DIRECT WRITING CRYSTALLOGRAPHIC ORIENTATIONS TO …

The Pennsylvania State University

The Graduate School

DIRECT WRITING CRYSTALLOGRAPHIC ORIENTATIONS TO TAILOR

PROPERTIES OF PIEZOELECTRIC CERAMICS

A Dissertation in

Materials Science and Engineering

by

Rebecca L. Walton

© 2020 Rebecca L. Walton

Submitted in Partial Fulfillment

of the Requirements

for the Degree of

Doctor of Philosophy

August 2020

ii

The dissertation of Rebecca L. Walton was reviewed and approved by the following:

Gary L. Messing

Distinguished Professor of Ceramic Science and Engineering

Dissertation Co-Advisor

Co-Chair of Committee

Richard J. Meyer

Associate Professor of Materials Science and Engineering

Senior Scientist, Applied Research Laboratory

Dissertation Co-Advisor

Co-Chair of Committee

James H. Adair

Professor of Materials Science and Engineering, Biomedical Engineering, and

Pharmacology

Michael T. Lanagan

Professor of Materials Science and Engineering

Mark A. Fanton

Special Member

Senior Scientist, Applied Research Laboratory

John C. Mauro

Professor of Materials Science and Engineering

Intercollege Graduate Degree Program Chair

Associate Head for Graduate Education, Materials Science and Engineering

iii

Abstract

Crystallographically texturing piezoelectric ceramics is a powerful method to bring

the piezoelectric properties of polycrystalline ceramics closer to those of single crystals.

Crystallographic orientation in piezoelectric ceramics is primarily achieved by tape casting

and slip casting to align large, anisotropic template particles via shear stress in a randomly

oriented piezoelectric matrix. For this research, the process of shear alignment in a model

alumina tape casting system was explored to link common forming parameters, such as

slurry viscosity, casting head aspect ratio, and casting rate to the magnitude and gradient

of applied torque. Using Multiphysics modeling in COMSOL, it was determined that as

slurry viscosity, casting head aspect ratio, and casting rate increased, so did the magnitude

and gradient of torque during casting. As the magnitude and gradient of applied torque

increased, the volume fraction of aligned particles and misalignment angle of the particles,

as characterized by XRD rocking curves, increased by 14%, and decreased by 7°

respectively.

Dispersion characteristics of the piezoelectric system of interest, Pb(In1/2 Nb1/2)O3-

Pb(Mg1/3Nb2/3)O3-PbTiO3 (PIN-PMN-PT), and the acrylic binder system were

characterized to develop a direct writing paste with appropriate rheology. Ceramic particle

surface charge, characterized by zeta potential measurements, was adjusted via pH to

maximize binding of the organic to the powder surface. Polymer conformation was also

controlled with pH to produce an electrosterically stabilized dispersion. The rheology of

the ceramic paste was characterized with oscillatory cone-and-plate rheometry and had an

equilibrium storage modulus of 105 Pa, a yield stress of 520 Pa, and a recovery time of 7

seconds. Rheology was further tailored with the addition of 10 volume percent 20 – 40 µm

iv

wide barium titanate platelet particles, to serve as crystallographic templates for texturing,

to produce a paste which filled space upon deposition but held the as-deposited shape and

extruded at pressures manageable for the printing hardware.

Additive manufacturing techniques offer access to crystallographic orientations and

textured shapes that are not possible with tape and slip casting. To tailor the alignment of

barium titanate particles during direct writing by altering the shear field, custom SLA

nozzles with aspect ratios 2 – 5 were designed and printed at Penn State. A series of samples

were printed at rates from 5 mm/s to 20 mm/s with nozzles of aspect ratios 2 and 3. All

printed ceramic samples were sintered to 98% density, measured by the Archimedes

method, at 1050 °C for 10 h in flowing O2, which produced a fully textured microstructure.

Increasing the aspect ratio from 2 to 3 and printing rate from 5 mm/s to 20 mm/s in turn

increases the magnitude and gradient of torque generated during printing, as modeled with

COMSOL. As torque is increased via printing rate the average angle of misalignment

decreases by 10° and as torque is increased by increasing deposition nozzle aspect ratio

from 2 to 3 the average angle of misalignment decreases by 6°. As misalignment angle in

textured piezoelectric ceramics is decreased, the piezoelectric coefficient increases. In

direct written PIN-PMN-PT decreasing the misalignment angle by ~5°, by increasing the

printing nozzle aspect ratio from 2 to 3, increases the piezoelectric coefficient, as measured

by strain-voltage loops, by 20%.

v

Table of Contents

List of Figures ................................................................................................................... vii

List of Tables ..................................................................................................................... xi

Acknowledgements ........................................................................................................... xii

Chapter 1. Introduction ................................................................................................... 1

1.1 Thesis Motivation ................................................................................................. 1

1.2 Crystallographically Textured Ceramics .............................................................. 1

1.2.1 Motivation for Textured Ceramic Manufacturing ........................................ 1

1.2.2 Characterizing Crystallographic Texture ...................................................... 2

1.2.3 Textured PIN-PMN-PT ................................................................................. 3

1.2.4 Production of Crystallographic Texture........................................................ 3

1.2.5 Shear Alignment of Anisotropic Particles .................................................... 6

1.3 Additive Manufacturing Techniques .................................................................. 12

1.3.1 Slurry-based Additive Manufacturing Techniques ..................................... 12

1.3.2 Direct Writing ............................................................................................. 16

1.3.3 Selection of an Additive Manufacturing Technique ................................... 25

Chapter 2. Tailoring Particle Alignment and Grain Orientation during Tape Casting

and Templated Grain Growth ........................................................................................... 26

2.1 Publication Disclosure........................................................................................ 26

2.2 Introduction ........................................................................................................ 26

2.3 Experimental Procedure ..................................................................................... 28

2.3.1 Slurry Preparation ....................................................................................... 28

2.3.2 Rheological Measurements and Flow Simulations ..................................... 30

2.3.3 X-Ray Measurements and Analysis ............................................................ 30

2.4 Tailoring Alignment during Tape Casting ......................................................... 32

2.4.1 Effect of Slurry Viscosity on Alignment .................................................... 32

2.4.2 Effect of Gap Height on Alignment ............................................................ 35

2.4.3 Effect of Casting Rate on Alignment .......................................................... 40

2.4.4 Settling Considerations ............................................................................... 41

2.4.5 Concluding Remarks on Torque and Alignment ........................................ 42

Chapter 3. Dispersion and rheology for direct writing lead-based piezoelectric

ceramics pastes with anisotropic template particles ......................................................... 45

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3.1 Publication Disclosure........................................................................................ 45

3.2 Introduction ........................................................................................................ 45


3.3.1 Powder and Paste Preparation ..................................................................... 48

3.3.2 Zeta potential and solubility measurements ................................................ 50

3.3.3 Rheological measurements and printing ..................................................... 51

3.4 Surface Chemistry and Dispersion ..................................................................... 53

3.5 Rheology of Direct Writing Pastes..................................................................... 57

3.5.1 Effect of Anisotropic Particles on Paste Rheology ..................................... 61

3.6 Rheological Effects on Direct Writing ............................................................... 65

3.7 Summary ............................................................................................................ 67

Chapter 4. Direct Writing of Textured Ceramics with Anisotropic Nozzles ............... 69

4.1 Introduction ........................................................................................................ 69


4.3 Particle Alignment During Direct Writing ......................................................... 78

4.4 Densification of Printed Ceramics ..................................................................... 84

4.5 Piezoelectric Properties of Printed Ceramics ..................................................... 86

4.6 Summary ............................................................................................................ 87

Chapter 5. Future Work and Summary ......................................................................... 88

5.1 Prospect for AM of Textured Ceramics ............................................................. 88

5.2 Modifying the Direct Writing Process ............................................................... 90

5.3 Thesis Summary ................................................................................................. 93

Chapter 6. Appendix for COMSOL Multiphysics Simulations ................................... 96

References ......................................................................................................................... 97

vii

List of Figures

Figure 1.1. Simulated and calculated (A) velocity and (B) shear rate curves for tape

casting of non-Newtonian fluids, with (C) the rheological behavior of the fluid showing

the important information for the calculation of torque on anisotropic particles during

tape casting where z = 0 is the carrier tape surface and z = 2 mm is the doctor blade

surface.[16] ......................................................................................................................... 8

Figure 1.2. Schematic of a (A) tape casting setup illustrating (B) the velocity profile

under the doctor blade and (C) the resulting microstructure of a laminated and sintered

TGG ceramic.[34] ............................................................................................................. 10

Figure 1.3. Doppler velocity measurements of pressure driven flow for suspensions of

oil and starch across the diameter (D) of an extrusion nozzle displaying shear thinning

and yield stress behavior showing the constant velocity plug flow region fit with

calculated flow profiles compared to a Newtonian fluid.[37] .......................................... 11

Figure 1.4. Schematic of layer-wise slurry additive manufacturing via

photopolymerization (A)[42] and by binder gelation (B).[49] ......................................... 12

Figure 1.5. Schematic of a direct writing 3D printer where the deposition nozzle moves

in x-z and the stage moves in y showing the paste extrusion mechanism and resulting

flow field. .......................................................................................................................... 17

Figure 1.6. Representative velocity (A) and torque (B) profiles for an arbitrary pressure-

driven flow system illustrating the plug flow characteristic of pressure-driven flow

systems of yield stress fluids............................................................................................. 20

Figure 1.7. SEM images of filaments of alumina platelets printed using different nozzle

lengths, showing the effect of nozzle length on the level of concentric platelet

alignment.[39] ................................................................................................................... 20

Figure 2.1. Schematic of a (A) tape casting setup illustrating the (B) velocity profile


TGG ceramic. .................................................................................................................... 26

Figure 2.2. Backscatter SEM image of alumina platelets. ............................................... 29

Figure 2.3. (A) Experimentally determined rheological behavior for each alumina slurry

examined in this study and (B) COMSOL calculated torque gradients through the

thickness of the slurry as a function of slurry solids loading (h = 0.254 mm, v = 2.9mm/s).

........................................................................................................................................... 33

Figure 2.4. (A) ϴ-2ϴ scans and (B) rocking curves for textured alumina cast at h = 254

µm and v = 2.9 mm/s as a function of slurry powder content........................................... 35

Figure 2.5. X-ray diffraction data for textured alumina (A) rocking curves for samples

cast at varying gap heights (v = 2.9 mm/s, 30 vol% powder content) and (B) 2ϴ

diffraction patterns for randomly aligned alumina and {0001} aligned alumina. ............ 36

Figure 2.6. Normalized torque gradients (position in gap height, y, divided by total gap

height, h) calculated in COMSOL as a function of gap height (v = 2.9 mm/s, powder

content of 30 vol%). .......................................................................................................... 37

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Figure 2.7. Polished cross-sections of samples cast at 2.9 mm/s from the 30 vol% slurry

cast at gap heights of: (A) 60 µm, (B) 127 µm, (C) 203 µm, (D) 254 µm, and (E) 330

µm. Localized areas of misalignment in the 60 µm and 127 µm samples are shown in the

dotted ovals. ...................................................................................................................... 39

Figure 2.8. Variations in the (A) velocity profiles and (B) torque profiles as a function of

casting rate when gap height is 254 µm and powder content is 30 vol%. ........................ 41

Figure 2.9. The relation between r and torque for all sample sets studied. The data point

marked with an asterisk corresponds to the 254 µm gap height, 2.9 mm/s casting rate, 30

vol% condition which was included in the data for each parameter set discussed

previously. ......................................................................................................................... 43

Figure 2.10. A comparison of full width at half maximum (FWHM) achieved in previous

TGG tape casting studies which utilize platelet-like template particles.[12,26,85] ......... 44

Figure 3.1. Backscattered SEM images of (A) PIN-PMN-PT matrix powder around a

BT template particle (arrowed) and (B) BT template particles showing the size difference

between matrix powder and template particles and the geometry of the template particles.

........................................................................................................................................... 49



flow field. .......................................................................................................................... 53

Figure 3.3. Zeta potential as a function of pH for 0.08 vol% PIN-PMN-PT suspensions

with and without the acrylic binder system exhibiting the surface charge modification

enacted by acrylic binding to the particle surface. Where error bars are not visible the

error was less than the height of the data point. ................................................................ 55

Figure 3.4. Solubility of 0.10 vol% PIN-PMN-PT + CuO + barium titanate suspensions

aged for 1 h as a function of pH showing incongruent dissolution of the M2+ cations. ... 56

Figure 3.5. Storage modulus (solid data points) and loss modulus (hollow data points) as

a function of applied stress for PIN-PMN-PT pastes formulated at pH 5 with 28, 30, or 35

vol% powder loading illustrating the increase in storage modulus and yield stress as

powder content increases. ................................................................................................. 58

Figure 3.6. (A) Storage modulus (filled points) and loss modulus (hollow points) as a

function of applied stress for 28 vol% PIN-PMN-PT pastes formulated at different initial

pHs and the PAA binder system. Printing tests of 28 vol% PIN-PMN-PT pastes

formulated at (B) pH 1 and (C) pH 5 illustrating the importance of a paste with a steep

drop in storage modulus with increasing applied stress for consistent printing. .............. 60

Figure 3.7. Storage modulus (filled points) and loss modulus (hollow points) as a

function of applied stress for 28 vol% ceramic pastes formulated at pH 5 with either 0.3

or 1.4 vol% 2 – 40 µm anisotropic barium titanate (BT) platelet particles illustrating the

decrease in storage modulus and increase in yield stress as anisotropic platelet content

increases. ........................................................................................................................... 62

Figure 3.8. Storage modulus as a function of applied stress for 28 vol% ceramic pastes

formulated at pH 5 with different barium titanate platelet sizes and amounts. The storage

modulus dramatically increases as platelet size decreases. Rheologies marked with a (*)

are referred to in Figure 8. ................................................................................................ 64

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Figure 3.9. Photographs of representative direct written PIN-PMN-PT samples of 28

vol% ceramic loading pastes formulated at pH 5 and printed at 5 mm/s with (A) top-view

and (B) cross-section for 2.6 vol% BT platelets 20 µm < x < 40 µm and (C) top-view and

(D) cross-section for 2.6 vol% BT platelets 5 µm < x < 20 µm illustrating the difference

in printing behavior generated by increasing 𝐺eq′ and decreasing recovery time. .......... 66



flow field. .......................................................................................................................... 70

Figure 4.2. Backscatter scanning electron microscope image of barium titanate template

particles. ............................................................................................................................ 74

Figure 4.3. Backscatter scanning electron microscope image of a sintered filament cross-

section with (A) an overlay of the nozzle outline, (B) the platelets highlighted and

concentric sections of the cross-section indicated, (C) the radial division of the filament,

and (D) schematic of angle measurement relative to the tangent angle. .......................... 76

Figure 4.4. (A) Schematic of the serial sections and XRD process with (B) a

representative set of scans showing a decrease in crystallographic texture as depth into

the filament increases. ....................................................................................................... 77

Figure 4.5. (A) Torque profile at the outlet of the nozzle for a nozzle of aspect ratio 3

and printing rate of 20 mm/s. Dotted line indicates position of minor axis calculations in

(B) torque profiles calculated along the minor axis at 20 mm/s printing rate for each

aspect ratio nozzle and (C) torque profiles for aspect ratio 3 at increasing printing rates.

........................................................................................................................................... 79

Figure 4.6. The average misalignment angle (A) and standard deviation (B) of platelet

particles relative to the nozzle surface as a function of nozzle aspect ratio and printing

rate where each data point is the average of three samples per printing condition. ......... 80

Figure 4.7. The average alignment angle (A) and standard deviation (B) of template

particles relative to the nozzle surface as a function of filament cross-section for

filaments printed with aspect ratio 2 and 3 nozzles at 20 mm/s printing rate averaged for 3

samples per printing condition. ......................................................................................... 81

All samples exhibit the highest texture quality on the surface of the filament, but as the

aspect ratio of the nozzles and the printing rate changes the extent of alignment relative to

the surface changes dramatically. For the aspect ratio 1 nozzle, the degree of texture (i.e.

F) at the surface ranges from 27% to 39% at 5 mm/s and 20 mm/s, respectively, while the

aspect ratio 5 nozzle exhibits a range from 41% to 47% as the printing rate increases. The

aspect ratio 2 nozzle exhibits a trend opposite to that of the aspect ratio 1 and 5 nozzles

with the degree of texture on the surface decreasing from 41% to 30% as the printing rate

increases from 5 to 20 mm/s. The percent of the filament that exhibits some alignment,

defined here as having a Lotgering factor ≥ 0.10 is also significantly different between

nozzle aspect ratios. For the nozzles of aspect ratios 1, 2, and 5 the aligned portion of the

filament ranges from 9 to 23%, 12 to 25%, and 22 to 30% of the filament radius,

respectively. Figure 4.8. Lotgering factor as a function of position (position/diameter)

for samples printed at various printing rates with (A) an aspect ratio 1 nozzle, (B) an

x

aspect ratio 2 nozzle, and (C) an aspect ratio 5 nozzle showing higher overall Lotgering

factors for the aspect ratio 5 nozzle prints. Trendlines are included to guide the eye. ..... 81

Figure 4.9. Lotgering factor (data points) and torque (solid line) as a function of position

in the filament (position/diameter) for samples printed at 20 mm/s with (A) an aspect

ratio 1 nozzle, (B) an aspect ratio 2 nozzle, and (C) an aspect ratio 5 nozzle showing

strong correspondence between the high slope areas of the torque profile and the aligned

areas of the filament. Trendlines are included to guide the eye. ....................................... 83

Figure 4.10. TMA densification curves for samples printed (A) with aspect ratio 2 and 3

nozzles at 5 mm/s and (B) with aspect ratio 3 nozzles at increasing printing rates. Final

relative densities are low due to lead loss during sintering. ............................................. 85

Figure 4.11. Strain versus applied voltage for sintered direct written PIN-PMN-PT

ceramics printed at 20 mm/s showing an increase in piezoelectric response when

templates are added and when the templates are better aligned with higher aspect ratio

printing nozzles. ................................................................................................................ 86

Figure 5.1. (A) Typical platelet orientation and geometry for templated tape cast

ceramics, (B) geometry possible with tape casting with platelet orientation only possible

through additive manufacturing, and (C) geometry and platelet orientation only possible

with additive manufacturing. ............................................................................................ 89

Figure 5.2. Torque profile during printing for nozzles of aspect ratios 5 and 20 at 20

mm/s printing rate showing increased torque magnitude and gradient as nozzle aspect

ratio increases.................................................................................................................... 91

Figure 5.3. Model of proposed baffled direct writing nozzle with (A) an expanded side

view, (B) expanded outlet view, and (C) expanded inlet view showing the inclusion of

flat baffles to the interior of a standard tapered nozzle. .................................................... 92

Figure 5.4. Torque profiles for baffled and un-baffled nozzles at a 20 mm/s printing rate

showing the elimination of constant torque regions with the addition of flat baffles....... 93

xi

List of Tables

Table 1.1. Comparisons of relevant parameters for layer-wise additive manufacturing

techniques with tape casting systems that exhibit particle alignment............................... 15

Table 1.2. Comparisons of relevant parameters for direct writing/robocasting systems

which produce aligned particles compared to systems with no goal of alignment. .......... 22

Table 3.1. Compositional ranges for 28 – 35 vol% ceramic PIN-PMN-PT pastes used in

this study. .......................................................................................................................... 51

Table 3.2. Isoelectric points for metal oxides related to PIN-PMN-PT showing a wide pH

range of low surface charge. ............................................................................................. 55

xii

Acknowledgements

The old saying that it takes a village to raise a child is also true of PhD students, I

could not have accomplished all of this without a lot of help and support. First, thank you

to Dr. Messing for deciding that a plucky college senior desperately trying to pull her group

through their Capstone project might make a good PhD candidate. I am truly thankful to

have been given the opportunity to get my PhD in this research group. Along those lines, I

would also like to thank Dr. Kupp for her invaluable mentoring and support, as well as my

groupmates Brova and Beecher for their camaraderie and help, both scientific and

emotional.

Thank you also to my thesis committee, for their patience and excellent feedback,

all of you have truly made my thesis a better body of work. Special thanks to Dr. Meyer,

for being a tireless champion for our entire research project, without whom we would not

have had the support for any of our work. I would like to thank Professor James H. Adair

of the Department of the Materials Science and Engineering at Penn State for invaluable

discussions about zeta potential and isoelectric point of mixed metal oxides. I would also

like to thank to Professor Michael Hickner and his research group at Penn State, who

provided the 3D printer for my thesis work as well as patient and helpful training on the

machine, and Professor Ralph Colby and his research group at Penn State for providing the

rheometer and training to collect rheological data for my thesis.

It would be impossible for me to write an acknowledgements section without

talking about the group of people who have collectively been my rock, both for my thesis

and before. To my friends, both new and old, your love and support has kept me going

xiii

through this process. Audrey, Zoe, Beca, Buddy, Chris, Ian, Erica, Melissa, Nadia, Tom,

Angela, Namjun, and so many others, thank you for sticking with me through this journey.

Desmond, my constant furry companion, comforted me and gave me a sense of purpose in

a way only a cat can. Finally, to my family, Mom, Dad, Amanda, Emily, and the rest of my

extended family, the belief and love you all have shown me throughout my life made this

possible, thank you for always believing in and supporting me.

This material is based upon research supported by, or in part by, the

U. S. Office of Naval Research under award number N00014-18-1-2498.

1

Chapter 1. Introduction

1.1 Thesis Motivation

Crystallographically texturing piezoelectric ceramics is a powerful method to bring

the piezoelectric properties of polycrystalline ceramics closer to those of single crystals.

Currently, crystallographic orientation in piezoelectric ceramics is primarily achieved by

tape casting and slip casting to align large, anisotropic template particles via shear stress in

a randomly oriented piezoelectric matrix. Additive manufacturing techniques offer access

to crystallographic orientations and textured shapes that are not possible with tape and slip

casting. The focus of this thesis is to provide a comprehensive basis for additively

manufacturing dense, crystallographically oriented ceramics. To achieve this, we outline

important aspects of the shear alignment process for both tape casting and additive

manufacturing processes and explore the specific characteristics of dispersion and rheology

that are necessary to produce alignment during additive manufacturing.

1.2 Crystallographically Textured Ceramics

1.2.1 Motivation for Textured Ceramic Manufacturing

Single crystals often have superior properties relative to polycrystalline ceramic

counterparts. While many applications require the use of single crystals, for other

applications single crystals are cost prohibitive and suffer from non-uniform composition

when grown in large volumes.[1] For these reasons, ceramics with crystallographically

oriented microstructures, also known as textured ceramics, have garnered significant

interest as alternatives for single crystals and randomly oriented ceramics. For example,

crystallographically oriented polycrystalline piezoelectric ceramics with textured volume

2

fractions (the volume fraction of the polycrystalline ceramic which exhibits the desired

crystallographic orientation) > 0.9 have piezoelectric coefficients (d33) 1.5 to 3 higher than

polycrystalline ceramics and coupling coefficients (k33) comparable to single crystals.[1,2]

In textured ceramics, the textured volume fraction significantly affects this increase in

piezoelectric coefficient, but the misalignment angle among the oriented grains, or the

quality of crystallographic alignment, also has a major influence on the final properties of

the textured ceramic.[2]

1.2.2 Characterizing Crystallographic Texture

Degree of texture in a textured ceramic can be calculated compared to a reference

random ceramic of the same composition through the Lotgering factor (Equation 1.1).[3]

The Lotgering factor (𝐹) is calculated using θ-2θ scans to calculate 𝑃 and 𝑃0. Here 𝑃 is

the ratio of all peak intensities and the texture peak intensities in the textured ceramic XRD

scan and 𝑃0 is the ratio of all peak intensities and the texture peak intensities in an

untextured reference XRD scan.

𝐹 = 𝑃−𝑃0

1−𝑃0 (1.1)

Texture in crystallographically oriented ceramics can also be quantified via rocking

curve analysis. Rocking curves are collected by positioning the x-ray collector at the 2θ

position of an XRD peak indicative of the crystallographically textured direction and tilting

the sample angle relative to the x-ray source. The resulting curve is fit with the March-

Dollase equation (Equation 1.2) to obtain f and r. From this fit f is the textured volume

fraction and r is a dimensionless alignment quality factor where as r approaches 0 the

crystallographic alignment is oriented more precisely to the sample surface.

3

𝐹(𝑓, 𝑟, 𝜔) = 𝑓 (𝑟2𝑐𝑜𝑠2(𝜔) +𝑠𝑖𝑛2(𝜔)

𝑟)

−32⁄

+ (1 − 𝑓) (1.2)

1.2.3 Textured PIN-PMN-PT

PIN-PMN-PT (Pb(In1/2Nb1/2)O3-Pb(Mg1/3Nb2/3)O3-PbTiO3) was chosen as a model

system for this thesis work because it is a piezoelectric system which is of interest for high

power applications. This chemistry can be crystallographically oriented via TGG and

exhibits high piezoelectric coefficients and low dielectric loss in both the polycrystalline

and textured form. Furthermore, the properties and densification of the PIN-PMN-PT

system can be tailored using various additives, making this chemistry appealing for a wide

range of applications.[4–7]

There has been significant work on this piezoelectric system in the single crystal,

polycrystalline, and textured forms with which direct written ceramics can be compared.

Hosono et al. initially reported that single crystals of PIN-PMN-PT had a piezoelectric

coefficient of 2200 pC/N and randomly oriented polycrystalline ceramics had piezoelectric

coefficients between 510 and 430 pC/N depending on the proportions of PIN to PMN to

PT.[8,9] Later work by Chang et al. reported significant increases in the piezoelectric

coefficient of PIN-PMN-PT when crystallographically textured with barium titanate

template particles, with a maximum piezoelectric coefficient of 927 pC/N when copper

oxide was added as a sintering aid to promote densification and grain growth.[6,10]

1.2.4 Production of Crystallographic Texture

Textured technical ceramics are commonly fabricated by the templated grain

growth (TGG) process in which relatively larger morphologically anisotropic single crystal

particles of a known crystallographic orientation (i.e. template particles) are aligned,

4

morphologically and crystallographically, in a matrix of equiaxed submicron powder. The

anisotropic template particles are usually plate- or needle-like and typically comprise 1

volume % to 15 volume % (vol%) of the solid particles in the slurry.[11–13]

Crystallographically oriented grains then grow from the aligned templates during sintering

to form a crystallographically oriented microstructure. Thus, the initial alignment of the

anisotropic template particles in the matrix is directly mapped to the final textured grain

orientation.[11]

Tape casting, and other shear forming techniques, such as screen printing and slip

casting, are used to physically orient the high aspect ratio, single crystal template particles

during TGG. Tape casting relies on the movement of slurry under a doctor blade to generate

a shear field which aligns the anisotropic template particles dispersed in the slurry. Because

of the importance of grain alignment quality on the properties of textured ceramics, the

relationship between tape casting parameters and resulting crystallographic alignment is of

great interest.

While fluid flow under a doctor blade has been thoroughly modeled,[14–20] there

are few studies regarding the influence of processing parameters during shear forming

techniques on particle or grain alignment quality. As such there is little fundamental

understanding about how tape casting process parameters control alignment quality in tape

cast ceramics. Kim et al. simulated the tape casting process assuming a Newtonian fluid

and concluded that increasing the viscosity of the slurry, the casting rate, and the volume

fraction of template particles may increase the volume fraction of texture in TGG

ceramics.[14] Wonisch et al. also simulated the tape casting process with a variety of

doctor blade geometries and powder morphologies, and compared average particle

5

orientations for each between experimental and calculated.[21] However, the volume

fraction and alignment quality of the oriented microstructures were not thoroughly

characterized (via rocking curve or θ-2θ scan). The case of anisotropic particles was also

carried out with 100 vol% anisotropic particles,[16] as opposed to a minority of anisotropic

particles common in templated grain growth methods.

Snel et al. investigated the relationship between tape casting parameters (gap

height, powder loading, casting velocity, and de-airing time) and textured fraction

(calculated using Lotgering factor),[22] but alignment quality was not measured.

Alignment quality relationships have been reported for sintering temperature,[11,23,24]

sintering time,[11] template concentration,[11–13,23–25] annealing time,[26] and template

aspect ratio.[23,27] Sintering temperature was demonstrated to have little effect on r,

however Jones et al. noted the necessity of high density (> 90%), and thus higher sintering

temperatures, to facilitate increased the degree of orientation.[24]

Conflicting results have been reported for template fraction. Seabaugh et al.

reported that increasing the volume percent of template particles in the initial slurry from

1% to 25% (dry volume basis, dvb) decreased the quality of grain alignment (i.e., r

increased from 0.18 to 0.30)[11]. Pavlacka et al. showed that r increased from 0.13 to 0.17

when the concentration of alumina platelets was increased from 1 vol% to 15 vol%

(dvb).[12] In contrast, Wei et al. reported that as the volume percent of alumina platelets

was increased from 2.4 vol% to 9.1 vol% r decreased from 0.6 to 0.4, however platelet

concentrations greater than 9.1% yielded no further improvement in r.[13] Based on the r

values the degree of crystallographic texture was not as high as the studies by Seabaugh

and Pavlacka, however, which suggests a fundamental difference in the study parameters.

6

Jones et al. increased the template fraction of Bi4Ti3O12 platelets in a Na0.5Bi4.5Ti4O15

matrix from 0 weight % to 25 weight % and observed a linear increase in the degree of

orientation.[24]

1.2.5 Shear Alignment of Anisotropic Particles

Template particle alignment has been limited primarily to shear forming techniques

such as tape casting to produce dense, well-aligned ceramic bodies. Magnetic alignment

techniques, where application of a strong magnetic field aligns suspended ceramic powder

based on magnetically susceptible crystallographic directions, are also used to fabricate

textured ceramics.[28–30] The process of magnetic alignment generally does not utilize

anisotropic template particles, but Poterala et al. demonstrated alignment and subsequent

TGG of sodium bismuth titanate-lead titanate platelet particles in a lead magnesium

niobate-lead titanate system.[30] However, this thesis will focus on shear alignment of

template particles.

To predict the extent of anisotropic particle alignment during tape casting the

rheological properties of the dispersion and the flow conditions during casting must be

known. An early study by Watanabe et al. with tape casting slurries of 20 – 33 vol%

Bi4Ti3O12 platelet particles explored how altering casting rate, gap height, and powder

content influenced the shear rate during casting and the resultant degree of orientation of

the platelet particles, but they concluded that only powder content affected the degree of

orientation.[31] In this study shear rate was calculated by combining the equations for drag

flow and pressure-driven flow and assumed Newtonian viscosity.[31] Later studies of flow

during tape casting began to consider more fluid behaviors such as shear thinning,

viscoelastic, and yield stress fluids.[14,18,19,32,33] Simulations of flow during tape

7

casting by Wonisch et al.[16] compared flow profiles of slurries with Newtonian and shear

thinning behaviors as casting rate increased (Figure 1.1A), from which they calculated the

shear rate profiles (Figure 1.1B). Velocity profiles for the Newtonian case in this study

were calculated by combining the equations for drag and pressure-driven flow, while the

shear thinning velocity profile was simulated using the Navier-Stokes equation and the

measured rheological behavior of the slurry (Figure 1.1C). These simulations showed that

while the velocity profile during casting for both Newtonian and shear thinning fluids is

similar, the maximum shear rates differ. This difference combined with the dramatic

changes in viscosity as shear rate changes for shear thinning fluids points to the need for

more detailed simulations to understand flow and alignment of particles during tape

casting.

8

Figure 1.1. Simulated and calculated (A) velocity and (B) shear rate curves for tape

casting of non-Newtonian fluids, with (C) the rheological behavior of the fluid showing

the important information for the calculation of torque on anisotropic particles during

tape casting where z = 0 is the carrier tape surface and z = 2 mm is the doctor blade

surface.[16]

If the viscosity behavior of the casting slurry is known, then the shear stress (𝜏)

gradient though the slurry can be calculated by multiplying the shear rate (��) by the

viscosity at that shear rate (𝜂𝐷), shown in Equation 1.3. Park et al. showed that the shear

stress gradient, along with the geometry of an aligning particle, can be used to calculate

the torque applied to a whisker-shaped particle during casting (Equation 1.4).[20] Torque

(M) on a particle is calculated by multiplying the difference in shear stress at the ends of

the particle (𝜏𝑦+𝛿𝑦, 𝜏𝑦) by the projection height of the particle (𝛿𝑦).

𝜏 = ��𝜂𝐷 (1.3)

9

𝑀 = (𝜏𝑦+𝛿𝑦 − 𝜏𝑦)𝛿𝑦 (1.4)

After the slurry exits the space under the doctor blade and is no longer influence of drag

flow, torque goes to zero and thus the template particles remain aligned.

The velocity profile during tape casting does not have any areas of zero slope

because drag flow results in a velocity profile with constant slope which is then influenced

by pressure behind the casting head to generate a velocity profile with constantly changing

slope (Figure 1.1A). Therefore no areas of constant shear stress (i.e. zero torque) exist and

alignment of anisotropic particles parallel to the carrier tape is consistent through the

thickness of the ceramic slurry (Figure 1.2).[34] Methods for increasing alignment quality

during tape casting generally depend on increasing the torque applied to template particles

during casting as in studies by Wu and Messing,[35] Iverson et al.,[33] Snel et al.,[22] and

Walton et al.[34] where alignment of particles during tape casting is improved by

increasing the casting viscosity and casting rate as well as decreasing the gap height. For

the alignment of needle-like particles further modifications to the tape casting process are

necessary to apply sufficient torque for particle alignment. The so-called gated doctor blade

employed pins spaced along the length of the doctor blade to serve as additional shearing

surfaces and more finely align needle-like particles.[20,35,36]

10

Figure 1.2. Schematic of a (A) tape casting setup illustrating (B) the velocity profile


TGG ceramic.[34]

In contrast to the drag flow which occurs during tape casting, forming techniques

which rely on pressure-driven flow of yield stress fluids, such as extrusion, exhibit plug

flow.[37] This flow regime is characterized by a sharp velocity gradient near the

constraining walls of the nozzle or die and a constant velocity region in the center of the

fluid volume (Figure 1.3). In the constant velocity plug region, there is no shear stress

applied to the fluid volume since the slope of the velocity profile is 0.

11

Figure 1.3. Doppler velocity measurements of pressure driven flow for suspensions of oil

and starch across the diameter (D) of an extrusion nozzle displaying shear thinning and

yield stress behavior showing the constant velocity plug flow region fit with calculated

flow profiles compared to a Newtonian fluid.[37]

Due to this zero shear stress region, the torque necessary to align anisotropic particles in

the plug volume is also zero, causing a core of unaligned material in the extruded fluid

volume.[38–40] Compared with drag-driven flow in tape casting, which applies torque to

the entire fluid volume, pressure-driven forming methods such as extrusion or direct

writing will result in lower volumes of aligned material if no modifications are made to the

forming process. Therefore, additive manufacturing methods with drag-driven flow

regimes are well suited to fabricate well-aligned ceramics.

12

1.3 Additive Manufacturing Techniques

1.3.1 Slurry-based Additive Manufacturing Techniques

There are three main methods of layer-wise slurry additive manufacturing. One

involves a slurry containing ceramic particles and a photoactive polymer deposited in a

layer. The polymer is cross-linked with light in patterns of the desired shape which are built

up into the 3D shape (Figure 1.3A).[41–46] Another method builds the ceramic shape via

drying of ceramic slurry in cross-sections using a laser, forming 3D shapes in a similar

manner to the photo-polymerization method (stereolithography).[47,48] Gelation of the

binder in the slurry in cross-sections of the desired shape (Figure 1.3B) is another approach

to form individual layers.[49–51] In all methods the ceramic slurry is deposited as a layer

by a moving doctor blade, which creates a shear field similar to that observed during tape

casting. Particle alignment in slurry-based additive manufacturing has primarily been

achieved via application of electric or magnetic field to ceramic whiskers in polymers as

opposed to ceramic slurries.[52,53]

Figure 1.4. Schematic of layer-wise slurry additive manufacturing via

photopolymerization (A)[42] and by binder gelation (B).[49]

13

The rheology for layer-wise slurry-based additive techniques and tape casting is

similar.[34,54] Both forming techniques require a slurry which is shear-thinning so the

slurry viscosity drops when it is sheared during casting, but increases after the casting stress

is removed so the layer of slurry remains in place and does not flow. The doctor blade used

to spread new layers of slurry for stereolithography, or drying, in slurry-based additive

techniques generates a similar flow profile to that of tape casting. Table 1.1 classifies

slurry-based layer-wise additive techniques that produce dense ceramics including some

typical tape casting formulations. It is clear from this table that the ceramic formulations

for tape casting and laser-wise AM have similar ceramic powder and solvent/polymer

contents. Additionally, the rheological behavior and layer heights of layer-wise AM and

tape casting fall within the same ranges. The time for complete curing of the ceramic

volume by layer-wise slurry additive manufacturing can be much shorter than the drying

time for tape casting with total time depending on the number of layers times the individual

layer solidification rate (i.e. 1 – 10 s) time whereas tape casting drying times can be as long

as 1 – 2 h for aqueous formulations.

Challenges for using slurry-based layer-wise additive manufacturing to align

anisotropic particles include particle settling in the slurry reservoir, changes in the

refractive properties of the slurry due to the large template particles and producing a

uniform flow field. To satisfy conditions for alignment during tape casting, template

particles are anisotropic in shape and typically >10 µm in cross-section by < 1 µm in

thickness When suspended in a submicrometer particle dispersion such large particles can

settle out of low viscosity suspensions. Generally, the casting and drying processes during

tape casting are rapid enough because the casting process is continuous, that settling of

14

template particles is not an issue. In contrast, the process of building a shape by layer-wise

AM can take hours since after deposition of each layer a drying or curing step is required.

Particle settling during layer-wise AM techniques is primarily an issue when the printed

geometry is built from the bottom up and/or when the geometry is solidified within a vat

of slurry. However, in the case of slurries with extreme particle size differences, settling of

large particles within slurry layers has been observed despite layer curing times of

approximately 4 s.[45] To mitigate this issue Tian et al.,[55] Lüchtenborg et al.,[47] Zocca

et al.,[49,51] and Lima et al.[50]separated the slurry reservoir from the print bed and

incorporated a stirring mechanism to keep particles in suspension before printing a layer.

15

Table 1.1. Comparisons of relevant parameters for layer-wise additive manufacturing techniques with tape casting systems that

exhibit particle alignment.

Publication Ceramic

Systems

Slurry

Formulations Curing Method

𝜼𝟎

(mPa·s)*

𝜼∞

(mPa·s)**

Sintered

Density

Layer

Height

(μm)

Total

Curing

Time

(m)

Deposited

Geometry

Griffith et

al.[41]

Chartier et

al.[42] An et

al.[43] Yanhui

et al.[46] Bae

and

Halloran[45]

Silica,

fused

silica,

alumina,

zirconia

10 – 50 vol%

ceramic, 50 –

90 vol% water

and organics

Photopolymerization 84 –

200,00

125 –

10,000 82 – 99%

40 –

800 NR

Simple and

complex

shapes

between 0.8

mm and 3 cm

Tian et al.[55]

Lüchtenborg

et al.[47]

Porcelain

, silicon

nitride

26 vol%

ceramic, 74

vol% water

Laser drying NR NR 87% -

99%

100 –

500 120

6 cm wide

complex

shapes

Zocca et

al.[49] Lima

et al.[50]

Zocca et

al.[51]

Alumina,

porcelain

, silicon

carbide

34 vol%

ceramic, 66

vol% water and

organics

Alginate gelling 1,500 100 91 – 98% NR NR

Simple and

complex

shapes

between 0.25

cm and 6 cm

Iverson et

al.[33]

Walton et

al.[34]

Lead

metaniob

ate,

alumina

18 – 30 vol%

ceramics, 70 –

82 vol% water

and organics

Tape casting 2,500 –

18,000

400 –

7,000 NR

60 -

330 5

2 x 2 x 0.25

cm plates

NR = Not reported

*Value read from graph of η versus shear rate (��) at �� ≈ 0 s-1.

**Value read from graph of η versus shear rate (��) at the value where η stabilizes.

16

Platelet particles are also problematic in photopolymerization-based additive

techniques because the large surfaces align parallel to the layer surface and thus have an

exaggerated effect on light reflection and refraction relative to the submicrometer particles,

in addition to shielding the curing agent on the opposite side of the platelet from the light.

For this reason, slurry-based additive techniques which do not rely on photopolymerization

would be better suited for printing textured ceramics fabricated by TGG. Finally,

differences in the shape of the flow field during tape casting and layer-wise AM should be

considered. Tape casting utilizes a stationary doctor blade with a consistently moving

carrier tape at a constant gap height and thus maintains a uniform and unchanged flow field

during the casting process. In contrast, during slurry-based additive manufacturing the

doctor blade is moving and the previously printed layer acts as the stationary surface for

drag flow. The shape and distance of the stationary surface can therefore change with each

deposited layer, which could cause perturbations in the velocity and torque profiles during

printing, resulting in variable alignment quality during printing of the ceramic. Detailed

simulations of the flow fields during printing, as well as fine control of layer height will be

critical to fabricate consistent alignment in templated ceramics by slurry-based additive

manufacturing techniques.

1.3.2 Direct Writing

Direct writing, or robocasting, was first demonstrated by Cesarano et al.[56,57]

with high viscosity aqueous ceramic pastes containing 60 vol% equiaxed ceramic powder

and less than 1 vol% organic additives. Direct writing involves the extrusion of filaments

of ceramic paste through a nozzle, like the fused deposition of polymers, and the layering

of these filaments to form macroscopic geometries (Figure 1.5). Printed filaments maintain

17

shape by rapid drying[56–58] and/or rheological recovery[59–61] to produce both

spanning lattices and macroscopically dense structures. Printed structures then go through

binder burn-out, if necessary, and sintering to produce dense ceramic parts.



flow field.

Initial work with this additive method was primarily with alumina, but ZnO, kaolin,

and PZT were also explored.[56] Alumina ceramics formed by this technique were shown

to have comparable densities and mechanical properties to traditionally formed ceramics,

thereby supporting the use of robocasting, or direct writing, to produce dense ceramics with

novel microstructures and geometries.[58] It is noteworthy that the process was

18

commercialized in 2007 by Robocasting Enterprises LLC to fabricate unique ceramic

components. Since these initial studies, further work has been conducted to direct write

various dense ceramics,[59–72] and some research has explored the alignment of high

aspect ratio ceramic particles within these dense ceramics.[38,39,73,74] Fu et al. aligned a

minority fraction of alumina templates (15 vol% dry ceramic basis) with equiaxed alumina

in a 50 vol% ceramic paste to create spanning templated grain growth (TGG) alumina

scaffolds.[38] Feilden et al.,[39] García-Tunón et al.,[73] and Lorenz et al.[74] printed

pastes made of majority alumina platelets into both spanning scaffolds and macroscopically

dense parts. Walton et al. recently aligned a minority volume fraction of barium titanate

platelet particles (2.6 vol%) in Pb(In1/2Nb1/2)-Pb(Mg1/3Nb2/3)O3-PbTiO3 (PIN-PMN-PT) to

create crystallographically-oriented piezoelectric ceramics in both scaffold and space-

filling structures.[40,75]

Each of the alignment studies, and all the previous work on equiaxed ceramic

systems, has the commonality of yield stress rheological behavior in the printed pastes.

This rheological behavior is necessary for robocasting and direct writing to facilitate

extrusion of the paste, as well as to ensure the printed part maintains its shape after

deposition. Studies of robocasting and direct writing systems indicate that there are three

important aspects to the yield stress behavior of pastes to produce printable suspensions:

𝐺eq′ , 𝜎y, and 𝜂0. 𝐺eq

′ , or the equilibrium storage modulus, is the value of the storage

modulus at low values of stress before the yield stress (𝜎y) is achieved. This value dictates

the extent that the fluid will elastically absorb energy to resist flow and is referred to as the

stiffness of the paste. 𝜎y is defined as the stress state at which the storage modulus is

19

exceeded by the loss modulus (𝐺′′) and begins to flow. Finally, the rest viscosity (𝜂0) is

the extrapolated viscosity of a fluid at zero shear.

Table 1.2 summarizes direct writing studies in terms of formulation, rheology, and

mechanics of the direct writing system. Printable pastes are defined as pastes which extrude

as filaments of consistent dimensions and hold shape when additional filaments are

deposited in subsequent layers. Most pastes used for direct writing exhibit 𝐺eq′ values

between 10 and 1,000 kPa, yield stresses between 250 and 800 Pa, and low shear viscosities

of 200 to 2,000 Pa·s, Macroscopically dense samples, such as bend bars, should be printed

with paste which exhibits flow for a short window of time after deposition so adjacent

filaments knit together to fill inter-filament pores. Spanning structures, such as lattices,

should be printed with paste which displays minimal flow upon deposition and is stiff

enough to resist deformation after printing. Generally, pastes with high 𝐺eq′ (> 40 kPa) will

print as spanning structures and pastes with lower 𝐺eq′ (< 40 kPa) will print as space filling

filaments.

When yield stress fluids are subjected to pressure-driven flow the velocity profile

that develops in the fluid is classified as plug flow,[76] which is characterized by a velocity

gradient near the walls confining the paste and an area of constant velocity in the center of

the paste body (Figure 1.6A). This flow profile arises due to yielding of the fluid near the

walls where drag occurs creating a layer of flowing material, shielding the core of the fluid

body from being subjected to shear. The torque profile which is generated by this flow type

therefore has the highest magnitude and slope near the walls constraining the fluid where

the velocity gradient is greatest (Figure 1.6B).

20

Figure 1.6. Representative velocity (A) and torque (B) profiles for an arbitrary pressure-

driven flow system illustrating the plug flow characteristic of pressure-driven flow

systems of yield stress fluids.

Alignment of anisotropic particles in additive techniques utilizing pressure-driven flow

systems is therefore limited to the regions near the walls of the deposition nozzle or other

shearing surfaces, as previous studies have noted.[38,39] This cortical alignment (Figure

1.7) is useful for creating bio-inspired ceramics,[38,39] but is difficult to quantify and not

appropriate for other applications.

Figure 1.7. SEM images of filaments of alumina platelets printed using different nozzle

lengths, showing the effect of nozzle length on the level of concentric platelet

alignment.[39]

Table 1.2 compares studies which have aligned anisotropic particles in dense

ceramics using direct writing with direct writing processes for equiaxed ceramic pastes.

21

When degree of alignment is reported in these studies, it is generally measured by percent

of oriented particles[38] or by apparent width of unaligned core in the filament.[39] A wide

range of paste formulations and anisotropic particle concentrations have been successfully

printed, however the printing resolution (nozzle diameter) for templated systems is still

worse than that of equiaxed systems. This is likely due to large anisotropic particles

forming flocculate complexes and clogging nozzles with smaller diameters.

22

Table 1.2. Comparisons of relevant parameters for direct writing/robocasting systems which produce aligned particles compared to

systems with no goal of alignment.

Publication Ceramic

System(s)

Paste

Formulation(s)

𝑮𝐞𝐪′ *

(kPa)

𝝈𝐲

(Pa)

η

(Pa·s)**

Printing

Pressure

(kPa)

Deposition

Rate

(mm/s)

Alignment Nozzle

Diameter(s)

Deposited

Geometry

Fu et al.[38]

Alumina

(85%

equiaxed,

15%

platelets)

50 vol%

ceramic, 50

vol% water and

organics

40 340 500 DBE 10

Outer 60%

of each

filament

aligned to

the nozzle

wall

0.5 mm

diameter

circular

nozzle

20-30 mm

wide

scaffolds

Feilden et

al.[39]

Alumina

(30%

equiaxed,

70%

platelets)

31 vol%

ceramic, 69

vol% water and

organics

38 885 780 DBE 10

Outer 70%

of each

filament

aligned to

the nozzle

wall

0.2 – 1.6

mm

diameter

circular

nozzle

40 x 4 x 3

mm dense

test bars

García-

Tunón et

al.[73]

Alumina

and

graphene

oxide (28

vol%

alumina

platelets,

1.1 vol%

graphene

oxide

flakes)

29 vol%

ceramic, 71

vol% water

NR NR NR NR 6 – 12 NR

0.51 mm

diameter

circular

nozzle

40 x 4 x 3

mm test

bars

Lorenz et

al.[74]

Alumina

(70 – 80%

equiaxed,

51 vol%

ceramic, 49

vol% water and

organics

200 –

7,000

265 –

633

600 –

700 100 - 220 10 – 40 NR

0.5 mm

diameter

circular

nozzle

20 mm

wide

scaffolds

23

20 – 30%

platelets)

Walton et

al.[40,75]

PIN-

PMN-PT

+ barium

titanate

platelets

28 vol%

ceramic, 72

vol% water

and orgaincs

60 –

1,000

530

–

1,60

0

NR 800 -

1200 5 - 20

Out 18 –

60% of

each

filament

aligned to

the nozzle

wall

580 µm

diameter

circular

nozzle, 870

µm x 430

µm, 750

µm x 250

µm, and

1560 µm x

300 µm

oval

nozzles

15 x 10 x

3 mm

dense

plates

and

scaffolds

Equiaxed[56

–61,63–

65,67–

69,72,77]

Alumina,

ZnO,

zirconia,

PNZT,

PZT,

silica,

kaolin,

mullite,

barium

titanate,

boron

carbide

35 vol% ≤

ceramic ≥ 60

vol%, 40 vol% ≤

water and

organic ≥ 65

vol%

0.9 –

1,000

3 –

350

200 –

2,000 DBE 0.007 - 20 -

0.025 mm –

0.5 mm

diameter

circular

nozzles

5 mm

wide

scaffolds

– 50 mm

wide

dense

crucibles

NR = Not reported; DBE = Displacement based extrusion

*Value read from graph of 𝐺′ versus stress at σ ≈ 0 Pa.

**Value read from graph of viscosity versus shear rate at �� = 1 s-1.

24

Relatively little work has been conducted on alignment of anisotropic particles in

dense ceramics formed by direct writing. Therefore, there are several promising avenues

for future direct writing research. One example is altering the deposition nozzle geometry

to align anisotropic particles in new modes of orientation by tailoring the shear field

generated during printing. Preliminary work on the application of anisotropic nozzles for

the alignment of platelet particle during direct writing has shown that altering the aspect

ratio of printing nozzle controls torque during printing and thus the alignment behavior of

platelet particles.[40] Additionally, while piezoelectric ceramics have been fabricated

using direct writing,[60,64,66,78] textured piezoelectric ceramics made using direct

writing have not yet been thoroughly studied. To date, direct written textured piezoelectric

ceramics display lower textured volume fractions than tape cast counterparts, but

improvements to texture quality of 10% and piezoelectric properties of 12% have been

realized by increasing the printing nozzle aspect ratio.[40] Combining the ferroelectric

property increases which result from crystallographic orientation[2] and the unique

alignment profiles and flexibility of build geometry of direct writing would open up

significant potential for novel textured piezoelectric ceramics and devices.

Some challenges associated with using direct writing for the production of

templated ceramics include rheological tailoring of the printing pastes, integrity of the

ceramic during printing and drying, and control of the unaligned core of deposited

filaments. Due to the specific rheology needed for direct writing, care must be taken when

formulating direct writing pastes with different ceramic chemistries and template particles.

Changing the powder and solvent chemistries, content of anisotropic particles, and size of

anisotropic particles all affect rheology dramatically[74,79] and need to be tailored for each

25

ceramic system and application. Printing complex shapes, or printing simple shapes in

varying orientations, necessitates the capability to print compatible support structures for

the printed ceramics. Therefore, to maximize the flexibility of direct written templated

ceramics, use of a multi-material printer would be beneficial to print supports in a

sacrificial material while the templated ceramic is printed. Control of the unaligned core

which develops during the flow regime of direct writing can be achieved through altering

the geometry of the printing nozzle, thereby altering the magnitude and shape of the applied

torque field.

1.3.3 Selection of an Additive Manufacturing Technique

Direct writing was chosen as the additive manufacturing technique of interest for

this thesis because it offers excellent flexibility of printed chemistries and printed

geometries. It also displays similarities to forming techniques already used to produce

textured piezoelectric ceramics, namely tape casting, if the aspect ratio of the deposition

nozzle is increased. Both techniques use shear forces to aligned anisotropic template

particles for subsequent crystallographic alignment of the ceramic via template grain

growth during sintering. Therefore, knowledge from the tape casting of templated ceramics

can be directly applied to the direct writing process. Additionally, the unique flow fields

which arise during direct writing could offer interesting possibilities for the alignment of

anisotropic particles.

26

Chapter 2. Tailoring Particle Alignment and

Grain Orientation during Tape Casting and

Templated Grain Growth

2.1 Publication Disclosure

The work in this section was previously published in The Journal of the American

Ceramic Society and the publisher, Wiley, allows reproduction for thesis and/or non-

commercial use. Publication is citation [34] in references.

2.2 Introduction

Orientation of anisotropic particles during tape casting is related to the velocity

profile in the slurry and the resistance to motion of the viscous slurry as the slurry passes

under the doctor blade. The velocity profile under the doctor blade can be described as a

combination of pressure-driven flow and drag driven flow[14–16,18,80] (Figure 2.1B),

and is primarily dominated by drag driven flow under typical tape casting conditions (e.g.

2 mm/s - 50 mm/s casting velocity, 0.25 mm – 2 mm gap height, 2 mm – 30 mm reservoir

height).[15,16,19]

Figure 2.1. Schematic of a (A) tape casting setup illustrating the (B) velocity profile


TGG ceramic.

27

The shear rate at any point in the velocity profile is calculated by taking the slope

of the velocity profile. If the rheological behavior of the slurry is known, the gradient in

the shear stress under the doctor blade can be determined. Further, the shear stress (τ) acting

on the surface of the template particle at any position in the under the doctor blade can be

calculated for a known shear rate (γ) and the experimentally determined dynamic viscosity

(ηD) using Equation 2.1.

𝜏 = ��𝜂D (2.1)

The gradient in shear stress across the major axis of the template particle (i.e.

diameter or length) generates a torque that rotates and aligns the template particle parallel

to the velocity profile. Equation 2.2 is a 1D torque approximation,[20] where M is the

torque, δy is the projection height of the particle, and τy+δy and τy are the shear stress values

on either end of the particle.

𝑀 = (𝜏𝑦+𝛿𝑦 − 𝜏𝑦)𝛿𝑦 (2.2)

When a platelet particle is oriented perpendicular to the casting direction, the projection

height (δy) is at a maximum at the platelet or fiber major dimension, but as the platelet

angle relative to the casting direction approaches 0°, the projection height approaches the

thickness of the platelet (approximately zero as platelet thickness << platelet diameter)

when perfectly aligned, i.e. the diameter of the platelet or fiber length is parallel to the

direction of the applied shear. The dynamic viscosity (resistance to shear flow) of the slurry

creates resistance to the template particle changing orientation, and thus the magnitude of

the viscous resistance depends on the dynamic viscosity, rotational velocity of the platelet,

and the surface area of the template.[81] Particle alignment under any set of tape casting

28

conditions therefore depends on how the magnitude of torque balances with the viscous

resistance of the slurry. If the torque generated during casting is sufficient to overcome the

viscous resistance and rotate the particle while it is under the doctor blade, then the template

particles will become well aligned. After casting the templates will remain well aligned,

since the aligned particles must overcome the rest viscosity (i.e. zero shear rate) of the

slurry to rotate further.

2.3 Experimental Procedure

2.3.1 Slurry Preparation

Slurries with 15 vol%, 20 vol%, and 30 vol% 200 nm alumina powder (AKP-50®,

Sumitomo Chemical, Japan) of which 5 vol% (dvb) is ~11 µm diameter by 200 nm thick

alumina platelets (Ronaflair® White Sapphire, EMD Performance Materials/Rona,

Germany, Figure 2.2) were prepared to investigate the effect of tape casting parameters on

the texture quality of final TGG textured parts. All samples were made with a doped

alumina slurry containing 0.25 wt% (dry weight basis, dwb) of CaO and SiO2 (1:1 mole

ratio) as template growth aids. The CaO source was Ca(NO3)2·4H2O (ACS Grade, Alfa

Aesar) dissolved in the aqueous binder and the SiO2 source was a vapor phase synthesized

30 nm silica (Aerosil®, Evonik, Germany). Platelets were used as received. In reference to

concentration of platelets, dry weight basis (dwb) and dry volume basis (dvb) are

equivalent because the matrix powder and platelets are both alumina. The powder mixtures

were dispersed in an aqueous acrylic binder (WB4101, Polymer Innovations, California).

The alumina powder and dopants were first ball milled with the acrylic binder for 24 h,

then platelets were added, and the slurry was ball milled for an additional 30 min. Finally,

the milling media was removed and the slurry de-aired by gentle stirring for 24 h.

29

Figure 2.2. Backscatter SEM image of alumina platelets.

After de-airing, the 30 vol% slurry was cast on the hydrophilic side of mylar tape

at gap heights from 60 µm to 330 µm (at a constant casting rate of 2.9 mm/s) and casting

rates from 2.9 mm/s to 25.7 mm/s (at a constant gap height of 254 µm). The 15 vol% and

20 vol% slurries were cast at a gap height of 254 µm and a casting rate of 2.9 mm/s. The

gap heights were selected based on the typical range of tape thicknesses (20 µm to 160 µm)

used for fabrication of multilayer ceramic parts. The doctor blade had a flat casting face of

6mm width, similar to that shown in Figure 1. Once cast and air-dried, tapes were cut and

20 – 25 layers were stacked to achieve green samples approximately 2.5 mm thick. 10 cm

sections at the beginning and end of the tape, as well as a 1 cm wide strip along each edge

of the tape, were not used when cutting samples to eliminate any edge effects from casting.

Subsequently, each sample was heated to 75 °C and uniaxially pressed at 10 MPa to lightly

tack the layers together, then laminated isostatically at 20.7 MPa and 75 °C before binder

burn-out. Binder burn-out was performed in a two-step process with a 9 h hold at 350 °C

30

and a 4 h hold at 450 °C. After binder burn-out the samples were cold isostatically pressed

at 196 MPa before being sintered at 1550 °C for 4 h to densify the ceramic and induce

template growth to achieve a high textured volume fraction in the ceramic.

2.3.2 Rheological Measurements and Flow Simulations

Slurry rheology was characterized with a cup and bob viscometer via shear sweep

tests (Bohlin, Visco88). To mimic the shear rate range during casting,[12,13,22,23,25–27]

applied shear rates ranged from 14 s-1 to 600 s-1 and the viscosity versus shear stress

response was measured while the shear rate was increasing and decreasing. Viscosity

measurements were collected within time spans similar to that of the tape casting process

(second longer intervals between measurements at different shear rates) to simulate the

rheological environment during tape casting. The viscosity behavior was then fit with a

power law equation to extrapolate the viscosity at lower shear rates (11 s-1) than measurable

with the cup and bob rheometer. Representative steady state tape casting velocity profiles

for all casting conditions studied were simulated in COMSOL Multiphysics (COMSOL

Inc.) which combined the experimentally determined rheological behavior of each slurry,

the geometry of the tape casting system, and the Navier-Stokes equation.

2.3.3 X-Ray Measurements and Analysis

X-ray θ-2θ scans were collected over a range of 20° - 118° at a step size of 0.03°

and a dwell time of 0.4 s using a PANalytical 4-Circle X'Pert3 MRD x-ray diffractometer

with a Cu x-ray tube. Additionally, rocking curve omega (ω) scans were conducted at the

θ-2θ value of the (000.12) (here l = 12 in the hkil notation) peak with a step size of 0.25°

and a step time of 1.3 s. The (000.12) peak was selected because it is the highest angle peak

31

(90.7°) from the (0001) planes of the alumina template particles. For use in rocking curve

corrections, high resolution θ-2θ scans of the (000.12) peak were collected with a 0.005°

step size and a dwell time of 1.3 s. Irradiation depth for each rocking curve was

approximately 5% of the total sample volume, which corresponds to ≈107 grains. Several

rocking curves were collected and compared from a subset of samples to determine if each

rocking curve was representative of the real alignment in a sample, and nominally no

difference was observed for each sample.

Rocking curve analysis of the x-ray diffraction patterns was conducted with the

rocking curve correction and analysis software TexturePlus and MD_fit, developed at

NIST. [82] Each rocking curve was corrected in TexturePlus with the corresponding high

resolution (000.12) peak scan to correct for the defocusing of the x-ray beam and variation

of the irradiated area, as demonstrated by Vaudin et al.[82] The FWHM of the corrected

rocking curve was determined by TexturePlus, then the corrected rocking curve was fit

with the March-Dollase equation (Equation 2.3) in the MD_fit program to obtain f and r.

Residual values for each fit iteration on the corrected rocking curve were recorded and

minimized to provide the f and r values which best fit the data.

𝐹(𝑓, 𝑟, 𝜔) = 𝑓 (𝑟2𝑐𝑜𝑠2(𝜔) +𝑠𝑖𝑛2(𝜔)

𝑟)

−32⁄

+ (1 − 𝑓) (2.3)

Cross-sections of each sample were polished and thermally etched at 1450 °C for 2

h. Scanning electron microscopy (SEM) images of etched textured microstructures were

obtained using a Phenom ProX tabletop SEM (Nanoscience Instruments, Phoenix, AZ).

SEM image areas were selected at random from an optical cross-section to reduce influence

by observational bias.

32

2.4 Tailoring Alignment during Tape Casting

2.4.1 Effect of Slurry Viscosity on Alignment

As seen in Fig. 2.3A, all slurries exhibited shear thinning behavior with the 30 vol%

slurry having the largest viscosity difference (1.26 Pa·s) between the slowest and fastest

shear rates measured compared to maximum viscosity differences of 0.06 Pa·s and 0.18

Pa·s for the 15 vol% and 20 vol% slurries, respectively. None of the slurries exhibited

hysteretic behavior in the rheology when comparing increasing and decreasing shear rate

data. When cast at 2.9 mm/s and a gap height of 254 μm, the apparent viscosity at a shear

rate of 11.6 s-1 (the average shear rate through the thickness of the casting height) in the 30

vol% system was 2.27 Pa·s, or roughly an order of magnitude greater than the viscosities

of 0.10 Pa·s and 0.30 Pa·s in the 15 vol% and 20 vol% systems, respectively (Figure 3a).

The torque profiles under the doctor blade were determined by combining the shear

rate profile calculated for each slurry composition and the experimental rheological

behavior. Equation 2 was then applied to the shear rate profile by integrating the profile.

Simulations showed that the difference in the casting rheology generated significant

differences in the torque experienced by the platelets during casting (Figure 2.3B). For

example, there is almost no gradient in torque under the doctor blade for the 15 vol% and

20 vol% slurries whereas the torque at the top of the 30 vol% cast slurry is 0.4 N/mm and

0.35 N/mm at the bottom. Furthermore, the magnitude of the torque in the 30 vol% slurry

is nominally 8 times greater than that of the 20 vol% slurry.

33

Figure 2.3. (A) Experimentally determined rheological behavior for each alumina slurry

examined in this study and (B) COMSOL calculated torque gradients through the

thickness of the slurry as a function of slurry solids loading (h = 0.254 mm, v = 2.9mm/s).

XRD ϴ-2ϴ scans and rocking curves are shown in Figure 2.4 for the three slurries

cast at v = 2.9 mm/s and a gap height of 254 µm. Both the XRD ϴ-2ϴ scan and rocking

curve of the 15 vol% slurry show many peaks in addition to the (000.12) basal peak

indicating that this slurry led to poor template orientation. Values for r and f could not be

calculated for the 15 vol% slurry because the crystallographic orientation of the (000.12)

was too poor for March-Dollase fitting. In contrast, the ϴ-2ϴ scans of the 20 vol% and 30

vol% slurries shown in Fig. 2.4A appear to indicate that they both exhibit large textured

volume fractions, but the rocking curves (Figure 2.4B) differ significantly. The 20 vol%

slurry resulted in a textured alumina with an r of 0.25, while the 30 vol% slurry resulted in

34

an r of 0.15. The increased alignment quality in the 30 vol% slurry is attributed to

significantly higher torque acting on the particles and the larger gradient in torque acting

on particles through the slurry depth below the doctor blade. The larger torque during

casting of the 30 vol% slurry is sufficient to overcome the higher viscous resistance. The

rotation of the particles to lower angles (i.e. more parallel to the casting direction) decreases

the projection length of the template (δy) and the resultant rotational torque. Once the shear

during casting is removed, it is proposed that the rest viscosity (i.e. zero shear rate) of the

slurry inhibits further rotation of the templates. As a result, the particles are effectively

frozen at a low misorientation angle upon exiting the shear field. Therefore, the rest

viscosity of the slurry (2.5 Pa·s, 0.3 Pa·s, and 0.1 Pa·s for 30 vol%, 20 vol%, and 15 vol%

respectively) is important because higher rest viscosity stabilizes the alignment of the

templates after casting.

35

Figure 2.4. (A) ϴ-2ϴ scans and (B) rocking curves for textured alumina cast at h = 254

µm and v = 2.9 mm/s as a function of slurry powder content.

2.4.2 Effect of Gap Height on Alignment

The effect of casting height on particle alignment was explored for the 30 vol%

slurry cast at 2.9 mm/s for gap heights ranging from 60 µm to 330 µm. As seen in Figure

2.5A the sharpness of the rocking curves increases with increasing gap height. All of the

XRD ϴ-2ϴ patterns for the textured ceramics produced under these conditions were similar

to the pattern shown for the 330 µm casting height (Figure 2.5B). Apart from the 60 µm

curve, each of the rocking curves corresponds to a textured volume fraction (f) of > 95%.

Figure 2.5B shows a representative ϴ-2ϴ pattern for these f > 95% samples compared to

36

a random alumina sample. As textured volume fraction increases, the (0006) and (000.12)

peaks increase in intensity while the non-basal peaks decrease in intensity.

Figure 2.5. X-ray diffraction data for textured alumina (A) rocking curves for samples

cast at varying gap heights (v = 2.9 mm/s, 30 vol% powder content) and (B) 2ϴ

diffraction patterns for randomly aligned alumina and {0001} aligned alumina.

Figure 2.6 shows how the torque profiles change as a function of normalized gap

height (position in gap height divided by total gap height) for the 30 vol% slurry when cast

at 2.9 mm/s. Increasing gap height is seen to decrease the magnitude of the torque in the

alumina slurry while casting.

37

Figure 2.6. Normalized torque gradients (position in gap height, y, divided by total gap

height, h) calculated in COMSOL as a function of gap height (v = 2.9 mm/s, powder

content of 30 vol%).

The effect of decreasing torque on grain alignment is observed in Figure 2.7. At all

gap heights a number of pockets of a few misaligned grains are observed. These small

misoriented grain clusters may arise due to a fraction of small (< 5 µm) of low aspect ratio

particles in the as received template powder. At the lower gap heights (Figures 2.7 A and

B, highest torque) clusters of misoriented grains (indicated by the dotted ovals) persisted

in an otherwise well-aligned grain structure. One factor leading to these misaligned regions

could be the low platelet diameter to gap height ratio. At the smallest gap height (i.e. 60

µm) the average platelet diameter (11 µm) is only about one-fifth of the available space for

the slurry to rotate. It is conjectured based on simulations by Wonisch et al.[16] that the

doctor blade and moving tape boundaries result in edge effects in the shear rate profile

during the tape casting process. These abrupt changes in shear rate, and thus shear stress,

alter the torque profile which interferes with template rotation, reduces the shear alignment

effect, and increases overall misorientation. At larger gap heights (203 µm to 330 µm)

these edge effects will not have a significant impact on overall alignment as the region

unaffected by the edge effects (approx. 75% of the gap height)[16] is still more than 14

38

times larger than the average template diameter. However, at smaller gap heights (60 µm

and 127 µm) the region free from edge effects is only 4-8 times the average template

diameter, and as such perturbation of template particles by edge effects will decrease

overall alignment quality. It is clear comparing r and the increase in torque that increasing

torque alone during casting does not always result in an improvement in grain alignment.

Therefore, the ability of the template particles to rotate freely could play a critical role in

alignment, similar to cases where increased template particle concentration negatively

affected alignment quality.[11,12]

39

Figure 2.7. Polished cross-sections of samples cast at 2.9 mm/s from the 30 vol% slurry

cast at gap heights of: (A) 60 µm, (B) 127 µm, (C) 203 µm, (D) 254 µm, and (E) 330

µm. Localized areas of misalignment in the 60 µm and 127 µm samples are shown in the

dotted ovals.

40

2.4.3 Effect of Casting Rate on Alignment

Figure 2.8 compares the velocity (Fig. 2.8A) and torque (Fig. 2.8B) gradients as a

function of casting velocity for 30 vol% slurries cast with a 254 µm gap height. The fastest

casting rate results in the highest torque of 1.3 N/mm and greatest torque gradient observed

in this study. As seen in Figure 2.8B it is observed that high quality alignment is observed

for all casting rates with r ranging between 0.15 and 0.2. The best alignment was observed

for the slowest and fastest casting speeds. At the slowest casting velocity (2.9 mm/s) the

time spent by the slurry under the doctor blade was approximately 2.1 seconds, while at

the highest velocity (25.7 mm/s) the time spent under the doctor blade was just 0.2 seconds.

At the slowest casting rate, the viscosity of the slurry will be high (2.27 Pa·s) and thus the

torque and rotational velocity are lower, but the longer casting time facilitates alignment.

At the fastest casting rate, the lower viscosity of the slurry (0.86 Pa·s) and higher torque

results in higher rotational velocity of the template, and thus a shorter casting time still

produces well aligned templates. This suggests that, while the ability of the torque to

overcome the viscous resistance imposed by the slurry plays a major role in template

alignment, the length of time the template is exposed to the torque is also important during

tape casting.

41

Figure 2.8. Variations in the (A) velocity profiles and (B) torque profiles as a function of

casting rate when gap height is 254 µm and powder content is 30 vol%.

2.4.4 Settling Considerations

A modified Stokes equation (Eqn. 2.4)[83] was used to determine whether settling

of the large template particles could lead to particle reorientation. Equation 4 was

determined by balancing the drag force on the template and the buoyancy of the template

in the slurry against the weight of the template. The terminal velocity (vT) of an aligned

template particle is obtained as a function of the difference between the density of the

template and the density of the slurry (ρT and ρs respectively), average radius of the platelet

(r), platelet thickness (h), the gravitational constant (g), dynamic viscosity (ηD, 2.5 Pa·s

for the 30 vol% slurry), a shape correction factor (k) to account for non-spherical particle

42

geometries, the equivalent spherical diameter (ds) of the template. A k of 1.35 was used in

this case to approximate a high aspect ratio cylinder at a Reynold’s number of

approximately 10-3.

𝑣T = (𝜌𝑇 − 𝜌𝑠)𝑟2ℎ𝑔

3𝜂D𝑘𝑑s (2.4)

Using Eqn. 2.4 the terminal velocity of an 11 µm diameter by 200 nm thick template

particle was calculated to be approximately 0.7 nm/s. This extremely slow settling velocity

is attributed to ds being very small, due to the high aspect ratio of the platelets, as well as

the relatively small difference between the densities of the platelet and the slurry (ρT = 3.98

g/cm3, ρs ≈ 2 g/cm3). The density of the alumina slurry was calculated by weighted average

based on the densities and proportions of the slurry components. Therefore, settling of

aligned platelets during casting and drying processes is unlikely to affect alignment quality.

Misaligned templates will settle differently than aligned templates, which potentially

accounts for the orthogonal grains observed in Figure 2.7, however further experiments

are required to study the origin of the misaligned grains.

2.4.5 Concluding Remarks on Torque and Alignment

Overall, once the torque exceeds approximately 0.2 N/mm there is a sharp increase

in crystallographic alignment (decrease in r) as seen in Figure 2.9. FWHM follows the

same trend as torque. In the powder loading series FWHM ranged from 11.7° (20 vol%,

0.05 N/mm) to 6.0° (30 vol%, 0.37 N/mm), in the gap height series FWHM ranged from

7.3° (60 µm, 0.89 N/mm) to 4.5° (203 µm, 0.44 N/mm), and in the casting rate series

FWHM ranged from 8.6° (8 mm/s, 0.75 N/mm) to 5.8° (25.7 mm/s, 1.23 N/mm). FWHM

and r are obtained in different ways, so the difference between the two should be kept in

43

mind when comparing them. FWHM is obtained from the full width at half of the maximum

intensity in the rocking curve, and as such describes only those grains captured in the peak

of the rocking curve. However, r fits the entire rocking curve pattern, which includes both

the peak and the tails of the orientation distribution function, so r describes a larger range

of data than FWHM.

Figure 2.9. The relation between r and torque for all sample sets studied. The data point

marked with an asterisk corresponds to the 254 µm gap height, 2.9 mm/s casting rate, 30

vol% condition which was included in the data for each parameter set discussed

previously.

It is important to recall that each of the casting parameters will influence the shear

field and alignment process through different mechanisms (torque magnitude and gradient,

distance between edge effect layers, duration of exposure to shear stress), and as such in

future work it will be important to consider these mechanisms rather than attempting to

produce an “ideal” torque value. Compared to previous works by Brosnan et al. (h = 200

µm , v = 10 mm/s)[26,84] and Pavlacka et al. (h = 376 µm, v = 5 mm/s),[12] the FWHM

was decreased to 4.5° for lower aspect ratio templates (Figure 2.10) by carefully

controlling casting parameters to maximize template alignment. To lower the FWHM and

r values further (FWHM ≤ 1°, r < 0.1), the effect of additional factors such as the length of

44

the doctor blade parallel to the casting plane, doctor blade thickness, varying the number

and geometry of the doctor blade(s), and processing the template particles to remove

templates which have a diameter of less than ~5 µm should be explored in the context of

TGG template alignment.

Figure 2.10. A comparison of full width at half maximum (FWHM) achieved in previous

TGG tape casting studies which utilize platelet-like template particles.[12,26,85]

45

Chapter 3. Dispersion and rheology for direct

writing lead-based piezoelectric ceramics pastes

with anisotropic template particles

3.1 Publication Disclosure

The work in this section has been submitted and accepted for publication to the

Journal of the American Ceramic Society, and the accepted manuscript is citation [75]. The

publisher, Wiley, allows for the reproduction of published content for the purposes of non-

commercial/educational purposes.

3.2 Introduction

Direct writing is a method of additive manufacturing where a filament of ceramic

paste is extruded from a nozzle and rastered to build up a shape layer-by-layer.[86–88]

This method, also called robocasting,[56,57,89] was first developed, and subsequently

used, to 3D print a variety of structural,[69,70,72,73,90,91] electrical,[59–61,66,68,92–94]

and textured ceramics.[38,39] Direct writing offers unique possibilities for tailoring

crystallographically textured ceramics via templated grain growth. In this case, the shear

stress during printing facilitates alignment of anisotropically-shaped template particles, and

subsequently, the crystallographic alignment of the printed ceramic after sintering and

templated grain growth. Direct writing produces complex shapes and offers the flexibility

of orienting the shape in relation to the print head, and thus depositing template particles

with various orientations relative to the shape of the print. Tailoring the crystallographic

orientation relative to the ceramic geometry has the potential to generate ceramics with

novel microstructures and thus unique mechanical, piezoelectric, and other properties.

46

Rheological control is of paramount importance for direct writing because the

process involves the extrusion of paste through a small diameter nozzle. The paste must

exhibit a sharp yield behavior to facilitate both the shearing and flow of the paste through

the nozzle and for the paste to hold its shape after deposition.[61] The yield stress (σy) and

the equilibrium storage modulus (𝐺eq′ ) are two important parameters for determining the

viability of a paste for printing. 𝐺eq′ is a measure of the stiffness of a fluid and represents

the resistance to flow at rest for that fluid.[39] Minimum values of yield stress and 𝐺eq′ for

successful direct writing have been reported as σy > 50 Pa and 𝐺eq′ > 104 Pa.[39,61,72]

Factors that affect the rheology of ceramic pastes with a specified particle loading include

suspension pH,[61,67,95] particle size and size distribution,[73,96–100] particle

geometry,[73,79,100–102] and organic additives.[59,60,66,67,71,72,103,104]

The pH of the paste can dramatically affect particle surface charge and organic

molecule conformation, and subsequently cause the viscosity of the paste to change by

orders of magnitude.[61,67,95] For direct writing some degree of flocculation or polymer

chain entanglement is needed to produce a paste with a distinct yield stress as a result of

floccules being broken down and entangled polymer chains being untangled.[61,67]

Flocculation has been controlled by gelling or coagulating an organic additive[61] as well

as mildly inhibiting the adsorption of dispersant polymers to the surface of the ceramic

particles[67] with as little pH change as 1.

Varying the particle size of the ceramic powder can change the viscosity and yield

stress of a paste by orders of magnitude.[96,105] As particle size decreases, holding

volume percent (vol%) constant, the total surface area of the suspended particles increases

and the interparticle distance decreases. Decreased spacing increases both the number of

47

particle interactions and the strength of particle-particle interactions, causing a higher

viscosity and yield stress.[96,99] Especially at high particle concentrations ( > 25 vol%),

replacing portions of a particle population with particles of a smaller size increases the

yield stress dramatically.[96] In some cases addition of a low fraction of highly charged

nanoparticles decreases the viscosity of a suspension of larger particles.[97] In this case

the large particles alone have low surface charge and the nanoparticles create a “halo” of

charge around the larger particles, causing the larger particles to repel one another and

resist flocculation.[97]

Particle shape plays a critical role in suspension rheology. Suspension viscosity

increases exponentially at lower powder concentrations as particles become more

anisotropic (aspect ratio increases).[100–102] This is because non-spherical particles have

larger ellipsoids of revolution compared to spherical particles of the same volume, causing

increased interparticle interaction and thus more agglomeration at lower solids loadings

than spherical particles.[100–102] The viscosity of suspensions of anisotropic particles

decreases if the suspension is subjected to shear conditions which align the particles.[100]

Increasing the volume fraction of platelet particles in pastes containing more than 20 vol%

(dry powder basis) platelets has been reported to decrease the storage modulus and yield

stress of pastes.[74]

PIN-PMN-PT (Pb(In1/2Nb1/2)O3-Pb(Mg1/3Nb2/3)O3-PbTiO3) was chosen as a model

system for this study because textured, lead-based piezoelectric ceramics have much better

properties than polycrystalline ceramics and approach those of single crystal analogs. Also,

PIN-PMN-PT aqueous dispersion chemistry is representative of other aqueous-processed

lead-based piezoelectric ceramics. The specific system studied here consists of 1 – 10 vol%

48

BaTiO3 platelet particles and 90 – 99 vol% PIN-PMN-PT powder; a system that results in

high quality textured piezoelectric ceramics.[4–6] CuO nanoparticles were added at 0.25

weight % (PIN-PMN-PT basis) to lower the sintering temperature. The results reported in

this paper serve as the foundation for a study on the additive manufacturing of textured

piezoelectric ceramics by direct writing.

In this paper we show how the surface chemistry of the PIN-PMN-PT powder and

binder system are affected by pH, as well as how size and concentration of BT templates

affects rheology. The rheology of suspensions was measured to establish relations between

paste formulation and conditions for direct writing. The effect of 𝐺eq′ and yield stress on

the printing behavior of the pastes was correlated with the necessary printing pressure to

extrude the paste, the consistency of filament thickness upon printing, the degree of space

filling, and the ability of the deposited filaments to hold shape.


3.3.1 Powder and Paste Preparation

A perovskite Pb(In1/2Nb1/2)O3-Pb(Mg1/3Nb2/3)O3-PbTiO3 (PIN-PMN-PT) (Applied

Research Lab, Freeport, PA), which is a solid solution with the molar ratios 0.28PIN-

0.40PMN-0.32PT,[9] was used as the matrix powder (Figure 3.1A). The as-received BT

(BaTiO3) platelet particles (Entekno, Eskisehir, Turkey), had a width of 2 – 40 µm and

thickness of 0.5 – 1 µm (Figure 3.1B). CuO nanoparticles of < 50 nm diameter (Sigma

Aldrich, St. Louis, MO) were added at 0.25 wt% (PIN-PMN-PT basis) as a sintering aid.

All PIN-PMN-PT powders used in this study were vibratory milled with zirconia media

for 96 h. CuO nanoparticles were added to the PIN-PMN-PT powder during this step.

49

Figure 3.1. Backscattered SEM images of (A) PIN-PMN-PT matrix powder around a

BT template particle (arrowed) and (B) BT template particles showing the size difference

between matrix powder and template particles and the geometry of the template particles.

After vibratory milling, powders were dry sieved to < 88 µm to obtain a monomodal

particle size distribution with a d50 of 280 nm. For conciseness, PIN-PMN-PT will be used

to refer to all pastes which contain both PIN-PMN-PT and CuO. BT platelets were

separated into different sizes by first dispersing with 0.1 wt% dispersant (DS001, Polymer

Innovations, Vista, CA) and then settled for 2 min. The supernatant particles were

suctioned off to obtain a population of platelets 20 – 40 µm in width in the sediment,

referred to as large platelets. The supernatant was then stirred and settled for 3 min, again

suctioning off the supernatant particles to remove platelets < 5 µm and obtain platelets 5 –

20 µm in width in the sediment, referred to as small platelets.

A commercial binder system consisting of an aqueous acrylic-based

polymer (WB4101, Polymer Innovations, Vista, CA) of pH 6.5 and a plasticizer (PL008,

Polymer Innovations, Vista, CA) of pH 12.5 was used. This binder system was selected

due because is had earlier been established with the vendor (Polymer Innovations, Inc.) to

be compatible for tape casting PIN-PMN-PT. Because it is a commercial system, the details

50

of the organic binder and plasticizer are unknown. However, to the best of our knowledge

the polymer is poly(acrylic) acid (PAA). The standard binder mixture for all pastes was 40

weight % (wt%) DI water, 30 wt% WB4101, and 30 wt% PL008. The concentrations of

binder and plasticizer in the final 28 vol% wet ceramic pastes were 21.5 and 22 vol%,

respectively, and 42 vol% total in the green ceramic body. Powders and binder systems

were mixed in a SpeedMixer (DAC 600, FlackTek Inc., Landrum, SC) at 800 – 2000 rpm.

If BT platelets were added they were pre-dispersed in a portion of the binder system by

manual stirring, then added to the powder and remaining binder portion before mixing.

Platelet concentrations of 0.3, 1.4, and 2.6 vol% of the total paste volume, or 1, 5, and 10

vol% relative to the PIN-PMN-PT powder were studied.

3.3.2 Zeta potential and solubility measurements

Zeta potential was measured with a Malvern Zetasizer ZS (Malvern Panalytical,

Westborough, MA) with 3 runs of 100 measurements for each sample. Suspensions for

zeta potential measurements consisted of dilute suspensions of 0.08 vol% PIN-PMN-

PT/CuO in either DI water or a solution containing the organic binder in the same

proportion to the powder as used in the 28 vol% pastes. The suspensions were adjusted to

pHs of 1 – 12.5 prior to powder addition using nitric acid (HNO3) or ammonium hydroxide

(NH4OH). All suspensions were aged for 24 h and then the pH of the suspension was

remeasured immediately before zeta potential measurements which are the reported pH

values for zeta potential. Suspensions with the binder equilibrated to different pH values

than the suspensions with no binder because the plasticizer has a pH of 12.5.

Solubility of 0.10 vol% PIN-PMN-PT + CuO + BT platelets (0.3 vol% CuO and 10

vol% BT on a dry PIN-PMN-PT basis) was measured at pH 1, 5, 9, and 13. Suspensions

51

were aged 1 h after shaking vigorously, then centrifuged at 4000 rpm for 1 h to remove the

powder particles. The cation concentrations in the clear supernatant were measured via

Inductively Coupled Plasma Emission Spectrometry (ICP-AES) (Thermo iCAP 7400,

Thermo Scientific, Waltham, MA).

3.3.3 Rheological measurements and printing

Rheological measurements were performed on pastes of 28 – 35 vol% solids

(compositions shown in Table 3.1) with an oscillatory rheometer (ARES-LS, TA

Instruments, New Castle, DE) using a cone-and-plate sensor (0.1 rad cone angle) at a 48

µm gap height at room temperature on (1) pastes with no templates while varying ceramic

loading and pH and (2) pastes with different platelet contents at a constant pH. The yield

behavior of each paste was evaluated using strain sweep tests from 0.01% to 200% strain

at a shear rate of 100 s-1. The yield stress is defined as the stress at which the loss modulus

(𝐺′′) exceeds the storage modulus (𝐺′), and the equilibrium storage modulus (𝐺eq′ ) was

determined by extrapolating the low stress plateau in storage modulus to zero stress.[39]

For select pastes, recovery behavior was also measured with a time sweep test at a constant

shear rate of 100 s-1 and strain of 0.01% for 10 min. Recovery measurements were

performed immediately after the 200% strain measurement from the rheology test.

Recovery time is the time necessary for the storage modulus to exceed the loss

modulus.[106]

Table 3.1. Compositional ranges for 28 – 35 vol% ceramic PIN-PMN-PT pastes used in

this study.

Material Function Volume

fraction (%)

Weight

fraction (%)

Density

(g/mL)

PIN-PMN-PT Ceramic

28 – 35 vol%

Ceramic matrix 25.48 – 31.82 70.36 – 75.47 8.19

BT Crystallographic

template 2.55 – 3.18 5.17 – 5.55 6.02

52

DI water

Solvent and

Binder

72 – 65 vol%

Solvent 27.76 – 25.07 9.36 – 7.26 1.00

WB4101 Binder 21.56 – 19.47 7.27 – 5.64 1.03

PL008 Plasticizer 22.21 – 20.05 7.48 – 5.81 1.00

DS001 Dispersant 0.22 – 0.20 0.07 – 0.06 1.00

DF002 Defoamer 0.22 – 0.20 0.07 – 0.06 1.00

Samples of 28 vol% solids were printed on Parafilm (Sigma, Saint Louis, MO) at

880 – 1250 kPa using a high pressure piston (HPx High Pressure Dispensing Tool,

Nordson, East Providence, RI) and pressure controller (Ultimus V High Pressure

Dispenser, Nordson, East Providence, RI) attached to a Cartesian 3D printer (MakerBot,

Brooklyn, NY). A schematic of the 3D printer is shown in Figure 3.2. Printed samples

were evaluated for consistency of paste extrusion, degree of space filling by the extruded

filaments, and pressure necessary to extrude at a printing rate of 5 mm/s. Green cross-

section images were collected after the printed samples dried in a 95% relative humidity

container for 4 d to prevent drying warpage. Binder burn-out, sintering, and densities of

similar samples are outlined in a subsequent study.[40]

53



flow field.

3.4 Surface Chemistry and Dispersion

The surface chemistry of lead-based perovskites like PIN-PMN-PT is highly

complex due to the multiple multivalent cations and interactions with the polymer system.

Figure 3.3 shows changes in zeta potential as a function of pH for PIN-PMN-PT with and

without the organic binder. From approximately pH 3.5 to pH 9 the surface charge density

of the powder is low (i.e. ≤ 5 mV), likely due to the different isoelectric points (IEP) of the

components of the PIN-PMN-PT solid solution, 5.8 for PMN (Pb(Mg1/3Nb2/3)O3), 8 for PT

(PbTiO3), and unknown for PIN (Pb(In1/2Nb1/2)O3).[107,108] Additionally, the isoelectric

54

points of the constituent oxides span a wide range of pH (Table 3.2). The zeta potential of

oxide systems with more than 3 elemental constituents has not been studied, but lead

magnesium niobate (PMN)[107] and lead zirconium titanate (PZT)[109] display similar

low charge density regions at pHs between the isoelectric points of their constituent oxides.

At pH 1 and 13 the zeta potentials of PIN-PMN-PT are 18 and -35 mV, respectively, which

could provide effective electrostatic stabilization.

The double IEP for the bare powder in Figure 3 is consistent with other perovskites

and complex metal oxides in aqueous suspension.[110–112] The fundamental mechanism

for the double IEP is that complex metal oxides are incongruent as a function of suspension

pH as shown in Figure 4.[111] This is a general issue because all complex metal oxides

consist of a basic metal oxides in solid solution with acidic metal oxides, even complex

materials systems such as PIN-PMN-PT. The single component basic metal oxides, i.e.

PbO, are acid soluble through the mid- pH range with lower solubility at alkaline pH. Also,

most of these divalent species form a stable metal carbonate or hydroxy-metal carbonate

solid in the ambient environment starting at pH 8.5, with the metal oxide emerging above

about pH 12. Thus, the double IEP is created in part by the leaching of basic cations through

a sparingly soluble acidic oxide matrix.[111] Additionally, the specific adsorption of the

basic cations leached from the surface contributes to the double IEP where basic cations

specifically adsorb on the acid metal oxide-enriched surface.[113]

55

Figure 3.3. Zeta potential as a function of pH for 0.08 vol% PIN-PMN-PT suspensions

with and without the acrylic binder system exhibiting the surface charge modification

enacted by acrylic binding to the particle surface. Where error bars are not visible the

error was less than the height of the data point.

Table 3.2. Isoelectric points for metal oxides related to PIN-PMN-PT showing a wide pH

range of low surface charge.

Material Isoelectric Point

PbO 10[107,114]

MgO 10 – 12[107,114]

Nb2O5 3[107,114]

TiO2 2.4 – 6[114]

In2O3 7 – 8.7[115]

Pb(Mg1/3Nb2/3)O3 (PMN) 5.8[107]

PbTiO3 8[108]

Pb(In1/2Nb1/2)O3-Pb(Mg1/3Nb2/3)O3-PbTiO3 (PIN-

PMN-PT)

3 – 8*

*This work

Particle solubility can have a dramatic effect on particle interactions due to the

increase in ionic strength of the suspension from dissolved multivalent cations.[114,116]

Figure 3.4 shows the solubility of M2+ ions from a mixture of PIN-PMN-PT, CuO, and BT

as a function of pH. Due to the low ion concentrations in the majority of this pH range,

56

destabilization of the dispersion from these dissolved species was not observed. Pb2+

concentration is highest at pH 1 at approximately 5.6 x 10-3 M. The concentrations of the

other metal ions are an order of magnitude lower at pH 1, suggesting there is a lead-

depleted layer on the surface of the PIN-PMN-PT particles at extremely low pHs.[117] The

concentrations of Pb2+ and Cu2+ drop by 4 – 5 orders of magnitude as the pH becomes more

basic, but increase again at pH 12. The concentrations of all metal ions are each less than

2 x 10-4 M at pH 12.

Figure 3.4. Solubility of 0.10 vol% PIN-PMN-PT + CuO + barium titanate suspensions

aged for 1 h as a function of pH showing incongruent dissolution of the M2+ cations.

The addition of the polyacrylic acid (PAA) based binder system increases the

magnitude of zeta potential over a wide range of pH starting at pH 5 (Figure 3.3). At pH

< 5 PAA exists in a globular conformation in suspension with negligible fractional

charge.[118] This conformation and lack of charged monomers impedes interaction

between the PAA and the particle surfaces, which is suggested by the positive zeta potential

for particles both with and without the acrylic binder. Beginning at pH 5, PAA is partially

57

charged and the polymer chain is partially unfolded. Due to this and the near neutral surface

charge of PIN-PMN-PT in this pH range, there is an increasing degree of adsorption of

PAA to the particle surfaces leading to a zeta potential of -25 mV.[95] The change in zeta

potential from zero to -25 mV suggests the PIN-PMN-PT is electrosterically stabilized. At

higher pH the PAA monomer groups are negatively charged and are fully charged polymer

chains at approximately pH 11.[118] The zeta potential reaches a stabilized value of -35

mV at pH 12 for suspensions with and without the PAA present, suggesting that the

negatively charged polymer chains do not contribute to the zeta potential of the suspended

powder at pH 12.

Polyacrylic acid can be crosslinked by M2+ metal ions.[119] The solubility trends

in Figure 4 suggest that if metal ions cross-link PAA in this system then it is most likely

at pH 1. Significant cross-linking is not expected at pH 12.5 due to the relatively low

concentration of M2+ cations. Based on Pourbaix diagrams the divalent cations exist

predominantly as simple metal hydroxides at pH 12.5.[120–123] Despite the extreme pH

of the suspension, acrylic polymer hydrolysis is not considered in this analysis because

PAA does not significantly hydrolyze within the short mixing times of this study at room

temperature.[124,125]

3.5 Rheology of Direct Writing Pastes

Rheology was evaluated as a function of powder loading for pastes containing only

PIN-PMN-PT, the acrylic binder system, and water of pH 5. As powder loading increased

from 28 vol% to 35 vol% the stiffness and yield stress of the paste each increase

dramatically (Figure 5) from 𝐺′= 110 kPa and σy = 520 Pa for the 28 vol% paste to 𝐺′= 420

58

kPa and σy = 1300 Pa for the 35 vol% paste. It is well known that as powder content

increases the stiffness and yield stress of suspensions increase due to increasing

interparticle forces.[96,99] In order to maintain stiffness and yield stress values which are

amenable to the pressure-driven direct writing system used for this study (𝐺′≈ 100 kPa, σy

≤ 1500 Pa), further exploration of rheological properties was carried out on 28 vol%

ceramic loading pastes because of anticipated increases in paste stiffness and yield stress

with the addition of anisotropic platelet particles.

Figure 3.5. Storage modulus (solid data points) and loss modulus (hollow data points) as

a function of applied stress for PIN-PMN-PT pastes formulated at pH 5 with 28, 30, or 35

vol% powder loading illustrating the increase in storage modulus and yield stress as

powder content increases.

Pastes of 28 vol% ceramics were prepared to study the effects of surface chemistry

and ceramic-binder interactions on rheology. Figure 3.6A shows the rheological behavior

of three pastes in which 28 vol% PIN-PMN-PT powder was first mixed with deionized

water adjusted to pH 1, 5, or 13 with nitric acid (HNO3) or ammonium hydroxide (NH4OH)

59

and then with the PAA binder system. The pastes composed of 28 vol% PIN-PMN-PT

equilibrated to pH 12.5 within 1 h after mixing with the binder system.

The pH 1 paste has an equilibrium storage modulus (𝐺eq′ ) of 180 kPa and a yield

stress of 1450 Pa with a gradual drop in storage modulus with increasing applied stress.

The water and powder suspension begins at pH 1, well below the isoelectric point of PIN-

PMN-PT and increases in pH to 12.5 when the polymer is added. This change likely causes

the paste pH to pass through the isoelectric point of PIN-PMN-PT and could cause

flocculation. At pH 1, the PAA phase separates in a globular conformation within the

suspension and has negligible fractional charge[118] while the surface of the powder is

positively charged (Figure 3.3). Due to crossing the isoelectric point of PIN-PMN-PT

during equilibration, and the probability that the PAA does not interact with the powder

particles, the paste is flocculated, causing the high 𝐺eq′ and yield stress. The pH 1 paste

exhibits a gradual drop in storage modulus when printed and as seen in Figure 3.6B the

filaments are inconsistent in uniformity and width.

60

Figure 3.6. (A) Storage modulus (filled points) and loss modulus (hollow points) as a

function of applied stress for 28 vol% PIN-PMN-PT pastes formulated at different initial

pHs and the PAA binder system. Printing tests of 28 vol% PIN-PMN-PT pastes

formulated at (B) pH 1 and (C) pH 5 illustrating the importance of a paste with a steep

drop in storage modulus with increasing applied stress for consistent printing.

The pH 5 paste has a 𝐺eq′ of approximately 130 kPa with a yield stress of 530 Pa

and a steep drop in 𝐺′ with increasing applied stress which could be attributed to more

61

effective binding of the PAA to the particle surface producing an electrosterically stabilized

suspension.[95] Additionally, the sharp decrease in 𝐺′ could be due to polymer chain

entanglement caused by the partial unfolding of PAA bound to the particle surface. The

lower 𝐺eq′ and yield stress of this paste, when compared to the paste mixed at pH 1, suggest

that the paste mixed at pH 5 is better dispersed. The pH 5 paste exhibited a steep drop in

storage modulus and prints as well-defined filaments of consistent width (Figure 3.6C).

Paste mixed at pH 13 displays rheological behavior similar to paste mixed at pH 1,

with a 𝐺eq′ of 70 kPa, a yield stress of 1550 Pa, and a gradual drop in storage modulus with

increasing stress. The PAA chains are completely unfolded at pH 13 and have a high

fraction of negatively charged monomers.[118] The unfolded conformation, negative

charge of PAA, and negatively charged surface of the PIN-PMN-PT (Figure 3.3) suggest

that the PIN-PMN-PT particles and PAA do not interact at pH 13 and the paste is well

dispersed. The high yield stress of the pH 13 paste could be attributed to hydrogen bonding

between PAA chains that is more likely as the pH increases and the polymer chains

unfold.[118] When the paste mixed at pH 13 was printed it behaved similarly to paste

mixed at pH 1.

3.5.1 Effect of Anisotropic Particles on Paste Rheology

The size, concentration, and aspect ratio of particles have a significant effect on the

rheology of ceramic suspensions. All pastes with BT platelets were mixed at pH 5 with 28

vol% ceramics and 72 vol% binder solution. Figure 3.6 shows the rheological response of

pastes mixed with 0.3 and 1.4 vol% anisotropic BT template particles ranging in width

between 5 and 40 µm. The addition of large, anisotropic particles reduced 𝐺eq′ from 130

62

kPa (no templates) to 78 and 70 kPa for the 0.3 and 1.4 vol%, respectively, and reduced

the slope of storage modulus versus stress. The measured differences in 𝐺eq′ were apparent

in the pastes post-mixing, as each of the pastes containing BT platelets flowed immediately

after mixing and the paste without BT platelets did not. The yield stress was approximately

constant at 1200 Pa as BT platelet content increased from 0.3 vol% to 1.4 vol% and is

significantly higher than the yield stress of pastes without BT platelets (530 Pa).

Figure 3.7. Storage modulus (filled points) and loss modulus (hollow points) as a

function of applied stress for 28 vol% ceramic pastes formulated at pH 5 with either 0.3

or 1.4 vol% 2 – 40 µm anisotropic barium titanate (BT) platelet particles illustrating the

decrease in storage modulus and increase in yield stress as anisotropic platelet content

increases.

The addition of large equiaxed particles into a suspension typically lowers the yield

stress of the suspension.[96] In contrast, suspensions of randomly oriented anisotropic

particles have much higher yield stresses than suspensions of equiaxed particles.[101,102]

Compton and Lewis showed that the addition of 13.6 vol% anisotropic platelet particles to

63

a Newtonian polymer resin increased 𝐺eq′ by 3 orders of magnitude and produced a distinct

yield stress behavior.[79] In contrast to their work the concentration of anisotropic particles

in our pastes is much lower at ≤ 2.6 vol%. At low concentrations large anisotropic particles

may lower 𝐺eq′ , due to the relative size of the platelets to the equiaxed matrix particles, but

increase yield stress due to alignment of the platelets as the paste is sheared. Lorenz et al.

reported a similar effect on 𝐺eq′ for pastes of equiaxed alumina and alumina platelets.[74]

In their work they showed that 𝐺eq′ decreased by an order of magnitude when the platelet

fraction increased from 10 to 15 vol%.

Figure 3.8 shows the rheological response of pastes made with platelets of different

sizes (i.e. width, x). Paste with 1.4 vol% small platelets (5 µm < x < 20 µm) had a high

𝐺eq′ and yield stress of 1000 kPa and 1370 Pa, respectively. In comparison 1.4 vol% of

large platelets (20 µm < x < 40 µm) significantly decreased 𝐺eq′ to approximately 60 kPa,

but had a similar yield stress of 1500 Pa. Increasing the platelet concentration of large

templates to 2.6 vol% increases 𝐺eq′ to 180 kPa, leads to almost no change in yield stress

of 1600 Pa, and exhibits a sharp drop in storage modulus approaching the yield stress. It is

interesting to note that as this paste yields and the storage modulus of the paste decreases

the measured stress on the paste decreases, resulting in an “S” shaped curve. Compared to

the large platelets, 2.6 vol% of small platelets increased 𝐺eq′ by almost an order of

magnitude to 1000 kPa while the yield stress of the paste was similar at 1400 Pa.

64

Figure 3.8. Storage modulus as a function of applied stress for 28 vol% ceramic pastes

formulated at pH 5 with different barium titanate platelet sizes and amounts. The storage

modulus dramatically increases as platelet size decreases. Rheologies marked with a (*)

are referred to in Figure 8.

Platelet size has a significant effect on paste rheology due to the effect of torque on

particle alignment. As the platelet size increases, the projection height (𝛿𝑦) of the platelet

increases, which in turn increases the torque (𝑀) on the platelet during shear (Equation

3.1).[20,34] For the same applied shear gradient (𝜏𝑦+𝛿𝑦 − 𝜏𝑦), the smaller platelets

experience ~2.5 times less torque than the larger platelets because of the smaller average

sizes.

𝑀 = (𝜏𝑦+𝛿𝑦 − 𝜏𝑦)𝛿𝑦 (3.1)

This alignment process during shear is believed to be one reason for the decrease in stress

as some of the pastes approach the yield stress in Figure 3.8 as well as the dramatic

difference in the 𝐺eq′ of the pastes formulated with large and smaller platelets.

65

3.6 Rheological Effects on Direct Writing

Altering the surface chemistry, binder behavior, and platelet content of direct

writing pastes influenced three rheological characteristics of the pastes: 𝐺eq′ , yield stress,

and the slope of the storage modulus versus stress. Two representative samples have been

chosen to highlight the effect of these parameters on the printing behavior of the paste in

relation to three key print properties: retention of printed shape, printing pressure, and

space filling of the deposited filaments (Figure 3.9). Each paste was mixed at pH 5 with a

total ceramic content of 28 vol%, of which 2.6 vol% was BT platelets of different size

ranges, and 72 vol% binder solution, printed at 5 mm/s with printing pattern dimensions of

10 x 15 x 2 mm. The rheology of the printed pastes is shown in Figure 3.8 (marked).

The samples in Figures 3.9A and 3.9B were printed with a paste containing 2.6

vol% large BT platelet particles. The paste had a 𝐺eq′ of 180 kPa and a yield stress of 1600

Pa. Due to the high stiffness and yield stress these samples maintained the as-deposited

shape during printing and printed at an applied pressure of 883 kPa. As-printed dimensions

for this paste were 10.1 x 15.2 x 1.9 mm, showing slight (1-2%) increases in the lateral

dimensions and 4% decrease in height due to slumping and space filling upon deposition.

Additionally, filaments of this paste exhibited space-filling flow between the deposited

filaments during printing, seen in Figure 3.9B where the printed part has a fill fraction of

approximately 100% as determined visually from the cross-section. This space filling

behavior is attributed to the measured 7 s recovery time of the paste. During the recovery

time the paste can flow and fill spaces between the deposited filaments. For the samples

printed here, it takes 3 s at 5 mm/s to print one full filament length of 15 mm. Filament

knitting thus occurs because the recovery time is longer than the filament deposition time.

66

Depending on printing rate and pattern, it is easy to appreciate that as adjacent filaments

are printed the previous filaments are still flowing and knitting together.

Figure 3.9. Photographs of representative direct written PIN-PMN-PT samples of 28

vol% ceramic loading pastes formulated at pH 5 and printed at 5 mm/s with (A) top-view

and (B) cross-section for 2.6 vol% BT platelets 20 µm < x < 40 µm and (C) top-view and

(D) cross-section for 2.6 vol% BT platelets 5 µm < x < 20 µm illustrating the difference

in printing behavior generated by increasing 𝐺eq′ and decreasing recovery time.

Figures 3.9C and 3.9D show samples printed with a paste containing 2.6 vol%

small BT platelet particles. The paste had a 𝐺eq′ of 1000 kPa and a yield stress of 1400 Pa.

The high stiffness and yield stress of the paste allowed the printed paste to hold the as-

deposited shape and resist slumping upon filament layering. The higher 𝐺eq′ necessitated a

higher printing pressure of 1241 kPa to print at 5 mm/s. As-printed dimensions for this

paste were 10.0 x 13.0 x 1.8 mm or, 0 – 14% smaller in lateral dimensions and 10% shorter

height due to under-filling of the printing pattern by the more viscous paste. In contrast to

67

the paste in Figures 3.9A and 3.9B, the paste in Figures 3.9C and 3.9D exhibits spanning

behavior with little to no flow between deposited filaments and has a fill fraction of 89%

in the cross-section. Lack of complete flow between deposited filaments is due to the

shorter recovery time (2 s) of the paste but is sufficient to cause necking between filaments

to hold the print together.

The pastes in Figure 3.9 exhibit a similar yield stress, which suggests 𝐺eq′ and

recovery time have a stronger influence on printing behavior in these samples. Each paste

meets the previously reported threshold for maintaining printed shape (σy > 50 Pa and 𝐺eq′

> 10 kPa) and are suitable for 3D printing structures. However, it is interesting that

drastically different stiffnesses, recovery times, and printing behaviors can be achieved by

altering the size of platelet particles in the paste. Space filling pastes with higher recovery

times are useful for the production of dense piezoelectric ceramic parts, while spanning

pastes with low recovery times may be used to create ceramic-polymer composite green

bodies depending ceramic part objective.

3.7 Summary

Rheological control of direct writing pastes is key to the production of high quality

printed shapes. For the ceramic system of PIN-PMN-PT + CuO + BT and a commercial

polyacrylic acid binder system it was critical to control the degree of interaction between

the PAA and the ceramic powder by starting at an initial pH of 5 which resulted in the PAA

interacting with the surface of the powder to provide electrosteric stabilization. This

stabilization produced a paste with some polymer chain entanglement, which resulted in a

yield stress greater than 300 Pa but was dispersed enough to flow upon yield. The addition

68

of BT platelet seeds for templated grain growth dramatically changed 𝐺eq′ , 𝜎𝑦, and the

effect of applied stress on the storage modulus. As the size of the BT platelets decreased

and the concentration increased, the 𝐺eq′ and yield stress of the pastes increased

substantially. This is attributed to the alignment process of the initially randomly aligned

platelet particles. Controlling these factors enables the 3D printing of ceramics with unique

microstructures and shapes ranging from dense solids to spanning structures.

69

Chapter 4. Direct Writing of Textured Ceramics

with Anisotropic Nozzles

4.1 Introduction

High quality crystallographic alignment in polycrystalline ceramics (i.e. texture) is

essential for fabrication of high performance textured piezoelectric transducer components,

and other texture-engineered ceramic properties.[1,2] Crystallographic alignment is

commonly achieved by tape casting, slip casting, or magnetic alignment of ceramic slurries

with a minority volume percentage of anisotropic template particles by templated grain

growth (TGG).[2] Upon sintering, the anisotropic template particles nucleate and grow

crystallographically-oriented grains, resulting in a crystallographically-oriented

microstructure and access to texture sensitive properties. The aligned volume fraction of

the ceramic and the degree of misalignment between aligned grains directly impact the

piezoelectric properties of textured piezoelectric ceramics.[126] Thus, particle alignment

during forming has been studied extensively for tape casting[11–16,25–27,34,127] and

magnetic alignment.[128–131]

Additive manufacturing techniques that can align template particles during

forming, such as direct writing or layer-wise slurry deposition, open opportunities for

fabricating novel textured ceramics. Direct writing, or robocasting, is an additive

manufacturing technique in which a ceramic paste is extruded through a nozzle that is

rastered over a build plate onto which the paste is printed to construct a 3D geometry layer-

by-layer (Figure 4.1). Such an approach can create monolithic 3D shapes, as well as

periodic lattice structures.[87,88]

70



flow field.

Robocasting was invented by Cesarano et al. and applied to the printing of high

solids loading (60 vol%) alumina pastes.[57] Printing resolution was limited because pastes

with 60 vol% solids loading dried too rapidly. To reduce evaporation rate and obtain finer

resolution parts, they used lower powder content pastes, or printed in an oil bath.[65,90]

Cesarano et al. further demonstrated robocasting of lead zirconium titanate (PZT) pastes

to form spanning structures, and demonstrated the importance of pH manipulation in the

paste to control the rheology.[61]

Fiber alignment during polymer fused deposition [132–134], and particle alignment

during direct writing of pastes [38,39,74,79,135] have been explored to create reinforced

composites and biomimetic structures, respectively. Raney et al. demonstrated that rotation

71

of the nozzle while direct writing carbon fiber-filled resins can alter the alignment angle of

the carbon fibers in relation to the printing surface and thus create components with

multidirectionally-oriented fibers.[135] Fu et al. linked the shear alignment of anisotropic

particles with position in the printed filament for a ceramic paste of 7.5 vol % alumina

platelets and 42.4 vol% equiaxed alumina[38] during direct writing with a circular nozzle.

They observed that template particles in the outer 4/7 of the filament were aligned nearly

parallel to the nozzle surface and the inner 3/7 of the filament was nominally randomly-

oriented.[38] Feilden et al. showed for a paste of 18 vol% alumina platelets that the time

for platelet orientation could be increased with longer nozzles, and thus increase the

volume of oriented material.[39] They also showed that nozzle diameter had little effect on

the degree of alignment. Lorenz et al. simulated the process of platelet alignment during

extrusion and concluded that platelet alignment improved as the duration of applied shear

during extrusion increased in systems that contained greater than 10 vol% platelet

particles.[74]

The mechanism for alignment of anisotropic particles during direct writing is

similar to shear alignment during tape casting.[38,39] In tape casting, and other shear

alignment techniques, anisotropic particles are aligned due to the velocity gradient that

arises from the movement of slurry or paste relative to the stationary nozzle or doctor blade.

This velocity gradient generates a shear rate (��), which combined with the rheological

behavior of the paste (evaluated at a single shear rate as η), gives rise to a shear stress (τ)

(Eqn. 4.1).

𝜏 = 𝜂�� (4.1)

72

Because the shear stress changes through the volume of slurry or paste, a torque (M) (Eqn.

4.2)[20] is generated that aligns each anisotropic particle with the major axis parallel to the

direction of applied velocity.[16,20,34] The aligned state is self-stabilizing when

anisotropic particles are aligned parallel to the velocity direction (i.e. δy, the projection

height, is zero) and thus the torque acting on the particle is zero.

𝑀 = (𝜏𝑦+𝛿𝑦 − 𝜏𝑦)𝛿𝑦 (4.2)

In tape casting systems drag flow dominates[15,16,19] so there is a torque applied

to the entire volume of the slurry.[34] This leads to a tape with uniform alignment through

the tape thickness. In contrast, the pressure-driven flow during direct writing results in a

central core of constant velocity in the filament known as plug flow. Because there is no

torque on the anisotropic particles, the core is comprised of unaligned material. [38,39]

Feilden et al. showed that the unaligned core cross-section for a circular nozzle could be

reduced to near the theoretical limit of 30% by increasing the nozzle length.[39]

Tape casting studies show that altering the aspect ratio (major axis divided by minor

axis) of the casting head opening (doctor blade length divided by gap height) has a

significant effect on the magnitude and slope of the torque gradient, and subsequently on

the alignment of platelet-shaped particles.[22,34] It is reasonable to conclude that

deposition nozzles with an aspect ratio > 1 can improve alignment of platelet-like particles

during direct writing. In this paper we explore the effects of nozzle aspect ratio on the

quality of particle alignment during direct writing for a system containing platelet-shaped

BaTiO3 (BT) particles which are designed to serve as template particles for TGG of a

textured piezoelectric ceramic. The PIN-PMN-PT (Pb(In1/2Nb1/2)-Pb(Mg1/3Nb2/3)O3-

PbTiO3) piezoelectric system was chosen for this study due to interest in textured

73

piezoelectric materials for high power transducer devices.[10,136] Additionally, this

system is representative of other templated piezoelectric chemistries which are currently

oriented via tape casting.[6,10]

We first simulate how nozzle aspect ratios of 2, 3 and 5 and printing rate affect

torque in the printed filament for a model PIN-PMN-PT paste containing 2.6 vol% BT

platelets using COMSOL Multiphysics (abbreviated as COMSOL). Alignment of the

template particles was measured in green filament cross-sections as a function of nozzle

aspect ratio and casting rate and correlated to the predicted torque distribution. We also

measured the texture fraction distribution through the thickness of dense textured filaments

by x-ray diffraction of serial-sectioned ceramics. The largest aspect ratio and fastest

printing rate are shown to yield the best texture quality and piezoelectric strain. COMSOL

simulations for printing nozzles with an aspect ratio of 20 and a baffled nozzle design show

that nozzle design is a key factor in establishing torque fields to maximize particle

alignment and textured ceramics by TGG.


A high powder loading (28 vol%) paste of phase-pure perovskite PIN-PMN-PT

powder made in house according to Watson et al.,[7] 0.25 wt% CuO powder (Sigma

Aldrich, St. Louis, MO) on the basis of PIN-PMN-PT weight, and 10 vol% barium titanate

(BT) platelet particles (Applied Research Laboratory, Freeport, PA) on a dry powder basis

(2.6 vol% of the total mixed paste) was used for this study. Barium titanate platelet widths

ranged from 20 – 40 µm and thicknesses from 0.5 – 2 µm (Figure 4.2). The dry powder

was mixed with an aqueous acrylic-based binder and plasticizer (WB4101 and PL008,

74

Polymer Innovations, Vista, CA). Formulation and mixing of the direct writing paste are

detailed in Chapter 3.

Figure 4.2. Backscatter scanning electron microscope image of barium titanate template

particles.

The printing syringe was loaded with the outlet facing upwards to remove excess

air from the syringe and then spun in a SpeedMixer (DAC 600, FlackTek Inc., Landrum,

SC) at 2300 rpm for 3 min to remove air bubbles in the paste. Nozzles were attached to the

syringe and samples of 1 cm x 1.5 cm x 2 mm were printed with each of 4 nozzle designs

at 5 mm/s, 10 mm/s, and 20 mm/s using a high pressure piston (HPx High Pressure

Dispensing Tool, Nordson, East Providence, RI) and pressure controller (Ultimus V High

Precision Dispenser, Nordson, East Providence, RI) attached to a Cartesian 3D printer

(MakerBot, Brooklyn, NY). The nozzles were 24 mm long and had 6 mm diameter circular

inlets which taper to outlet cross-sections of 580 µm x 580 µm (aspect ratio 1), 870 µm x

430 µm (aspect ratio 2), 750 µm x 250 µm (aspect ratio 3), and 1560 µm x 300 µm (aspect

75

ratio 5). Tapered nozzles were used to reduce the printing pressure necessary to print

continuous filaments. Nozzles with aspect ratios greater than 1 were custom made via

stereolithography (3DSystems, State College, PA).

Ceramics were printed on Parafilm (Sigma, Saint Louis, MO) and dried in a 95%

relative humidity container for 4 d before binder burn out at 0.1 °C/min to 375 °C with a 9

h hold. Samples printed with nozzles of aspect ratio 2 and 3 were partially sintered by

heating at 10 °C/min to 1250 °C, then immediately furnace cooled. The printing pattern of

the samples was controlled in such a way that individual filaments would not completely

flow together, so the outline of the filaments would be easily identifiable for alignment

characterization. An additional set of macroscopically-dense, textured samples printed

with nozzles of aspect ratios 1, 2, and 5, was sintered at 1050 °C for 10 h in 0.2 L/min

flowing O2.

Macroscopically-porous samples sintered to 1250 °C for 0 min were fractured and

individual filament cross-sections were imaged with scanning electron microscopy (SEM)

using a Phenom ProX tabletop SEM (Nanoscience Instruments, Phoenix, AZ). Images

were collected in back-scattered electron mode to distinguish between the BT platelets and

the surrounding PIN-PMN-PT matrix (Figure 4.3A). To measure platelet alignment, single

filaments were identified, and the outline of each nozzle cross-section was drawn on the

micrograph of the cross-section filament (Figure 4.3B). The cross-section of the filament

was divided into sectors of equal area by drawing lines from the center of the filament to

the surface (Figure 4.3C). The angular alignment of platelets was measured relative to the

filament surface between the endpoints of the individual sectors (Figure 4.3D). Platelet

alignment was measured as a function of cross-sectional position by dividing the filament

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image into 10 concentric rings. The same angular measurements as described above were

obtained for each ring. The alignment of BT templates relative to the ring surface was

analyzed and averaged for three different cross-sections per sample.

Figure 4.3. Backscatter scanning electron microscope image of a sintered filament cross-

section with (A) an overlay of the nozzle outline, (B) the platelets highlighted and

concentric sections of the cross-section indicated, (C) the radial division of the filament,

and (D) schematic of angle measurement relative to the tangent angle.

Additional alignment analysis of samples printed with nozzles of aspect ratios 1, 2, and 5

was performed via serial x-ray diffraction (Figure 4.4). Lotgering factor was determined

as a function of depth by removing 20 µm increments from the surface of each sample and

doing XRD of the thinned filament. XRD scans were collected on a PANalytical Aeris with

a 0.04° step size and 1.7 s dwell time from 20° to 70° 2θ. The Lotgering factor (𝐹) was

calculated using Equation 4.1[3] where 𝑃 is the ratio of all peak intensities and the texture

peak intensities in the textured ceramic XRD scan and 𝑃0 is the ratio of all peak intensities

and the texture peak intensities in an untextured reference XRD scan. Phase-pure PIN-

PMN-PT powder with no BT templates was used for the untextured reference scan.

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𝐹 = 𝑃−𝑃0

1−𝑃0 (4.1)

Figure 4.4. (A) Schematic of the serial sections and XRD process with (B) a

representative set of scans showing a decrease in crystallographic texture as depth into

the filament increases.

Steady-state velocity profiles for each printing condition were calculated using

COMSOL Multiphysics (COMSOL Inc.). The CFD Module in COMSOL Multiphysics

was used to simulate flow through the nozzle in direct writing assuming laminar flow and

an incompressible fluid. Viscosity behavior was accounted for in the simulation by

inputting coefficients from the power law model fit to the experimentally measured

rheology of PIN-PMN-PT/BT pastes in Walton et al.[75] 3D nozzle geometries were

imported and the boundary conditions for the simulation were set as the printing pressure

on the inlet of the nozzle and the printing rate on the outlet of the nozzle, with no slip

specified for the constraining nozzle walls. Torque profiles were calculated using

Equations 1 and 2, and the velocity, shear rate, and viscosity profiles generated from the

simulation. The local torque was calculated for an average template particle size of 30 µm

from the steady-state velocity profiles as determined for the specific printing conditions

(nozzle geometry, printing rate).

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Electromechanical strain of dense ceramics was measured as a function of applied

field for 98% dense ceramic parts printed at 20 mm/s with nozzle aspect ratios 2, 3, and 5.

The printed ceramic parts were sintered at 1050 °C for 10 h in 0.2 L/min flowing O2. Silver

electrodes (DuPont 6160, DuPont, Research Triangle Park, NC) were painted on the

sintered and polished ceramics and fired to 750 °C for 1 h. Electroded ceramics were poled

at 30 kV/cm for 15 min at room temperature before measuring the unipolar strain response

up to 25 kV/cm at 1 Hz.

4.3 Particle Alignment During Direct Writing

Torque Simulations

Figure 4.5A shows the torque distribution changes across the filament cross-

section for a filament printed with an aspect ratio 3 nozzle at 20 mm/s. The torque

decreases from 6.5 mN.mm at the surface to ~ 1 mN.mm in the core of the film. The central

core of low, constant torque is evidence of plug flow and would induce much less

orientation than near the surface. The slope in torque from the surface to the core parallel

to the minor axis of the nozzle is shown in Figure 4.5B for aspect ratio 2, 3, and 5 nozzles

at 20 mm/s printing rate and in Figure 4.5C for aspect ratio 3 nozzles at 5, 10, and 20 mm/s

printing rates. Figure 4.5B shows that as the aspect ratio of the nozzle increases from 2 to

5 the torque at the surface increases from 3.2 to 11.5 mN.mm for a printing rate of 20 mm/s.

The aspect ratio 5 case experiences a steeper torque gradient through 72% of the minor

axis radius compared to the aspect ratio 2 nozzle which exhibits a torque gradient over 58%

of the minor axis radius. Additionally, as printing rate increases for the aspect ratio 3 nozzle

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the magnitude of torque generated during printing increases (Figure 4.5C) and a greater

cross-section of the printed filament experiences torque with increasing printing rate.

Figure 4.5. (A) Torque profile at the outlet of the nozzle for a nozzle of aspect ratio 3 and

printing rate of 20 mm/s. Dotted line indicates position of minor axis calculations in (B)

torque profiles calculated along the minor axis at 20 mm/s printing rate for each aspect

ratio nozzle and (C) torque profiles for aspect ratio 3 at increasing printing rates.

Particle Alignment in the Cross-section

Platelet misalignment was measured with respect to the nozzle walls by measuring

the angle of platelets relative to the surface tangent in each section (Figure 4.3). Average

misalignment angles and standard deviations, taken as a measure of alignment quality

along the major axis over the entire volume of the filament, are plotted for each printing

condition in Figure 4.6. The average angle of misalignment decreased (i.e. better

alignment) for the aspect ratio 3 nozzle from approximately 38° for the 5 mm/s printing

rate to 29° for the 20 mm/s printing rate (Figure 4.6A). In the aspect ratio 2 condition the

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average misalignment angle was nearly the same for the 5 mm/s and 10 mm/s printing rates

at 39° and decreased to 35° at 20 mm/s. Standard deviation in alignment along the major

axis decreased by 4° in the aspect ratio 3 case as printing rate increased (Figure 4.6B). The

standard deviation was relatively constant at ~26° as a function of printing rate for the

aspect ratio 2 nozzle. These results correlate well with the torque simulations in Figure

4.5. That is, the platelet particles align better (lower angle and standard deviation) for the

higher aspect ratio nozzles because of the higher torque and increasing depth of the filament

experiencing the torque gradient.

Figure 4.6. The average misalignment angle (A) and standard deviation (B) of platelet

particles relative to the nozzle surface as a function of nozzle aspect ratio and printing

rate where each data point is the average of three samples per printing condition.

Platelet alignment is plotted in Figure 4.7 as a function of position relative to the

filament surface. For the aspect ratio 3 nozzle printed at 20 mm/s, the average misalignment

angle (Figure 4.7A) and standard deviation (Figure 4.7B) along the major axis were the

lowest in the outermost 20% of the filament diameter. Similarly, the average misalignment

angle and standard deviation were lowest in the outer 20% of the filament cross-section for

the aspect ratio 2 nozzle printed at 20 mm/s. In the case of both nozzles, the center 20% of

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the minor axis radius is small and does not contain enough oriented platelets to obtain

reliable averages and standard deviations.

Figure 4.7. The average alignment angle (A) and standard deviation (B) of template

particles relative to the nozzle surface as a function of filament cross-section for

filaments printed with aspect ratio 2 and 3 nozzles at 20 mm/s printing rate averaged for 3

samples per printing condition.

Texture Relative to Printed Surface

Serial x-ray diffraction scans of the textured ceramic filaments were used to

quantify the alignment of template particles, and thus the crystallographically-oriented

TGG PIN-PMN-PT. Lotgering factor as a function of depth into the filament is shown in

Figure 4.8 for printing nozzles of aspect ratios 1, 2, and 5 and printing rates of 5, 10, and

20 mm/s. In Figure 4.8, position zero corresponds to the filament surface and 0.5 indicates

the filament center. For all samples, Lotgering factor decreases (i.e. texture quality

increases) from the surface to the core of the filament and reaches near zero close to the

core of the filament.

All samples exhibit the highest texture quality on the surface of the filament, but as

the aspect ratio of the nozzles and the printing rate changes the extent of alignment relative

to the surface changes dramatically. For the aspect ratio 1 nozzle, the degree of texture (i.e.

F) at the surface ranges from 27% to 39% at 5 mm/s and 20 mm/s, respectively, while the

aspect ratio 5 nozzle exhibits a range from 41% to 47% as the printing rate increases. The

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aspect ratio 2 nozzle exhibits a trend opposite to that of the aspect ratio 1 and 5 nozzles

with the degree of texture on the surface decreasing from 41% to 30% as the printing rate

increases from 5 to 20 mm/s. The percent of the filament that exhibits some alignment,

defined here as having a Lotgering factor ≥ 0.10 is also significantly different between

nozzle aspect ratios. For the nozzles of aspect ratios 1, 2, and 5 the aligned portion of the

filament ranges from 9 to 23%, 12 to 25%, and 22 to 30% of the filament radius,

respectively.

Figure 4.8. Lotgering factor as a function of position (position/diameter) for samples

printed at various printing rates with (A) an aspect ratio 1 nozzle, (B) an aspect ratio 2

nozzle, and (C) an aspect ratio 5 nozzle showing higher overall Lotgering factors for the

aspect ratio 5 nozzle prints. Trendlines are included to guide the eye.

Figure 4.9 overlays the torque and texture profiles for each nozzle aspect ratio at a

printing rate of 20 mm/s. The regions which exhibit a Lotgering factor ≥ 0.10 fall within

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the high slope regions of the torque profile, while the near zero slope region of the torque

profile in the center of the filament corresponds to the randomly oriented region. Surface

Lotgering factors are correlated to the magnitude and gradient of the applied torque. For

the aspect ratio 1, 2, and 5 20 mm/s cases the maximum torques are approximately 3.5, 3,

and 11.5 mN·mm and the surface Lotgering factors are 0.39, 0.30, and 0.47, respectively.

Figure 4.9. Lotgering factor (data points) and torque (solid line) as a function of position

in the filament (position/diameter) for samples printed at 20 mm/s with (A) an aspect

ratio 1 nozzle, (B) an aspect ratio 2 nozzle, and (C) an aspect ratio 5 nozzle showing

strong correspondence between the high slope areas of the torque profile and the aligned

areas of the filament. Trendlines are included to guide the eye.

The aligned portions of the filaments printed at 20 mm/s with 1, 2, and 5 aspect ratio

nozzles are 46, 50, and 60% of the filament diameter, respectively. Based on the high slope

portions of the torque profiles, 50, 58, and 72% of the filament radius are predicted to

aligned during printing for the aspect ratio 1, 2, and 5 nozzles. This suggests that more time

(i.e. a longer nozzle design) is needed to align the platelet particles while under the

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influence of the high torque zone to approach the theoretical limits.[39] It is clear from

these overlays that a higher magnitude and gradient of torque results in more alignment of

template particles throughout the printed filament.

4.4 Densification of Printed Ceramics

The green density and degree of densification was found to be heavily dependent

on printing nozzle aspect ratio and on printing rate. Figure 10 shows the densification

process of samples printed with different conditions. It is important to note that the final

relative densities shown are low due to lead loss in the TMA and that under controlled

sintering conditions prints reach > 92% density. The sample printed with nozzle of aspect

ratio 2 experiences 24% shrinkage during sintering, while the sample printed with nozzle

of aspect ratio 3 experiences 34% shrinkage (Figure 4.10A). It is known that rigid

inclusions, such as the barium titanate platelet particles, can cause constraint during

sintering, resulting in less shrinkage and densification.[137,138] Due to these inclusions

being misaligned to a greater extent in the aspect ratio 2 sample, it is possible that the

contributions from constrained sintering have a greater effect, and thus impede the

densification more than a sample with better alignment such as the aspect ratio 3 system.

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Figure 4.10. TMA densification curves for samples printed (A) with aspect ratio 2 and 3

nozzles at 5 mm/s and (B) with aspect ratio 3 nozzles at increasing printing rates. Final

relative densities are low due to lead loss during sintering.

Differences in the densities of samples printed at increasing printing rates are

apparent primarily in the green density of the samples (Figure 4.10B). Samples printed at

5 mm/s had a green density of approximately 34%, while samples printed at 10 and 20

mm/s had green densities of 53 and 62%, respectively. These dramatic differences in green

density are attributed to lower printing viscosities as the printing rate increases. From

COMSOL simulations, the high shear viscosity during printing decreases by a factor of 3

as the printing rate is increased from 5 to 20 mm/s. Decreased viscosity during printing

allows for rearrangement and compaction of the ceramic particles to a greater extent,

thereby increasing the green density of the print. A similar phenomenon can be observed

in the work of Fu et al. where the density in the center of the printed filament, where the

printing viscosity is high, is visibly lower than the density on the edges of the filament,

where the printing viscosity is lower.[38]

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4.5 Piezoelectric Properties of Printed Ceramics

Figure 4.11 compares the electromechanical strain vs. applied voltage loops for

ceramic samples printed at 20 mm/s with no template particles (random crystallographic

alignment) and textured samples printed at 20 mm/s with aspect ratio 2 and 3 nozzles. The

average high field piezoelectric coefficients obtained for 3 samples were 340, 420, and 480

pC/N for the random, aspect ratio 2, and aspect ratio 3 samples, respectively.

Figure 4.11. Strain versus applied voltage for sintered direct written PIN-PMN-PT

ceramics printed at 20 mm/s showing an increase in piezoelectric response when

templates are added and when the templates are better aligned with higher aspect ratio

printing nozzles.

Improving the alignment of template particles during printing by increasing the

torque during printing results in significant improvements to the piezoelectric properties of

the printed ceramics. While the differences in alignment angles and alignment quality in

Figures 4.6 and 4.7 may seem small, the importance of such differences is clear as

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increasing the nozzle aspect ratio from 2 to 3 increases the high field piezoelectric

coefficient by 12%, and aligning PIN-PMN-PT via direct writing increases the high field

piezoelectric coefficient by 29% when compared to the unaligned printed ceramic. It

should be recognized that the sintering and template growth conditions were not optimized

for the PIN-PMN-PT samples in this study but, as shown in the literature, if the Lotgering

factors can be increased to >90% then these textured materials will have competitive

properties with textured ceramics fabricated by tape casting.

4.6 Summary

Alignment of anisotropic particles during direct writing, and subsequently the

electrical properties, has been shown to be strongly dependent on printing conditions. As

the aspect ratio and printing rate increase, thereby increasing the torque applied to template

particles during printing, the alignment of barium titanate template particles in the PIN-

PMN-PT matrix improves when measured by average alignment angle as well as Lotgering

factor. In addition, the volume of material which is aligned via torque during printing

increases as the nozzle aspect ratio and the printing rate increases. Improving the alignment

of barium titanate platelets during printing in turn increases the piezoelectric coefficient of

the sintered TGG ceramic by 35% relative to the random ceramic.

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Chapter 5. Future Work and Summary

5.1 Prospect for AM of Textured Ceramics

Additive manufacturing in ceramics creates unique opportunities for manufacturing

novel crystallographic orientations in textured ceramics. Tape casting, the current standard

for textured ceramic production, is limited by possible part geometries to simple high

aspect ratio shapes and limits possible particle orientations in relation to the macroscopic

form of the ceramic (Figure 5.1). To increase the flexibility of textured ceramic

fabrication, it is therefore important to explore other forming techniques which allow for

the production of dense, complex-shaped ceramics and still result in the shear alignment of

anisotropic particles to provide crystallographic and/or morphological texture.

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Figure 5.1. (A) Typical platelet orientation and geometry for templated tape cast

ceramics, (B) geometry possible with tape casting with platelet orientation only possible

through additive manufacturing, and (C) geometry and platelet orientation only possible

with additive manufacturing.

It is clear from the similarities in equipment (i.e. using a doctor blade to deposit

thin layers of ceramic slurry) and the slurry formulation (shear thinning, ceramic content ≥

20 vol%) that tape casting and layer-wise slurry deposition additive techniques could be

combined to address challenges in each forming method. While tape casting offers the

ability to tailor microstructures by the inclusion of anisotropic template particles to create

crystallographic and morphologic texture, the possible part geometries made via tape

casting are limited to simple, high aspect ratio forms. One novel use of tape casting to

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access <001> radially textured cylinders by winding oriented tapes on a mandrel which

was subsequently removed.[139]

Layer-wise 3D printing can produce complex and finely featured ceramic

geometries, on the order of 10 μm,[140] but has not yet been used to tailor the

microstructure of dense ceramic bodies. Combining the knowledge of how to tailor particle

alignment in tape casting and the geometric flexibility of layer-wise 3D printing would

allow for the creation of complex, dense ceramics with novel crystallographic and

morphologic texture. In addition, the unique flow fields present during additive

manufacturing and the ability to alter the orientation of these flow fields layer-by-layer

while printing offers unique capabilities to tailor the microstructure of printed ceramics.

For example, particle alignment generated by extrusion-based additive techniques such as

robocasting is similar to the cortical structure of bone and can be tailored by changing

deposition nozzle length.[39] This novel alignment pattern can be used to create bio-

inspired ceramics which have levels of patterning from the macroscale to the

microscale,[38,39] which is an area of research already being pursued with tape

casting.[141,142]

5.2 Modifying the Direct Writing Process

The direct writing process can be modified in a number of ways to change the

alignment behavior of anisotropic particles during sintering. Of particular interest in the

scope of this thesis is the altering of nozzle geometry. A number of nozzle geometries have

been modeled in COMSOL for this work, but not yet tested experimentally. Increasing the

aspect ratio of the printing nozzle from 5 to 20 at a 20 mm/s printing rate would double the

torque magnitude during printing and dramatically decrease the constant torque section of

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the flow profile, effectively decreasing the volume of randomly aligned material left after

printing (Figure 5.2). The aspect ratio 20 nozzle modeled here has an outlet measuring 4

mm x 0.2 mm and the aspect ratio 5 nozzle has an outlet measuring 1.56 mm x 0.3 mm.

Figure 5.2. Torque profile during printing for nozzles of aspect ratios 5 and 20 at 20

mm/s printing rate showing increased torque magnitude and gradient as nozzle aspect

ratio increases.

Estimated from the torque profiles, the volume of unaligned material would decrease from

approximately 40% in the aspect ratio 5 case to 15% in the aspect ratio 20 case. To make

such high aspect ratio nozzles high resolution stereolithography would have to be

employed.

More complex nozzle designs have also been modeled to align a larger volume of

material at lower angles, primarily a nozzle which has flat “baffles” dividing the volume

to act as additional shearing surfaces (Figure 5.3). The flat baffles are placed such that they

bisect the volume of paste, which is unaligned during the direct writing process, effectively

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eliminating areas of unaligned material and aligning anisotropic particles at lower angles

than the curved walls of the nozzle.

Figure 5.3. Model of proposed baffled direct writing nozzle with (A) an expanded side

view, (B) expanded outlet view, and (C) expanded inlet view showing the inclusion of

flat baffles to the interior of a standard tapered nozzle.

Figure 5.4 shows the torque profile of the baffled nozzle as compared with a nozzle of the

same geometry without the flat baffles. The volume of the center baffle has been excluded

to compare just the paste volumes. It is clear from Figure 5.4 that the addition of flat baffles

in the nozzle both increases the torque magnitude during print, due to the increase in aspect

ratio of the outlet and eliminates the constant torque region at the core of the paste volume.

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Figure 5.4. Torque profiles for baffled and un-baffled nozzles at a 20 mm/s printing rate

showing the elimination of constant torque regions with the addition of flat baffles.

Because randomly aligned material exists primarily in this constant torque region, it is

hypothesized that the use of baffled nozzles would effectively eliminate randomly aligned

regions in the direct written ceramic. However it is important to note that the addition of

such baffle has been calculated to increase the pressure drop along the nozzle during

printing by a factor of 5, so it is likely that printing with a baffled nozzle will require high

powered extrusion systems.

5.3 Thesis Summary

This thesis has demonstrated the importance of torque for considerations of

anisotropic particle alignment during shear forming techniques, both for traditional

forming techniques such as tape casting and cutting edge forming techniques such as direct

writing. Physical and crystallographic alignment of anisotropic template particles is shown

to be directly linked to the casting rate, gap height, and casting viscosity during tape

casting. These parameters are shown to affect the shape and magnitude of the shear rate

94

profile under the doctor blade during casting which in turn causes a gradient in the torque

acting on anisotropic particles. The magnitude of the torque, the time the slurry is exposed

to torque during casting, and the ratio of casting height to template diameter are

demonstrated to enable the particle alignment process to be tailored to produce well aligned

template particles. Crystallographic alignment of the textured ceramic was quantified by

grain misalignment angle (full width at half maximum, FWHM) and degree of orientation

(r) and is directly correlated to the degree of torque during casting. High quality alignment

(FWHM = 4.5°; r = 0.13) was demonstrated in the model TGG system consisting of

submicron alumina and 5 vol% 11 µm diameter template platelet particles.

Ceramic pastes were formulated to explore the relation between surface chemistry

and rheology of complex pastes of Pb(In1/2Nb1/2)O3-Pb(Mg1/3Nb2/3)O3-PbTiO3 (PIN-PMN-

PT) powder, large barium titanate platelet particles, and a commercial poly(acrylic) acid-

based binder system. Zeta potential of the ceramic powder, the conformation of the

poly(acrylic) acid, and the effect of these factors on rheology were evaluated as a function

of suspension pH. Effective dispersion and amenable rheology for direct writing were

achieved at mixing pH 5. Barium titanate additions of 0.3 to 2.6 vol% dramatically altered

the rheology of the pastes due to the shear alignment of the platelet particles. Powder-

organic interactions and the size and concentration of barium titanate platelet particles can

be tailored to direct write either space-filling filaments to form dense ceramics or non-

flowing filaments to form spanning ceramic structures.

The alignment of tabular barium titanate template particles in a PIN-PMN-PT

matrix during direct writing can be significantly improved by using anisotropic nozzles at

high printing rates. As predicted with COMSOL simulations these conditions lead to

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maximum torque acting on the template particles. The quality of particle orientation in the

deposited filament, and texture degree distributions in the sintered ceramic, closely follow

the predicted torque profiles generated during printing. Electromechanical strain properties

of the textured piezoelectric ceramic are significantly improved relative to random

ceramics when printed with anisotropic nozzles and thus demonstrate a new means to tailor

properties during 3D printing.

96

Chapter 6. Appendix for COMSOL Multiphysics

Simulations

Steady-state velocity profiles for the tape casting and direct writing systems in this

dissertation were calculated using COMSOL Multiphysics (COMSOL Inc.). The CFD

Module in COMSOL Multiphysics was used to simulate flow under the doctor blade or

through the nozzle assuming laminar flow and an incompressible fluid. Viscosity behavior

was accounted for in the simulation by inputting coefficients from the power law model fit

to the experimentally measured rheology of alumina tape casting slurries and PIN-PMN-

PT/BT pastes. 3D tape casting and nozzle geometries were imported to COMSOL after

being modeled in a free 3D modeling software. The boundary conditions for the tape

casting simulation were set as the rate of the moving carrier tape and the stationary doctor

blade which was specified as a no slip surface. For the direct writing system, the boundary

conditions were set as the printing pressure on the inlet of the nozzle and the printing rate

on the outlet of the nozzle, with no slip specified for the constraining nozzle walls. Torque

profiles were calculated using Equations 1.3 and 1.4, and the velocity, shear rate, and

viscosity profiles generated from the simulation. The local torque was calculated for an

average template particle size of 11 µm for the tape casting system and 30 µm for the direct

writing system from the steady-state velocity profiles as determined for the specific casting

or printing conditions (gap height, casting rate, casting viscosity, nozzle geometry, printing

rate).

97

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Vita

Becca Walton was born in Fort Belvoir, VA and grew up in Lakeridge and Manassas, VA.

She attended The Pennsylvania State University for her undergraduate studies and earned

a Bachelor of Science in Materials Science and Engineering in May of 2016. As an

undergraduate, Becca was privileged to work in the group of Dr. Zi-Kui Liu assisting with

research on magnesium alloys phase diagrams. She also worked with Corning Inc. to

complete a Capstone project on processing phase-pure complex ceramics using the seeding

method for high temperature applications. Becca joined the group of Dr. Gary Messing at

The Pennsylvania State University in June of 2016. Her graduate research was funded by

the Office of Naval Research through The Applied Research Laboratory at The

Pennsylvania State University.

List of publications written with Becca as a first author while at Penn State:

1. Walton, R. L.; Vaudin, M. D.; Hofer, A. K.; Kupp. E. R.; Meyer, R. J.; Messing, G.

L.; Tailoring particle alignment and grain orientation during tape casting and templated

grain growth. J. Am. Ceram.Soc. 102 (2019), 2405-2414.

2. Walton, R. L.; Fanton, M. A.; Meyer, R. J.; Messing, G. L.; Dispersion and rheology

for direct writing lead-based piezoelectric ceramic pastes with anisotropic template

particles. J. Am. Ceram. Soc. Accepted and publication in process.

3. Walton, R. L.; Brova, M. J.; Watson, B. H.; Kupp. E. R.; Fanton, M. A.; Meyer, R. J.;

Messing, G. L.; Direct writing of textured ceramics with anisotropic nozzles. J. Eu.

Ceram. Soc. In review.

4. Walton, R. L.; Kupp. E. R.; Messing, G. L.; Layer-wise additive manufacturing of

textured ceramics – A review. In preparation.

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