled the reaction kinetic between Ba(NO3)2 and TiO2-c. This is in good agreement with the results obtained by H. Tagawa et al., 1985, using isothermal TG method for kinetic analysis. The agreement is not only in the kinetic model i.e. phase boundary controlled, but also in the activation energies, which were 212±3, 231±6 and 184±8 kJ/mole for the three previously mentioned stages of the reaction. They classified the 1st and 2nd stages as solid-state reaction and the 3rd as solid-liquid reaction. In this respect the second state should be for solid-solid-congruent liquid reaction. As the liquid in this reaction is molten Ba(NO3)2, the difference in the activation energies for the reaction between the first and the second stages - 105 - which is 19.6 kJ/mole might be the enthalpy of melting of Ba(NO3)2, in agreement with H. Tagawa et al., 1985. Table-5.1: Activation energies (in kJ/mole) obtained for BaTiO3 powder prepared from Ba(NO3)2/TiO2 powder mixture using: a) Model-free and b) Reaction kinetic model equations a) Model-free Reaction kinetic Temperature range 530-560°C 560-580°C 590-740°C 1- OZAWA (TG) 210.44 ± 29.7 232.62 ± 25.9 181.83±15.63 2- Kissinger (DTA) 212.14 ± 20 226.33 ± 22 180 b) Reaction kinetic model Temperature range 530-560°C 560-580°C 590-740°C Contracting volume (TG) 208.6±23 248.1±27.3 177.1±18 5.3. Reaction mechanism 5.3.1. BaCO3/TiO2-c system The schematic representation shown in Figure (5.2) illustrates the sequence of the reactions that take place for the formation of BaTiO3 from BaCO3 and TiO2-c. Slide (A) represents the as milled mixture where BaCO3 large spherical particle (core) is surrounded by microspheres of the fine TiO2 powder as a shell. Upon heating, the reactants start to react: in the first step a layer of BaTiO3 is formed between BaCO3 and TiO2, in the temperature interval 600- 700°C as shown in Figure (5.2-B). This is confirmed by the XRD pattern, Figure (4.13), made for milled powder calcined for one hour at different temperatures. These XRD patterns show that BaTiO3 started to form at 600°C. Moreover, the thermodynamic calculations of the change in Gibbs free energy (∆G) versus temperature for the different possible reactions that could take place during the calcination of BaCO3 and TiO2; showed to be in favor of the - 106 - direct reaction between BaCO3 and TiO2-c to form BaTiO3. The relation between ∆G and temperature manifests itself in a straight line relationship, Figure (5.3). A byproduct of this reaction is CO2 gas which, when released leads to the formation of pores and cracks in the newly formed layer of BaTiO3. Further, the BaTiO3 layer acts as a barrier between the TiO2-c and BaCO3. However, upon increasing the temperature to 800°C a thin layer of the intermediate phase Ba2TiO4 is formed as a result of the reaction between BaCO3 and the previously formed BaTiO3 layer as shown schematically in Figure (5.2-C). The XRD pattern of the powder calcined at 800°C (Figure-4.13) showed a very small peak at 2θ 28.6°, which corresponds to that of Ba2TiO4 intermediate phase. Upon prolonged heating at 800°C or heating up to 900°C, the titanium from the shell and barium from the core will diffuse towards either the centre or the shell in a spherical symmetry, most probably by surface diffusion through the cracked BaTiO3 layer. The titanium might first react with the tiny amount of the intermediate phase and the barium will react with the titanium dioxide forming BaTiO3 as represented in slides D to F (Figure 5.2). If the diffusion of Ba+2 cations on surface of the microcracks- formed in the BaTiO3 layer- is faster than the diffusion of Ti+4 cations, then a void will be formed in the centre in place of the BaCO3 particles previously existing. This is in agreement with our reaction kinetic results which showed that a contracting volume model prevails. The XRD made on the calcined powder at 800°C for one hour (Figure-4.13), showed a very tiny amount of the intermediate phase Ba2TiO4 beside a considerable amount of the BaTiO3, which is larger than the amount formed upon calcination at 700°C for one hour. This might be explained as follows: - 107 - (1) The formation of BaTiO3 layer is between the dissimilar contact surfaces of BaCO3 and TiO2 as schematically illustrated-Figure (5-2, B). (2) At 800°C the formation of the intermediate compound Ba2TiO4 through the reaction between BaTiO3 layer and BaCO3 is not thermodynamically possible as shown in Figure (5.3). The only thermodynamically possible reaction to form Ba2TiO4 at this temperature is: 2BaCO3 + TiO2 → Ba2TiO4 + CO2. However, this is not feasible because the BaTiO3 layer acts as an isolation between the BaCO3 and TiO2 reactants. Yet, if somehow a quantity of the intermediate phase Ba2TiO4 was formed, most of it will disappear when reacting with CO2 gas trapped in the reaction zone. This will take place according to a thermodynamically possible reaction as follows: Ba2TiO4 + CO2 → BaTiO3 +BaCO3 Where: ∆G= -20.3 Kj/mole - 108 - D CO ↑ A TiO2 2 Ti+4 Ti+4 Ba+2 Ba+2 BaCO3 ←CO2 CO2 → BaCO3 Room Temperature Long calcination time or heat up BaCO3 +TiO2 milled mixture Ba2TiO4 + TiO2 → 2BaTiO3 CO B CO2 ↑ E 2 Ti+4 void Ti+4 Ba+2 Ba+2 ←CO2 CO2 → Ba+2 BaCO3 CO2↓ CO2 BaCO3 600-700°C 800°C and more BaCO +TiO →BaTiO +CO BaCO3 +TiO2→BaTiO3+CO2 3 2 3 2 C CO2 ↑ F void BTO BTO ←CO2 CO2 → BTO BTO BTO BTO BaCO3 BTO CO2↓ 700-800°C Complete formation of BaTiO3 BaCO3+BaTiO3→Ba2TiO4+CO2 TiO2 BaCO3 Ba2TiO4 BaTiO3 Figure (5.2): Schematic diagram of the mechanism of formation of BaTiO3 phase from BaCO3/TiO2-c powder mixture - 109 - 400 1-BaCO3+TiO2→BaTiO3+CO2 300 2-BaCO3→BaO+CO2 3-BaTiO3+BaCO3→Ba2TiO4+CO2 200 4-Ba2TiO4+TiO2→2BaTiO3 G ∆ 6-2BaCO3+TiO2→Ba2TiO4+2CO2 100 0 0 200 400 600 800 1000 1200 1400 1600 Free energy change, energy Free -100 -200 -300 Temperature,°C Figure (5.3): The change in Gibbs free energy (∆G) versus temperature for the different possible reactions that could take place during the calcination of BaCO3 and TiO2-c - 110 - It is worthwhile here to examine the different reactions that have been proposed for the formation of barium titanate from BaCO3 and TiO2 precursors. V. P. Pavlović et al., 2008 proposed the following reactions sequence, which is in good agreement with the descriptive illustration shown on Figure (5.2). BaCO3 + TiO2 → BaTiO3 + CO2 BaTiO3+ BaCO3 → Ba2TiO4 + CO2 Ba2TiO4 +TiO2 → 2BaTiO3 Meanwhile L. S-Seveyrat et al., 2007 emphasized on the reaction: BaCO3 + TiO2 → BaTiO3 + CO2 as a major contributor to the formation of BaTiO3 with a trace amount of Ba2TiO4 which is in agreement with our XRD results obtained for milled powder after calcination at 800°C for one hour. On the other hand, L. B. Kong et al., 2002 (using probably non-stoichiometric quantities of BaCO3 and TiO2 in a heterogeneous mixture) proposed the following scheme which had been proposed long ago by Galagher et al., 1965: 2BaCO3 + TiO2 → Ba2TiO4 + 2CO2 Ba2TiO4 +TiO2 → 2BaTiO3 Although their XRD patterns showed that BaTiO3 phase was formed before Ba2TiO4 phase. A. Beauger et al., 1983 proposed two schemes The first was: BaCO3 → BaO + CO2 2BaO+ TiO2 → Ba2TiO4 Ba2TiO4 +TiO2 → 2BaTiO3 And the second: BaCO3 → BaO + CO2 BaO + TiO2 → BaTiO3 BaTiO3+ BaCO3 → Ba2TiO4 + CO2 Ba2TiO4 +TiO2 → 2BaTiO3 - 111 - These schemes based on the decomposition of BaCO3 contradict with the thermodynamic data of the decomposition of BaCO3, which occurs at relatively higher temperature than that for direct reaction between BaCO3 and TiO2. From the above discussion it can be deduced that the model represented in Figure (5.2) can not fully explain the mechanism of BaTiO3 formation. The reason for that was due to the appearance of the intermediate phase in the XRD pattern for the powder mixture calcined at 800°C for one hour. This in fact contradicts with the thermodynamic data obtained for the geometrically possible reaction between BaTiO3 and BaCO3. This reaction can not take place at 800°C but at rather higher temperature i.e 900°C. Thus a more realistic approach to the reaction mechanism will be given in the following section. 5.3.1.1. Realistic approach to the reaction mechanism The SEM of the as milled powder, Figure (4.6), showed that the powder consists of large agglomerates of bimodal particles of fine TiO2-c and coarse BaCO3. The arrangement in the model described earlier could be assumed to be repeated inside each agglomerate with some heterogeneity. That is some of the contacts between the particles must not be always dissimilar. On the other hand, peripheries or the outer surface of each agglomerate will have less surface contact with both BaCO3 and TiO2-c particles. When the agglomerated mixture schematically shown on Figure (5.4-A) is heated up to 600-700°C, a reaction between BaCO3 and TiO2-c to form BaTiO3 will take place at all the dissimilar contacts inside each agglomerate and as well in the contact surfaces between the agglomerates as schematically shown on Figure (5.4-B). The XRD made on BaCO3/TiO2-c mixture calcined at 600°C showed the formation of BaTiO3. This reaction produces CO2 gas, most of it was trapped inside each agglomerate. The gas will develop pressure which will create slowly a network of microcracks through which it will escape from the reaction zones. This can be seen from the TG curve, Figure (4.4), which shows a - 112 - relatively low rate for the weight loss. The thermomechanical analysis TMA showed a shrinkage which occurs as a result of release of CO2. This shrinkage will be accompanied by particle rearrangement inside each agglomerate as well as agglomerates rearrangement. As a result new dissimilar contacts inside and outside the agglomerates will be created and the reaction proceeds again. In this stage of the reaction which occurs in the temperature range 700-800°C, more BaTiO3 was formed and the new surfaces of contacts between the agglomerates rich in BaCO3 and intermediate phase Ba2TiO4 were formed as shown in Figure (5.4-C). The XRD made on the powder mixture calcined at 800°C showed a trace amount of the intermediate phase, which indicates that the heterogeneities in the powder are very little. This supports the idea that this reaction occurs on few places at the new contact surfaces between the agglomerates, where dissimilar contacts rich in BaCO3 exist. This step also will be accompanied by further shrinkage (shown on TMA curves) and rearrangements, which will create new dissimilar contacts during the course of heating up. The reaction will then proceed at relatively higher rate as shown on the TG, Figure (4.4), as a result of the increase of temperature and the ease of the CO2 release. In this range of temperature the TiO2 will react with both the intermediate phase and the residual BaCO3 to form BaTiO3. This is shown on Figure (5.4-D), where BaTiO3 fine particles and voids were formed. It should be noted here that the particle size of the initial powder is a very important factor in the determination of the reaction mechanism. J. C. Niepce et al., (1990) and M. I. Buscaglia et al. (2005) showed that it is possible to prevent the formation of Ba2TiO4 phase by controlling the particle size of both BaCO3 and TiO2 powders. - 113 - A C TiO2 BaCO3 Room Temperature 700-800°C As milled BaCO3 /TiO2-c mixture 1-BaCO3 +TiO2→BaTiO3+CO2 2-2BaCO3+TiO2→Ba2TiO4+CO2 3- Particles Rearrangement B D BT BT BT BT BT BT BT BT BT BT BT BT BT BT BT BT BT BT BT BT BT BT BT BT BT BT BT BT BT BT BT BT BT BT BT BT BT BT BT BT BT BT 600-700°C Long calcination time or heat up 1- BaCO3 +TiO2→BaTiO3+CO2 And Complete formation of BaTiO3 2- Particles Rearrangement 1- Ba2TiO4 + TiO2 → 2BaTiO3 2- BaCO3 +TiO2→BaTiO3+CO2 BT BaCO3 TiO2 Ba2TiO4 BaTiO3 Figure (5.4): Schematic diagram for the realistic approach describing the reaction mechanism of formation of BaTiO3 from BaCO3/TiO2-c powder mixture - 114 - 5.3.2. BaTiO3 Prepared from the Ba(NO3)2/TiO2-c mixture According to the thermodynamic calculations given in Table (4.5), the formation of BaTiO3 phase from Ba(NO3)2 and TiO2 mixtures (reaction-8) has a heat of formation less than the heat of decomposition of Ba(NO3)2 to BaO phase (Reaction-7) and the free energy change for Reaction-8 is more negative than that for Reaction-7. This indicates that reaction-8 is more favorable than Reaction-7. Combining these results with those obtained from the DTA/TGA curves (Figure 4.4), the formation of BaTiO3 phase from Ba(NO3)2 and TiO2 powder mixture can be described, Figure-5.5, as follows: First a solid-state reaction between Ba(NO3)2 and TiO2 powders occurred (first peak in the DTA curve- Figure 4.20). Upon further heating, the Ba (NO3)2 powder partially melted and reacted with the TiO2 powder (the second peak in the DTA curve). Continuing heating caused a complete melting of the remaining Ba(NO3)2 powder which reacted with the residual TiO2 (the third peak in the DTA curve). The formation of BaTiO3 was accompanied by the release of NO2 and O2 gases, and proceeded according to the following equation: Ba (NO3)2+TiO2→BaTiO3+2NO2+1/2O2) Ba(NO3)2 BaTiO3 TiO2 2nd step Ba(NO3)2 /TiO2-c First step TiO2 Ba(NO3)2 rd BaTiO3 3 step BaTiO3 Figure (5.5): Schematic diagram of the mechanism of formation of BaTiO3 phase from Ba(NO3)2/TiO2-c powder mixture - 115 - 5.4. Characterization of the sintered barium titanate 5.4.1. Densification and microstructure The densification of the compacts made from the as milled BaCO3/TiO2-c powder mixture, showed that the shrinkage of the compacts continue upon increasing the temperature up to 1400°C. Thus the densification needs higher temperature and/or long time to be attained. This indeed leads to a sintered barium titanate having coarse grained microstructure. In the present work, it was found that the addition of polyvinyl alcohol increased the green density of the compacts. Sintered densities in the range between 90 to 98% T.D (Table- 4.7) could be obtained upon sintering at 1300°C/3h, depending on the compacting pressure or the green density, while samples sintered without PVA addition showed lower sintered densities. The microstructure showed a bimodal grain structure of small and large grains from 2 to 5μm, similar results have been published by S. B. Deshpand et al., 2006. Samples sintered at higher temperature of 1350°C/3h showed very coarse grain structure, the grain size being in the range from 30-50μm. In order to obtain fine grained microstructure particular pressing and sintering procedure were employed (C. J. Xiao et al., 2009; Y. Kinemuchi et al., 2005; A. B. Alles et al., 2005). To attain fine grained microstructure at low sintering temperatures, glass additives were used (D. Prakash et al., 2000; C-H. Hsi et al., 2008; H-I. Hsiang et al., 2009; H. N-Zadeh et al., 2011). 5.5. Electrical properties of BaTiO3 A great variation appears in the measured dielectric constant in the different investigations. This may be attributed to different reasons. For example: S-W. Kwon et al., 2007 stated that tetragonality is correlated to ferroelectricity that is characterized by high dielectric constant. M. H. Frey et al., 1996 showed that tetragonality is an increasing function of processing temperature, while L. Wu et al., 2009 showed that the grain size affect both the room - 116 - temperature and Curie temperature dielectric constant in such a way that; less dense and lower tetragonality but smaller grain size sintered BaTiO3, will have higher dielectric constant than the larger grained materials. In contrast, W. Li et al., 2009 showed that coarse grained BaTiO3 ceramics showed higher dielectric constant than the finer one. In addition, A. B. Alles et al., 2005 showed that for large grain size and high sintered density, higher values for both room and curie temperature dielectric constants could be obtained for BaTiO3 having Ba to Ti ratio of 1.007 if compared to that having a ratio of 0.993. Nano-sized BaTiO3 ceramics prepared by T. Ahmed et al., 2005 showed very low values of the dielectric constant. This has been attributed to a very week tetragonal distortion in the nano size structure. The sintered density of BaTiO3 should have an effect on the values of the dielectric constant, because the density is a measure of the porosity that exists in the sintered BaTiO3. This porosity in its amount is not as important as its distribution which could be a detrimental factor on the values of the dielectric constant. This reaches its atmost harmful effect when the pores get agglomerated in the form of a large pore in a lateral position inside the sintered BaTiO3 disk, which could form series capacitors or reduce the effective capacitance area of the BaTiO3 sample, resulting in low overall capacitance and consequently low dielectric constant. The presence of porosity in the sintered barium titanate not only decreases its relative permittivity but also increases the dissipation factor in agreement with the published results of H-I Hsiang et al., 1995 A. B. Alles et al., 2005 and V. P. Pavlović et al., 2007. The relative permittivity measured at room temperature is important for the application of energy storage; the values obtained in the present work are comparable to that obtained in some previously published data by C. N. George et al., 2009; X. Wang et al., 2004 and M. Cernea, 2005. In order to study the effect of the porosity on the relative permittivity of the sintered barium titanate compacts; J. C. Maxwell Garnett, 1904, formula have been used to calculate the effective relative permittivities. The best data - 117 - published by C. Miclea et al., 2007 for dense and fine grained barium titanate having 1μm grain size were used. The model is based on considering the dielectric as a two phase mixture: the BaTiO3 as the matrix and the other is the porosity. The following Maxwell Garnett formula has been recently employed by H-M. Chang et al., 2011. ε P εm εr εm 3Pεm ε P 2εm P(ε P εm ) Where εr is the effective permittivity, εm is the permittivity of the matrix (BaTiO3), εP is the permittivity of the pores and P is the porosity. H-I. Hsiang et al., 1995 showed the validity of Maxwell Garnett model when applied for fine grained BaTiO3 having a porosity approaching 20%. A comparison between the calculated results according to Maxwell-Garnet formula, the present study results obtained for the samples sintered at different temperatures and some of the previously published results are presented in Figures (5.6-a, b). Figure (5.6, a) shows the relative permittivity values measured at room temperature, while Figure (5.6, b) shows the values measured at Curie temperature. It can be seen in general that the results obtained in the present work are comparable to the previously published results. The straight line fitting of the data of the relative permittivities versus the porosities, shown in the figures are nearly parallel to that obtained from Maxwell-Garnet formula calculated values. This means that, the results of the present and the previously published results are in reasonable agreement with the Maxwell-Garnett model. The difference in the values of the permittivities from the C. Miclea et al., 2007 values, could be attributed to the difference in grain size and/or to the variation in domain densities and domain orientations. In fact there is a tremendous amount of published permittivity results but unfortunately they can not be used for comparison because the relative densities of the samples were not given. - 118 - 7000 Theoretical Maxwell-Garnett model, 1 μm Present work 6000 Alles Ba/Ti=1.007 Alles Ba/Ti=0.999 Alles, 2005-28 μm 5000 Seveyrat 2005 Wu et al 2009-1 μm Li W. et al 2009, 5 μm 4000 y = -6652x + 4958.5 R2 = 0.9995 3000 y = -9217.1x + 3736.1 2000 R2 = 0.684 Relative Permittivity Relative (εr) y = -6225.7x + 2752.1 y = -7946.9x + 3140.5 1000 R2 = 0.5216 R2 = 0.9344 0 0 0.05 0.1 0.15 0.2 0.25 0.3 Porosity, % (a) 18000 Theoretical Maxwell-Garnett model, 1 μm 16000 1 present work,3-5 μm 2 present ork, 30-50 μm 14000 Kim et al 2004, 1 and 10.3 μ m Severyat et al,2005 12000 Alles 2005 y = -18620x + 13884 10000 R2 = 0.9996 8000 y = -17500x + 10162 6000 R2 = 1 4000 y = -22308x + 8689.4 y = -8836.7x + 7170.8 2 Relative Permittivity (εr) Permittivity Relative 2000 R2 = 0.4687 R = 0.9954 0 0 0.05 0.1 0.15 0.2 0.25 0.3 Porosity, % (b) Figure (5.6): A comparison between the calculated results of the relative permittivities according to Maxwell-Garnet formula, the present study results obtained for the samples sintered at different temperatures, and some of the previously published results (a) the relative permittivity values measured at room temperature (b) the relative permittivity values measured at Curie temperature - 119 - CHAPTER (6) Conclusions Conclusions In this study, the BaTiO3 was synthesized by using the solid-state reaction method, starting with two different precursors each having 1:1 molar ratio; the BaCO3/TiO2-c and the Ba(NO3)2/TiO2-c. From the study the following main conclusions are summarized: A) BaCO3/TiO2-c system 1- Milling for 7.5h of BaCO3/TiO2-c powder mixture followed by calcination for 10h at 750°C was found enough to form a single phase BaTiO3. 2- The use of a very reactive TiO2 in an equimolar BaCO3/TiO2-c mixture, followed by mechanical activation, using planetary mill, led to lowering the formation temperature of BaTiO3 (from ~1200 to 750°C). 3- Irrespective of the milling time, the rate of formation of BaTiO3 phase increases with calcination time and calcination temperature. 4- The TMA results showed that, the shrinkage of compacts, made from BaCO3/TiO2-c milled mixture, proceeds in two stages: the stage of reaction and particle's rearrangement, and the stage of sintering. In the first stage, the shrinkage rate decreased with the increase of milling time. While in the second stage, the shrinkage rate increased with the increase of the milling time. 5- The activation energy for the reaction between BaCO3 and TiO2-c milled powders is independent of the milling time; activation energies of 190±7, 202±20 and 196±9 kJ/mole were obtained for the reactions of the powders milled for 7.5, 10, 12.5h respectively 6- The DTA-TG, XRD and the thermodynamic analyses showed that, the formation of BaTiO3 proceeds through a direct reaction between BaCO3 and TiO2, not through the decomposition of BaCO3 to BaO neither through the formation of Ba2TiO4 intermediate phase. 7- The kinetic analysis showed that the formation reaction of BaTiO3 was controlled by contracting volume (phase boundary reaction model). - 120 - 8- A reaction mechanism was proposed depending on the morphology of the milled powder and on the experimental results obtained from SEM, TG, TMA and XRD analyses. The agglomerated nature of the milled powder, its rearrangement during the course of the reaction, the particle size of BaCO3 and TiO2 and the effect of CO2 gas in the reaction zone are the major factors affecting the mechanism of reaction between BaCO3 and TiO2. 9- The tetragonality of BaTiO3 ceramics increases with the sintering temperature 10- The relative permittivity and the dielectric loss, measured at room temperature and 1 kHz, were 2028.5 and 0.043, respectively. B) Ba(NO3)2/TiO2-c system 1- A single phase BaTiO3 was formed from the Ba(NO3)2-TiO2-c powder mixture after calcination at 600°C for 6h, which is 150°C lower than that for the BaCO3/TiO2-c system. 2- The kinetic analysis showed that the phase boundary mechanism controlled the reaction between Ba(NO3)2 and TiO2-c which proceeded during heating up in three consecutive stages: the solid-solid reaction between Ba(NO3)2 and TiO2 powders, the reaction between the partially melted Ba(NO3)2 and TiO2-c), and finally the reaction of the molten Ba(NO3)2 with the residual TiO2. These stages of the reaction are characterized by activation energies of: 212±3, 231±6 and 184±8 kJ/mole, respectively. 3- The mechanism of the reaction was explained on the basis of thermogravimetric reaction kinetics results. 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Powder Characterization 70 anatase 60 (101) 50 anatase anatase (200) anatase Rutile anatase 40 (110) (211) Rutile anatase (002) (201) Rutile (112) (210) I, I, a. u. (311) 30 Anatase (B) (101) RutileRutile Rutile 20 Anatase Rutile (110)(101) Rutile Anatase (211) (110) Rutile Rutile Rutile (210) (200) (002) 10 (220) (311) (200) (A) 0 20 30 40 50 60 70 80 2^Theta Figure (6.1): XRD patterns for the TiO2 powder calcined at: (A) 300°C, (B) at 500°C 100 90 80 70 60 50 I, a. u. 40 30 (B) 20 10 (A) 0 20 30 40 50 60 70 80 2^theta Figure (6.2): XRD patterns for the BaCO3 powder: (A) as recieved, (B) calcined at 1000°C - 134 - 160 BaCO3 -γ 140 TiO2 120 BaTiO 15h 100 3 80 10h I,u. a. 60 7h 40 5h 20 1h 0 20 30 40 50 60 70 80 2^Theta A) 700°C BaCO3-γ TiO2 BaTiO3 10h I,u. a. 7h 5h 1h 20 30 40 50 60 70 80 2^Theta B) 750°C 160 BaCO3-γ 140 TiO2 120 BaTiO3 Ba TiO 100 2 4 80 5h I,u. a. 60 3h 40 2h 20 1h 0 20 30 40 50 60 70 80 2^Theta C) 800°C Figure (6.3): Effect of calcination time for the BaCO3/TiO2-c mixture powders milled for 10h, at different calcination temperatures - 135 - BaCO3-γ TiO2 BaTiO3 15h I, a. u.a. I, 10h 7h 1h 20 30 40 50 60 70 80 2^Theta A) 700°C BaCO3-γ TiO2 BaTiO3 Ba2TiO4 10h I,u. a. 7h 5h 1h 20 30 40 50 60 70 80 2^Theta B) 750°C BaCO3-γ TiO2 BaTiO3 Ba2TiO4 5h I, a. u. a. I, 3h 2h 1h 20 30 40 50 60 70 80 2^Theta C) 800°C Figure (6.4): Effect of calcination time for the BaCO3/TiO2-c mixture powders milled for 12h, at different calcination temperatures - 136 - 2. Reaction Kinetics 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 Fraction (α) Reacted Fraction 700°C 0.2 750°C 0.1 775°C 800°C 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Cacination time, h Figure (6.5): The fraction reacted (α) versus time (t) curves obtained from the XRD analysis for reaction of BaCO3/TiO2-c powder mixtures (milled for 10h and calcined at different temperatures) 11 10.5 10 9.5 9 8.5 ln t ln alfa=70% 8 alfa=64% 7.5 alfa=56% y56%= 2.1484x - 12.386 E56% = 7 y64%= 2.6946x - 17.273 E17964.%6kJ =/ mole225.2 6.5 y70%= 2.2751x - 12.809 EkJ70/mole% = 190.19 6 9.1 9.3 9.5 9.7 9.9 10.1 10.3 10.5 10-E4/T Figure (6.6): Arrhenius plot of ln(t) versus 1/T for reaction of BaCO3 /TiO2-c powder mixture milled for 10h and calcined at different temperatures - 137 - 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 700°C Fraction (α) Reacted Fraction 0.2 750°C 0.1 775°C 800°C 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Calcination time, h Figure (6.7): The fraction reacted (α) versus time (t) curves obtained from the XRD analysis for reaction of BaCO3/TiO2-c powder mixtures (milled for 12.5h and calcined at different temperatures) 12 11 alfa=70% alfa=64% 10 alfa=56% 9 ln t ln 8 y56% = 2.2378x - 13.195 E 56% = 187.1kJ/mole 7 y64% = 2.3414x - 13.744 E 64% = 195.74 kJ/mole y70% = 2.4564x - 14.593 E 70% = 205.36 6 kJ/mole 9.2 9.4 9.6 9.8 10 10.2 10.4 10.6 10-E4/T Figure (6.8): Arrhenius plot of ln(t) versus 1/T for reaction of BaCO3 /TiO2-c powder mixture milled for 12.5h and calcined at different temperatures - 138 - 3. Thermodynamic Data Table6 6-1: The standard thermodynamic data for ∆Ho, ∆So, and cp Constants Entropy, Enthalpy, at at 298°K 298°K Substances a b c S298, kJ/mole H298 , kJ/mole BaCO3** 21.5 11.06 2.96 0.112024 -1218.888 BaO** 11.79 1.88 0.88 0.0702658 -553.432 BaTiO3* 20.03 2.04 4.58 0.1079276 -1659.7944 Ba2TiO4* 43 1.6 6.96 0.1966272 -2242.988 CO2** 10.57 2.16 2.06 0.2134726 -394.00262 TiO2 17.83 0.5 4.23 0.0502854 -943.844 Ba(NO3)2** 30.05 35.7 4.01 0.213598 -990.9108 NO2** 10.26 2.04 1.61 0.239932 33.44 O2** 0.20482 * O. Kubaschewski and C. B. Alcock, "Metallurgical Thermochemistry", Pergamon press, 1979. ** M. Kh. Karapetyants, "Chemical Thermodynamics", MIR Publishers- Moscow, 1978. - 139 - Table-6.2: The enthalpies and entropies calculated for different substances at different temperatures, and used for the calculation of the change in the Gibbs free energy for the different reactions given in Tables (4.5) and (4.6) BaCO3 T, K Hcp H298 HT Scp S298 ST 873 64.5048 -1218.89 -1154.38 0.11702 0.112024 0.22905 973 77.6132 -1218.89 -1141.27 0.13124 0.112024 0.24326 1073 91.2111 -1218.89 -1127.68 0.14453 0.112024 0.25656 1173 105.292 -1218.89 -1113.6 0.15708 0.112024 0.26910 1273 119.850 -1218.89 -1099.04 0.16899 0.112024 0.28101 1373 134.882 -1218.89 -1084.01 0.14799 0.112024 0.26001 BaO T Hcp H298 HT Scp S298 ST 873 30.1699 -553.432 -523.262 0.055659 0.070266 0.12593 973 35.7801 -553.432 -517.652 0.061743 0.070266 0.13201 1073 41.4770 -553.432 -511.955 0.067315 0.070266 0.13751 1173 47.2585 -553.432 -506.173 0.072466 0.070266 0.14273 1273 53.1232 -553.432 -500.309 0.077264 0.070266 0.14753 1373 59.0700 -553.432 -494.362 0.081761 0.070266 0.15203 BaTiO3 T Hcp H298 HT Scp S298 ST 873 46.7815 -1659.79 -1613.01 0.085372 0.107928 0.19330 973 55.7158 -1659.79 -1604.08 0.095059 0.107928 0.20299 1073 64.7773 -1659.79 -1595.02 0.103923 0.107928 0.21185 1173 73.9553 -1659.79 -1585.84 0.112101 0.107928 0.22003 1273 83.2425 -1659.79 -1576.55 0.119698 0.107928 0.22763 1373 92.6337 -1659.79 -1567.16 0.126799 0.107928 0.23477 - 140 - Table-6.2: Continued Ba2TiO4 T Hcp H298 HT Scp S298 ST 873 99.1719 -2242.99 -2143.8 0.18257 0.19663 0.379193 973 117.421 -2242.99 -2125.6 0.20236 0.19663 0.398982 1073 135.800 -2242.99 -2107.2 0.22034 0.19663 0.416962 1173 154.294 -2242.99 -2088.7 0.23681 0.19663 0.433441 1273 172.893 -2242.99 -2070 0.25203 0.19663 0.448655 1373 191.584 -2242.99 -2051 0.26616 0.19663 0.46279 CO2 T Hcp H298 HT Scp S298 ST 873 26.54147 -394.003 -367.461 0.04839 0.21347 0.26187 973 31.69172 -394.003 -362.311 0.05398 0.21347 0.26745 1073 36.95115 -394.003 -357.051 0.05913 0.21347 0.27259 1173 42.31493 -394.003 -351.688 0.06391 0.21347 0.27738 1273 47.77974 -394.003 -346.223 0.06838 0.21347 0.28185 1373 53.34325 -394.003 -340.659 0.07258 0.21347 0.28606 TiO2 T Hcp H298 HT Scp S298 ST 873 39.65003 -943.844 -904.194 0.070717 0.050285 0.121002 973 47.08773 -943.844 -896.756 0.078601 0.050285 0.128886 1073 54.58512 -943.844 -889.259 0.085771 0.050285 0.136057 1173 62.13228 -943.844 -881.712 0.092347 0.050285 0.142633 1273 69.72242 -943.844 -874.122 0.09842 0.050285 0.148705 1373 77.3507 -943.844 -866.493 0.104062 0.050285 0.154347 - 141 - Table-6.2: continued Ba(NO3)2 T Hcp H298 HT Scp S298 ST 873 118.759 -990.91 -872.152 0.21247 0.21360 0.42608 973 144.896 -990.91 -846.014 0.24081 0.21360 0.45441 1073 172.563 -990.91 -818.348 0.26786 0.21360 0.48146 1173 201.748 -990.91 -789.162 0.29386 0.21360 0.50746 1273 232.447 -990.91 -758.463 0.31896 0.21360 0.53256 1373 264.654 -990.91 -726.256 0.34331 0.21360 0.55691 NO2 T Hcp H298 HT Scp S298 ST 873 26.04326 33.44 59.4833 0.04765 0.23993 0.287584 973 31.03977 33.44 64.47977 0.05307 0.23993 0.293002 1073 36.13632 33.44 69.57632 0.05806 0.23993 0.297987 1173 41.32914 33.44 74.76914 0.06268 0.23993 0.302613 1273 46.61563 33.44 80.05563 0.06701 0.23993 0.306938 1373 51.99395 33.44 85.43395 0.07107 0.23993 0.311005 - 142 - 4. Electrical Properties 5000 εr at 500 Hz 0.5 4500 4477.115989 εr at 1KHz 0.45 εr at 10KHz 4000 εr at 20KHz 0.4 εr at 100KHz 3500 tanδ at 500Hz 0.35 tanδ at 1kHz 3000 tanδ at 10kHz 0.3 tanδ at 20kHz 2500 tanδ at 100kHz 0.25 2000 0.2 1407.017074 1500 0.15 dielectric loss, tanδ loss, dielectric Relative permittivity Relative 1000 tanδ=0.0875 0.1 tanδ=0.056 tanδ=0.0279 500 0.05 tanδ=0.0175 tanδ=0.0105 tanδ=0.00175 0 0 0 50 100 150 200 250 Temperature, °C Figure (6.9): Dielectric properties as a function of temperature and frequency for BaCO3/TiO2-c powder mixture, milled for 10h, calcined at 800°C/3h, and sintered at 1300°C/3h 0.0014 y = 1E-05x - 0.0009 0.0012 R2 = 0.999 0.001 0.0008 0.0006 0.0004 Reciprocal permittivity Reciprocal 0.0002 0 120 140 160 180 200 220 Temperature, °C Figure (6.10): Reciprocal of relative permittivity versus temperature at T>Tc, for the sintered BaTiO3 prepared from BaCO3/TiO2-c powder mixture, milled for 10h - 143 - 6000 εr at 500Hz 1 εr at 1kHz 0.9 5000 5040.075414 εr at 10kHz εr at 20KHz 0.8 εr at 100KHz 4000 tanδ at 500z 0.7 tanδ at 1kHz 0.6 tanδ at 10kHz 3000 tanδ at 20kHz 0.5 tanδ at 100khz 0.4 1806.057113 2000 0.3 dielectric loss, tanδ loss, dielectric Relative permittivity Relative tanδ=0.173 tanδ=0.209 1000 0.2 tanδ=0.0105 tanδ=0.00698 0.1 0 0 0 50 100 150 200 250 Temperature, °C Figure (6.11): Dielectric properties as a function of temperature and frequency for BaCO3/TiO2-c powder mixture, milled for 12.5h, calcined at 800°C/3h, and sintered at 1300°C/3h 0.0014 y = 1E-05x - 0.0012 0.0012 R2 = 0.9671 0.001 0.0008 0.0006 0.0004 Reciprocal permittivity Reciprocal 0.0002 0 120 140 160 180 200 220 Temperature, °C Figure (6.12): Reciprocal of relative permittivity versus temperature at T>Tc, for the sintered BaTiO3 prepared from BaCO3/TiO2-c powder mixture, milled for 12.5h - 144 - الملخص تى تحضيش تيتبَبث انببسيىو ببستخذاو طشيقت انتفبعم فً انحبنت انصهبت يٍ خهيطيٍ يختهفيٍ هًب: كشبىَبث انببسيىو/ أكسيذ انتيتبَيىو و َيتشاث انببسيىو/ أكسيذ انتيتبَيىو. و قذ وجذ أٌ طىسا واحذا يٍ يبدة تيتبَبث انببسيىو انًعذة قذ تكىٌ بعذ انحشق عُذ 750 دسجت يئىيت نًذة 10 سبعبث و عُذ 600 دسجت يئىيت نًذة 6 سبعبث، نهخهيطيٍ األول و انثبًَ عهً انتىانً. استخذو كم يٍ، و حيىد األشعت انسيُيت فً دساست كيُبتيكيت تكىيٍ تيتبَبث انتحهيم انحشاسي انببسيىو. و قذ وجذ أٌ ًَىرج األَكًبش انحجًً هى انزي يحكى حشكت انتفبعم فً كال انتفبعهيٍ. و تى اقتشاح تصىس واقعً نًيكبَيكيت انتفبعم. كًب تى دساست وقيبس خصبئص انعزل انكهشبً نتيتبَبث انببسيىو انًحشوقت. و وجذ أٌ انسًبحيت انُسبيت و انفقذ فً انعزل انكهشبً يقبسيٍ عُذ دسجت حشاسة انغشفت و عُذ ربزبت واحذ كيهى هشتز نتيتبَبث انببسيىو انًعذة يٍ كم يٍ خهيظ كشبىَبث انببسيىو/ أكسيذ انتيتبَيىو و خهيظ َيتشاث انببسيىو/ أكسيذ انتيتبَيىو هًب 2028.5 و0,043 نألونً و 1805,33و0,41 نهثبَيت. حصُيع و دراست خىاص يبدة حيخبَبث انببريىو انفيزوانيكخزيك إعداد كهثىو إسًبعيم عثًبٌ رسبنت يقديت إنً كهيت انهُدست- جبيعت انقبهزة كجشء يٍ يخطهببث انحصىل عهً درجت اندكخىراِ فً هُدست انفهشاث كهيت انهُدست – جبيعت انقبهزة انجيشة – جًهىريت يصز انعزبيت 2011 حصُيع و دراست خىاص يبدة حيخبَبث انببريىو انفيزوانيكخزيك إعداد كهثىو إسًبعيم عثًبٌ رسبنت يقديت إنً كهيت انهُدست- جبيعت انقبهزة كجشء يٍ يخطهببث انحصىل عهً درجت اندكخىراِ فً هُدست انفهشاث ححج اشزاف أ.د. فىسي عبد انقبدر انزفبعً قسى انفهشاث- جبيعت انقبهزة أ.د. يصطفً يحًىد انسيد عهً قسى انفهشاث- هيئت انطبقت انذريت أ.د. راَدا أحًد عبد انكزيى قسى انفهشاث- جبيعت انقبهزة كهيت انهُدست – جبيعت انقبهزة انجيشة – جًهىريت يصز انعزبيت 2011 حصُيع و دراست خىاص يبدة حيخبَبث انببريىو انفيزوانيكخزيك اعداد كهثىو إسًبعيم عثًبٌ رسبنت يقديت إنً كهيت انهُدست- جبيعت انقبهزة كجشء يٍ يخطهببث انحصىل عهً درجت اندكخىراِ فً هُدست انفهشاث يعخًد يٍ نجُت انًًخحُيٍ أ.د. فىسي عبد انقبدر انزفبعً قسى انفهشاث- جبيعت انقبهزة أ.د. يصطفً يحًىد انسيد عهً قسى انفهشاث- هيئت انطبقت انذريت أ.د. سعد يجبهد انزاجحً قسى انفهشاث- جبيعت انقبهزة أ.د. وفبء إسًبعيم عبد انفخبح انًزكش انقىيً نهبحىد كهيت انهُدست – جبيعت انقبهزة انجيشة – جًهىريت يصز انعزبيت 2011