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

The first is the M A phase, characterized by c m > am and b m with the spontaneous polarization vector lying in {110}pc-type mirror planes, where subscript m and pc denotes the monoclin

Chapter 6 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

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 M A phase,

characterized by c m > am and b m 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 M B phase, having

similar mirror planes as in the M A phase but is characterized by c m < am and b m (Figure

6.1b) The third is the M C phase, characterized by c m>am and b m 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 a m and c m vectors but

not in the b m vector The degenerated a m and c m vectors are bounded by the monoclinic

Figure 6.1 (a) M A , (b) M B , (c) M C , and (d) the relation between M C and O

Orthorhombic lattice

ao/2

c o /2

Monoclinic lattice

β

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

<111>pc R and <001>pc T directions for the case of M A and M B phases In the M C phase,

the vector is free to lie within the {100}pc planes bounded by the <110>pc O and

<100>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 M C phase, when a m = cm, the crystal structure is best interpreted as

the O phase The relation between the M C and O phase lattices is shown in Figure

6.1(d) The O phase, characterized by a o ≠ bo ≠ co and mutually orthogonal crystal axes,

is thus the limiting case of M C phase when the lattice parameters a m 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

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

Monoclinic (mirror) plane and

characteristics of a m,

b m and c m [1]

Relationship between monoclinic and pseudocubic

axes

Characteristics of

apc, bpc, and cpc in (002)mapping

leading to c m > a m and bm forthe M A phase but c m < a m and bm for the MB phase

[3]

The O phase may be treated as a special case of the M C , of which c m = am and the

volume of an O cell is approximately double that of corresponding pc cell

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 do 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

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

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

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-M C , M B-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-M A

and R-M B 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

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]

Pm3m (Cubic)

P4mm

(Tetragonal)

Amm2 (Orthorhombic)

R3m (Rhombohedral)

Pm (Monoclinic C)

Cm (Monoclinic B)

P1 (Triclinic)

Cm (Monoclinic A)

6.3 Evidence of tetragonal micro/nanotwins in PZN-9%PT at room

temperature

As described above, the out-of-plane diffractions can arise from either the M

diffractions or T* diffractions, where T* denoted T micro/nanotwin inclusively In this

work, to ascertain whether the out-of-plane diffractions correspond to the true M

phases or the T* diffractions, structural studies on unpoled PZN-9%PT via HR-XRD

were carried out To avoid undesired surface effects produced by mechanical polishing

as described in Chapter 5, only fractured surface were used in the HR-XRD

measurements The incident x-ray beam, of 8.048 keV in energy, had typical

divergence of about 0.01°, with the best divergence being 0.006° A series of rocking

(∆ω) scans at a range of 2θ was carried out to form the RSM The rocking scans were

performed at the step size of 0.02° with the counting time of 0.5 s for every rotating

step Further experimental details can be found in Chapter 4

Figure 6.4 shows the (002) RSM of an unpoled (annealed) (001)-oriented

PZN-9%PT taken at increasing temperature At 25 °C, seven diffraction peaks were

detected, marked by d1 to d7 in Figure 6.4(a) These peaks lie in three diffraction

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 ω = 0° plane, while the remaining peaks lie out of the

plane, i.e., ∆ω ≠ 0° According to the analysis given in Section 6.2, the diffraction

patterns may be assigned as: (a) M C (d1, d3, d7, d4, and d6, d7 being the b m 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 T R-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 T R-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 M C (assuming b m diffraction being very weak) or T

The following two observations help rule out M C 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,

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