Chapter Rhombohedral Micro/Nanotwins and Thermally-induced Phase Transformations in Unpoled PZN-4.5%PT 7.1 Introduction The existence of the M phases remains a subject of much debate when the adaptive phase model proposed by Viehland and coworkers [43-45] has pointed out that the reported M reflections could indeed be those of micro- and nanoscale twinned R and T domains instead While direct evidence of nanotwin domains has only been reported by TEM [49, 51, 52], support for the M phases (i.e., MA, MB, and MC) has been elicited by high-resolution x-ray diffraction study [30-32, 34-36, 38-40, 66, 93] The concept of nanotwin diffraction theory has been employed by Wang [46-48] to explain the diffraction pattern produced by nanotwins in perovskite ferroelectrics The diffraction peaks of the nano-scale twin domains exhibit streaked behavior and their interference cannot be fully explained by the conventional diffraction theory, which perceived the diffraction pattern as that arising from the M phases instead The nanotwin diffraction theory has yet to be utilized to interpret the complicated diffraction patterns of relaxor ferroelectric single crystals In this chapter, diffraction profiles of the R phase were projected onto the 104 RSM using micro/nanotwin diffraction theory The projections can compared with the experimental diffraction patterns obtained from the HR-XRD study of [100]L×[010]W×[001]T PZN-4.5%PT single crystals 7.2 Theoretical considerations of rhombohedral micro/nanotwin diffractions Figure 7.1(a) illustrates a schematic domain configuration of an unpoled R crystal structure with spontaneous polarization directed along eight pc directions The four-fold degenerated R domains is shown in Figure 7.2(a) To understand how the (002) diffraction pattern is affected by: (a) the four structural variants of the R structure, i.e., r1, r2, r3, and r4, and (b) its domain size, the diffraction produced by the eight pc domain variants of the R phase are represented by means of the stereographic projection technique shown in Figure 7.1(b) When projected to the (002) plane, only four of the eight pc domain variants are relevant, as shown in Figure 7.2(a) This is because stereographic projection does not distinguish domain variants of opposite polarization In Figure 7.2(b), each variant diffraction is represented by circles of half-intensity contours Since the R phase of PZN-PT is elastically soft, individual variant diffractions broaden as a result of residual stresses arising from the crystal growth process and accompanied phase transformations during cooling of the crystal to room conditions As shown in 105 [ 111 ] [ 111 ] [ 111 ] [111] (b) Figure 7.1 (a) Schematic domain configuration of an unpoled R crystal structure with spontaneous polarization directed along eight pc direction (b) Three dimensional illustration of a stereographic projection of the unpoled R structure In the two dimensional plane, only the four pc variants are projected 106 this figure, peak convolution would occur as a result of the small twin (or tilt) angle in both the ω and 2θ planes among the four domain variants, giving rise to an extremely broad diffraction as shown in Figures 7.2(c) and (d) In addition to peak convolution, it should also be noted that the four-fold degenerated R domains not only has a ∆ω component but also the 2θ tilt of (002) component, a result of the polarization vectors along the eight pc directions Since the high precision diffractometer used in the HR-XRD study only allows direct (nearly untilted) diffracted beam in the 2θ plane to be detected, what actually detected by the diffractometer are not the direct diffractions of the R variants but their convoluted peak(s) In the actual mapping, the detected diffractions are restricted to within the region of dotted lines The resultant RSM pattern is given in Figures 7.2(b)-(d) As shown, only two convoluted diffractions could be detected by the high-precision diffractometer used in the HR-XRD study This is especially true for small R tilt angle (i.e., 90º - αR) and when the residual stress in the crystal is sufficiently high The projection of the convoluted peak(s) on (002) RSM is illustrated in Figure 7.2(d) Note that in the four-fold degenerated R domains may form twins of either a {100}-type or {110}-type R twin plane For R microtwins, the streaking effect is minimum The actual type of twins in this case could not be that easily identified The 107 (a) r1 r2 r4 r3 (b) Diffracted signal detected by HR-XRD (c) Figure 7.2 (d) Convoluted peak (a) Four of the eight pc domain variants with tilt angle in both the ω and 2θ planes (b) Each variant diffraction is represented by circles of half-intensity contours Individual variant diffractions broaden as a result of residual stresses arising from the crystal growth process and accompanied phase transformations during cooling of the crystal to room conditions The resultant RSM pattern is given in (b)-(d) In the actual mapping, the detected diffractions are restricted to within the region of dotted lines in (b) (d) The projection of the convoluted peak(s) on (002) RSM 108 two different types of R microtwin domains thus give rise to identical diffraction behavior on (002) RSM, as projected in Figure 7.2(d) For R nanotwins, the 2θ diffraction position and the R tilt angle of the four-fold remain unchanged However, the diffractions become streaked in the direction of the thinnest dimensions of the diffracting structure, i.e., normal to the twin plane The streak direction can thus be used conveniently to identify the type of the R nanotwin domains For instance, diffractions streaking along pc crystal direction indicate the presence of {100}-type R nanotwins (Figure 7.3); while those streaking along the pc indicate the {110}-type R nanotwins (Figure 7.4) An extra peak joining the two parent nanotwin diffractions may occur as a result of the constructive interference effect of the streaked behavior as discussed earlier in Section 6.2.2 The resultant nanotwin diffractions for {100}-type and {110}-type R nanotwins are illustrated in Figures 7.3(b) and 7.4(b), respectively As discussed above, only detected diffraction laid within the region of dotted lines could be detected when the R nanotwins were performed with high-resolution diffractometer Figures 7.3(c) and 7.4(c) show the corresponding diffraction pattern on the (002) RSM for the respective {100}-type and {110}-type R nanotwins, respectively Figure 7.5(a) shows the coexistence of both the {100}-type and {110}-type R nanotwins coexist and their various diffractions are resolvable, while Figure 7.5(b) shows the case of the 109 (a) (b) (c) ∆ω Figure 7.3 (a) The constructive interference effect of the two parent streaked of {100}-type R nanotwin diffractions (b) The resultant nanotwin diffractions for {100}-type R nanotwins (c) The projection of such extra peak joining the two parent nanotwins diffractions on (002) RSM for the {100}-type R nanotwins Traces of the twin type are laid along the pc direction 110 (a) (b) (c) Figure 7.4 (a) The constructive interference effect of the two parent streaked of {110}-type R nanotwin diffractions (b) The resultant nanotwin diffractions for {110}-type R nanotwins (c) The projection of such extra peak joining the two parent nanotwins diffractions on (002) RSM for the {110}-type R nanotwins Traces of the respective twin type are laid along the pc direction 111 (a) {100}-type R {110}-type R nanotwins nanotwins + = ∆ω (b) Convoluted peak {110}-type R nanotwins {100}-type R nanotwins + + = ∆ω Figure 7.5 (a) The projection of coexistence of the {100}-type and {110}-type R nanotwins onto the (002) RSM (b) The projection of the coexistence of R micro- and nanotwins onto (002) RSM 112 coexistence of R micro- and nanotwin domains on (002) RSM 7.3 Evidence of rhombohedral micro/nanotwins in PZN-4.5%PT at room temperature Figure 7.6 show the HR-XRD (002) RSMs of unpoled (annealed) (001)-oriented PZN-4.5%PT single crystals taken at room temperature (i.e., 25 °C) Figure 7.6(a) shows a single extremely broad peak at 2θ ≈ 44.58° This peak is in good agreement with the projection on (002) RSM as discussed in Figure 7.2(d) This broad peak is thus the convoluted peak of the {100}-type and/or {110}-type R microtwin domains, a result of the large diffraction width associated with the fine domain structure and the extreme compliant nature of the R phase The diffraction pattern indicating possible coexistence of {100}-type and {110}-type R* domains is shown in Figure 7.6(b), which was obtained from another unpoled (annealed) PZN-4.5%PT single crystal This figure shows three distinguishable diffraction peaks, marked d1 to d3, lying along the same Bragg’s position (2θ ≈ 44.63º) This diffraction pattern agrees with the predicted projections of R micro- and nanotwin mixture illustrated in Figure 7.5 The main R peak (d2) may be assigned to that arising from {110}-type R nanotwin, while the remaining two off ω = 0º plane peaks (d1 and d3) are those arising from the {100}-type R* 113 (a) (b) Figure 7.6 Room temperature HR-XRD (002) RSM of unpoled (annealed) PZN-4.5%PT single crystals (a) shows a broad convoluted R peak while (b) shows evidence of R micro- and nanotwins These diffraction patterns indicate the possible coexistence of {100}-type and {110}-type R* (see text for details) 114 7.4 Thermally-induced phase transformations in unpoled PZN-4.5%PT 7.4.1 Temperature dependent polarization characteristics Figures 7.7(a) and (b) show the ZFH ε’ at various frequencies (0.5 – 500 kHz) and the thermal current, respectively, during ZHH of unpoled (annealed) PZN-4.5%PT single crystals As seen in Figure 7.7(a), the ε’ increases fairly smoothly over the entire temperature range from room temperature to Tmax ≅ 157 °C, at which the ε’ is maximum The dielectric anomaly at Tmax shows a broad frequency dependence, which has been attributed to the dynamic relaxation processes of polar nanoclusters [95, 96] In contrast, the thermal current (Figure 7.7b), which are mainly associated with temporal dynamics of spontaneous polarization, shows two anomalous responses over the above temperature range, one over the temperature of 125-135 °C and the other of 140-150 °C 7.4.2 Structural studies The HR-XRD (002) RSMs as a function of temperature are given in Figure 7.8, in which the intensity contours are on log scale At 25 ºC, the mapping of the sample revealed a rather broad single peak with 2θ ≈ 44.58º (Figure 7.8a), being the convoluted peaks of the four degenerated R domains (see Section 7.2 for details) The R phase remained as the stable phase at 125 ºC (Figure 7.8b) At about 115 ε' (x104) (a) Tmax 0.5 kHz 10 50 100 500 TC TR-T (T* R* (R* + T) C + C) (b) (ii) J (mA/m2) 0.001 140 0.000 145 150 (i) -0.001 126 128 130 132 -0.002 40 60 80 100 120 140 160 180 200 220 Temperature(oC) Figure 7.7 (a) ZFH ε’ and (b) ZFH J of unpoled (annealed) PZN-4.5%PT crystal The sample thickness is 1.0 mm A broad-diffuse and dispersive phase transition in ε’ not only gives rise to a range of Tmax, but may mask the weak anomalies in the ε’ curves 116 129 ºC, a splitting of the reflection at 2θ ≈ 44.68º with ∆ω ≈ 0.30° became evident in the (002) RSM (Figure 7.8c), suggesting that some structural changes must have occurred The observed pattern of peak splitting may arise from either of the two following causes Firstly, the diffraction may indicate the occurrence of a new M phase Table 6.1 gives the relationships between the m axes and the pc axes of the various M phases and the O phase Judging from the nature of splitting, these diffraction peaks may be assigned to the MB-type phase When referred to the pc coordinates, we have for the MB system, cpc (≈ cm) < apc = bpc (≈ (am/2)2 + (bm/2)2 ) and that cpc, apc, and bpc are all two-fold degenerated This diffraction pattern is consistent with the diffraction patterns shown in Figure 7.8(c), which shows clearly degenerated diffraction peaks of cpc at 2θ ≈ 44.66º (∆ω ≈ 0.40º), while the bpc and apc diffractions may be responsible for the relatively broad convoluted peak at 2θ ≈ 44.46º Alternatively, the diffractions may arise from T*, as explained in Chapter The two likely assignments of the diffractions at 129 °C are hereafter referred to as (T+T*) or MB diffractions At 135 °C, in addition to the (T+T*) or MB diffractions, a new diffraction peak was detected This new peak, at 2θ ≈ 44.66º and lying in the ω = 0° plane (Figure 7.8d), can be assigned to that of the (100)T diffraction Our results thus suggest that the (T+T*) or MB phases coexisted over the temperature range of 135-144 ºC At 145 ºC 117 (Figure 7.8e), only two peaks at 2θ ≈ 44.66º and 2θ ≈ 44.50º were detected, both lying in the ω = 0º plane This indicates that the T phase is the dominant phase at this temperature At 146 ºC (Figure 7.9f), several new diffraction peaks appeared Figure 7.9(g) is the mapping taken at 148 ºC at which the main T diffractions faded away It is evident that the new phase shows clear splitting of the peaks at 2θ ≈ 44.60° (with ∆ω ≈ 0.30°) and 2θ ≈ 44.50° (with ∆ω ≈ 0.10°) but no observable splitting for the peak at 2θ ≈ 44.58° Again there are two possible assignments for the new diffractions The first is that it may be a new M phase, which is likely a MC phase in this case The MC phase has pc–type mirror planes and the various diffractions, when referred to the pc system are characterized by cpc(≈ cm) >bpc(≈ bm) >apc(≈ am) with degeneracy in both cpc and apc but not bpc [31, 32, 98, 99, see also Table 6.1] The various diffraction peaks in Figure 6.3(g) may thus be assigned to that of apc(≈ am) at 2θ ≈ 44.66° with ∆ω ≈ 0.30°, bpc(≈ bm) at 2θ ≈ 44.58° with ∆ω ≈ 0° (i.e., no degeneracy), and cpc(≈ cm) at 2θ ≈ 44.50° with ∆ω ≈ 0.10° The second assignment is that the ∆ω ≠ 0° diffractions are those of the T* domains (see Chapter 6) The diffraction at 2θ ≈ 44.58°, in turn, can be assigned to that of the C phase On further heating to 155 ºC (Figure 7.8h), the various diffraction peaks gradually coalesced into a single C peak located at 2θ ≈ 44.58° At 160 ºC, only the C phase diffraction was detected (Figure 7.8i) 118 (a) 25ºC: R* (b) 125ºC: R* (c) 129ºC: (T+T*) (d) 135ºC: (T+T*) (e) 145ºC: (T+T*) (f) 146ºC: (T+T*+C) (g) 148ºC: (T*+C) (h) 155ºC: (T*+C) (i) 160ºC: C Figure 7.8 Temperature dependent (002) RSMs taken from fractured surface of annealed PZN-4.5%PT crystal obtained at (a) 25 ºC, (b) 125 ºC, (c) 129 ºC, (d) 135 ºC, (e) 145 ºC, (f) 146 ºC, (g) 148 ºC, (h) 155 ºC, and (i) 160ºC The intensity contours are on log scale The PZN-4.5%PT undergoes a transformation sequence of R*–(R*+T+T*)–T–(T+T*+C)–C upon heating 119 To ascertain if the out-of-plane diffractions with ∆ω ≠ 0° in Figures 7.8(d) and (f) are M diffractions or diffractions arising from T*, the observed phase transformation sequence was compared with the thermal current signals Note that the R-MA and R-MB transformations, being of first-order [25, 42], would give rise to anomalous responses in dielectric behaviors and thermal current signals should MA and MB phases act as the intermediate phase between R-T transformation Note also that when the diffractions are those of the M phases, the deduced transformation path should be R-MB-T-MC-C In this case, four clear thermal current signals are expected despite their relative strengths Examination of Figure 7.7(b), however, revealed that only two thermal current signals were detected More interestingly, there was no obvious thermal current signal over the temperature range from 150-170 °C, over which the T-MC-C transformation occurred This rules out T-MC-C being the transformation path and renders strong support for (T+T*)-(T+T*+C)-C, or T-C being the actual transformation path at higher temperatures Now, assuming the diffractions in Figure 7.9(d) pertain to that of MB-type monoclinic phase The expected transformation path is thus: R-MB-T-C, suggesting that three thermal current signals are to be expected As mentioned above, only two thermal current signals were detected, ruling out this possibility The only option left is that the new diffractions in Figure 7.8(d) in fact 120 pertain to that of (T+T*), while that in Figure 7.8(g) pertain to those of (T*+C) Should this be so, the expected transformation path is R*–(R*+T+T*)–T–(T+T*+C)–C, or R-T-C for short These deductions are consistent with the crystal group theory As shown in Figure 6.3, the M-C and MB-T phase transformations in piezoelectric are forbidden [42, 94].The two thermal current signals thus correspond to the R*–(R*+T+T*) and T–(T+T*+C), or R-T and T-C for short, transformations, respectively Figure 7.9 shows the domain structures obtained by the PLM as a function of temperature At 25 ºC, the crystal exhibited complete optical extinction at only P/A = 45º (Figure 7.9a), indicating that the room temperature phase is the R phase The R phase remained as the stable phase upon being heated to 125 ºC Above 127 ºC, a gradual change in the extinction angle was observed (Figure 7.9b), suggesting that some structural changes must have occurred Above 135 ºC, scattered areas started to exhibit extinction at P/A = 0o, which may arise from the T phase (Figure 7.9c) Above 145 ºC, scattered areas started to exhibit extinction at most P/A angles, suggesting the occurrence of the C phase (Figure 7.9d) Above Tmax, the sample exhibited a total extinction indicating the presence of the C phase only (Figure 7.9e) It has been reported that R-T and T-C phase transformations are of first order [25, 42] with accompanied dielectric anomalies notably for poled crystals [28, 100- 121 (a) 25 °C P/A = 0° P/A = 45° (b) 126 °C (c) 136 °C P/A = 0° P/A = 0° P/A = 45° (d) 146 °C P/A = 45° P/A = 0° (e) 154 °C P/A = 45° [100] P/A = 0° 150 µm [010] Figure 7.9 ZFH domain structures of annealed PZN-4.5%PT crystal observed by the PLM at (a) 25 ºC, (b) 126 ºC, (c) 136 ºC, (d) 146 ºC, and (e) 154 ºC The sample thickness is about 50 µm The PLM observation is consistent with the HR-XRD results 122 102] Despite so, the present work and other reported works in the literature [102] have repeatedly shown that during ZFH, the ε’ of unpoled (annealed) bulk PZN-4.5%PT crystal increases smoothly with temperature until Tmax with no obvious anomaly This observation suggests that for PZN-xPT crystals with low PT contents (say, x < 5%PT), the strong dynamic relaxation processes associated with the polar nanoclusters can easily mask the weak anomalies in the ε’ of the unpoled (annealed) material, giving rise to the smoothly increasing ε’ curve observed The slight difference in the transformation temperature can be attributed to the different experimental set-up and temperature controlling and monitoring devices used 7.5 Summary of main observations (a) The present work showed that the observed HR-XRD (002) RSMs of PZN-4.5%PT single crystals can be understood from the micro- and nanotwin diffraction theory of R phase in the material (b) For PZN-4.5%PT at room temperature, the {100}R diffractions manifest as an extremely broad peak at 2θ = 44.58°-44.63° Bragg’s position, being the convoluted peak of the degenerated R microtwins In addition to the extremely broad convoluted R peak, streak representative of nanotwin diffractions have also been detected They arise from {100}-type and {110}-type R nanotwins in 123 the material (c) Experimental analysis involving polarization and structural characteristics combined with the crystal group theory suggest that the PZN-4.5%PT undergoes a phase transformation sequence of R*-(R*+T+T*)-T-(T+T*+C)-C, or R-T-C for short upon heating (d) Both the R-T and T-C transformations occur over a range of temperature bounded by a two-phase field involving T* domains, which are formed possibly as a means to relax the associated transformation stresses in the crystal 124 ... projection of the coexistence of R micro- and nanotwins onto (002) RSM 112 coexistence of R micro- and nanotwin domains on (002) RSM 7.3 Evidence of rhombohedral micro/nanotwins in PZN- 4 .5% PT at... domains, a result of the large diffraction width associated with the fine domain structure and the extreme compliant nature of the R phase The diffraction pattern indicating possible coexistence... diffraction may indicate the occurrence of a new M phase Table 6. 1 gives the relationships between the m axes and the pc axes of the various M phases and the O phase Judging from the nature of