High resolution x ray diffraction study of phase and domain structures and thermally induced phase transformations in PZN (4 5 9)%PT 5

Chapter Tetragonal Micro/Nanotwins and Thermally-induced Phase Transformations in Unpoled PZN-9%PT 6.1 Introduction According to Neumann’s principle [92], changes in polarization possessed by a non-centrosymmetry must conform to the symmetry element of the crystal concerned In other words, the polarization behavior and the structural evolution of a non-centrosysmmetry crystal, such as PZN-PT, are interrelated Neumann’s principle also states that the property depends only on the point group, and hence the orientation of the crystal, but not on the space group This means that the study of polarization behaviour alone may not be sufficient to distinguish the type of crystal structure It is thus important to study both the polarization and structural behaviors of PZN-PT single crystal when examining the structural phase transformation of the crystal In this chapter, while the structural information of unpoled (annealed) PZN-9%PT single crystal was studied by means of HR-XRD and PLM, its polarization behaviors were determined by means of dielectric permittivity (ε’) and thermal current density (J) measurements Noticing that mechanical polishing induced surface layer gives rise to possible complication in x-ray diffraction structural studies, fractured 78 surfaces are used in this work during the HR-XRD measurements 6.2 Theoretical considerations of diffractions from (002) planes of perovskite crystals 6.2.1 Monoclinic diffractions In PZN-PT single crystals, three different types of M phases have been reported thus far by means of high-resolution diffraction The first is the MA phase, characterized by cm > am and bm with the spontaneous polarization vector lying in {110}pc-type mirror planes, where subscript m and pc denotes the monoclinic and pseudocubic axes, respectively (Figure 6.1a) The second is the MB phase, having similar mirror planes as in the MA phase but is characterized by cm < am and bm (Figure 6.1b) The third is the MC phase, characterized by cm>am and bm with the spontaneous polarization vector lying in {100}pc-type mirror planes (Figure 6.1c) Since the M phases are thought to help minimize the free energy path during the phase transformation [23-25], their presence is highly possible The presence of the E-field and temperature induced M phases has been evidenced experimentally, mostly via HR-XRD studies [31, 32, 34, 35, 93] The above-described M phases show degeneracy in the am and cm vectors but not in the bm vector The degenerated am and cm vectors are bounded by the monoclinic 79 (a) (b) cpc ≈ cm cpc ≈ cm β bpc bm apc am bpc ββ bm apc (c) am (d) cpc ≈ cm cm co/2 Orthorhombic ao/2 Monoclinic β bpc ≈ bm Figure 6.1 apc ≈ am lattice lattice Cubic lattice β am (a) MA, (b) MB, (c) MC, and (d) the relation between MC and O lattice [66] 80 angle, β, where β ≠ π/2 As the mirror plane is formed by the degenerated vectors, the spontaneous polarization vector is free to lie within the mirror plane bound by the pc R and pc T directions for the case of MA and MB phases In the MC phase, the vector is free to lie within the {100}pc planes bounded by the pc O and pc T polarization directions As mentioned, the various M phases could act as structural bridges for the R-T phase transformation, facilitating the polarization rotation mechanism For the MC phase, when am = cm, the crystal structure is best interpreted as the O phase The relation between the MC and O phase lattices is shown in Figure 6.1(d) The O phase, characterized by ao ≠ bo ≠ co and mutually orthogonal crystal axes, is thus the limiting case of MC phase when the lattice parameters am and cm are equal Because reciprocal lattice points in HR-XRD RSM are projected with respect to the pc axes, it is important to establish the relationship between the pc axes and the axes of the various M and the O phases of the perovskite crystal Table 6.1 contains the relationship between the (002) diffractions of the m and pc axes for the various M phases and the O phase described above in the unpoled state Since β ≠ π/2, in the (002) RSM, the M phase diffractions will be tilted out of the ω = 0° plane The out-of-plane diffractions (i.e., with ∆ω ≠ 0º) in the RSM may thus indicate possible presence of an M phase 81 Table 6.1 Relationship between the m and pc axes for various M phases and the O phase in the unpoled state Type of Monoclinic (mirror) Relationship between Characteristics of monoclinic plane and monoclinic and pseudocubic apc, bpc, and cpc in (002) characteristics of am, axes mapping bm and cm MA [2] [1] {110}pc; β > π/2 apc2 = bpc2 = (am/2)2 +(bm/2)2; degeneracy in apc, bpc, cpc ≈ cm cm > am/√2 and bm/√2 cpc > apc = bpc; and cpc possible MB [2] {110}pc; β > π/2 cm < am/√2 and bm/√2 apc2 2 = bpc = (am/2) +(bm/2) ; cpc ≈ cm cpc< apc = bpc; degeneracy in apc, bpc, and cpc possible {100}pc; β > π/2 apc ≈ am; cpc > apc and bpc; cm > am and bm bpc ≈ bm; No degeneracy in bp cpc ≈ cm MC [3] in but degeneracy in apc and cpc possible {100}pc; β > π/2 apc ≈ am; cpc = apc > bpc; cm = am > bm bpc ≈ bm; both ap and cpc cpc ≈ cm O [3] degenerated but not bpc cm and am are always bounded by the monoclinic angle β in the monoclinic (mirror) plane, where β ≠ π/2 [1] [2] Both MA and MB phases are similar in nature in that the am and bm axes are rotated 45° about the [001]pc direction and are bounded by the monoclinic angle, β ≠ π/2 They are both characterized by cpc≈ cm and apc2 = bpc2 = (am/2)2 + (bm/2)2 because am and bm are bounded by β = π/2 They, however, differ in the spontaneous strain, leading to cm > am and bm for the MA phase but cm < am and bm for the MB phase [3] The O phase may be treated as a special case of the MC, of which cm = am and the volume of an O cell is approximately double that of corresponding pc cell 82 6.2.2 Tetragonal micro/nanotwin diffractions It should be noted that in addition to the M phases, off ω = 0º plane diffractions may also arise from T micro- and nanotwin domains Figures 6.2(a)-(c) schematically illustrate diffraction intensity weighted distribution around the (002) of T micro- and nanodomains and Figures 6.2(d)-(h) are the corresponding diffraction patterns on the (002) RSM To explain how domain size may affect the (002) diffraction profiles, we begin with diffractions arising from untilted T microdomains By microscale domains, we mean here coarse domains of which the diffractions can be predicted by means of the conventional diffraction theory, as opposed to nanoscale domains described in Ref [47, 48] The projection of untilted (100)T and (001)T microdomains in the RSM is shown in Figure 6.2(d), in which only two diffractions lying in the ω = 0° plane at the respective 2θ positions are noted For tilted (100)T and (001)T microdomains, their diffraction peaks are tilted out from the ω = 0° plane, forming a {110}-type T twin The tilt angle (∆ω), also called the offset angle, indicates that for a set of tilted microdomains structure the twin diffractions not lie in the ω = 0° plane, as illustrated in Figure 6.2(e) Now, let’s consider the diffractions from the nanotwin domains, i.e., twins of nanometers in thickness Although the Bragg’s diffraction positions of the nanotwin diffractions remain unchanged, they become streaked in the twin thickness direction, a 83 (d) (f) (a) ∆ω ≠ 0º (e) (g) Tetragonal microdomains (b) Tetragonal nanodomains (h) T1 2θ T2 T3 T7 (c) Coexistence of tetragonal T4 micro/nanodomains T5 T6 T ω = 0° Figure 6.2 (002) diffraction intensity weighted distributions arising from (a) T microdomains, (b) interference effect of T nanodomains and (c) combined effect of (a) and (b) (d) to (g) show the projections of various T diffractions onto the (002) RSM; i.e., diffractions arising from (d) untilted T microdomains; (e) tilted T microdomains; (f) streaking effect of untilted T nanodomains, (i) streaking effects of tilted T nanodomains, and (l) combined diffraction patterns of T micro/nanodomains of all configuration 84 result of their nano-size thicknesses, as illustrated in Figures 6.2(f)-(g) Wang [47, 48] has shown that additional peaks may arise as a result of the constructive interference effect of the streaked nanotwin diffractions This new nanotwin peak lies along the line joining the two parent nanotwin diffractions, of which the exact position is determined by the lever rule according to the intensity of respective parent diffractions which, in turn, is determined by the volume fractions of respective nanotwins in the material [47, 48] This is illustrated in Figures 6.2(f)-(g) It should be mentioned that this streaking effect is enhanced as the twin thickness decreases Note also that the streaking effect is not as obvious for microdomains, as illustrated in Figures 6.2(d)-(e) When T micro- and nanotwin domains coexist, the intensity-weighted distribution is displayed in Figure 6.2(c), which is the combination of Figures 6.2(a) and (b) The overall projection onto RSM is illustrated in Figure 6.2(h), being a combination of Figures 6.2(d)-(g) Judging from the above interpretation, peak T2 and T5 located at ω = 0° plane correspond to the untilted (100)T and (001)T microdomains, respectively; while the out-of-plane peaks T1, T3, T4, and T6 are from diffractions of tilted (100)T and (001)T microdomains and their streaking effects are those of tilted nanodomains Peak T7 is the additional peak resulting from the coherent interference of (100)T-(001)T nanodomains as shown in Figures 6.2(d)-(g) Other than the streaking phenomenon shown by the nanodomain, the micro- and nanoscale domains also differ 85 in FWHM because peak broadening increases as the domain thickness decreases 6.2.3 Crystal group theory of phase transformation Landau theory of phase transformation has been the most widely used method in analyzing structural relations in crystals Figure 6.3 shows the diagram of transformations of various phases between a crystal group and its subgroups Solid and dashed lines indicate the transformations of first and second order, respectively According to Landau theory, two criteria are necessary for second order phase transformations The first criterion is that crystal symmetry involved in a phase transformation must obey group-subgroup relation, i.e., a phase of lower symmetry is the subgroup of a phase of higher symmetry, as indicated by the dashed lines in Figure 6.3 Thus, any M-C, and the R-MC, MB-T, and MA-O phase transformations in piezoelectric perovskites are forbidden [42, 98], as so illustrated in Figure 6.3 The second criterion is that no third order invariant is allowed in any second order transformation between a group-subgroup Examples of such include the R-MA and R-MB group-subgroup transformations These two transformations cannot be of second order because it allows a cubic invariant and violate the Landau condition [42] These two group-subgroup transformations, should they occur, must thus be of first order, as indicated by the solid lines in Figure 6.3 86 Pm3m (Cubic) P4mm (Tetragonal) Amm2 (Orthorhombic) R3m (Rhombohedral) Pm (Monoclinic C) Cm (Monoclinic A) Cm (Monoclinic B) P1 (Triclinic) Figure 6.3 Lines between space groups indicate a group-subgroup relationship Solid lines indicate a first-order transformation Dashed lines indicate a second-order transformation [42, 94] 87 patterns may be assigned as: (a) MC (d1, d3, d7, d4, and d6, d7 being the bm diffraction) + T (d2 and d5), (b) T (d2 and d5) + T* (d1, d3, d4 and d6) + R (d7), or (c) T (d2 and d5) + T* (d1, d3, d4, d6, and d7, d7 being the T nanotwin diffraction here) Subtle changes of the various diffractions with increasing temperature indicate that these diffractions is a mixture of R phase and the coherent effects of (100)T-(001) T nanodomain diffractions (Figure 6.4a), i.e., case (b) above The first evidence comes from the disappearance of d7 at TR-T at 70 °C (Figure 6.4b) while other peaks (i.e., d1 to d6) persisted, which indicates that peak d7 is likely to arise from a different phase while the rest of the peaks are from another phase which remains stable above TR-T It is thus logical to assign d7 to that of the R phase The second evidence comes from the highly coordinated manner of the remaining peaks (d1 to d6) on further heating which eventually coalesced into C phase (2θ ≈ 44.74°, ω = 0°) at 180 °C (Figures 6.4b-e) These peaks, i.e., d1 to d6, thus pertain to the same phase, and may be assigned to that of either MC (assuming bm diffraction being very weak) or T The following two observations help rule out MC phase being a likely phase Firstly, since the M and the T phases have different lattice constants, should these off ω = 0° peaks pertain to those of the M phases, then their Bragg’s position would differ from those of (100)T and (001)T (d2 and d5) diffractions because the M and the T phases have different lattice constants Being at the same Bragg’s positions with d2 and d5, 89 respectively, d1 and d3 peaks can only arise from (100)T plane and d4 and d6 from (001)T planes but not any of the M diffractions Secondly, all the d1-d6 peaks shifted and disappeared in a coordinated manner and transformed to the C phase at 180°C (Figure 6.4e) This indicates that these peaks cannot arise from any of the M phase as, according to the crystal group theory, all the three M-C transformations are forbidden in piezoelectric perovskites (see Section 6.2.3 for details) It is also interesting to note that the obvious streak joining d2-d5 diffractions but less pronounced streaks joining d1-d6 and d3-d4 diffractions (Figures 6.4b-d) These streak-like features are manifestations of nanodomains in the material Despite the streaks, peaks d1 to d6 have an average FWHM ≅ 0.08°, indicating that these peaks arise largely from T microscale domains instead Our RSM results thus show that both T micro- and nanotwins coexisted in the crystal despite the dominance of the former twin type Both untilted and tilted (100)T and (001)T twin components exhibit identical Bragg’s positions, giving a = 4.0302(2) Å, c = 4.088(2) Å at 25 °C The tilt angle for (100)T and (001)T components of the tilted {110}-type T twin, can be determined from the RSM, as shown in Figure 6.5 The obtained tilt angels, are different from the two twin components, being ∆ω/2 ≅ 0.22° and ≅0.61°, respectively This may be attributed to the difference in elastic stiffness and hence shear strains experienced by respective 90 (a) 25 °C: (R*+T+T*) (b) 70 °C: (T+T*) (c) 125 °C: (T+T*) (101) (d) 170 °C: (T+T*) Figure 6.4 (101) (e) 180 °C: C Temperature dependent (002) RSMs taken at (a) 25 ºC, (b) 70 ºC, (c) 125 ºC, (d) 170 ºC, and (e) 180 ºC The {110}-type T twin planes are indicated by white dashed line in (c) The intensity contours are on log scale 91 twin components [43-45] Using these findings, the detailed configuration of the {110}-type T* are constructed and shown schematically in Figure 6.6 The tilting effect of these twinned T domains is probably a means to help relax the various stresses in the crystal The ∆ω/2 and Bragg’s positions of (100)T and (001)T as a function of temperature have been determined in the present work The results are shown in Figures 6.7(a) and (b) 6.4 6.4.1 Thermally-induced phase transformations in unpoled PZN-9%PT Temperature dependent polarization characteristics Fresh PZN-9%PT samples of [100]Lx[010]Wx[001]T cut were used in this work All the samples were annealed at 257 °C for h prior to any measurements Their ε’ and J as a function of temperature were measured under ZFH conditions Figure 6.8(a) shows the ZFH ε’ at various frequencies (0.1 kHz – MHz) of the unpoled (annealed) PZN-9%PT sample The ε’ increased gradually with temperatures initially, followed by a weak anomaly at 65 °C The anomaly is barely perceptible even in the 1/ε’ versus temperature plot (see the inset of Figure 6.8a) Upon heating to higher temperatures, a clear anomaly in ε’ (and a step-like decrease in 1/ε’) was observed over the temperature range of 175-179 °C The latter anomaly was followed by a frequency dependent ε’ maximum (at Tmax) which may be attributed to 92 Rocking scan Microscale Nanoscale: Coherency effect ω = 0º (a) θB 2θB (b) ∆ω ≠ 0º 2θB θB θB 2θB Δω Figure 6.5 Δω The projection of the diffraction peaks onto RSM for micro- and nanoscale domains for rocking scan (a) ∆ω/2 and (b) Bragg’s position of (100)T and (001)T components of the {110}-type T twins as a function of temperature 93 ∆ω(001)T /2 ≅ 0.61º Figure 6.6 ∆ω(100)T /2 ≅ 0.22º (001) plane Schematic illustration of coexistence of both untilted and tilted (100)T and (001)T micro/nanodomains in PZN-9%PT single crystal The tilted twins give rise to the off ∆ω = 0° diffractions with ∆ω/2 ≅ 0.22º for the (100)T component and ∆ω/2 ≅ 0.61º for the (001)T component, respectively The {110}-type T twin planes are indicated by red dashed lines 94 0.7 0.21 0.6 ∆ω(100) T/ 0.18 0.5 0.15 0.4 0.12 0.09 0.06 0.3 ∆ω(100) Τ/ ∆ω(001) Τ/ 0.2 0.03 0.1 44.9 (100)T (001)T 44.8 TC C 44.7 2θ ∆ω(001) T/ 0.24 44.6 44.5 (100)T (001)T 44.4 44.3 44.2 20 40 60 80 100 120 140 160 180 200 Temperature (oC) Figure 6.7 (a) ∆ω/2 and (b) Bragg’s position of (100)T and (001)T componenets of the {110}-type T twins as a function of temperature The T-C phase transformation occurs at 180 ºC 95 (a) ε' (x104) 1/ε' (x10-3) 0.2 TR-T TC Tmax TC 0.1 0.0 0.1 kHz 0.5 10 50 100 500 MHz 50 100 150 200 (R+T+T*) TR-T C (T+T*) J (mA/m2) 0.002 (b) 0.000 -0.002 -0.004 40 60 80 100 120 140 160 180 200 220 Temperature (oC) Figure 6.8 (a) ZFH ε’ and (b) ZFH J of unpoled (annealed) PZN-9%PT crystal The sample thickness is 1.0 mm 96 the dynamic relaxation processes of polar nanoclusters in the material [95, 96] It is interesting to note that, besides the ε’ at Tmax, frequency dispersion was also noted at low temperature, i.e., ≤ 65 °C, a phenomenon attributed to the low temperature dielectric relaxation process by earlier researchers [97] In what follows, we shall focus our discussion in the temperature region of room temperature, 25 °C to Tmax The J measurement as a function of temperature of the unpoled PZN-9%PT single crystal was shown in Figure 6.8(b) Two groups of current signals were detected upon heating The first group, being multiple but very weak, was displayed at about 60 °C The current signals are enlarged in the inset of Figure 6.8(b) for easy reference There followed by a region where no current activities were noted on further heating until about 175 ºC The second group shows a string of strong current activities spreading over the temperature region of 175-185 ºC 6.4.2 Structural studies A similar fracture procedure was used to prepare the unpoled (annealed) PZN-9%PT single crystal for the heating HR-XRD study The (002) RSMs, of which a part has been shown in Figure 6.3 earlier, are shown in Figure 6.9 over the temperature region of 25-185 °C As described in Section 6.3, at 25 °C, the diffraction pattern of PZN-9%PT 97 contains of seven diffraction peaks, marked as d1 to d7 in Figure 6.9(a), which lie in three Bragg’s positions, with d1 to d3 lying at 2θ ≈ 44.95°, d4 to d6 at 2θ ≈ 44.28°, and d7 at 2θ ≈ 44.70° Peaks d2, d5, and d7 lie in the ω = 0° plane, while the remaining peaks lie out of the plane, i.e., ∆ω ≠ 0° While peak d7 may be attributed to the rhombohedral domains, peaks d1, d2, d3, d4, d5 and d6 have been attributed to the T* diffractions in unpoled PZN-9%PT (see Section 6.3 for details) The room temperature structure of unpoled PZN-9%PT is thus a mixture of (R+T+T*) domains As temperature increased further, all the six diffraction peaks gradually coalesced into a single peak Above 178 °C, only the single peak at 2θ ≈ 44.74° (∆ω = 0°) was detected (Figure 6.9i) This peak pertains to the C phase of the crystal Similar to the analysis for the diffractions at low temperatures, the out-of-plane peaks (i.e., d1, d3, d4, and d6) at higher temperatures (from 100ºC to Tmax) may also be assigned to either those of the MC phase or the (T+T*) diffractions A number of observations shown below have led us to conclude that the room temperature phase pertains to those of (T+T*) instead Firstly, should the phase present be the MC phase, the d1, d3, d4, and d6 diffraction peaks would have faded away simultaneously at 70 °C, leaving only d2 and d5 peaks The diffraction patterns in Figures 6.9(c)-(h), however, show that other than the d7 peak, the remaining peaks persisted upon heating Secondly, from above 100°C 98 to Tmax, all the six peaks (i.e., d1 to d6) shifted in a coordinated manner and eventually coalesced into a single peak, C phase This strongly suggests that they arise from the same phase Since it is thus unlikely that he MC phase is present at room temperature, the peaks can only be those of T* domains The forbidden of the MC-C transformation by the crystal group theory (see also Section 6.2.3) also rules out the presence of the MC phase at high temperatures The various diffractions which are present over the temperature range from 100 °C to Tmax, are thus those pertaining to the T* domains PZN-9%PT single crystal thus undergoes the (R+T+T*)-(T+T*)-C transformation path during ZFH The above finding is supported by our PLM observation Figure 6.10 gives the PLM micrographs of the unpoled (annealed) PZN-9%PT sample in the temperature region of 25-185 °C At 25 ºC, only a small fraction of the domains (as encircled by the dash lines in Figures 6.10a-b) reveals an extinction at P/A= 45°, while the remaining domains exhibited the optical extinction at P/A= 0° This suggests that the (R+T) two phases coexisted in unpoled PZN-9%PT at room temperature with the T phase being dominant The R domains persisted even at 55 ºC (Figure 6.10c) At 65 ºC (Figure 6.10d), the whole sample displays extinction at P/A=0° instead This indicates that the small fraction of R domains must have undergone structural changes to the T phase The observed phenomenon correlates well with the disappearance of d7 peak 99 (a) 25ºC: (R*+T+T*) (b) 55ºC: (R*+T+T*) (c) 70ºC: (T+T*) (d) 100ºC: (T+T*) (e) 125ºC: (T+T*) (f) 140ºC: (T+T*) (g) 160ºC: (T+T*) (h) 170ºC: (T+T*) (i) 178ºC: C Figure 6.9 Temperature dependent (002) RSMs taken from fractured surface of annealed PZN-9%PT crystal obtained at (a) 25 ºC, (b) 55C (c) 70 ºC, (d) ºC, 100 ºC, (e) 125 ºC, (f) 140 ºC , (g) 160 ºC, (h) 170 ºC, and (i) 178 ºC The intensity contours are on log scale The PZN-9%PT crystal consists of T micro- and nanotwin domains and undergoes a sequence of (R*+T+T*)–(T+T*)–C phase transformation upon heating 100 (a) 25 ºC P/A= 0º (b) 25 ºC P/A= 45º R R R T R (c) 55 ºC P/A= 0º (d) 65 ºC P/A= 0º R R (e) 125 ºC P/A= 45º P/A= 0º (f) 145 ºC P/A= 0º P/A= 45º (g) 170 ºC P/A = º P/A= 45º (h) 178 ºC P/A= 45º T C T P/A= 45º [100] 200 µm T C [010] Figure 6.10 ZFH domain structure of 45º P/A= annealed PZN-9%PT crystal observed at by the PLM (a) 25 ºC (P/A = 0º), (b) 25 ºC (P/A = 45º), (c) 55 ºC, (d) 65 ºC, (e) 125 ºC, (f) 145 ºC , (g) 170 ºC, and (h) 178 ºC The sample thickness is about 100 µm The dominant T domains coexist with the small fraction of R domains at 25 °C The PLM observation is consistent with the HR-XRD results 101 in the HR-XRD results (Figures 6.9a-c) and the anomalous responses in both the ε’ and J measurements (Figure 6.8) in the temperature region of 60-70 ºC The sample remained in extinction at P/A = 0° over the temperature range from 125-170 ºC (Figures 6.10e-g) At 178 ºC, scattered areas started to exhibit extinction at most P/A angles, indicating the occurrence of the C phase (Figure 6.10h) The PLM observation is consistent with the HR-XRD results presented above Despite undergoing the first-order R-T phase transformation over the temperature range from 60 ºC to 70 ºC, no perceptible anomaly was noted in the ε’ of the unpoled PZN-9%PT upon heating, except at the Tmax This phenomenon can be attributed to the following observations Firstly, the dynamic relaxation processes at low temperature may have masked the anomalies in the ε’ displayed by the R-T transformation Secondly, since only a small fraction of the R domains are present in the sample (Figure 6.10a) The R-T phase transformation thus involves only a minor R phase and thence the associated electric behavior many not be conspicuous in Figure 6.8(a) These findings are summarized in Figure 6.8(a) for easy reference 6.5 (a) Summary of main observations Evidence for T micro- and nanotwin domains in unpoled PZN-9%PT has been obtained by means of HR-XRD study 102 (b) The present work showed that at room temperature, unpoled PZN-9%PT single crystals consists predominantly of the T phase of both micro- and nanotwin domains, although a small amount of the R phase may also be present (c) Experimental analysis involving polarization and structural characteristics combined with the crystal group theory suggest that the PZN-9%PT undergoes a phase transformation sequence of (R+T+T*)-(T+T*)-C, or R-T-C for short, upon heating (d) Instead of clear TR-T and TC locus as depicted in earlier works, both R-T and T-C transformations occur over a range of temperature bounded by two-phase coexistence field 103 ... RSM To explain how domain size may affect the (002) diffraction profiles, we begin with diffractions arising from untilted T microdomains By microscale domains, we mean here coarse domains of which... micro/nanodomains T5 T6 T ω = 0° Figure 6.2 (002) diffraction intensity weighted distributions arising from (a) T microdomains, (b) interference effect of T nanodomains and (c) combined effect of (a) and. .. 6.10a-b) reveals an extinction at P/A= 45? ?, while the remaining domains exhibited the optical extinction at P/A= 0° This suggests that the (R+T) two phases coexisted in unpoled PZN- 9%PT at room temperature