LIST OF TABLES
Table 1.1. Values of the close packing factor t for some perovskite-type compounds 8
Table 2.1. Calculation results of grain size, lattice constant and average ceramic density of MP sample group from SEM analysis and X-ray diffraction 42
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Table 2.2. Calculation results of grain size, lattice constant and average ceramic density of MZ sample group from SEM analysis and X-ray diffraction 46
Table 2.3. Polynomial coefficients of (2.14) and (2.15). 54
Table 3.1. Average values of dielectric constant and dielectric loss tan of sample groups MP, MZ at room temperature at frequency 1kHz
................................................................ ................................................................ ... 59
Table 3.2. Values of maximum dielectric constant max , temperature corresponding to maximum dielectric constant T m and blurring of sample groups MP, MZ measured at frequency 1kHz 63
Table 3.3. Parameters obtained from fitting data to the Vogel – Fulcher formulas 68
Table 3.4. Parameters characterizing the ferroelectric properties of PZT-PZN- PMnN ceramics at room temperature: residual polarization P r , electric field resistance E C
................................................................ ................................................................ ... 69
Table 3.5. Parameters characterizing the ferroelectric properties of PZT-PZN- PMnN ceramics according to temperature: residual polarization P r , electric field resistance E C72
Table 3.6. Average values of electromechanical coupling coefficients k p , k 31 , k t , pressure coefficient
electrical properties d 31 and mechanical quality factor Q m of PZT-PZN-PMnN ceramics
................................................................ ................................................................ ... 76
Table 3.7. Comparison of properties of manufactured ceramics with ceramics of other works 79
Table 4.1. Results of grain size and ceramic density calculations of the MF sample group from SEM analysis 83
Table 4.2. Average values of dielectric constant and dielectric loss tan of MF samples at room temperature at 1kHz frequency. 84
Table 4.3. Values of maximum dielectric constant max , temperature corresponding to maximum dielectric constant T m and blurring of MF samples at 1kHz frequency 88
Table 4.4. Average values of electromechanical coupling coefficients k p , k t , k 31 , piezoelectric coefficient d 31 and mechanical quality factor Q m of Fe 2 O 3 doped PZT-PZN-PMnN ceramics92
Table 4.5. Parameters characterizing the ferroelectric properties of Fe 2 O 3 doped PZT-PZN- PMnN ceramics : residual polarization Pr , electric field resistance E C ... 95
Table 4.6. Comparison of properties of manufactured ceramics with ceramics of other works with the same Fe 2 O 3 impurities95
Table 4.7. Ceramic density, dielectric constant, tan loss , coefficient k p of sample M0- 1150 97
Table 4.8. Calculation results of grain size, lattice parameters and ceramic density of MC sample group from SEM analysis and X-ray diffraction 104
Table 4.9. Average values of dielectric constant and dielectric loss tan of MC samples measured at room temperature at 1kHz frequency 105
Table 4.10. Values of maximum dielectric constant max , temperature corresponding to maximum dielectric constant T m and blurring of MC samples at frequency 1kHz 106
Table 4.11. Average values of electromechanical coupling coefficients k p , k t , k 31 , piezoelectric coefficient d 31 and mechanical quality factor Q m of CuO-doped PZT-PZN-PMnN ceramics 108
Table 4.12. Parameters characterizing the ferroelectric properties of CuO-doped PZT-PZN- PMnN ceramics: residual polarization Pr , electric field resistance E C ... 110
Table 4.13. Comparison of properties of manufactured ceramics with ceramics of other works with the same type of CuO 111 impurities
Table 4.14. Resonance characteristics of toroidal transformer 113
LIST OF DRAWINGS
Figure 1.1. Cubic perovskite unit cell (a) and three-dimensional BO 6 lattice (b).. 7
Figure 1.2. Crystal structure of BaTiO 3 (a) cubic structure (b) tetragonal structure 9
Figure 1.3. Free energy diagram according to spontaneous polarization at different temperatures
................................................................ ................................................................ ... 11
Figure 1.4. Dependence of dielectric constant on temperature of ferroelectric ceramics
................................................................ ................................................................ ... 12
Figure 1.5. Schematic diagram of a typical ferroelectric hysteresis loop 13
Figure 1.6. Diagram demonstrating the influence of external electric field on a) first-order phase transition; b) second-order phase transition and the shift of the transition point when the temperature increases or decreases; c) T C shifts to a higher temperature for first-order phase transition; and d) T C does not shift for second-order phase transition. 15
Figure 1.7. Schematic diagram showing some types of domains: a) domains antiparallel to the 180 o walls ; b) domains with 180 o and 90 o walls ; and c) a mixture of domains in the c and a axis directions (the a axis is perpendicular to the c axis). 17
Figure 1.8. Relative dielectric constant spectra versus temperature measured at different frequencies of the single-crystal material system Pb(Mg 1/3 Nb 2/3 )O 3 : (a) typical relaxor; (b) blurred phase transition of the crystal, from normal ferroelectric to relaxor ferroelectric at T c < T m ; (c) phase transition of the crystal, from normal ferroelectric to relaxor ferroelectric at T c < T m ; (d)
phase transition of the crystal, from normal ferroelectric to relaxor ferroelectric at T c = T m ; (CRD). 21
Figure 1.9. Crystal structure of complex perovskite compound on lead base, with formula Pb(B'B'')O 322
Figure 1.10. Differences between conventional ferroelectrics and phase-shifted ferroelectrics; (a) Shape of the ferroelectric hysteresis loop; (b) Dependence of spontaneous polarization on temperature; (c) Dependence of dielectric constant on temperature and frequency 23
Figure 2.1 . DTA and TGA thermal analysis diagrams of the compound (Zn,Mn)Nb 2 (Zr,Ti)O 637
Figure 2.2. X-ray diffraction spectrum of the compound (Zn,Mn)Nb 2 (Zr,Ti)O 637
Figure 2.3. DTA and TGA thermal analysis diagrams of the compound: 38
Figure 2.4. X-ray diffraction spectrum of MP80 pre-calcined at 850 o C 39
Figure 2.5. Technological process for manufacturing PZT-PZN-PMnN ceramic system by BO method 40
Figure 2.6. X-ray diffraction spectra of samples belonging to the MP sample group: MP65 (0.65 mol PZT), MP70 (0.7 mol PZT), MP75 (0.75 mol PZT), MP80 (0.8 mol PZT), MP85 (0.85 mol PZT) and MP90 (0.9 mol PZT).. 41
Figure 2.7. Dependence of c/a ratio on PZT concentration 43
Figure 2.8. Scanning electron microscopy images of samples belonging to the MP sample group: MP65 (0.65 mol PZT), MP70 (0.7 mol PZT), MP75 (0.75 mol PZT), MP80 (0.8 mol PZT), MP85 (0.85 mol PZT) and MP90 (0.9 mol PZT) 44
Figure 2.9. Dependence of ceramic density (a) and average grain size (b) on PZT concentration 44
Figure 2.10. X-ray diffraction spectra of samples belonging to the MZ group: MZ46 (Zr/Ti = 46/54), MZ47 (Zr/Ti = 47/53), MZ48 (Zr/Ti = 48/52), MZ49 (Zr/Ti = 49/51), MZ50 (Zr/Ti = 50/50), MZ51 (Zr/Ti = 51/49) 45
Figure 2.11. Dependence of c/a ratio on Zr/Ti concentration 47
Figure 2.12. Scanning electron microscopy images of samples belonging to the MZ group: MZ46 (Zr/Ti = 46/54), MZ47 (Zr/Ti = 47/53), MZ48 (Zr/Ti = 48/52), MZ49 (Zr/Ti = 49/51), MZ50 (Zr/Ti = 50/50), MZ51 (Zr/Ti = 51/49) 47
Figure 2.13. Dependence of density (a) and ceramic grain size on Zr/Ti ratio 48
Figure 2.14. EDS spectrum of PZT–PZN–PMnN 48 ceramics
Figure 2.15. Equivalent diagram of piezoelectric oscillator near resonance .. 51 Figure 2.16. Sawyer-Tower circuit diagram 55
Figure 2.17 . PE 55 electric rail delay line
Figure 3.1. Dependence of dielectric constant and dielectric loss on temperature
Measurements at 1kHz of the MP (a) and MZ (b) sample groups 60
Figure 3.2. Dependence of ln(1/ -1/ max ) on ln(TT m ) at T T m of samples MP (a) and MZ (b) 62
Figure 3.3. Dielectric constant with temperature at different frequencies of the MP sample group: MP65 (0.65 mol PZT), MP70 (0.7 mol PZT), MP75
(0.75 mol PZT), MP80 (0.8 mol PZT), MP85 (0.85 mol PZT), and MP90 (0.9 mol PZT) 64
Figure 3.4. Dielectric constant with temperature at different frequencies of the MZ sample group: MZ46 (Zr/Ti = 46/54), MZ47 (Zr/Ti = 47/53), MZ48 (Zr/Ti = 48/52), MZ49 (Zr/Ti = 49/51), MZ50 (Zr/Ti = 50/50), MZ51 (Zr/Ti = 51/49) 65
Figure 3.5 . Experimental and Vogel-Fulcher fitting curves of MP samples: MP65 (0.65 mol PZT), MP70 (0.7 mol PZT), MP75 (0.75 mol PZT), MP80 (0.8 mol PZT), MP85 (0.85 mol PZT) and MP90 (0.9 mol PZT) 67
Figure 3.6. Experimental and Vogel-Fulcher fitting curves of MZ samples: MZ46 (Zr/Ti = 46/54), MZ47 (Zr/Ti = 47/53), MZ48 (Zr/Ti = 48/52), MZ49 (Zr/Ti = 49/51), MZ50 (Zr/Ti = 50/50), MZ51 (Zr/Ti = 51/49) 67
Figure 3.7. Hysteresis curve shape of MP 68 group samples
Figure 3.8. Hysteresis curve shape of MZ 69 group samples
Figure 3.9. Dependence of the resistive electric field and residual polarization on concentration
PZT (a) and Zr/Ti ratio (b) 70
Figure 3.10. Hysteresis curve of MZ48 sample according to temperature 71
Figure 3.11. Temperature dependence of residual polarization P r and electric field resistance E C of sample MZ48 (Zr/Ti =48/52) 72
Figure 3.12. Radial vibration spectrum of MP 74 ceramic samples
Figure 3.13. Radial vibration spectrum of MZ 74 ceramic samples
Figure 3.14. Thickness variation spectrum of MP 75 ceramic samples
Figure 3.15. Thickness variation spectrum of MZ 75 ceramic samples
Figure 3.16. Dependence of piezoelectric parameters of PZT-PZN-PMnN ceramics on PZT concentration (a) and Zr/Ti concentration (b) 77
Figure 4.1. X-ray diffraction pattern of PZT–PZN–PMnN ceramic doped with Fe 2 O 3 82
Figure 4.2. Lattice constant (a) and tetragonal phase concentration (b) of Fe 2 O 3 doped PZT–PZN–PMnN ceramics82
Figure 4.3. Scanning electron microscopy images of samples belonging to the MF 83 sample group
Figure 4.4. Dependence of dielectric constant and dielectric loss of Fe 2 O 3 doped PZT-PZN-PMnN ceramics84
Figure 4.5 . Temperature T m of PZT-PZN- PMnN ceramics with different Fe 2 O 3 concentrationsdifferent 85
Figure 4.6. Raman scattering spectrum of PZT–PZN–PMnN doped with Fe 2 O 386
Figure 4.7. Raman scattering spectrum of PbTiO 3 (a) [1]; Pb(Zr,Ti]O 3 (b) [67] 87
Figure 4.8. Raman modes (a) and mode shifts (b) in Fe 2 O 3 doped PZT– PZN-PMnN ceramics88
Figure 4.9. Dependence of Ln(1/ −1/ max ) on ln(T−T m ) (a) and HWHM width (b) of Fe 2 O 3 doped PZT – PZN – PMnN ceramics89
Figure 4.10. EDS spectrum of Fe 2 O 3 doped PZT–PZN–PMnN ceramics91
Figure 4.11. Radial (a) and thickness (b) vibrational resonance spectra of MF4 92
Figure 4.12. Dependence of piezoelectric parameters of PZT-PZN-PMnN ceramics on Fe 2 O 3 concentration93