High resolution x ray diffraction study of phase and domain structures and thermally induced phase transformations in PZN (4 5 9)%PT 6

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 produc

Chapter 7 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

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%PTsingle 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 <111>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

<111>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 <111>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

Figure 7.1 (a) Schematic domain configuration of an unpoled R crystal

structure with spontaneous polarization directed along eight

<111>pc direction (b) Three dimensional illustration of a

stereographic projection of the unpoled R structure In the two

dimensional plane, only the four <111>pc variants are projected

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 <111>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

Figure 7.2 (a) Four of the eight <111>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

(d) Convoluted peak (c)

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 <100>pc crystal direction

indicate the presence of {100}-type R nanotwins (Figure 7.3); while those streaking

along the <110>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

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 <100>pc direction

(a)

(b)

∆ω

(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 <110>pc direction

(a)

(b)

(c)

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

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*

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)

(b) (a)

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’ increasesfairly smoothly over the entire

temperature range from room temperature to T max ≅ 157 °C, at which the ε’ is

maximum The dielectric anomaly at Tmaxshows 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

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

7 (a)

500

(b)

*

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) < a pc = 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

cpcat 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 6 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

(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 clearsplittingof 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 <001>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(≈ b m ) at 2θ ≈ 44.58° with ∆ω ≈ 0° (i.e., no degeneracy), and cpc(≈ c m ) 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