Jones-2007-1-JACS Texture and Ani Sot Ropy of Piezoelectrics

8/2/2019 Jones-2007-1-JACS Texture and Ani Sot Ropy of Piezoelectrics

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Texture and Anisotropy of Polycrystalline Piezoelectrics

Jacob L. Jones

Materials Science and Engineering, University of Florida, Gainesville, Florida 32611

Benjamin J. Iverson and Keith J. Bowmanw

Materials Engineering, Purdue University, West Lafayette, Indiana 47907

Piezoelectricity is manifested in ferroelectric ceramics by induc-ing a preferred volume fraction of one ferroelectric domain vari-ant orientation at the expense of degenerate orientations. Thepiezoelectric effect is therefore largely controlled by the effec-tiveness of the electrical poling in producing a bias in ferroelec-tric (1801) and ferroelastic (non-1801) domain orientations.Further enhancement of the piezoelectric effect in bulk ceram-ics can be accomplished by inducing preferred orientationthrough grain-orientation processes such as hot forging ortape casting that precede the electrical-poling process. Coupled

crystal orientation and domain orientation processing yields ce-ramics with an even greater piezoelectric response. In this paper,preferred orientations of domains and grains in polycrystallinepiezoelectric ceramics generated through both domain- andgrain-orientation processing are characterized through pole fig-ures and orientation distribution functions obtained using datafrom a variety of diffraction techniques. The processing methodsused to produce these materials and the methods used to eval-uate preferred orientation and texture are described and dis-cussed in the context of prior research. Different sample andcrystal symmetries are explored across a range of commercialand laboratory-prepared materials. Some of the variables pre-sented in this work include the effects ofin situ thermal depolingand the detailed processing parameters used in tape casting ofmaterials with preferred crystallite orientations. Preferred ori-

entation is also correlated with anisotropic properties, demon-strating a clear influence of both grain and domain orientationson piezoelectricity.

I. Introduction

A MATERIAL with a crystallographic texture is best describedas a polycrystal with a nonrandom distribution of crystalorientations or a preferred crystallographic orientation. This isunique from a polycrystal with a morphological texture, orpreferred grain shape orientation, although they are frequentlycorrelated.

Because most crystalline properties are a function of crystal-lographic direction (anisotropic), the distribution of crystals and

the intrinsic crystalline anisotropy is coupled to the macroscopicanisotropy of textured polycrystalline materials. This is illus-trated in Fig. 1. Fundamental to these textureanisotropy rela-tionships is the requirement of a quantitative description of theorientation of crystals. Preferred orientation is most completelydescribed by an orientation distribution function (ODF), whichgives the relative presence of each possible crystal orientationrelative to that in a random distribution of orientations. Panel Adescribes this further.

Researchers in the metallurgy and geology communities pro-duced the first publications on crystallographic textures tied todirectional deformation in the first half of the 20th century.5,6

The Laue diffraction experiments by Wever5 tied forming to thesubsequent concentration of orientations in polycrystal alumi-num and iron through the first use of X-rays to describe the

development of preferred orientations. Because these first ex-amples of crystallographic texture arose from large-scale plas-ticity in ductile metals, quantitative measures of texturedevelopment in polycrystalline ceramics were at first limitedand tied to textures arising from green body processing of ma-terials with nonequiaxed particles (e.g., Pentecost and Wright7

and Bowman8) until hot working of ceramics was used to eval-uate the orientation effects on the optical properties of aluminumoxide9,10 and the potential for improved performance in struc-tural applications.11

The motivation in most engineering applications for inducingcrystallographic texture is the desire to optimize a particularproperty, its anisotropy, or both.1 Crystallographic texture maybe correlated or uncorrelated with the directional morphologyof crystals or defects that may otherwise result from the direc-

tionality of processing. In the last two decades, research oncrystallographic texture in ceramics related to high-temperatureforming operations has been broadened to include a wide rangeof processes for introducing texture, including templating

Feature

D. Greencontributing editor

This research was supported by the U.S. National Science Foundation under awardnumbers DMR-0224991 and OISE-0402066 and the Indiana 21st Century Research andTechnology Fund No. 092200-0076. This work has benefited from the use of the Los Al-

amos Neutron Science Center at the Los Alamos National Laboratory, funded by the U.S.Department of Energy under Contract W-7405-ENG-36 and the NSLS at BrookhavenNational Laboratory, supported by the U.S. Department of Energy, Division of MaterialsSciences and Division of Chemical Sciences, under Contract No. DE-AC02-98CH10886.

wAuthor to whom correspondence should be addressed. e-mail: [email protected]

Manuscript No. 22750. Received January 30, 2007; approved April 17, 2007.

Journal

J. Am. Ceram. Soc., 90 [8] 22972314 (2007)

DOI: 10.1111/j.1551-2916.2007.01820.x

r 2007 The American Ceramic Society


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processes for bulk,12 and thin-film materials.13 Incidentally,most of these processes take advantage of the intrinsic surfaceenergy anisotropy of the crystal structure to synthesize texturedmaterials, which, in effect, is used to generate anisotropy inmacroscopic properties. Other attributes of anisotropy have alsobeen explored that can occur within the crystals of a polycrys-talline material. Phase transformations within crystals or thedevelopment of biased domains or twins have recognized con-tributions to anisotropy in noncubic ceramics. These effortshave resulted in an ever increasing range of anisotropic proper-

ties including elasticity, strength, fracture toughness, opticalproperties, conductivity, thermoelectricity,1416 superconductiv-ity,17 magnetic properties,18 shape-memory properties,19 and pi-ezoelectricity.12,20 In this last category, our recent research hasshown that the behavior of domains inherent to most ceramicpiezoelectrics couples with crystallographic texture and concur-rent changes in other property tensors. In this paper, we describethe context and characteristics of these coupled textures andshow new examples of how this coupling can be exploredthrough tailored processing, rigorous quantitative texture as-

sessments, and property evaluations.Piezoelectricity in polycrystalline ceramics depends on theorientation achieved from poling of non-centrosymmetric ma-terials that are also ferroelectric. Until a macroscopic electricdipole is formed, a piezoelectric material will not demonstratepiezoelectricity. The noncubic materials that exhibit piezoelec-tricity typically have a domain structure that is inherited duringa phase transformation from a higher temperature phase of ahigher symmetry. On cooling through the temperature at whichthe phase transformation occurs (Curie temperature), the break-ing of symmetry results in a multiplicity of orientations consis-tent with the change in symmetry.21 Without an externalmechanical or electrical field biasing the formation of these do-main orientations, it is expected that they will form with nearlyequal fractions within each crystal. The orientation variants can

(a) (b)micro-anisotropy

of the crystals

macro-anisotropy

of the material

Fig. 1. Influence of micro-anisotropy of the crystals on the macro-anisotropy of the material, after Bunge and Schwarzer.96

Panel A: The Orientation Distribution Function

The ODF is a means of describing the probability of every possible crystal orientation relative to the probability in a randomlyoriented material. Many reference texts have been written on texture and the ODF14 and the description provided in this panel isintended only to be a brief introduction.

To describe the probability of certain crystallite orientations in a polycrystalline material quantitatively, two definitions arerequired:

(1) a description of the individual crystallite orientation relative to the specimen coordinate axes and(2) a measure of the frequency at which a particular orientation is preferred relative to that in a random distribution of crystal-

lites. This value can also be described as the density, or amplitude, of preferred orientation.For the former, (1), three angles are required to transform the specimen coordinate axis to the grain coordinate axis or vice versa.

There are various definitions of these three angles based on the sequence of rotations. We adopt here the Bunge notation, wherein

the first angle, j1, is a rotation about the specimen Z-axis. The second angle, F, is a tilting of the crystallite z-axis from thespecimen Z-axis about the crystallite x-axis. The third angle, j2, is a rotation about the new specimen z-axis.

2 These angles areillustrated in Fig. A1.

For a definition of frequency, (2), the degree of preferred orientation can be described as a multiple of a random distribution(mrd). In other words, the density of each crystallite orientation is described relative to its density in a randomly oriented ceramic.For example, a crystallite orientation that is twice as probable in a textured material as in a randomly oriented material isdescribed as having a density of 2 mrd. The three-dimensional (3D) ODF, f(j1, F, j2), therefore consists of the densities, f, of allorientations j1, F, and j2.

The ODF is difficult to represent linearly in two dimensions and pole figures or inverse pole figures are typically sufficient fordescribing textures in real materials. Pole figures and inverse pole figures are integrations of the ODF in two dimensions andrepresent either the densities of a single crystallographic direction in sample orientation directions (pole figure) or the densities of

all crystallographic directions in a single sample direction (inverse pole figure). Pole figures are usually plotted on an equal areaprojection, while inverse pole figures are typically plotted on a stereographic projection.

Fig. A1. Angles describing a coordinate transformation, j1, F, and j2, from Bowman.97

2298 Journal of the American Ceramic SocietyJones et al. Vol. 90, No. 8


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be generated by either 1801 rotations or non-1801 rotations,corresponding to the so-called 1801 and non-1801 domains.With piezoelectric ceramics, orientation is conventionally in-duced by applying an electric field to an initially untextured ce-ramic at temperatures near the Curie temperature to increase thesize of domains aligned with the applied electric field. This pro-cess, termed poling, is an orientation-inducing process thatchanges the fraction of the 1801 domains and can change thefraction of non-1801 domains. Figure 2(a) illustrates the reori-entation of non-1801 domains, or expansion of favored orien-tations from domain wall motion, resulting from the applicationof an electric field.

Through this poling process and the development of an elec-

tric dipole, piezoelectric ceramics can demonstrate the piezo-electric effect, whose direct effect is described by the linearrelation

Di dijsj (1)

where Di is the electric displacement, dij is the piezoelectric mod-ulus, and sj is the applied stress (i51, 2, and 3; j51, 2, y 6).The poling process provides a method for tuning the domainorientation distribution to optimize the coefficients ofdij. Detailsof the dielectric properties, dielectric anisotropy, elastic behav-ior, and elastic anisotropy become very complex once a polar-ization has been introduced, in turn producing piezoelectricstresses, and electric fields in the system. Unlike texture chang-es from plastic deformation, recrystallization, or grain growth,

the property changes resulting from domain textures can bemodulated with only slight changes in defect content, grainshape, grain size, grain boundary structure, and grain boundarychemistry. Additionally, within ranges allowed by internalstresses and fatigue effects, the orientation process and proper-ties can be reversible.

The remainder of the paper is divided as follows: Section IIdescribes the evolution of domain structure and piezoelectricproperties through the poling and thermal depoling process ininitially randomly oriented lead zirconate titanate (PZT) ceram-ics. Sections III and IV are devoted to describing property andtexture measurements in ceramics with an initial texture in theunpoled state. Because the domain textures and the resultingproperties are coupled to the initial grain orientation, the per-formance potential is superior to conventionally processed ma-

terials.12,20,2227 Figure 2(b) illustrates the alignment of domainsbefore and after poling in ceramics that possess an initial crys-

tallographic texture. Materials exhibiting an Aurivillius28 orTungstenbronze2931 crystal structure are particularly valuablefor generating ceramics with an initial crystallographic texturebefore poling because of the large surface energy anisotropy oftheir structures. Sections III and IV describe the synthesis ofinitially textured ceramics of these two respective crystal systemsand the evolution of their domain structures and piezoelectricproperties through electrical poling. In Section V, other textureanisotropy relationships are explored with a focus on polariza-tion in materials exhibiting monoclinicity. Finally, Section VI

summarizes the results of the preceding sections.

II. Initially Randomly Oriented PZT Ceramics

PZT materials remain widely used despite reservations over theirlead content. The well-developed understanding of these mate-rials and the ability to fine tune their performance using well-investigated doping strategies are confounded by limited under-standing of the domain character of these materials. Our limitedunderstanding of how domain walls move and overcome obsta-cles to their motion has not changed significantly despite theirwide range of applications. Even the static nature of the domainconfigurations is disputed, particularly at the morphotropicphase boundary where both a monoclinic structure and nano-domains of a high-symmetry phase are argued to exist.3234 Re-gardless of the static structure, the process of electrical polingestablishes a bias in domain configurations that enables thefunctionality of these materials. This section demonstrates thatthe degree of domain texture established in conventional polingprocesses is constrained by microstructural aspects of these ma-terials and can be quantitatively correlated with the measurablemacroscopic properties.

(1) Experimental Procedure

Soft PZT ceramics (K350; Piezo Technologies, Indianapolis, IN)were obtained from the supplier in dimensions of 1 cm 1cm 1 cm. Gold electrodes were sputtered onto two opposingsides. The samples were immersed in silicon oil and electricallypoled using electric fields in the range 0.51.75 kV/mm for 10

min at room temperature. The sample dimension through whichthe electric field was applied was measured before and after pol-ing. The d33 was measured on a Berlincourt d33 meter (APCInternational, Ltd., Mackeyville, PA) 24 h after poling.

Preferred orientation after electrical poling was measured us-ing the texture diffractometer High Pressure-Preferred Orienta-tion (HIPPO) (Panel B). The software package MAUD41,42

(Panel B) was used to analyze the measured diffraction data inthe range 1.05 A odo2.25 A using the Rietveld method.38,39

The starting crystallographic information (lattice parameters,atomic coordinates, etc.) was taken from prior refinements ofthis material.45 The time-of-flight (TOF) calibration constantdifc was first refined for each detector, followed by refinement ofindividual spectra intensities and polynomial background co-efficients. In the subsequent refinement, lattice constants and

texture were refined. Texture was modeled using a fourth-orderSH (Panel B). In our earlier work, a fourth-order SH was de-termined to be sufficient for describing the small degrees of pre-ferred orientation and wide distributions in non-1801 domaintextures.45,46 After refinement of the texture using a samplesymmetry of 1, fiber symmetry was enforced about the max-imum of the 002 peak. This direction corresponds to the axis ofthe electric field during poling.

For the strain and polarization hysteresis measurements, asample of the same composition and from the same manufac-turing lot as those used for the diffraction measurements wasreceived from the manufacturer in the shape of a disk of 10-mmdiameter and 1-mm thickness. After thermal annealing at 6001Cfor 2 h, a silver electrode was painted on the major faces of thesample and the polarization and strain response were measured

using a SawyerTower circuit with a laser interferometer in re-sponse to a 2.3 mHz triangular waveform.

E E

(a) (b)

Fig. 2. Grain and non-1801 domain distribution in a ceramic with noinitial preferred orientation in the unpoled state (a) and with preferredorientation in the unpoled state (b). After electrical poling through theapplication of electric field, E, certain domain orientations increase indirections relative to the electric field.

August 2007 Texture and Anisotropy of Polycrystalline Piezoelectrics 2299


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Panel B: Diffraction Methods for Measuring Texture

Diffraction methods for measuring texture must enable a quantitative and statistically significant interpretation of the orientationof domains and grains in the polycrystalline material. Today, diffraction techniques are most widely used for texturemeasurements35 and in this work, we have used a variety of approaches using X-ray and neutron diffraction. The bestmethod for texture measurements is often dependent on the material being examined and the availability of the given diffractioninstruments. The continuity and statistical accuracy of a given texture measurement can be affected by the relationship betweengrain size and counting statistics. While different methods may obtain different results, trends should be consistent with theexpected textures developed across all methods. Here, a brief examination of some of the capabilities and limitations of theseapproaches is given. The two primary considerations in these approaches are: (1) instrument selection and (2) the method of

interpretation of information contained in the diffraction pattern.Many different diffraction instruments are available by which to perform texture measurements. These range from spallationneutron sources to synchrotron sources to laboratory diffractometers. In this work, we have performed measurements using allof these various instrument types. Neutron diffraction typically gives a better sampling of the bulk material and therefore hasbeen used whenever possible. When higher resolution measurements are required, synchrotron sources have been used,sometimes in three-crystal mode (a crystal analyzer on the diffracted beam). When surface-sensitive measurements or a largenumber of measurements are required, the laboratory diffractometer has an advantage. The diffraction patterns of the soft PZTceramic used in Section II obtained from three of these instruments is shown in Fig. B1, illustrating some of the unique features ofthese instruments. For example, the relative intensities in neutron and X-ray patterns are different as a result of the difference inatomic scattering and Lorentz-polarization factors. Other differences are not apparent in Fig. B1 and yet are critical to thecapabilities of the instrument. For example, the diffractometer HIPPO at the Los Alamos Neutron Science Center, Los Alamos

National Laboratory, has 30 detector panels at fixed diffraction angles of 1501, 901, and 401 that are used for texturemeasurements, all of which collect diffracted intensities as a function of TOF.36,37 Each TOF pattern is effectively a measuredinverse pole figure for one sample direction. Typically, four sample rotations are used for collection of 120 diffraction patterns.The resolution of these detectors depends on the scattering angle, with improved resolution available at higher scattering angles.HIPPO also has a high count rate that results from its short (9 m) initial flight path.

Once a diffraction pattern or a series of patterns are obtained, a method of interpretation of information contained within the

pattern is necessary. For grain texture measurements, the ODF can be calculated by pole figure inversion. Pole figure inversion isthe reconstruction of the 3D ODF from measurements of the intensities of crystal poles (the distribution of a single-crystal pole insample space is a pole figure and the distribution of crystal poles in a single sample direction is an inverse pole figure). To obtainpole figures or inverse pole figures from diffraction data for use in pole figure inversion, the intensities can be extractedindividually or as part of a whole powder pattern-fitting routine. For the latter, the Rietveld method38,39 is a common method ofmodeling the diffraction patterns and enabling intensity extraction. Commonly used software for using Rietveld methods fortexture analysis are General Structure Analysis System (GSAS)40 and Materials Analysis Using Diffraction (MAUD).41,42

MAUD was utilized for this purpose in this work. Details of pole figure inversion can be found in Kocks et al.,1 Bunge,2 Wenk,3

and Randle and Engler.4 The ODF can be described discretely, or continuously using spherical harmonic (SH) functions inFourier space.39,43

The large number of neutron diffraction patterns obtained on the texture diffractometer HIPPO at the Los Alamos NeutronScience Center (120 diffraction patterns are common for texture analysis)36,37,44 often necessitates, and benefits from, theRietveld method for texture analysis. The Rietveld method can also be used on X-ray diffraction patterns, but the number ofmeasurements required (largely a function of the materials symmetry) can be large. Therefore, other less complex texture

measurements are often desirable, which require fewer measurements. For domain textures of initially randomly orientedmaterials, where the texture is expressed completely by intensity interchanges in symmetry-dependent reflections, we have

Fig. B1. Diffracted intensities of the soft commercial lead zirconate titanate using three different diffraction instruments. At the bottom, the X-raypattern utilized a synchrotron source with a fixed wavelength in BraggBrentano geometry.98 In the middle, the neutron diffraction pattern wasobtained from the instrument MRPD at the HiFAR reactor at the Australian Nuclear Science and Technology Organisation (ANSTO) using a fixedwavelength.99,100 At the top, the neutron diffraction pattern was obtained on the TOF instrument HIPPO by summing all of the y5 901 fixed-angledetectors.45



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(2) Results and Discussion

The polarization and strain response of an initially unpoled softPZT bulk ceramic to a cyclic bipolar electric field are shown in

Fig. 3. The coercive field, defined here as the minimum value inthe strain hysteresis plot, is 1.0 kV/mm. Increasing the electricfield beyond the coercive field reorients both 1801 and non-1801domains, leading to polarization and strain accumulation that isretained upon removing the electric field, i.e., the remanent state.The polarization and strain hysteresis, shown in Fig. 3, is typicalof soft PZT ceramics measured in other commercially availablesoft PZT materials.47

Electrical poling of bulk ceramics induces domain reorienta-tion similar to that observed during polarization and strain hys-teresis measurements. However, static electric fields are appliedfor longer time periods during electric poling. Piezoelectricity isthen allowed in the initially randomly oriented ceramic after a netelectric dipole is developed in the bulk material through 1801 andnon-1801 domain switching. The longitudinal piezoelectric coeffi-

cient, d33, is shown as a function of electric field amplitude duringelectrical poling in Fig. 4. The d33 increases dramatically around apoling field of 1.0 kV/mm, identified from Fig. 3 as the coercivefield of this material. After poling with an electric field of 1.2 kV/mm, a d33 of 380 pC/N is achieved. Poling with higher electricfields yields nominally higher piezoelectric coefficients. Some do-main switching is expected during electrical poling below the co-ercive field because the electric field is applied over relatively longtimes. This small degree of domain switching results in a mea-surable value of d33 for poling fields below 1.0 kV/mm.

The macroscopic longitudinal strain generated from the elec-trical poling process is also shown in Fig. 4. This macroscopicstrain, ranging from 0% to 0.33%, is of the same order of mag-

nitude as the remanent strain obtained during measurement ofthe polarization and strain hysteresis (Fig. 3). However, themagnitude of strain is higher during electrical poling because the

electric field is applied for 10 min, whereas the positive portionof the electric field was applied for only B3 min during mea-surement of the strain in Fig. 4 and, moreover, was not constantduring this entire time (triangular waveform). The fact that thesestrains are different for different loading times provides someevidence of a time dependence of domain reorientation duringelectrical poling. The poling strain, or remanent strain obtainedafter poling, is a combination of both intergranular elastic strainand strain resulting from non-1801 domain switching (inter-changing of the long (002) and short (200) lattice planes). Themeasurable strain at subcoercive poling fields could be attribut-ed to either mechanism, although it will be shown later that acomponent of this strain is from non-1801 domain switching.

Preferred orientation induced through non-1801 domainswitching was measured after electrical poling using full-pattern

Rietveld refinement and pole figure inversion methods. Becausenon-1801 domain switching only occurs in this tetragonal struc-ture through an interchange of 002 and 200 poles, these poles arethe only texture components in this system. In other words, sig-nificant grain rotation or growth does not lead to preferred ori-entation in these or other poles during electrical poling.Therefore, the inverse pole figure parallel to the electric fieldconsists of a single maximum at 002 and a single minimum at200. Although the entire ODF is calculated through pole figureinversion methods, a single pole figure is sufficient to illustratethe results. The 002 pole density distributions are reproduced inFig. 5. The information presented in Fig. 5 is the same as thatgiven in pole figures with fiber symmetry, although the pole

2 1 2 10 1 240

20

0

20

40

Polarization[C/cm

2]

Electric Field [kV/mm]

0 1 20.1

0.0

0.1

0.2

0.3

Strain[%]

Electric Field [kV/mm]Fig. 3. Polarization and strain hysteresis behavior of the soft lead zirconate titanate ceramic.56

developed a simple calculation for determining the degree of domain preference based on the relative intensity of these peaks in asingle scattering direction. For tetragonal symmetries, the 001 pole density is given by45

f001 mrd 3 I00h=IR00h

I00h=IR00h 2Ih00=IRh00B 1

where IRhlk is the integrated intensity of the hklpeak in a randomly oriented sample (cooled in the absence of applied fields andunpoled). For orthorhombic symmetries with two possible orthogonal ferroelastic variants such as the bismuth titanate and leadmetaniobate structures in this work, the 100 pole density (or, conversely, the 010 pole density) pole is given by 20

f100 mrd 2 Ih00=IRh00

Ih00=IRh00 2I0h0=IR0h0B 2

Using Eqs. (B-1) and (B-2) on diffraction intensities obtained at various sample tilt angles (a), incomplete pole figures can bemeasured directly without the complexity of pole figure inversion or the Rietveld method. There exist some materials in which the(h00) and (0k0) peaks are either low in intensity or highly overlapped with other peaks and the use of Eq. (B-2) becomes difficult.Therefore, the use of Eq. (B-2) cannot always be directly applied. In these cases, any set of peaks with consistent c componentsand varying a and b components can be used for quantifying domain textures.21



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figure terminology is reserved for pole distributions plotted onan equal area projection. The angle a in Fig. 5 is the angle from

the poling axis.Before interpreting the results from Fig. 5, it is worthwhile

reviewing the character of these pole density representations.The principle of pole figure inversion involves a calculation ofthe ODF in three dimensions (Euler angles) from 2D data (poledensity values as a function of two sample directions in the formof pole figures or intensity deviations from a structure solutionin a diffraction pattern). Different methods have been developedfor the inversion procedure including discretization methods andthe use of series expansion. The data presented in Fig. 5 used theseries expansion representation of spherical harmonics. Becausethis series expansion method provides a continuous solution ofpole density in every possible sample direction (regardless of thediscrete measurement grid), the pole density distributions arerepresented as continuous functions. Furthermore, this method

of pole figure inversion does not yield errors associated witheach sample direction. In other words, no error bars are readilyavailable for a given sample direction and thus confidence inobserved trends has to be developed through other means.

One context for discussing the errors in these values isthrough a comparison of the results produced from the differ-ent methods of pole figure inversion. For example, Matthieset al.44 compare several different methods of pole figure inver-sion from data obtained using the same instrument as that used

in this work on a strongly textured aluminum sample and reporta wide range of maximum pole density values produced by thevarious methods. This seems to suggest that the use of differentpole figure inversion techniques may produce a wide range ofODFs. However, the domain textures produced by electrical pol-ing are weak by comparison and the width of the pole densitypeaks is broad. Therefore, such large differences are not expectedin these weaker textures. In earlier work, we have reported rea-sonable repeatability of pole density measurements using differentmeasurement techniques and pole figure inversion methods.45,46

For example, the maximum f002 values for compression domaintextures measured using two different orders of spherical har-monics were 1.62 (sixth order) and 1.50 (fourth order) mrd.46

Additionally, the use of different pole figure inversion methodsyielded maximum f002 values of 1.51 and 1.65 mrd for the samedata.46 The differences reported in these earlier examples are gen-erated using fundamentally different representations of the ODF.These differences are much larger than the approach expectedwithin the same pole figure inversion method such as those usedhere. Therefore, we expect the errors in the values reported inFig. 5 to be o0.1 mrd. The minimum change in the maximum

f002 values in the measured data of Fig. 5 is 0.06 mrd, which isseen between the highest electric fields. Thus, we have strongconfidence in the trends observed between 0 and 1.0 kV/mm andreasonable confidence in the increasing trend above 1.0 kV/mm.

It is therefore apparent from Fig. 5 that the preferred orien-tation of the 002 pole increases with an increasing electric fieldduring poling, consistent with observations in earlier work.45,46

Also shown in Fig. 5 is the theoretical saturation distributionspredicted from an analytical domain-switching model of tetrag-onal ferroelastic ceramics with an initial random orientation.21

The maximum density in the saturation distribution of 3 mrdresults from the three possible non-1801 domain orientations intetragonal ceramics. Electric field amplitudes below 1.0 kV/mmduring electrical poling generate maximum 002 density values ofo1.25 mrd. Because these experiments were conducted usingneutron diffraction, this is evidence of non-1801 domain switch-ing in the bulk of the material under application of static, sub-coercive electric fields. When the electric field amplitude duringelectrical poling exceeds the coercive field (1.0 kV/mm),

the maximum pole density value increases to the range 1.5 mrdof002o2.0 mrd. The presentation of the measured pole densitydistribution with the maximum saturation distribution high-lights opportunities for optimization in the degree of non-1801domain switching achieved during electrical poling. The strainassociated with domain switching and the mechanically con-strained boundary conditions of individual grains within the ce-ramic limit switching within individual grains and therefore limitthe degree of preferred orientation that can be attained.4851

Application of mechanical fields during the electrical poling pro-cess, or electromechanical poling, has recently shown promisefor attaining greater domain switching during this process.52,53

Qualitatively, the evolution of preferred orientation duringelectrical poling (Fig. 5) agrees with the trends observed inmacroscopic strain and d33 (Fig. 4). In bulk ceramics, the devel-

opment of a nonzero d33 coefficient is a function of 1801 andnon-1801 domain switching, both of which can lead to the devel-opment of a net electric dipole. 1801 domain switching is typicallyconsidered to be the primary contributor to this polarizationdevelopment. However, the non-1801 domain switching distribu-tions measured in Fig. 5 correlate with the evolution of d33 inFig. 4, indicating a likely concurrent progression of both 1801 andnon-1801 domain switching. Evolution of both types of domainswitching may progress in parallel, albeit within different grainswith different orientations as a means of balancing both mechan-ical strain and electrical charge at the domain wall interface.

Measurements of crystallographic texture are useful for qual-itative correlations to measured properties and material behav-ior. However, a benefit of quantitative texture measurements isthe capability to relate single-crystal properties and the poly-

crystalline ODF to bulk anisotropic properties (Fig. 1). For ex-ample, the domain distributions described here are related to the

Fig. 4. Measured Berlincourt d33 and poling strain evolution as a func-tion of the applied electric field during poling. Poling strain results fromnon-1801 domain switching and the evolution of intergranular elasticstrain. The domain-switching component is calculated from the domainorientation distributions (Fig. 5) using Eq. (2).

0 15 30 45 60 75 90

0.0

0.5

1.0

1.5

2.0

2.5

3.0

Random

f002[mrd]

[degrees]

Field [kV/mm]

1.75

1.501.25

1.00

0.75

0.50

Saturation

Fig. 5. 002 pole density (f002) distributions of tetragonal lead zirconatetitanate as a function of poling electric field. The units of f002 are mrd(Panel A). The solid line labeled saturation indicates the theoretical sat-uration distribution from Jones et al.21



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macroscopic poling strain because the measurements quantita-tively capture the degree of interchanging (switching) of thecrystallographic a and c lattice parameters in every possiblegrain orientation. This textureproperty relationship is best un-derstood by considering a grain orientation in which the pseudo-cubic crystal axes are coincident with the sample axes. The graincontains three non-1801 domain variants. Such a grain yields amacroscopic strain of 0.67(ca)/a if the two less-preferred do-main orientations switch entirely to the orientation where [001]is parallel to the electric field. For unsaturated switching, the

value of 0.67 and the associated strain are lower. For switchingin grain orientations that are not perfectly oriented with respectto the electric field, a second-rank tensor transformation yieldsan additional cos2a dependence, where a is the angle betweenthe axis undergoing lattice constant interchanging and the straindirection. An averaging of this domain-switching strain over allpossible grain orientations is represented as an integral over thetwo pole figure angles a and b, yielding21

SZZ S0lattice1

2p

Zp=2a0

Z2pb0

Df001a;b cos2 a

sina dadb (2)

Through Eq. (2), the change in the 001 pole density distribution(Df001) can be related to the macroscopic strain resulting fromnon-1801 domain switching. For the textures represented inFig. 5, the calculated component of the macroscopic strain re-sulting from non-1801 domain switching is shown in Fig. 4. At1.0 kV/mm and below, the measured poling strains and the cal-culated strains from non-1801 domain switching are compara-ble. Above 1.0 kV/mm, the calculated strains from non-1801domain switching comprise just over half of the measured polingstrain. This discrepancy above 1.0 kV/mm is contributed by theevolution of intergranular elastic strains. Some prior studieshave shown that the measured 111 lattice strains parallel to theloading axis can serve as an indicator of internal stress duringelectrical or mechanical loading.54,55 Hoffmann et al.47 have re-ported the 111 lattice strain hysteresis and observed the reman-

ent strains after similar loadings to be approximately 0.4%0.6%. These strains contribute to the difference between ourmeasured strain and calculated domain-switching strain values.In other words, the total measured macroscopic strain is a com-bination of both non-1801 domain switching (a small volumefraction of the material in which the a and c lattice parametersare interchanged) and intergranular elastic strains.

The extraction of the domain-switching strain componentfrom non-1801 domain distributions are one possible outcomeof coupling texture measurements and macroscopic properties.We have used this comparison in ferroelastic textures induced bymechanical compression46 and domain-switching strains pro-duced during higher frequency, subcoercive electric field cy-cling.56,57 The most significant error in such an approach isthat the lattice parameters are assumed to be constant. In me-

chanical compression, there is more elastic strain58 and thereforelarger errors in the application of Eq. (2).46 Ideally, coupling of alattice strain distribution function with a lattice ODF, althoughmore intensive, would produce a more accurate strain estimate.In the absence of such an approach, these efforts at coupling themacroscopic strain to texture remain a quantitative link betweentexture measurements and macroscopic properties of piezoelec-tric ceramics.

Figure 5 suggests that the highest degree of domain switchingis expected at the highest applied electric fields during poling.The ferroelectric hysteresis loops in Fig. 3 also imply that thereis some relaxation as the field is removed. The temperature atwhich poling is performed plays a similarly important role in theachievable degree of domain switching. As a piezoelectric ce-ramic cools from an elevated poling temperature, the increase in

tetragonality (c/a) and elastic stiffness can promote intergranu-lar elastic stresses. These stresses compete with a decreasing do-

main wall mobility to establish the final domain configurationfound at room temperature after poling.

As stated earlier, small changes in the composition and do-pant can strongly influence the behavior of these materials, in-cluding tetragonality and stiffness. Chang et al.59 have recentlyused thermal depoling experiments to demonstrate the changingmagnitudes of tetragonality and domain wall stability as a func-tion of temperature and dopant. These results are redrawn inFigs. 6 and 7. Thermal depoling is, in essence, the reverse effectof the cooling that occurs after poling at elevated temperatures.For the soft PZT ceramic reported thus far, the preference fornon-1801 domain orientations parallel to the poling axis initiallyincreases with increasing temperature (Fig. 6). However, thetetragonality decreases continuously with temperature until theCurie temperature is reached (Fig. 7). In contrast to that of thesoft PZT ceramic, the domain wall mobility of a Sr-doped (hard)PZT ceramic decreases as a function of temperature, although it

exhibits similarly decreasing tetragonality. A modified leadtitanate (PT) ceramic exhibits a smaller degree of domain ori-entation in the as-poled state as compared with the other ma-terials (T5251C in Fig. 6). The reduced domain wall mobility inthis material compared with the PZT compositions has also beenexpressed in its mechanical stressstrain behavior and reducedfracture toughness enhancement with crack extension.60 For thisPT ceramic, there is a small but steady increase in the preferencefor domain orientations parallel to the poling axis with increasing

0 50 100 150 200 250 300 3501.0

1.1

1.2

1.3

1.4

1.5

1.6

soft PZT

hard PZT

PT

f002[mrd]

Temperature [Celsius]

Fig.6. 002 pole density (f002) parallel to the poling axis for three differ-ent ceramic compositions measured in situ as a function of temperature,after Chang et al.59

0 100 200 300 4000.99

1.00

1.01

1.02

1.03

1.04

1.05

soft PZT

hard PZT

PT

c/aratio


Fig.7. Change in the tetragonality (c/a ratio) parallel to the poling axisfor three different ceramic compositions measured in situ as a function oftemperature, after Chang et al.59



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temperature (Fig. 6). Because this ceramic exhibits a strong de-crease in tetragonality with temperature (Fig. 7), this behavior isattributed to a reduced domain wall mobility resulting from dop-ing that is internally strengthened with increasing temperature.

Figure 8 shows the results of a similar in situ measurement oftextures generated initially by mechanical grinding of the softPZT and PT compositions. These samples were then subjectedto thermal cycling in increments of 501C to temperatures justbelow the Curie temperature. The data shown are for the heat-ing cycles up to 2501C only as a resolution of the peaks is diffi-cult at temperatures exceeding 2501C. For each of the two

materials, there is an increase in the surface domain textureswith increasing temperature. These experiments were repeatedtwo additional times and repeatability was demonstrated with-out substantial loss of the mechanically induced surface domaintexture. These results demonstrate that domain alignments canintensify as the elastic constants soften and the tetragonalitydecreases with increasing temperature. The strong degree of ini-tial domain texture relative to those achieved by electrical poling(Fig. 6) suggests a strong mechanical influence from surfacegrinding. This strong mechanical influence persists through re-peated thermal cycling and thermal depoling at temperaturesapproaching the Curie temperatures. In fact, the same materialsretain domain texture following brief excursions above theCurie temperature.61 Investigations of this type enable a newframework in which to investigate, understand, and describe the

role played by dopants that are designed to help pin or depindomain walls.

III. Textured Bismuth Titanate Oxides

The prototypical bismuth titanate structure, Bi4Ti3O12, containstwo pseudo-perovskite blocks separated by Bi2O2

21 layers, or theAurivillius-oxide crystal structure.28 Bismuth titanate ceramicsare preferred for high-temperature sensors because the structureremains piezoelectric at higher temperatures than in other com-mon ferroelectric ceramics.62 However, the piezoelectric d33 co-efficient is modest in bismuth titanate.63 The highly anisometric,plate-like morphology of bismuth titanate expressed in aniso-metric single crystals64 is easily exploited in engineered processes

to generate crystallographic texture, an established approach toincrease d33 in a preferred sample direction.

The earliest process used to induce a crystallographic texturein bismuth titanate ceramics was hot forging,23 in which a uni-axial force is applied to the ceramic at or near the sinteringtemperature, reorienting the (001) planes normal to the appliedforce. In the resulting texture, the maximum piezoelectric re-sponse is observed perpendicular to the pressing direction, in the(001) plane, because the spontaneous polarization direction isparallel to [100] and non-1801 domain switching occurs between[100] and [010]. Although hot forging is still being investigat-ed,27,65 tape casting was explored as a more commercially viable,

high-capacity process. The first tape-casting process used pow-der composed completely of platelet-shaped particles6668 andthe obtained textures are analogous to those produced by hotforging. The platelet-shaped particles are preferentially orientedparallel to the tape-casting plane by viscous forces during theshearing process (Panel C), promoting a 001 fiber texture aboutthe casting plane normal.

Because highly anisometric platelet-shaped particles are syn-thesized by a more complex route than conventional calcination,namely molten salt methods, more recent tape-casting work haslimited the quantity of platelets by including only a small frac-tion within a fine matrix powder.22,26,74 The larger platelets,preferentially oriented by tape casting, grow at the expense ofthe matrix powder during sintering, leading to a macroscopicfiber texture in the ceramic. This texturing mechanism has been

called templated grain growth (TGG), with the platelet-shapedparticles serving as templates for epitaxial grain growth throughthe fine matrix grains.75 A schematic of the tape-casting processand the resulting texture in the sintered ceramic are shown inFig. 9(a).

(1) Experimental Procedure

Textured ceramics were fabricated using templates of composi-tion Bi4Ti3O12 and a commercial, calcined Na0.5Bi4.5Ti4O15 ma-trix powder (K15; Piezo Technologies) in discrete fractionsranging from 0 wt% (untemplated) to 25 wt%. Details of theprocessing can be found in Jones.76 The Na0.5Bi4.5Ti4O15 struc-ture contains three pseudo-perovskite blocks separated byBi2O2

21 layers, and Na substitutes for Bi evenly and complete-

ly only in the pseudo-perovskite blocks.77

The ODF of the Na0.5Bi4.5Ti4O15 phase was determined usingboth neutron and X-ray diffraction in methods detailed earli-er.78 Neutron diffraction was used to measure the global texturein the bulk ceramic using the texture diffractometer HIPPO. Todescribe the texture on as-sintered and polished surfaces, an areadetector diffractometer was utilized using CuKa incident radi-ation. For both instruments, the software MAUD41,42 was usedto calculate the ODF as represented by a fourth-order SH func-tion by full-pattern Rietveld refinement of the obtained diffrac-tion patterns (Panel B). The recalculated 001 pole figures of theNa0.5Bi4.5Ti4O15 phase extracted from the ODF provide the dis-tribution of the 001 crystallographic pole throughout the entiresample orientation space.

For property and diffraction measurements, samples were cut

with different orientations relative to the sample axes. In bis-muth titanate, the tape-casting process produces a ceramic witha fiber symmetry axis parallel to the tape-casting normal direc-tion (ND). Within the tape-casting plane, the two directions de-fined by the tape-casting geometry are the tape-casting direction(TCD) and the transverse direction (TD), although they are in-distinguishable in both diffraction and property measurementsbecause the sample symmetry is transversely isotropic. Uniquesamples were cut in which measurements were taken both par-allel to the TCD and the ND. The samples were polished usingdecreasing grit coarseness to a final alumina grit size of 0.05 mm.Sputtered electrodes were applied to both major faces of thesamples and were thin enough for diffraction from the substrate.Electrical poling was performed in an oil bath heated to tem-peratures in the range 15012151C for 40 min. A temperature of

2151C and an electric field of 7.5 kV/mm were used for thesample on which diffraction measurements were made to deter-

50 100 150 200 250

1.6

1.7

1.8

1.9

2.0

2.1

2.2

2.3

soft PZT, 1

soft PZT, 2

soft PZT, 3

PT, 1

PT, 2

PT, 3f002[mrd]


Fig. 8. Domain alignment expressed in the unit mrd for soft lead zir-conate titanate (PZT) and a lead titanate (PT) material during repeatedthermal cycles (1, 2, and 3) of in situ heating to temperatures just belowthe Curie temperature. The materials have been ground to introducesurface residual stresses and initial domain textures. Although the sam-ples were heated to just below the Curie temperature of 3501C, the datashown are limited to 2501C due to the inability to quantify accurately thedegree of alignment in mechanically ground domain textures above this

temperature.



9/18

mine domain textures. These domain measurements usingdiffraction were conducted at the National Synchrotron LightSource (NSLS), beamline X18A, using a wavelength of 1.240 A

and a Ge (111) crystal analyzer detector on the diffractedbeam.20 This instrumental setup was required to resolve thesmall difference between the (100) and (010) lattice planes.79 Thesamples for which the piezoelectric d33 coefficient was measuredwere poled using an electric field of 6.5 kV/mm, and the d33coefficient was measured on a Berlincourt d33 meter 24 h afterpoling.


Figure 10 shows a micrograph of a section of a pyrolyzed, tem-plated sample. The templates can be identified as platelet-shapedparticles with a width in excess of 10 mm. Texture in the bulk as afunction of template fraction was measured using neutrondiffraction. The correlation between template fraction, density,and texture is shown in Fig. 11(a). The maximum value of the001 pole figure is reported in this paper as a texture indicatorbecause the pole figure is a smooth and broad distribution thatdoes not change unexpectedly with processing condition. Thepole figure is given explicitly in Jones et al.78 where it is com-pared with pole figures produced from other approaches.

According to Fig. 11(a), both density and texture increasewith increasing template fraction. Between 0% and 25% tem-

plate fraction, the maximum value of the 001 pole figure in-creases from 2.6 to 4.1 mrd, while the relative density increases

from 91% to 95%. Figure 10 shows that the templates are pref-erentially oriented during the tape-casting process, consistentwith the generally accepted theory of particle alignment in shear-based processes, which describes that the interaction of platelet-shaped particles leads to their mutual parallelism.67 Panel Cdescribes this process more completely. The initial preferred ori-entation of the templates then directs texture development of thematrix phase by epitaxial or topotaxial growth. Increasing thefraction of templates increases the sintered bulk texture becausethe templates possess an initial preferred orientation.

Prior investigators have used the Lotgering degree of orien-

tation indicator to describe the texture. Because we haveexplored the relationship between the Lotgering degreeof orientation indicator and the multiple in intensity ofthe 00l peaks,77 it is apparent that the textures produced inthis work are modest compared with those in the earlierliterature.2224,26,27,6568,74 Nonetheless, this modest degree oforientation still proves to be valuable. Recent numerical meth-ods demonstrate a high piezoelectric response in microstructureswith modest degrees of texture; the greatest piezoelectric re-sponse in textured BaTiO3 is found in microstructures with amaximum of 2.9 mrd.80

The residual texture observed in untemplated samples with amaximum of 2.6 mrd is obtained without the requirements oftemplate synthesis and incorporation. An untemplated, modestresidual texture (Lotgering factor

%30%) was also previously

acknowledged in Bi4Ti3O12 processed by TGG.74 To explore theuntemplated texture evolution in greater detail, quantitative

Panel C: Tape Casting and Texture Development

Tape casting ceramic powders with the inclusion of shaped seed particles is an effective way to induce grain textures in ceramicmaterials. While highly anisotropic ceramics can be created in this way, most investigations focus only on either the seed particleshape or the seed particle concentration in the slurry.6972

A thorough examination of the flow behavior of a ceramic slurry during tape casting was conducted by Kim et al.73 (Fig. C1).They assumed that the slurry would behave as a Newtonian fluid in order to simplify the analysis. Deformation during a processsuch as tape casting in any fluid can be due to both viscous- and pressure-driven forces. Kim et al. used a parameter,P, to quan-tify the ratio between the pressure forces to the viscous forces. Utilizing all process conditions and slurry viscosity, it is possible tocalculate P for a given tape-casting experiment for the following geometry from the equation

P DPH2

2mLUC 1

DPH2 is the pressure driven forces and 2mLU the viscous driven forces

where DP is the pressure exerted by the slurry head (DP5rslurry g Hslurry), H is the blade gap used, m is the viscosity of theslurry, L is the length of the doctor blade, and Uis the casting velocity. The ratio of the pressure forces to viscous forces determinesthe flow characteristics of the slurry. Viscous forces are the source of shear behavior necessary for particle rotation and alignment.Therefore, an increase in the ratio of viscous forces will result in an increased degree of particle orientation. From Kim et al.sanalysis, an increase in either the slurry viscosity or casting velocity will effectively increase the amount of viscous-driven forces.This increase in viscous-driven forces is expected to increase preferred orientation. Although the formulation used by Kim et al.was developed for Newtonian fluids, the effects of viscosity and casting velocity are expected to have similar effects on texture intape casting of even non-Newtonian fluids. From this analysis, three independent methods for increasing texture in tape-casting

systems can be devised: increasing the casting velocity, increasing the slurry viscosity, and increasing the template concentration.

H

L

Hslurry

x=L x=0

y

U

H xHo

HH1

Fig. C1. Casting geometry described in Kim et al.73



10/18

texture analysis using surface-sensitive X-ray reflection geometrywas used. The maximum value of the 001 pole figure on both thetop and bottom as-sintered surfaces and a polished internal sur-face are plotted with the relative density as a function of sinteringtemperature in Fig. 11(b). Little densification occurs at 10001C,only 1501C from the maximum sintering temperature. The 56%relative density at this sintering temperature is only slightly largerthan the relative density of the pyrolyzed ceramic, 51%. Densifi-cation accelerates at 11001C and plateaus near 11251C.

With increasing sintering temperature, preferred orientationon the as-sintered surface develops more rapidly than on theinternal polished surface. Because the degree of orientation at asintering temperature of 10501C is nearly equivalent at the sur-

face and in the bulk, it cannot be presumed that the texture inthis system is more significantly predisposed at the surface bysuch effects as particle settling (at the bottom surface) or particlereorientation from slurry surface tension (at the top surface).This is consistent with viscous forces as the mechanism of par-ticle rotation and alignment as described in Panel C. In fullysintered ceramics, however, it is apparent that the surface tex-ture is stronger than in the bulk. Because the surface is not ini-tially more predisposed to sources of texture than the bulk, thepossible mechanisms for the stronger surface texture are limitedto: (1) preferential growth of particles initially oriented parallelto the surface, (2) reorientation of particles early during thesintering process, or (3) a combination of preferential growthand reorientation mechanisms. A determination of the actingmechanism cannot be distinguished from these measurements.

However, the driving force for surface texture enhancement, re-gardless of the mechanism, is the promotion of relatively low-energy (001) surfaces.

Untemplated ceramics, or ceramics containing 0% templateparticles, were electrically poled for further domain texture andproperty measurements. The initial preferred orientation beforeelectrical poling is shown in Fig. 12(a). Recall for orthorhombicbismuth titanate such as Na0.5Bi4.5Ti4O15 that the directions ofpossible spontaneous polarization relative to the paraelectric

tetragonal unit cell are [100] and [010].77 High-resolution synch-rotron X-ray diffraction was used to characterize the domaintexture, or the preference for the [100] (parallel to the sponta-neous polarization) at the expense of the [010]. The volumefraction of the 100 domain orientation20 was measured as afunction of angle relative to the electric field by evaluating the(200) and (020) peaks. In initially textured ceramics, a represen-tation of domain switching by the value f200 calculated from Eq.(B-2) would imply a complete description of preferred orienta-tion. However, Eqs. (B-1) and (B-2) do not account for theinitial preferred orientation induced by grain-orientationprocessing because they are formulated on a relative change inintensities after application of an electric field. Equations (B-1)

and (B-2) are therefore reserved for initially randomly orientedceramics. For initially textured ceramics, the domain switchingcan instead be expressed by the volume fraction of the preferreddomain orientation, a measurement that is independent of theinitial preferred orientation of the grains. In orthorhombic bis-muth titanate, this volume fraction is given as20

Zh00 Ih00=I

Rh00

Ih00=IRh00 I0h0=IR0h0

12

(3)

where the relationship between the domain-switching fractionZh00 and the absolute pole density value fh00 calculated from Eq.(B-2) for initially randomly oriented ceramics is given by81

fh00mrd 2Zh00 1 (4)

The domain-switching fraction induced by electrical poling ininitially textured ceramics and calculated by Eq. (3) is shown inFig. 12(b).

Figures 12(a) and (b) illustrate the presence of both the initialcrystallographic texture of the grain structure and poling-induceddomain texture, respectively. Consideration of both texture con-tributions is necessary for interpreting the resulting propertiesbecause both forms of preferred orientation contribute to the ab-solute volume fraction of any given domain orientation. In otherwords, only a small absolute number of domains can be aligned inany specimen direction where the initial grain orientations pro-vide few possible domain orientation variants; such consider-

ations exist regardless of the domain-switching fraction. Likewise,even in a textured ceramic with nearly perfect orientation, thevolume fraction of certain domain orientations can be restrictedby the domain-switching fraction. The implication of this con-sideration is that the ferroelectric and piezoelectric properties arederived from contributions by both the grain orientation distri-bution and the domain orientation distribution.

In bismuth titanate ceramics with an initial preferred orien-tation of the grains, the grain fgrainhkl and domain-switching(Z200) orientation distributions can combine multiplicatively todescribe the total preferred orientation of the 200 pole f200 by81

f200 fgrain200 2Z200 1 (5)

where the 2Z20011 component transforms the domain-switching

fraction (Z200) into the unit mrd as described by Eq. (4).81 Inother words, the initial preferred orientation of the 200 pole

[001]

[001] [001]

[001]

[001]

[001]

[hk0]

(b)(a)

Fig. 9. Schematic of the tape-casting process and the resulting texture in the sintered ceramic for 001-oriented, platelet-shaped Bi4Ti3O12 templates (a)and 001-oriented, needle-shaped PbNb2O6 templates (b).

Fig.10. Section of a pyrolyzed tape containing 5% Bi4Ti3O12 templatesand a Na0.5Bi4.5Ti4O15 matrix powder. The tape-casting plane is hori-zontal in the image and normal direction is vertical.



11/18

resulting from tape casting (grain texture) is enhanced by poling(domain texture) and the preferred orientation induced by bothindependent processes combines multiplicatively to completelydescribe preferred orientation in ceramics with both texture

components.The final pole figure representing the degree of preference for

the 200 pole in the poled ferroelectric material is shown inFig. 12(c). The maximum 200 pole density value is approxi-mately 2.2 mrd. Thus, the process of electrical poling increasesthe 200 pole density value parallel to the electric field from 1.5mrd (Fig. 12(a)) to 2.2 mrd (Fig. 12(c)). The final state of themicrostructure as shown in Fig. 12(c) could be obtained bymeasuring 200 pole figures directly on the poled ferroelectricmaterial. However, the independent measurement methods de-scribed here are required to assess independently the grain anddomain orientation contributions to the final state of preferredorientation. Here, pole figures of the initially unpoled ceramicwere first generated, the domain orientation distributions weremeasured by evaluating the relative intensity of the 200 and 020

diffraction peaks, and the final state was calculated as a multipleof the two components.

By measuring these two forms of preferred orientation inde-pendently, we have also been able to demonstrate the influenceof initial grain orientation on the degree of non-1801 domainswitching. Jones et al.20 demonstrate that the maximum value ofdomain orientation when poled parallel to the tape-casting planeis Z20050.18 (Fig. 12(b)). However, no measurable degree ofdomain orientation was apparent when poled perpendicular tothe tape-casting plane. Thus, because non-1801 domain switch-ing involves mechanical straining or deformation of grains, thepreferred orientation or alignment of the individual componentstrains influences the degree of domain switching.

The piezoelectric d33 coefficient as a function of orientationand poling temperature is shown in Fig. 13 for samples con-taining 0% templates (untemplated) and range from 5 to 10 pC/N when poled parallel to the ND and from 19 to 30 pC/N when

poled parallel to the TCD. The randomly oriented ceramic poledunder equivalent poling conditions exhibits a piezoelectric d33coefficient between the values measured in the two directions ofa textured ceramic:B15 pC/N. A large temperature dependenceof poling on the d33 coefficient is apparent parallel to the TCD,the in-plane direction of the casting process. Parallel to the ND,however, the values are much smaller and less dependent ontemperature. The smaller values are the result of fewer favorablegrain orientations. In contrast to tetragonal or rhombohedralperovskite symmetries, the orthorhombic material here exhibitsonly two possible ferroelastic distortion directions.21 Therefore,grains with a [001] direction parallel to the electric field have lessof a tendency for ferroelectric switching and, therefore, contrib-ute less to the piezoelectric response of the bulk ceramic.

We have previously suggested that the easy realignment of the

ferroelastic distortion directions within the tape-casting planemay contribute to the strong dependence of d33 on direction.

20

Thus, the grain texture leads to easier domain switching in thetape-casting plane. This can then influence both the attainabledegree of switching during electrical poling as mentioned previ-ously and also promote possible extrinsic contributions to thed33 coefficient measured in this direction. With these mecha-nisms in mind, the temperature dependence of the d33 in theTCD may result from thermally activated ferroelectric domainwall motion in the tape-casting plane during electrical poling.There is a reduced temperature dependence when poled perpen-dicular to the tape-casting plane because domain wall motion isnot promoted in this direction.

0 5 10 15 20 2560

70

80

90

10(a) (b)0

2.0

2.5

3.0

3.5

4.0

4.5

5.0

RelativeDensity[%]

Template Fraction [weight percent]

950 1000 1050 1100 1150 12000

20

40

60

80

100

0.0

2.0

4.0

6.0

8.0

10.0

RelativeDensity[%]

Sintering Temperature [Celsius]

maximum(f001)[mrd]

maximum(f001)[mrd]

Fig.11. (a) Influence of template fraction on relative density (& ) and degree of preferred orientation () sintered at 11251C. Texture of the bulkceramic quantified using neutron diffraction measurements. (b) Influence of sintering temperature in an untemplated sample on preferred orientation ofthe top (n), bottom (H), and a polished internal surface (), and the relative density (& ). Texture of the as-sintered and polished internal surfacesquantified by surface-sensitive X-ray diffraction measurements.

Fig.12. (a) 200 pole figure of a textured bismuth titanate ceramic in units of mrd (redrawn from Jones et al.77). The tape-casting plane is parallel to thehorizontal plane of the pole figure. (b) Degree of domain switching (Z200) induced from electrical poling (from Jones et al.

20). (c) Resultant 200 pole figureafter poling considering the contributions of both preferred grain and domain orientations in units of mrd (after Jones et al.81). All plots are equal areaprojections.



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IV. Textured Lead Metaniobate Oxides

Ceramics of lead metaniobate, or PbNb2O6, find use where theirelevated Curie temperatures (%5601C), high d33/d31 ratio (%6),and low mechanical quality factor ( %15) can be exploited. Theferroelectric phase exhibits an orthorhombic tungstenbronzecrystal structure2931 where the a and b unit cell dimensions aresubstantially larger than the c dimension (a517.63 A , b517.92A , and c53.87 A ) and the b axis is defined as the axis of fer-roelastic elongation and is parallel to the spontaneous polariza-tion.30,82 Switching by 901 and 1801 domains occurs between[100], 100, [010], and 010, such that four possible coplanarpolarization directions exist.83 Similar to orthorhombic bismuthtitanate, polarization is confined to the ab plane of the crystal.

When poled, polycrystalline ceramics of lead metaniobateexhibit a modest longitudinal piezoelectric coefficient, d33 %80pC/N. Previous studies have shown that inducing crystallo-graphic texture before poling can lead to improvements in pi-ezoelectric properties.69,84 The inclusion of seed particles with ahigh morphological aspect ratio in a tape-casting process canallow for the development of grain textures through processessuch as TGG. Additionally, modifications to the tape-castingprocess itself can affect the degree of texture developed duringthe process. Here, texture developed in lead metaniobate islinked to variations in the tape-casting process. These resultsare compared with preferred domain orientation that is devel-oped due to the application of an electric field and the resultingpiezoelectric properties in initially textured and poled ceramics.

(1) Experimental ProcedureFor domain orientation measurements on initially untexturedceramics, commercial lead metaniobate ceramics (K81; PiezoTechnologies) were obtained in both an unpoled and poled con-dition. The commercial poling conditions used were 3.94 kV/mm for 25 min at a temperature of 1401C. Samples for X-raydiffraction were polished to a fine grit (1 mm) on the surfaceperpendicular to the poling direction in order to remove thesample electrode. Polishing the unpoled material to this finishproduces X-ray diffraction data that are indistinguishable fromsamples annealed above the Curie temperature.

Two methods were used to measure domain textures frompoled lead metaniobate using diffraction techniques: compari-son of (hk0)-type peaks using synchrotron X-ray diffractiondata and pole figure inversion methods using neutron diffraction

data and the Rietveld method. Both of these methods are de-scribed in Panel B. The 150/510 peak doublet was evaluated here

using a synchrotron X-ray source. Measurements of the peakdoublet were obtained at tilt angles (a) from 01 to 701 in 51 in-crements using Eq. (B-2), where intensities from the unpoledsample correspond to values of IRhkl. Domain textures were alsomeasured by whole pattern refinement via the Rietveld methodusing the neutron diffractometer HIPPO. The structure was firstrefined using data from an unpoled specimen and a startingstructure equivalent to that reported by Labbe et al.85 Domaintextures were represented in poled samples by using a second-order SH texture model with fiber symmetry enforced about the

poling axis. The details of these approaches are described inPanel B and Key et al. 86 and Iverson et al.87

Tape casting was performed using seeds to template preferredorientation. Acicular, single-crystal seed particles of the compo-sition PbNb2O6 were grown from a melt following the methodproposed by Li et al.88 These seeds were cast with a commercial,calcined PbNb2O6 matrix powder (K81; Piezo Technologies).For all formulations, a blade gap of 300 mm was used with aparallel doctor blade.

Using a rationale supported by Panel C, several variations ofthe tape-casting slurry were devised. Seed particle concentra-tions of 0%, 10%, and 20% by weight of ceramic were used withlow-viscosity slurries. The 10 wt% slurry was then cast at ratesof 20 and 80 cm/min, while all other slurries were cast at only20 cm/min. The high-viscosity slurries were cast only using a

5 wt% seed particle concentration at a casting rate of 20 cm/min.Increasing the casting velocity and slurry viscosity increases theshear behavior of the slurry, which can be tracked by quantify-ing the P value for each individual slurry.89

The general viscosity profiles for the two slurries containing aseed particle concentration of 5 wt% were measured using aBrookfield viscometer (Brookfield Engineering, Middleboro,MA). The shear rates developed during casting are estimatedto be the ratio of the blade gap to the casting velocity. Bothslurries exhibit shear thinning behavior and therefore the viscos-ities during casting can be estimated by fitting a best-fit line to theviscosity data. Using the estimates for the shear rate, the viscos-ities at casting are estimated to be: 6.5 Pa s for the high-viscosityslurry, 2.8 Pa s for the low-viscosity slurries cast at 20 cm/min,and 2.0 Pa

s for the low-viscosity slurry cast at 80 cm/min.

Green tapes were cut and laminated into stacks of 1020.These laminates were pressed at 6.9 MPa using heated platens ata temperature of 381C. The samples were heated to 6001C over 3h and held at this temperature for 2 h to burn out the binder.Temperature was then decreased to room temperature over a2-h span. For firing, samples were ramped to 12401C over 12 h,held at this temperature for 30 min, and furnace cooled to roomtemperature. Before all diffraction experiments, sample faceswere polished to a fine grit (1 mm). For property measurements,samples of the high-viscosity 5 wt% slurry were electricallypoled at a field of 3.94 kV/mm and a temperature of 1401 for25 min. These samples were poled parallel to the ND, TCD,and TD.

To describe the crystallographic texture of the grains, the Ri-etveld method was used to calculate ODFs from measured neu-

tron diffraction spectra using the instrument HIPPO andmethods described earlier. The ODF was represented as a sec-ond-order SH function and orthorhombic sample symmetry wasenforced. Because the strength of the induced texture is rela-tively weak, higher order spherical harmonics are not necessaryin representing the ODF.


In a randomly oriented ceramic, the volume fraction of domainswith crystallographic [h00] and [0k0] directions oriented in anygiven sample direction would be equal. Therefore, both the h00and 0k0 pole densities are 1 mrd. Changes from this value uponpoling indicate an increase in domain texture relative to a crys-tallographic pole. For an initially randomly oriented ceramic,

the maximum allowable 0k0 pole density parallel to the polingdirection is 2 mrd.21 This value would occur only if all 901

Fig.13. Piezoelectric d33 coefficient as a function of sample directionand poling temperature of textured Na0.5Bi4.5Ti4O15 obtained withoutthe use of templates and initially untextured, randomly oriented ceram-ics, from Jones et al.20 The tape-casting direction (TCD) is in the tape-casting plane of the sample in Fig. 9(a) and the normal direction (ND) isdirected out of the tape-casting plane.



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domains were reoriented. Because peaks of pure (h00) or (0k0)are either low in intensity or overlapped by other peaks in thisstructure, the use of direct peak intensity comparisons is limited

to those of (hk0) type, where hak. The (150) and (510) werechosen because there is a relatively shallow angle (B111) be-tween these crystal poles and the respective crystal axes, [100]and [010]. However, any set of peaks with consistent c compo-nents and varying a and b components can be used for quan-tifying domain textures.21

The 150 pole density distributions of an initially randomlyoriented lead metaniobate ceramic calculated using two differentmethods are shown in Fig. 14. One method involves domainorientation measurements at discrete sample orientations usingX-ray diffraction in reflection geometry and a calculation ofdomain orientations based on relative peak intensity changes.The second method involves pole figure inversion methods usingneutron diffraction data and a representation of the ODF usinga series expansion of spherical harmonics. The pole density dis-

tributions generated by the two methods exhibit a difference intheir absolute values and a difference in scatter. Domain densitydistributions calculated using the synchrotron diffraction dataare discrete because values are calculated from intensity mea-surements in discrete sample directions, whereas pole figuresobtained from an ODF are continuous because the ODF is rep-resented as a continuous SH function (similar to that of Fig. 5).There is more scatter in the discrete data because each value iscalculated individually, whereas pole figure inversion methodsutilizing series expansion representations produce data that are

continuous and provides an interpolation between measureddirections. Such an interpolation is commonly used as a filter forexperimental noise in measured intensities.

The two methods show agreement in that in both cases, themaximum 150 pole density value is parallel to the poling direction(a501) with decreasing values at higher angles to the poling di-rection. Differences between absolute values can be attributed todifferences between the penetration depth and sample volumeexamined during diffraction. The increase in 0k0-type texturequantified in all methods is attributed to an increase in the volume

fraction of domains oriented such that the angle between thepolarization direction and the electric field is minimized.Seed particles are used to fabricate textured ceramics.

Figure 15 shows a micrograph of these particles, which demon-strates a distinct elongated rectangular shape. The long axis ofthese particles is parallel to the crystallographic [001], with thecrystallographic [100] and [010] parallel to the shorter particledimensions. These particles were added to two slurries of differ-ent viscosity formulated after Galassi et al.90 During casting, theshear behavior of the slurry acts to align these particles withinthe tape-casting plane (Fig. 9(b)). These particles act as tem-plates for anisotropic grain growth in the fired ceramic. With thelong axis of the particles parallel to the crystallographic [001],general 001-type textures are expected to develop parallel to theTCD. Subsequently, 100- and 010-type textures are expected to

develop normal to the tape-casting plane.In addition to the template concentration, the degree of pre-

ferred orientation is dependent on other factors as described inPanel C. Slurry deformation during casting is composed of bothshear-driven and pressure-driven forces. Particle rotation andorientation is dependent on the amount of shear-driven forces.Therefore, if the amount of shear-driven forces occurring duringcasting is increased, the amount of particle orientation shouldalso be increased. With greater particle orientation before firing,stronger textures can be achieved when the ceramic is fired.

Accounting for the casting geometry and slurry viscosity,slurry deformation was determined to be dominated by shear-driven forces.89 This means that the inclusion of even smallamounts of seed particles should result in the development ofpreferred orientation.

A metal-rolling type, orthotropic sample symmetry resultswith a specific TCD and preferred normal plane correspondingto the tape-casting plane. The pole figures are recalculated fromthe ODF and are reproduced in Fig. 16. The 010 and 001 polefigures are shown for each of the investigated tape-casting vari-ations. With the exception of the 0 wt%, low-viscosity slurry, allof the laminates develop a maximum 010 texture parallel to theND and a minimum 010 texture parallel to the TCD. This be-havior inverts in the 001 pole figures with maxima in the TCDand minima in the ND.

During casting, shear forces will act to align seed particlesrelative to the tape-casting plane. The long axis of the particles isparallel to the [001] crystallographic direction and the [100] and[010] directions are parallel to the short particle direction. Dur-ing casting, the templates are subject to shear forces that rotate

the particles and align them within the tape-casting plane. Asillustrated in Fig. 9(b), alignment of the square-beam templateparticles in the tape-casting plane results in the development of[001]-type preferred orientation in the TCD and [100] and[010] preferred orientations in the normal and transverse direc-tions.87 This texture development is related to the morphology ofthe template particles and the degree of shear behavior devel-oped during casting. The pole figures in Fig. 16 correlate withthese predictions: a 001-type preferred orientation parallel to theTCD and a 010-type preferred orientation parallel to the ND.

Increasing seed particle concentration (Figs. 16(a)(c)) duringcasting increases the number of templates that become alignedduring casting, resulting in increased preferred orientation in theTCD and ND, respectively. Increasing the casting velocity (Figs.16(b) vs. (d)) results in an increase in both the 001 and 010 pole

densities without the use of additional seed particles. Increasingthe slurry viscosity (Fig. 16(e)) results in a higher 010 pole

0 15 30 45 60 75 90

0.0

0.5

1.0

1.5

2.0

2.5

3.0

Random

f150[mrd]

[degrees]

Synchrotron X-ray diffraction

Neutron diffraction

Saturation

Fig.14. 150 pole density (f150) distributions of orthorhombic leadmetaniobate. The solid line labeled saturation indicates the theoreticalsaturation distribution from Jones et al.21

Fig.15. Collection of acicular seed particles of lead metaniobate grownfrom a melt.



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density in the ND than all of the other cases with the use of thelowest fraction of seed particles. By increasing the casting ve-locity and slurry viscosity, the shear behavior of the slurrydeformation is increased.87,73 This equates to more particlerotation and orientation, resulting in an increase in preferredorientation.

The spontaneous polarization direction in lead metaniobate isparallel to [010]. Therefore, the piezoelectric response is depen-dent on the distribution of the 010 pole before electrical poling.For an originally random sample, the d33 value is approximately80 pC/N. When the 5 wt% high-viscosity laminate is poled par-

allel to the ND, TD, and TCD, three different longitudinal pi-ezoelectric coefficients are observed. Electrical poling parallel tothe ND (normal to the tape-casting plane) results in the largestpiezoelectric coefficient, d335110 pC/N. Electrical poling par-allel to the TCD results in a substantially lower piezoelectriccoefficient, d33510 pC/N. Unlike bismuth titanate, tape-castlead metaniobate exhibits orthotropic sample symmetry andthere are three distinct axes, two of which are in the tape-cast-ing plane (TCD and TD). Electrical poling parallel to the TDresults in a piezoelectric coefficient of d33570 pC/N, which is avalue between the two coefficients when poled parallel to theTCD and ND. These directionally dependent piezoelectric co-efficients correlate with the texture measurements in Fig. 16(e).To better illustrate these correlations, these texture and piezo-electric coefficient measurements are shown in parallel in

Fig. 17. The maximum 010 texture is found parallel to theND, followed by the TD, and the minimum 010 mrd is parallel

to the TCD. This indicates that increasing the preferred orien-tation of the 010 pole before electrical poling can increase thepiezoelectric response in this direction after poling. Differentstrengths of texture can be induced by altering the slurry vis-cosity, seed particle concentration, and casting velocity, suggest-ing that a tailored response can be induced through acombination of grain texturing, the magnitude of electric fieldand temperature during poling, and poling time.

V. Other TextureAnisotropy Relationships

There are a number of other piezoelectric systems not investi-gated in this work but are nonetheless interesting with regard tothe influence of texture, anisotropy, and symmetry on polycrys-talline anisotropy. For example, polycrystalline ceramics incor-porating increasingly complex crystal systems (e.g., those withmonoclinic symmetry or monoclinic distortions of the unitcell),32,33 yield unique domain distribution functions not yetconsidered. Nonetheless, these domain distributions will con-tribute to the enhanced performance in new functional materi-als, particularly with the increased availability of polycrystallineceramics of stable monoclinic symmetries with continuing pro-cessing advances.9193 Therefore, a discussion on the influence ofthese lower-symmetry systems on the domain distributions andpolycrystalline properties is relevant. In Section II, we described

the degree of non-1801 domain switching using a pole densitydistribution function. For tetragonal ceramics, the 001 pole den-sity distribution function described the distribution of the 001pole relative to the poling axis and the 001 and 001 pole areindistinguishable. In a similar manner, the degree of 1801 do-main switching can be represented by a polarization distributionfunction, where the polar direction, ~p, is unique from the anti-polar direction, ~p. These distributions cannot be measured di-rectly using the methods described here, although they areintrinsic to the behavior of polycrystalline ceramics in the poledstate.

The polarization distribution function as a function of crystalsymmetry and domain-switching can be calculated by modifyingour earlier non-1801 domain-switching simulation21 to accountfor polarization inversion (~p2

~p domain switching, or 1801

domain switching) and additional polarization reorientationsallowable by crystal symmetry. The incorporated symmetries

Fig.16. 010 (top) and 001 (bottom) pole figures for the various tape-casting processes plotted on equal area projections. (a)(c) are 0%, 10%, and 20%seed particles under the standard tape-casting conditions, (d) is the 10% seed particles with a blade speed of 80 cm/min, and (e) is the 5% seed particles

with a high-viscosity slurry.

ND TD

0.18

2.52 0.31

d33 [pC/N]

10

110 70ND

(a) (b) (c)

TD

0.18

2.52 0.31

f010 [mrd]

10

110 70

TCTCD

Fig.17. Sample axes definitions (a), the 010 pole density in each sampledirection (b), and the longitudinal piezoelectric coefficient measuredwhen electrical poling was performed parallel to each sample direction.



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include an MA-type monoclinic symmetry with a constrainedpolarization direction of 241 from the pseudo-cubic

o0014(g),94

and an MA-type monoclinic symmetry with an un-constrained polarization direction in the monoclinic (010) plane.Upon application of an electric field in the unconstrained case,non-1801 domain switching, polarization inversion, and polar-ization rotation may occur. In the constrained case (g5241),only non-1801 domain switching and polarization inversion mayoccur. Figure 18 presents the distribution functions of the po-larization direction ~p for various crystal systems, which are fur-ther described in Table I. In all cases with a finite number ofpolarization direction possibilities, the maximum value of fp isequal to the possible number of spontaneous polarization di-rections. In other words, the monoclinic and tetragonal symme-tries have maximum values fp524 and 6 mrd, respectively.

Because the polarization distribution function describes a sta-tistical probability of the spontaneous polarization direction in

every possible sample direction, the polarization distributionfunction can be integrated to calculate the effective grain-aver-aged polarization using the equation

p3h ip0

12

Zpa0

p a cosa sinada (6)

where /p3S/p0 is the fraction of single-crystal polarizationachievable in the polycrystalline material. Eq. (6) is analogousto Eq. (2), although the first-rank polarization tensor (vector) isprojected by a single cosine term, whereas the second-rank straint

Jones-2007-1-JACS Texture and Ani Sot Ropy of Piezoelectrics

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