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Electric-field-induced paraelectric to ferroelectric phase transformation in prototypical polycrystalline BaTiO₃

Citation: Wang, Zhiyang, Webber, Kyle G., Hudspeth, Jessica M., Hinterstein, Manuel and Daniels, John E. 2014, Electric-field-induced paraelectric to ferroelectric phase transformation in prototypical polycrystalline BaTiO₃, Applied physics letters, vol. 105, no. 16, 161903, pp. 1-5.

DOI: http://www.dx.doi.org/10.1063/1.4898573

© 2014, AIP Publishing

Reproduced with permission.

Downloaded from DRO: http://hdl.handle.net/10536/DRO/DU:30093852

Electric-field-induced paraelectric to ferroelectric phase transformationin prototypical polycrystalline BaTiO3

Zhiyang Wang,1 Kyle G. Webber,2 Jessica M. Hudspeth,3 Manuel Hinterstein,1

and John E. Daniels1,a)

1School of Materials Science and Engineering, UNSW Australia, Sydney, New South Wales 2052, Australia2Institute of Materials Science, Technische Universit€at Darmstadt, 64287 Darmstadt, Germany3European Synchrotron Radiation Facility, Grenoble 38043, France

(Received 2 September 2014; accepted 1 October 2014; published online 20 October 2014)

An electric-field-induced paraelectric cubic to ferroelectric tetragonal phase transformation has

been directly observed in prototypical polycrystalline BaTiO3 at temperatures above the Curie

point (TC) using in situ high-energy synchrotron X-ray diffraction. The transformation persisted to

a maximum temperature of 4 �C above TC. The nature of the observed field-induced transformation

and the resulting development of domain texture within the induced phase were dependent on the

proximity to the transition temperature, corresponding well to previous macroscopic measurements.

The transition electric field increased with increasing temperature above TC, while the magnitude

of the resultant tetragonal domain texture at the maximum electric field (4 kV mm�1) decreased at

higher temperatures. These results provide insights into the phase transformation behavior of a pro-

totypical ferroelectric and have important implications for the development of future large-strain

phase-change actuator materials. VC 2014 AIP Publishing LLC.

[http://dx.doi.org/10.1063/1.4898573]

Barium titanate (BaTiO3) is a classical prototypical fer-

roelectric material with well-understood structural and elec-

trical properties. It is often chosen as a model material for

perovskite ferroelectric studies. Above room temperature, a

first order polymorphic phase transformation from the ferro-

electric tetragonal (P4mm) phase to the high temperature

paraelectric cubic (Pm�3m) phase occurs at the Curie point

(TCffi 130 �C). This transition temperature is influenced by a

number of factors including the material type (single crystal

or polycrystalline)1 and grain size2 as well as external electri-

cal3–5 and mechanical1,6–9 fields. Applied electric fields3,5

and uniaxial6,7 and biaxial9 compressive loads have been

found to stabilize the ferroelectric order, increasing the Curie

point in both single crystal and polycrystalline BaTiO3. A

hydrostatic pressure,1,8 however, appeared to destabilize the

ferroelectric order, reducing the Curie point. The variation of

TC under the application of external electrical and mechanical

fields has been theoretically described in BaTiO3 with the

phenomenological Landau-Ginzburg-Devonshire (LGD)

theory.5,6

At fixed temperatures just above TC, the application of

electric fields results in double loop behavior characterized

by a closed unipolar polarization hysteresis.3 This behavior

has been assumed to result from an electric-field-induced

paraelectric–ferroelectric phase transformation,3,5 although

direct structural characterization has not yet been presented.

LGD theory predicts that the critical electric field needed for

the initiation of this transformation in BaTiO3 is a linear

function with temperature, in good agreement with the

results from the temperature-dependent electrical polariza-

tion and strain measurements.5

The behavior of BaTiO3 at temperatures just above TC is

analogous to that of reported high-strain lead-free piezoelec-

tric ceramics. Where, at room temperature, an applied electric

field can induce a structural phase transformation between a

pseudo-cubic and tetragonal10 or rhombohedral phase.11,12

Small variations in composition cause such phase transforma-

tions to either be irreversible10 or reversible.11 The phase

transformations are considered to contribute significantly to

the maximum electric-field-induced strain achievable in such

materials. Additionally, the electric-field-induced phase trans-

formation above TC in BaTiO3 acts as a model system for the

study of electrocaloric behavior in ferroelectrics.12 Such trans-

formations are associated with a change in entropy of the sys-

tem13,14 and thus have a resulting change in temperature.

Despite the numerous experimental and theoretical stud-

ies on the effect of electric fields on the phase transformation

behavior in BaTiO3, direct structural and domain texture in-

formation is lacking. This study presents in situ high-energy

synchrotron X-ray diffraction measurements on polycrystal-

line BaTiO3 during application of unipolar electric fields at

various temperatures above TC. The results confirm the

phase transformation from the high temperature paraelectric

cubic phase to a ferroelectric tetragonal phase during electri-

cal loading. However, the temperature threshold to observe

the transformation was only 4 �C above TC, significantly

lower than that predicted.5 Above this TCþ 4 �C tempera-

ture, an induced tetragonal structure cannot be observed,

however, it is known that strain is generated in the bulk ce-

ramic,5 suggesting an additional mechanism of strain exists

within the cubic state. These insights into the transformation

behavior of model BaTiO3 under applied electric fields are

important for theoretical understanding of high-strain lead-

free perovskite materials and electrocaloric mechanisms.

Polycrystalline BaTiO3 materials with a grain size of

�1–2 lm and a relative density of 98% were prepared from

a)Author to whom correspondence should be addressed. Electronic mail:

j.daniels@unsw.edu.au. Tel.: þ61 2 93855607.

0003-6951/2014/105(16)/161903/5/$30.00 VC 2014 AIP Publishing LLC105, 161903-1

APPLIED PHYSICS LETTERS 105, 161903 (2014)

high purity BaCO3 (Alfa Aesar, 99.95%) and TiO2 (Tronox

TR-HP2, 99.5%) powders using a solid state route. Details

of the sample processing can be found elsewhere.5 Bar-

shaped samples with dimensions of 1.0� 1.0� 5.0 mm3

were cut from the prepared ceramic disks using a diamond

saw. Silver paint electrodes were applied on two opposing

1.0� 5.0 mm2 faces of the bars. High-energy XRD experi-

ments were carried out at beamline ID15B of the European

Synchrotron Radiation Facility. The beamline was used in

Debye–Scherrer transmission geometry with a monochro-

matic beam of energy 87.12 keV (wavelength 0.1423 A). The

beam size on the sample was set to 200� 150 lm2. For the

electric-field- and temperature-dependent XRD tests per-

formed, the sample was placed inside an electric field cham-

ber equipped with a temperature stage.15 The sample was

cooled from 135 to 125 �C in steps of �1 �C. Temperatures

were allowed to equilibrate for approximately 8 min. At

each temperature a complete cycle of unipolar electric field

with maximum strength of 4 kV mm�1 was applied using a

triangular waveform in field steps of 0.4 kV mm�1. The tem-

perature stability during a full electric-field cycle was within

60.05 �C. Diffraction images at each field step were col-

lected over approximately 2 s using a Pixium 4700 flat panel

area detector.16 The acquired images were radially integrated

into 36 azimuthal sections of 10� widths to obtain one-

dimensional diffraction patterns using the software package

fit2d.17 These data represent diffraction information col-

lected with the scattering vector aligned from parallel to per-

pendicular to the applied electric field direction.

The Curie point of the polycrystalline BaTiO3 used for

the present experiment was found to be TC¼ 128 �C based on

the tetragonal to cubic phase transformation temperature at

zero electric field. This is in good agreement with the previ-

ous result from the permittivity-temperature measurements.5

Figure 1 demonstrates the ability of the technique used to

observe the electric-field-induced structural change. Here, the

222 and 004/400 diffraction peaks are shown for BaTiO3 at

129 �C (i.e., TCþ 1 �C) before electrical loading and under a

4 kV mm�1 electric field. Upon application of the field, the

paraelectric cubic 222 peak at initial zero field state remains

single and symmetric, while the paraelectric cubic 400

reflection splits into a doublet. This indicates an electric-

field-induced structural phase transformation from the high

temperature paraelectric cubic state to a tetragonal state. The

induced 400T and 004T peaks at TCþ 1 �C exhibit a marked

variation in their intensity ratio with scattering vector angle

to the applied field (Fig. 1). This observation indicates the

presence of a strong domain texture within the field-induced

tetragonal phase with c-axis components of the tetragonal

structure preferentially aligned close to the applied electric

field vector. This is consistent with previous investigations of

electric-field-induced phase transformations in the perovskite

0.93(Bi0.5Na0.5)TiO3–0.07BaTiO3 piezoelectric ceramics at

room temperature, where the induced ferroelectric domain

texture showed a similar distribution of the (002) pole.10,18

The diffraction data are consistent with the induced phase

being a polar tetragonal P4mm structure, i.e., the room tem-

perature BaTiO3 phase. The ferroelectric polarization within

the induced tetragonal phase is along the c-axis of the unit

cell, thus providing a driving force for the domain texture

development. Additionally, it is worth noting that the

electric-field-induced phase transformation was observed in

all grain orientations relative to the applied electric field

direction, although the electrical driving force for this trans-

formation is readily available only in those grains with a

cubic h001i-axis oriented close to the applied field direction.

A possible explanation for this behavior is that the phase

transformation is also driven by the intergranular stresses

generated for the accommodation of the elastic strains

between neighboring grains during electrical loading,19 con-

tributing to the occurrence of the phase transformation in all

grain orientations.

Figure 2 shows representative diffraction patterns near

the 004/400 reflections as a function of the applied electric

field amplitude measured at various temperatures above TC.

The observed electric-field-dependent diffraction patterns at

the temperatures of TCþ 1 �C (Fig. 2(a)), TCþ 2 �C (Fig.

2(b)), and TCþ 4 �C (Fig. 2(c)) clearly display peak splittings

when the applied field strength reaches a critical value, con-

firming the electric-field-induced cubic to tetragonal phase

transformations. A closer look at the diffraction data in

Figs. 2(a)–2(c) shows that the critical electric field required to

initiate a phase transformation (transformation field) increases

with increasing temperature. The field-induced symmetry-low-

ering transformation as indicated here was observed at

a maximum temperature of TCþ 4 �C. At temperatures

greater than TCþ 4 �C, it was not possible to observe a clear

FIG. 1. Representative diffraction peaks of BaTiO3 at TCþ 1 �C. (top,

black) Paraelectric cubic 222 and 400 diffraction peaks at zero electric field.

(lower, red) Ferroelectric tetragonal 222 and 004/400 peaks under an electric

field of 4 kV mm�1 as a function of scattering vector (q) angle to the applied

electric field (E).

161903-2 Wang et al. Appl. Phys. Lett. 105, 161903 (2014)

electric-field-induced transformation, as shown in Fig. 2(d)

for TCþ 5 �C. These observations imply that with increasing

temperature above TC, the electric-field-induced transforma-

tion into a tetragonal phase becomes increasingly difficult

and is no longer possible when reaching a specific tempera-

ture limit, qualitatively consistent with the Landau theory

predictions.5 It is also notable that the induced tetragonal

phase is stable at TCþ 1 �C after removal of the applied elec-

tric field (Fig. 2(a)) while at other temperatures the transfor-

mation is fully reversible (Figs. 2(b) and 2(c)). It is not clear

if the irreversibility at TCþ 1 �C is truly an intrinsic property

of the material or if the small temperature variations within

the experimental setup have caused the low-temperature

phase to remain.

To analyze the structural characteristics and domain tex-

ture changes in BaTiO3 during application of the electric

fields, the lattice parameters and the degree of the induced

domain texture were determined based on the peak positions

and integrated intensities. Specifically, the 400 cubic and

400/004 tetragonal peaks were fit using symmetric single

and double Gaussian peak profile functions, respectively.

The obtained peak positions were used to calculate the lattice

parameters, while the integrated intensity ratio of 004/400

tetragonal peaks (I(004)/I(400)) was used as a measure of the

degree of domain texture within the induced phase. Figure 3

shows the extracted lattice parameters and tetragonal domain

texture at various temperatures as a function of applied elec-

tric field with the scattering vector aligned parallel to the

field vector. There is no obvious change in the lattice param-

eters with further increasing field after the tetragonal phase

has been induced, implying that no significant (00l) or (h00)

lattice strains along the electric field direction were gener-

ated in this phase. Based on the lattice parameters of the

cubic and induced tetragonal phases, an estimate of the strain

contribution from the electric-field-induced cubic to tetrago-

nal phase transformation can be evaluated according to the

equation18

et33 ¼

1

3aTð Þ2 � cTð Þ � aCð Þ3

h i= aCð Þ3

n o; (1)

where et33 is the strain parallel to the electric field direction

that results from the phase transformation, aC is the lattice

parameter of cubic phase at zero field, and aT and cT are the

lattice parameters of the induced tetragonal phase. Using

only the lattice parameter data parallel to the electric field

direction presented in Fig. 3, phase transformation strains

(et33) of 0.02% and 0.01% were determined at the maximum

field of 4 kV mm�1, for temperatures of TCþ 1 and

TCþ 2 �C, respectively. This strain effect from the phase

transformation, in addition to the ferroelastic strain resulting

from the induced domain texture, is the origin of the macro-

scopic strain reported by Picht et al.,5 which shows a discon-

tinuous increase at temperatures slightly above TC. The

tetragonal domain texture, indicated by the intensity ratio of

the 004/400 peak doublet (Fig. 3), is found to be enhanced

with increasing electric field above the transition field, analo-

gous to the domain texture development behavior reported

previously in the stress-induced tetragonal phase in BaTiO3

at temperatures above TC.7 This observation further verifies

that the induced tetragonal phase is of a ferroelectric nature

and thus, the magnitude of the ferroelectric domain texture

FIG. 2. Representative diffracted intensities of the 004 and 400 peaks of

BaTiO3 during application of a triangular electric field waveform at (a)

TCþ 1, (b) TCþ 2, (c) TCþ 4, and (d) TCþ 5 �C. Here, the scattering vector

is parallel to the applied electric field vector.

FIG. 3. Unit cell lattice parameters and tetragonal domain texture indicated

by the intensity ratio of I(004)/I(400) with the scattering vector, q, parallel to

the applied electric field for four temperatures above TC (a)–(d). The dashed

red lines are the linear fits to the data points of I(004)/I(400) after the transfor-

mation, and their gradients indicate the rate of domain texture development.

161903-3 Wang et al. Appl. Phys. Lett. 105, 161903 (2014)

in the transformed phase increases with increasing field am-

plitude. Note that the rate of domain texture development

extracted from the gradient of the intensity ratio (I(004)/I(400))

after the transformation, as indicated by dashed red lines in

Fig. 3, is strongly dependent on the temperature above TC.

At temperatures of TCþ 1 �C and TCþ 2 �C, there are clear

ongoing developments of tetragonal domain texture with

increasing electric field, while at TCþ 3 �C and TCþ 4 �C,

the rate of domain texture enhancement with applied field is

significantly lower.

Figure 4 shows the changes of the critical electric field

magnitude of the cubic to tetragonal phase transformation,

the tetragonal domain texture at 4 kV mm�1 quantified by

the intensity ratio of the (004)/(400) tetragonal peaks (I(004)/

I(400)), and the final c/a ratio of the induced tetragonal phase

at 4 kV mm�1 as a function of temperature above TC. The

critical transition electric field, determined as the lowest

electric field under which an apparent phase transformation

was observed, displays a linear trend with increasing temper-

ature of 0.4 kV mm�1 �C�1 (Fig. 4(a)). This result, however,

is not consistent with the theoretical prediction based on the

Devonshire free energy expression or experimental results

determined from macroscopic strain measurements, which

showed the shift in the critical transition electric field with

temperature of 0.12 kV mm�1 �C�1 and 0.118 kV

mm�1 �C�1, respectively.5,20 It is possible that the origin of

the discrepancy between these results is related to the electri-

cal loading procedure, however, without concurrent strain

and diffraction measurements it is difficult to discern. As

shown in Fig. 4(b), at the maximum electric field of 4 kV

mm�1, a strong tetragonal domain texture exists at TCþ 1 �Cand TCþ 2 �C, while at higher temperatures of TCþ 3 �C

and TCþ 4 �C, the resultant domain texture is significantly

lower. This change in the resultant domain texture (Fig.

4(b)) correlates to the temperature-dependent macroscopic

electrical constitutive responses of BaTiO3 observed in a

previous work,5 which showed an evolution from a hystere-

sis loop at temperatures slightly above TC to a non-hysteresis

loop as the temperature further increasing above TC. The

final c/a ratio at 4 kV mm�1 reduces with increasing temper-

ature above TC (Fig. 4(c)).

Analogous to the electric-field-induced phase transfor-

mation reported here, a compressive uniaxial stress induced

paraelastic to ferroelastic phase transformation has also been

observed in polycrystalline BaTiO3 at temperatures above

TC.7 Similarly, the critical stress required to initiate a phase

transformation was found to increase with increasing temper-

ature above TC. These transformation behaviors of model

BaTiO3 under the influences of electric field and stress are of

great significance for the investigations into the high-strain

lead-free piezoelectric materials, where the electric field10

and stress21 induced phase transformations are known to

contribute significantly to the high-strain actuation.

Moreover, the obtained knowledge on the electric field

induced phase change is essential for understanding the elec-

trocaloric behavior near the ferroelectric phase transforma-

tion in ferroelectrics.

In situ high-energy X-ray diffraction has shown an

electric-field-induced phase transformation from a paraelec-

tric cubic to a ferroelectric tetragonal structure in the

polycrystalline BaTiO3 at temperatures above TC. The tem-

perature limit for this phase transformation was identified to

be 4 �C above TC. The critical electric field required to initiate

the phase transformation increases linearly with increasing

temperature above TC. After the transformation, the induced

tetragonal phase at temperatures of TCþ 1 �C and TCþ 2 �Cexhibit ongoing developments of domain texture with further

increasing electric field, resulting in a strong domain texture

at a maximum field of 4 kV mm�1. At higher temperatures

(TCþ 3 �C and TCþ 4 �C), the development rate and resultant

magnitude of the tetragonal domain texture both decrease

significantly. These results provide insights into the general

paraelectric to ferroelectric phase transformation behavior

and have important implications for the future development

of high-strain lead-free electromechanical materials.

J.E.D. acknowledges financial support from an AINSE

Research Fellowship and an ARC Discovery Project

(DP120103968). K.G.W. acknowledges support from the

Deutsche Forschungsgemeinschaft under WE 4972/1-1 and

WE 4972/2-1. Experimental beamtime was provided by the

European Synchrotron Radiation Facility.

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FIG. 4. (a) The critical phase transition field (estimated as the lowest electric

field at which an obvious phase transformation can be identified), (b) domain

texture at 4 kV mm�1 indicated by I(004)/I(400), and (c) final c/a ratio at 4 kV

mm�1 as a function of temperature above TC.

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161903-5 Wang et al. Appl. Phys. Lett. 105, 161903 (2014)