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研究生：	洪群雄 Hong, Cheng-Shong
論文名稱：	利用模糊相轉換模型、旋轉玻璃性模型及朗道相變理論探討MnO摻雜及製程條件對Pb(Fe2/3W1/3)O3-PbTiO3弛緩鐵電體介電特性的影響 Investigating the Effects of the MnO Additives and Process Conditions on the Pb(Fe2/3W1/3)O3-PbTiO3 Relaxor Ferroelectric Ceramics by Using the Diffuse Phase Transition Models, the Spin-Glass Model and the Modified-Landau Theory
指導教授：	朱聖緣 Chu, Sheng-Yuan
學位類別：	博士 Doctor
系所名稱：	電機資訊學院 - 電機工程學系 Department of Electrical Engineering
論文出版年：	2007
畢業學年度：	95
語文別：	英文
論文頁數：	162
中文關鍵詞：	弛緩體、旋轉玻璃、序向、介電、鐵電、模糊相轉換、朗道
外文關鍵詞：	relaxor, ferroelectric, diffuse phase transition, order, dielectric, Landau, spin-glass
相關次數：	點閱：70 下載：3
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本文以模糊相轉換定理、旋轉玻璃性模型、居里魏斯定理及修正式朗道理論，討論以Pb(Fe2/3Ti1/3)O3-PbTiO3陶瓷系統為基礎的低場介電行為，PbTiO3組成添加量之多寡、燒結溫度的高低、MnO雜質的摻雜及合成方法改變對介電特性、晶粒結構及晶格結構的影響均有詳細討論。
首先，以(1-x)Pb(Fe2/3Ti1/3)O3-xPbTiO3介電系統之實驗現象及統計迴歸理論分析Burfoot et al.及Eiras et al.所提出之模型所代表的物理及數學上的意義。觀其結果， Burfoot et al. 及 Eiras et al. 所提出之模型對於鐵電弛緩體的介電模糊相轉換現象存在相同的適合曲線，且不論鐵電弛緩體是屬完全模糊相轉換特性或非完全模糊相轉換特性，Burfoot et al.及Eiras et al.模型的估計偏離誤差均較Smolensky及Isupov et al.所提出的模型小。關於模型中的參數所代表之物理及數學上的意義，Eiras et al.所提出模型之參數數值大小較能合理解釋模糊相轉換介電行為之物理現象。
若探討不同燒結溫度對0.7Pb(Fe2/3Ti1/3)O3-0.3PbTiO3鐵電弛緩體的影響，可發現當燒結溫度愈高時，晶格結構由立方晶結構轉換到長方晶結構、介電模糊相轉換特性變差、旋轉玻璃性行為較不明顯。由相關實驗結果及理論模型分析，當燒結溫度愈高時，0.7Pb(Fe2/3Ti1/3)O3-0.3PbTiO3鐵電弛緩體愈傾向一般鐵電特性。
MnO雜質對(1-x)Pb(Fe2/3W1/3)O3-xPbTiO3陶瓷系統介電響應的影響，可由晶格結構及空間電荷極化的改變、模糊相轉換模型、居里魏斯定理、修正式朗道理論或及旋轉性玻璃理論加以討論。最後我們提出假設，Mn離子在(1-x)Pb(Fe2/3W1/3)O3-xPbTiO3扮演的角色應是取代鉛空缺或進入晶格間隙，使得鄰近的電偶極矩交互作用減少，而將材料特性調整為短程序向特性的弛緩体，至於PbTiO3組成則可加強長程序向鐵電特性。
為研究合成方法對陶瓷介電特性的影響，一般傳統陶瓷製程的氧化物直接合成法及不同於B位離子預先煆燒法的兩步驟間接合成法，被用來製造0.75Pb(Fe2/3W1/3)O3-0.25PbTiO3-0.15wt%MnO介電陶瓷系統，經由晶粒結構、晶格結構、空間電荷極化、模糊相轉換特性、介電常數的頻率散射、介電損失、居里魏斯行為及區域序向參數的討論，均可證明經由間接合成法可強化B位離子序向性，且材料特性由短程序弛緩體調整為長程序向鐵電特性。

In this thesis, the low-field dielectric behaviors of the Pb(Fe2/3Ti1/3)O3-PbTiO3 (PFW-PT) based ceramic system are investigated by using the diffuse phase transition (DPT) laws, the spin-glass model, the Curie-Weiss law and the modified-Landau theory. The effects of the PbTiO3 composition, the sintering temperature, the MnO dopant, and the synthesized method are discussed on the dielectric properties, the grain structure and the lattice structure.
In the first phase, we analyze the diffuse phase transition models in the (1-x)Pb(Fe2/3W1/3)-xPbTiO3 relaxor system by using the statistical regression theory. We find that the laws of both Burfoot and Eiras show the same adaptability and provide smaller estimation bias on the samples than the models of Smolensky and Isupov despite the complete or incomplete DPT characteristics. Regarding the physical and mathematical meanings of parameters in their laws, the law of Eiras is better to explain the behaviour of both the more complete relaxor system and the incomplete relaxor system.
The effects of the sintering temperature are investigated on the 0.7PbFe2/3W1/3O3-0.3PbTiO3 relaxor ferroelectrics sintered. We find that the lattice structure is changed from cubic to tetragonal, the diffuse phase transition characteristics and the spin glass behavior are deviated as the sintering temperature increases. In conclusion, the normal ferroelectric characteristics are more obvious as the sintering temperature increases in this system.
The low-field dielectric responses of pure and 0.15wt% MnO additive (1-x)Pb(Fe2/3W1/3)O3-xPbTiO3 were investigated by using the changes of the lattice structure and the space charge polarization, the diffuse phase transition model, the Curie-Weiss law, the modified-Landau theory and the spin-glass model. Furthermore, we suggest that the lead vacancy is substituted or the lattice interstice is intervened by manganese ions, and the ordering degree of B-site cations is enhanced by PbTiO3 compositions are possible mechanism.
The 0.75Pb(Fe2/3W1/3)O3-0.25PbTiO3-0.15wt%MnO ceramics are synthesized by two different methods. The low field dielectric properties are changed with the lattice structure, the grain structure, the space charge polarization, the diffuse phase transition characteristics, the frequency dispersion, the dielectric loss, the Curie-Weiss behavior and the local order parameters. Furthermore, we suggest that the ordering degree of B-site cations is enhanced by using the indirect synthesized (IS) method.

Table of Contents
List of Figures…………………………………………………………..…... X
List of Tables……………………………………………………………… XV
Chapter 1 Introduction…………………………………………………..….. 1
Chapter 2 Theory and Literature Review…………………………….……. 11
2.1 Structure of the large plate capacitance and the polarization principle………….… 11
2.2 Mechanisms of polarization and frequency response………………………….….. 12
2.3 Practical capacitance and dielectric loss……………………………………….….. 13
2.4 Debye theory and frequency behavior……………………………………….……. 14
2.5 Arrhenius law and relaxation time of polarization…………………………….….. 16
2.6 Perovskite structure and order-disorder model………………………………….… 17
2.7 Diffuse phase transition models…………………………………………………… 18
2.8 Curie-Weiss law and superparaelectric model………………………………….…. 21
2.9 Spin-glass model and correlation behavior of neighbor microregions………….… 22
2.10 Landau-Devonshire theory and polarization frozen process………………….…. 23
Chapter 3 Fabrication and measurement setups in PFW-PT based ceramics……………………………………………………...… 34
3.1 PFW-PT based sample preparation………………………………………………... 34
3.1.1 Conventional direct oxide synthesized process………………………...….… 34
3.1.2 Two-step indirect synthesized process……………………………..….……... 35
3.2 Measurement of dielectric properties………………………………………..…..… 36
3.3 Measurement of dc resistivities…………………………………………….……… 36
3.4 Measurement of density………………………………………………………..….. 37
3.5 Measurement of Curie temperature……………………………………………..… 38
3.6 X-ray patterns and phase analysis…………………………………………….…… 38
3.7 SEM analysis and grain size determination…………………………….……..…... 38
Chapter 4 The investigation of the diffuse phase transition models based on the statistic regression analysis and the experimental results of the (1-x)PFW-xPT ceramic system……………………………...…. 43
4.1 Diffuse phase transition models…………………………………………………… 43
4.2 Regression theory and evidence…………………………………………….…….. 44
4.2.1 Estimation of the parameters in Equation (4.3) by using the regression theory………………………………………………………………….....…... 44
4.2.2 Estimation of the parameters in Equation (4.4) by using the regression theory…………………………………………………………………….…... 45
4.2.3 Discussion……………………………………………………….……..….…. 47
4.3 The fitting adaptability discussion of the diffuse phase transition models based on the experimental results of (1-x)PFW-xPT ceramic systems…………………….……. 47
4.3.1 The dielectric properties of the (1-x)PFW-xPT ceramics………………….… 47
4.3.2 The fitting results of the diffuse phase transition models………………….… 48
4.3.3 The fitting bias comparing between different models…………………….…. 50
4.3.4 The variance of the dielectric constant…………………………………….… 51
4.4 Physical and mathematical theory and viewpoint……………………………….... 52
4.5 The discussion of the physical and mathematical meaning based on the experimental results of (1-x)PFW-xPT ceramic systems……………………………………...… 54
4.5.1 The effects of normalizing dielectric constant and shifting temperature….…. 54
4.5.2 The comparison of the models of Burfoot and Eiras based on the physical and mathematical meaning……………………………………………….….…… 57
4.6 Summary ………………..…………………............................................................ 59
Chapter 5 The effects of the sintering temperature on 0.7PbFe2/3W1/3O3- 0.3PbTiO3 Ceramics…………………………………………… 75
5.1 Interpretation of the e SEM images and the density………………………….…… 75
5.2 Interpretation of the X-ray patterns……………………………………………….. 76
5.3 Interpretation of the dielectric properties…………………………………………. 76
5.4 Interpretation of the dielectric data in the frame of the diffuse phase transition properties…………………………………………………………………….……. 78
5.5 Spin glass behavior………………………………………………………….…….. 79
5.6 Summary…………………………………………………………………………... 81
Chapter 6 Effects of the MnO additives on the properties of Pb(Fe2/3W1/3) -PbTiO3 relaxors……………………………………..…….….... 92
6.1 Interpretation of the X-ray patterns…………………………………………….….. 92
6.2 Interpretation of the dielectric properties and the charge compensation as adding with MnO additive……………………………………………………………………… 93
6.3 Interpretation of the dielectric characteristic in the frame of the diffuse phase transition law………………………………………………………………………. 98
6.4 Discussion of the roles of manganese ions…………………………………….….. 99
6.5 Interpretation of the dielectric data in the frame of the Curie-Weiss law and the spin-glass model………………………………………………………………….. 102
6.6 Interpretation of the dielectric data in the frame of the modified-Landau theory... 104
6.7 Summary…………………………………………..…………………………..…. 105
Chapter 7 The effects of the synthesized methods on the 0.75Pb (Fe2/3W1/3)O3-0.25 PbTiO3 based ceramics………………....… 121
7.1 Interpretation of the X-ray patterns and the SEM images……………………..…. 121
7.2 Interpretation of the dielectric properties and the frequency dispersion……….… 123
7.3 Interpretation of the dielectric data in the frame of the diffuse phase transition law……………………………………………………………………………....... 126
7.4 Interpretation of the dielectric data in the frame of the Curie-Weiss law and the spin-glass model…………………………………………………………………. 128
7.5 Interpretation of the dielectric data in the frame of the modified-Landau theory.. 130
7.6 Discussions and Summary…………………………………………………….…. 132
Chapter 8 Conclusions and Recommendations for Future Work……….… 147
8.1 Conclusions…..………………………………………………..………………..... 147
8.2 Suggestions for Future Work…………………………………………….….…… 149
References………………………………………………………………... 152
 
List of Figures
Fig. 2.1. The large plate capacitor………………………………………………………. 26
Fig. 2.2. The schematic representation of the polarization by the dipole chains and the bound charges…………………………………………………………………. 27
Fig. 2.3 Schematic representation of the various polarization mechanisms……….......... 28
Fig. 2.4. Frequency dependence of various polarization mechanisms………………..… 29
Fig. 2.5. Schematic representation of the equivalent circuit of a practical capacitor and the relation of the flow current and cross voltage……………………………….... 30
Fig. 2.6 The relaxation spectra of the real dielectric constant and the image dielectric constant for a Debye equations………………………………………….……. 31
Fig. 2.7. The schematic representation of the ABO3 perovskite structure……………… 32
Fig. 2.8. The schematic representation of the order and disorder structure…………..… 33
Fig. 3.1. Flow diagram of the sample preparation procedure………………….……….. 39
Fig. 3.2. Flow diagram of the 0.25PTMn sample preparation procedure……………… 40
Fig. 3.3. Flow diagram of the 0.2+0.3PTMn sample preparation procedure……...…… 41
Fig. 3.4. Flow diagram of the 0.1+0.4PTMn sample preparation procedure……...…… 42
Fig. 4.1. The dielectric constant as a function of temperature for 0.9PFW-0.1PT ceramics at different frequencies………………………………………………………….. 63
Fig. 4.2. Dielectric constant-temperature measurement and the fitting curves using different diffuse phase transition models in the (1-x)PFW-xPT (x = 0.1 – 0.4) system………………………………………………………………………… 64
Fig. 4.3. The dependence of the diffuse parameters, δ, σ and Δ on the x ratios in the (1-x)PFW-xPT system………………………………………………………… 65
Fig. 4.4. The dependence of the diffuse parameters, γ and ξ on the x ratios in the (1-x)PFW-xPT system………………………………………………………… 66
Fig. 4.5. The total estimation errors between the theoretical calculations and the experimental results in Eq. (4.1) ~ Eq. (4.4) as a function of x ratios in the (1-x)PFW-xPT system………………………………………………………… 67
Fig. 4.6. The relations between the dielectric constant variance at different x ratios and the deviated temperature region in the (1-x)PFW-xPT system…………………… 68
Fig. 4.7. The effects of the parameters (a) γ and (b) σ in Eq. (4.3) on the dielectric constant and the Tc probability distribution as a function of temperature……………… 69
Fig. 4.8. The effects of the parameters (a) ξ and (b) Δ in Eq. (4.4) on the dielectric constant and the Tc probability distribution as a function of temperature……………… 70
Fig. 4.9. The theoretical curve fitting result (Eqs. (4.3) and (4.4)) and the experimental results for in the PFW-PT system for x=0.4 and x=0.1, separately…………… 71
Fig. 4.10. The curve fitting results with different γ and σ values in Eq. (4.3) and the experimental results…………………………………………………………… 72
Fig. 4.11. The curve fitting results with different ξ and Δ values in Eq. (4.4) and the experimental results…………………………………………………………… 73
Fig. 5.1. SEM images of 0.7PFW-0.3PT ceramics with various sintering temperature of (a) 850°C (b) 880°C (c) 910°C (d) 950°C………………………………………… 83
Fig. 5.2. Density(g/cm3) and relative density(%) of 0.7PFW-0.3PT ceramics with various sintering temperature…………………………………………………………… 84
Fig. 5.3. XRD patterns of 0.7PFW-0.3PT ceramics with various sintering temperature… 85
Fig. 5.4. The dielectric constant as a function of temperature at different frequency of 0.7PFW-0.3PT ceramics sintered at 850°C…………………………………..… 86
Fig. 5.5. The 1-MHz dielectric constant as a function of temperature for the 0.7PFW-0.3PT ceramics sintered with different temperature………………………………….. 87
Fig. 5.6. The experimental and fitted dielectric constant vs temperature for various sintering temperature (a) 850°C (b) 880°C (c) 910°C (d) 950°C……………... 88
Fig. 5.7. The temperature dependence of the reciprocal dielectric constant and the fitting curve with the Curie-Weiss law for 0.7PFW-0.3PT sintered at 850°C………... 89
Fig. 5.8. The local order as a function of temperature for 0.7PFW-0.3PT sintered with different temperature………………………………………………………….. 90
Fig. 6.1. XRD patterns of (1-x)PFW-xPT and (1-x)PFW-xPT+0.15w%MnO ceramics with x=0.1, 0.2, 0.3, 0.4…………………………………………………………… 107
Fig. 6.2. The dielectric constant and dielectric loss as a function of temperature at different frequency of 0.7PFW-0.3PT ceramics……………………………………….. 108
Fig. 6.3. The dielectric constant and dielectric loss as a function of temperature at different frequency of 0.7PFW-0.3PT ceramics adding with 0.15w% MnO………….. 109
Fig. 6.4. The 1-MHz dielectric constant as a function of temperature for (1-x)PFW-xPT and (1-x)PFW-xPT+0.15w%MnO ceramics with x=0.1, 0.2, 0.3 and 0.4….... 110
Fig. 6.5. The composition dependence of the maximum dielectric constant and the corresponding temperature Tm for (1-x)PFW-xPT and (1-x)PFW-xPT +0.15w%MnO system……………………………………………………...… 111
Fig. 6.6. The composition dependence of the room temperature resistivity for (1-x)PFW-xPT and (1-x)PFW-xPT +0.15w%MnO system………………….. 112
Fig. 6.7. The experimental data and the fitting results of the dielectric constant- temperature dependence for (1-x)PFW-xPT and (1-x)PFW-xPT-0.15w%MnO ceramics with (a) x=0.1 (b) x=0.2 (c) x=0.3 (d) x=0.4………………………. 113
Fig. 6.8. The composition dependence of the diffuse parameters ξ for (1-x)PFW-xPT and (1-x)PFW-xPT-0.15w%MnO system………………………………………… 114
Fig. 6.9. The composition dependence of the diffuse parameters Δ for (1-x)PFW-xPT and (1-x)PFW-xPT-0.15w%MnO system………………………………………… 115
Fig. 6.10. The temperature dependence of the reciprocal dielectric constant and the fitting curve using the Curie-Weiss law for (1-x)PFW-xPT and (1-x)PFW-xPT +0.15w%MnO ceramics with (a) x=0.1 (b) x=0.2 (c) x=0.3 (d) x=0.4……… 116
Fig. 6.11. The compositional dependence of the temperature extension Tcw-Tm in (1-x)PFW-xPT and (1-x)PFW-xPT +0.15w%MnO ceramic system………… 117
Fig. 6.12. The local order as a function of temperature by using the spin-glass model for (1-x)PFW-xPT and (1-x)PFW-xPT+0.15wt%MnO ceramics with x=0.1, 0.2, 0.3, 0.4………………………………………………………………………….… 118
Fig. 6.13. The local order as a function of temperature by using the modified-Landau theory for (1-x)PFW-xPT and (1-x)PFW-xPT+0.15wt%MnO ceramics with x=0.1, 0.2, 0.3, 0.4…………………………………………………………………… 119
Fig. 7.1. XRD patterns (a) the diffraction peaks of 2  in the range between 20° to 80° and (b) detailed representation of (002) ~ (200) diffraction peaks after normalizing diffraction peaks of 0.25PTMn, 0.2+0.3PTMn and 0.2+0.4PTMn ceramics…………………………………………………………………….… 134
Fig. 7.2. SEM images of (a) 0.25PTMn (b) 0.2+0.3PTMn (c) 0.1+0.4PTMn ceramics.. 135
Fig. 7.3. The dielectric constant and dielectric loss as a function of temperature for 0.25PTMn ceramics………………………………………………………….. 136
Fig. 7.4. The dielectric constant and dielectric loss as a function of temperature for 0.2+0.3PTMn ceramics………………………………………………………. 137
Fig. 7.5. The dielectric constant and dielectric loss as a function of temperature for 0.1+0.4PTMn ceramics………………………………………………………. 138
Fig. 7.6. The frequency dispersion (ε1KHz-ε1MHz) as a function of temperature for 0.25PTMn, 0.2+0.3PTMn and 0.1+0.4PTMn ceramics………………………………….. 139
Fig. 7.7. The dielectric constant as a function of temperature for 0.25PTMn, 0.2+0.3PTMn and 0.1+0.4PTMn ceramics at f=1 MHZ……………………………………. 140
Fig. 7.8. The experimental and fitted dielectric constant vs temperature for (a) 0.25PTMn, (b) 0.2+0.3PTMn and (c) 0.1+0.4PTMn ceramics at f=1 MHZ……………... 141
Fig. 7.9. The dependence of the diffusive parameters ξ and diffusive extensions Δ on 0.25PTMn, 0.2+0.3PTMn and 0.1+0.4PTMn ceramics at f=1 MHZ………... 142
Fig. 7.10. The temperature dependence of the reciprocal dielectric constant and the fitting curve with the Curie-Weiss law for (a) 0.25PTMn, (b) 0.2+0.3PTMn and (c) 0.1+0.4PTMn ceramics at f=1 MHZ………………………………………… 143
Fig. 7.11. The dependence of the temperature parameters Tcw, Tm and Tcw-Tm for 0.25PTMn, 0.2+0.3PTMn and 0.1+0.4PTMn ceramics at f=1 MHZ………... 144
Fig. 7.12. The local order parameter as a function of temperature for 0.25PTMn, 0.2+0.3PTMn and 0.1+0.4PTMn ceramics based on the glassy polarization theory………………………………………………………………………… 145
Fig. 7.13. The local order parameter as a function of temperature for 0.25PTMn, 0.2+0.3PTMn and 0.1+0.4PTMn ceramics based on the modified-Landau theory……………………………………………………………………….... 146

 
List of Tables
Table 4.1. The fitting parameters of Eqs. (4.3) and (4.4) for x=0.1, 0.2, 0.3 and 0.4 on the (1-x)PFW-xPT system……………………………………………………… 74
Table 5.1. Fitting parameters of 0.7PFW-0.3PT with various sintering temperature at f=1MHz……………………………………………………………………... 91
Table 6.1. Fitting parameters of (1-x)PFW-xPT and (1-x)PFW-xPT+0.15w%MnO ceramics with x=0.1, 0.2, 0.3, 0.4 at f=1MHz……………………………………..… 120
                                    

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