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46
Table I Summary of the temperature-induced phase transitions of NaNbO3 characterized by X-
ray diffraction (XRD),98-102 Raman spectroscopy,102 dielectric analysis,102 and neutron powder diffraction (NPD)107.
XRD NPD XRD/Raman/Dielectric
Phase Symmetry Temp.
(ºC) Symmetry Temp. (ºC) Symmetry Temp. (ºC) N Rhombohedral (R3c) < -100 Rhombohedral (R3c) < 7 Rhombohedral (R3c) < -23 P Orthorhombic (Pbcm) -100 ~ 360 Orthorhombic (Pbcm) -258 ~ 407 Pm: Monoclinic -23 ~ 137 INC: Incommensurate 137 ~ 187 PO: Orthorhombic 187 ~ 360 R Orthorhombic (Pmnm) 360 ~ 480 Orthorhombic (Pbnm) 360 ~ 482 Orthorhombic (Pmnm) 360 ~ 480 S Orthorhombic (Pnmm) 480 ~ 520 Orthorhombic (Pbnm) 482 ~ 537 Orthorhombic (Pnmm) 480 ~ 527 T1 Orthorhombic (Ccmm) 520 ~ 575 Orthorhombic (Ccmm) 537 ~ 592 Orthorhombic (Ccmm) 527 ~ 575 T2 Tetragonal (P4/mbm) 575 ~ 640 Tetragonal (P4/mbm) 592 ~ 677 Tetragonal (P4/mbm) 575 ~ 640 U Cubic (Pm3m) > 640 Cubic (Pm3m) > 677 Cubic (Pm3m) > 640
47
Table II Summary of the temperature-induced phase transitions of AgNbO3.127-129 PE and AFE
stands for paraelectric and antiferroelectric, respectively.
Phase Temp. (ºC) Symmetry Tilting system Physical nature M1 < 67 Pmc21 (a-b-c+)/(a-b-c-) Uncompensated AFE
(ferrielectric) M2 67 ~ 267 Pbcm (a-b-c+)/(a-b-c-) AFE M3 267 ~ 353 Pbcm (a-b-c+)/(a-b-c-) AFE O1 353 ~361 Orthorhombic Undetermined PE O2 361 ~ 387 Cmcm a0b-c+ PE T 387 ~ 579 P4/mbm a0b0c+ PE C > 579 Pm3m a0a0a0 PE
48
Figure Captions:
Fig. 1. Structure models for PbZrO3-based antiferroelectrics. (a) The structure for PbZrO3,
redrawn from Ref. [2]. The orthorhombic unit cell is indicated by the red box. (b) The structure for PbZrO3-based solid solutions with incommensurate modulations. The
incommensurate modulation is suggested to be a mixture of commensurate modulations.60 Fig. 2. Evolution of the satellite reflections surrounding the (120)c and (210)c fundamental
diffraction spots in the <001>c-zone axis in Pb0.99Nb0.02[(Zr0.58Sn0.42)0.955Ti0.045]0.98O3.60 (a) E
= 0 kV/cm, (b) E = 8 kV/cm, (c) E = 20 kV/cm, (d) E = 30 kV/cm, (e) E = 40 kV/cm, and (f)
E = 60 kV/cm.
Fig. 3. Evolution of the <112>c-zone axis selected area diffraction pattern under applied electric
fields in Pb0.99Nb0.02[(Zr0.55Sn0.45)0.94Ti0.06]0.98O3.58 (a) E = 0 kV/cm, (b) E = 48 kV/cm, (c) E
= 56 kV/cm.
Fig. 4. The response of Pb0.99Nb0.02[(Zr0.57Sn0.43)0.94Ti0.06]0.98O3 (PNZST43/6.0/2) ceramics under
unipolar electric fields up to 140kV/cm.70 (a) The profile of the applied electric field. Point Z denotes the condition where the electric field-induced strains x33 and x11 are set to zero. (b)
The strains x33 and x11 developed under electric fields in segments A, B, C, and D, each with
a different color which corresponds to that in (a).
Fig. 5. The electric field-induced transverse strain x11 in PNZST43/6.0/2, 43/6.3/2, 43/6.7/2
ceramics. The point where x11 starts to decrease in the induced ferroelectric phase with
increasing field is marked.
Fig. 6. The compressive stress-strain curves of the PNZST43/6.0/2 ceramic in its antiferroelectric (25 C), multiple cell cubic (175 C), and single cell cubic (250 C) states.
Fig. 7. The polarization vs. electric field hysteresis loops with a peak field of 60 kV/cm in the PNZST43/6.0/2 ceramic under (a) uniaxial compressive pre-stresses, and (b) radial compressive pre-stresses.82
49
Fig. 8. The X-ray diffraction results from annealed ceramic specimens under electric fields at 25
C.92 (a) The pseudo-cubic {200}c peak, and (b) the pseudo-cubic {222}
c peak of
PNZST43/6.0/2. (c) The {200}c peak, and (d) the {222}c peak of PNZST43/7.1/2. The
evolution of the T(002) peak under different conditions is highlighted by the dashed boxes in (a) and (c).
Fig. 9. Calculated spontaneous polarization PS as a function temperature using the data of
Bi3+/Na+, Ti4+ displacements and unit cell volume from Ref. [144].
Fig. 10. The phase diagram for the (1-x)(Bi1/2Na1/2)TiO3–xBaTiO3 binary system under (a)
poled,37 and (b) unpoled conditions.154 The crystal structure and domain morphology at room temperature are highlighted as shaded boxes. Symbols of solid squares, open circles, and solid triangles represent Tm, TRE, and Td, respectively, determined from dielectric
measurements. PE, AFE, and FE stand for paraelectric, antiferroelectric, and ferroelectric, respectively.
Fig. 11. The P4bm uncompensated antiferroelectric (ferrielectric) phase with a nanodomain morphology. (a) The TEM bright field micrograph from an unpoled 0.93(Bi1/2Na1/2)TiO3–
0.07BaTiO3 ceramic at room temperature. The bright arrow in the electron diffraction pattern
indicates the 2 1
{ooe} superlattice spots. (b) A schematic diagram of the polar ferrielectric nanodomains in (1-x)(Bi1/2Na1/2)TiO3–xBaTiO3, refined from Ref. [154]. The ferrielectric
nanodomains (the grey islands in the diagram) with the P4bm symmetry are embedded in the undistorted cubic matrix (the white background in the diagram). The antiparallel arrow pairs with unequal amplitudes denote the cation displacements which fluctuate among the six equivalent <001>c directions.
Fig. 12. The electric field in situ TEM study on the P4bm-to-P4mm phase transition and the domain switching in the P4mm phase in the 0.93(Bi1/2Na1/2)TiO3–0.07BaTiO3 ceramic at
room temperature viewed with the <112>c-zone axis. (a) The bright field micrograph from
0.93(Bi1/2Na1/2)TiO3–0.07BaTiO3 ceramic at E = 0 kV/cm. (b) The electron diffraction
pattern reveals the presence of the 2 1
50
symmetry. (c) E = 5 kV/cm. The direction of the applied field is roughly along the bright arrow. (d) E = 7.5 kV/cm. (e) Selected area electron diffraction pattern from the lamellar domain area in the upper left portion of the grain shown in (d). (f) Diffraction pattern from the nanodomain area in the central portion of the grain. (g) E = 10 kV/cm. (h) E = 12.5 kV/cm. (i) E = 25 kV/cm.
(a) Fig. 1 (b) 8 8 7 4 4 51
Fig. 2
Fig. 3
0 30 60 90 120 150 E ( k V /cm) Seg. B Seg. C Seg. D Seg. A Z (a) 0 6 12 18 24 30 36 42 0.00 0.02 0.04 0.06 0.08 0.10 0.000 0.005 0.010 0.015 0.020 x 33 (%) Time (second) Seg. B Seg. D x 11 (%) (b) Seg. C Seg. A Fig. 4 54
0 20 40 60 80 100 120 140 160 0.00 0.02 0.04 0.06 0.08 PNZST43/6.3/2 PNZST43/6.7/2 x 11 (% ) E (kV/cm) PNZST43/6.0/2 Fig. 5 55
-0.5 -0.4 -0.3 -0.2 -0.1 0.0 -350 -300 -250 -200 -150 -100 -50 0 175°C 250°C PNZST43/6.0/2 Stres s (MPa) Strain (%) 25°C Fig. 6 56
-30 -20 -10 0 10 20 30 0 MPa 75 MPa 100 MPa 250 MPa P ( μ C/c m 2 ) (a) Axial -60 -40 -20 0 20 40 60 -30 -20 -10 0 10 20 30 0 MPa 90 MPa 135 MPa 180 MPa 360 MPa P ( μ C/cm 2 ) E (kV/cm) (b) Radial Fig. 7 57
Kα2 Kα 2 Co unts (a.u.) Virgin Fig. 8 -40kV/cm 0kV/cm (a) 43/6.0/2 Se qu en ce T(002) T(200) R(200) Virgin 0kV/cm (b) Kα2 T(222) -40kV/cm R(222)+ R(222) Kα2 43.5 43.8 44.1 44.4 44.7 Kα2 2θ Counts (a.u.) (c) Virgin +5kV/cm -25kV/cm 0kV/cm Seq uen c e 43/7.1/2 T(002) Kα2 T(200) R(200) 80.7 80.9 81.1 81.3 81.5 81.7 R(222)+ -25kV/cm Kα2 R(222) 2θ (d) Virgin Kα2 Kα 2 T(222) 58
300 350 400 450 500 550 -8 -4 0 4 8 12 16 Ca lc ula ted P S ( μ C/c m 2 ) T (oC) Fig. 9 59
0.04 0.06 0.08 0.10 0.12 -100 0 100 200 300 BT P4mm lamellar domain P4bm nanodomain relaxor AFE FE AFE T ( o C) x PE FE (a) (b) PE AFE FE FE R3c complex domain BNT Fig. 10 60
(b) <01 0 > <100> Fig. 11 61
Fig. 12