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[FOR MASTERS THESIS]
[TITLE OF THESIS]
BY
[YOUR NAME]
A THESIS
SUBMITTED TO THE FACULTY OF
ALFRED UNIVERSITY
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS
FOR THE DEGREE OF
MASTER OF SCIENCE
IN
CERAMIC ENGINEERING
[OTHER DEGREE CHOICES: GLASS SCIENCE, MATERIALS SCIENCE AND ENGINEERING,
ELECTRICAL ENGINEERING, MECHANICAL ENGINEERING OR BIOMEDICAL MATERIALS
ENGINEERING SCIENCE]
ALFRED, NEW YORK
JUNE, 2000
[Put month of defense]
[TITLE OF THESIS]
BY
[AUTHOR’s NAME]
B.S. [INSTITUTION] (Year)
SIGNATURE OF AUTHOR
APPROVED BY
[ADVISOR’S NAME], ADVISOR
[NAME], ADVISORY COMMITTEE
[NAME], ADVISORY COMMITTEE
CHAIR, ORAL THESIS DEFENSE
ACCEPTED BY
DOREEN D. EDWARDS, DEAN
KAZUO INAMORI SCHOOL OF ENGINEERING
[FOR DOCTORAL THESIS]
[TITLE OF THESIS]
BY
[YOUR NAME]
A THESIS
SUBMITTED TO THE FACULTY OF
ALFRED UNIVERSITY
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS
FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
IN
CERAMICS
{OR GLASS SCIENCE OR MATERIALS SCIENCE AND ENGINEERING}
ALFRED, NEW YORK
JUNE, 2000
[Note: Put month of defense]
[FOR DOCTORAL THESIS]
[TITLE OF THESIS]
BY
[YOUR NAME]
B.S. [INSTITUTION] (1998)
M.S. [INSTITUTION] (2000)
SIGNATURE OF AUTHOR _____________________________________
APPROVED BY _______________________________________________
[ADVISOR’S NAME], ADVISOR
________________________________________________
[NAME], ADVISORY COMMITTEE
________________________________________________
[NAME], ADVISORY COMMITTEE
________________________________________________
[NAME], ADVISORY COMMITTEE
________________________________________________
CHAIR, ORAL THESIS DEFENSE
ACCEPTED BY _______________________________________________
DOREEN D. EDWARDS, DEAN
KAZUO INAMORI SCHOOL OF ENGINEERING
ACCEPTED BY _______________________________________________
NANCY J. EVANGELISTA, ASSOCIATE PROVOST
FOR GRADUATE AND PROFESSIONAL PROGRAMS
ALFRED UNIVERSITY
[This blank page is necessary for submittal of your final copies. There should be nothing on it]
ACKNOWLEDGMENTS
iii
TABLE OF CONTENTS
Page
Acknowledgments ................................................................................................................iii
Table of Contents ................................................................................................................. iv
List of Tables ......................................................................................................................... v
List of Figures ...................................................................................................................... vi
Abstract ............................................................................................................................... vii
I
INTRODUCTION ................................................................................................... 1
A. Background on Ferroelectrics ........................................................................................ 2
B.
II
Instrumentation Background ......................................................................................... 4
1.
MTI Fotonic Sensor ............................................................................................................4
2.
Pulse-Echo Instrumentation ................................................................................................4
EXPERIMENTAL PROCEDURE ........................................................................ 5
A. Sample Sizes .................................................................................................................. 5
B.
Material Constant Calculations...................................................................................... 5
1.
C.
PZT Calculations ................................................................................................................5
Archimedes’ Principle ................................................................................................... 5
D. Analyses......................................................................................................................... 5
III
1.
X-ray Diffraction ................................................................................................................5
2.
SEM/EDS ...........................................................................................................................5
3.
Direct Measurement of Strain .............................................................................................5
4.
Pulse-Echo Measurements ..................................................................................................5
RESULTS AND DISCUSSION.............................................................................. 7
A. Results and Discussion for PZT .................................................................................... 7
E.
Results and Discussion for PMN-15.............................................................................. 7
IV
SUMMARY AND CONCLUSIONS...................................................................... 8
V
FUTURE WORK .................................................................................................... 9
REFERENCES ................................................................................................................ 10
APPENDIX ...................................................................................................................... 12
iv
LIST OF TABLES
Page
Table I. Calculated Values of d33 for Comparison with Berlincourt Measured Values .... 6
[Note: Tables have titles (in title capitalization) with Roman numerals. Titles in the list must line up (tab
after the number). If text of table title runs too close to the page number, add spaces until it wraps to the
next line.]
v
LIST OF FIGURES
Page
Figure 1. The Perovskite structure. .................................................................................... 3
Figure 2. Maximum dielectric constant for PZT P8 at various frequencies
during
heating. .............................................................................................................. 7
[Note: Use Arabic numbering for figure descriptions. They should be numbered consecutively throughout
the thesis. If there are too many, precede number with chapter number, Ex: I.1. They should line up and
not come too close to the page number (See List of Tables].]
vi
ABSTRACT
A stress rig was utilized to apply prestress. PMN-38 results showed that a DC
bias field of 0.35 MV/m with an AC excitation field of 0.16 MV/m at 1 Hz provided an
optimal linear d33-strain curve, both values being larger than results obtained with PZT.
Rings of PMN-38 were produced for prototype transducer fabrication. These prototypes
will be tested to determine to what degree the resonance and antiresonance frequencies
shift as a function of applied DC bias.
[1 ½ line spacing is preferred, but single space may be used to keep on one page.]
vii
INTRODUCTION
In ultrasonic systems, frequency modulation is difficult because resonant
frequencies are controlled by the elastic modulus, E, density, , and sample thickness, t:1
f 
1
2t
E

(1)
[Note: When a equation caption is generated, delete the word “Equation and put parentheses around the
equation number. Tab the equation away from the left margin. Tab to equation number]
For PZT, neither E nor  can be easily tuned to impart a significant change.
An
additional problem in PZT systems is the time dependent properties of the material; they
slowly degrade over time. PMN is an exception to both these considerations. If the PZT
component of transducers was replaced with PMN, it would allow the use of a DC bias to
vary PMN’s elastic modulus values, and hence the operating frequency, in order for the
transducer to suit the designer’s needs, giving a “degree of freedom” in design. This
would also alleviate the problem of time dependent properties of PZT shifting transducers
out of specification. Other benefits of utilizing PMN in place of PZT include a higher
dielectric constant for good electrical impedance matching, lower electrical loss,
relatively little aging with regard to polarization, fast polarization switching, and the
ability to induce a large polarization, hence large piezoelectric coefficients, by applying a
DC field.
In piezoelectrics, the properties are fixed with processing and output is usually
controlled with voltage. For PMN, strain is proportional to the square of polarization.
Because of this, it has been suggested that current could be used as the driving parameter
of the PMN transducers because of PMN’s diffuse transition region over a broad range of
temperatures. Instead of using a voltage driver, which would require observation and
adjustment by the user to maintain a specified level of output, a current driver would
allow the voltages to “self-fluctuate” in order to maintain a specific current driving level.
This thesis characterizes, in detail, a PZT composition currently used in ultrasonic
devices and explores the properties of two commercially available PMN compositions.
This information was then used in a joint project to determine the feasibility of replacing
1
PZT with PMN in an ultrasonic transducer, and to build and characterize a prototypeconcept PMN transducer.
A.
Background on Ferroelectrics
PZT possesses piezoelectric and ferroelectric properties which has made it a
popular material since the 1960’s. Using different dopants, the material properties have
been tailored to fit such varied applications as hydrophones, actuators, sonar, transducers,
medical ultrasound, and ultrasonic cleaners.2-5
A ferroelectric material possesses a polarization that can be reoriented by
application of an electric field. Piezoelectricity is the ability of a material to produce an
electric voltage in response to a mechanical stress. This is referred to as the direct
piezoelectric effect:3
Di  d ijk * T jk
(2)
where D is the dielectric displacement, d is the piezoelectric coefficient, and T is the
applied stress. For piezoelectrics, the converse is also true; strain can be generated as the
result of an applied electric field, referred to as the converse piezoelectric effect:
S ij  d ijk * E k
(3)
where S and E are the strain and electric field, respectively. Depending on the charge of
the applied electric field, the material will either stretch or compress. The subscripts i, j,
and k are directions that identify the piezoelectric constant as a third rank tensor which
connects a first and second rank tensor.
Ferroelectric behavior is dependent on crystal structure. The crystal must be
noncentric and have alternate atom positions or molecular orientations to permit the
reorientation of the dipole and the retention of polarization after the voltage has been
removed.4 PZT has a perovskite structure and has the general formula of ABO3. The
general unit cell is pictured in Figure I.1. Pb+2 ions reside in the corners, O-2 ions are
located at the face centers, and Zr+4 or Ti+4 occupies the body-centered position. In the
absence of a center of symmetry, a dipole is created which is based on the difference
between the positive and negative charge centers. When a stress is applied (either tension
2
or compression), the distance between the positive and negative ions changes (increases
or decreases, respectively). This causes an electric flux imbalance; to alleviate this
imbalance, surface charges appear. The net external charge created by the net internal
dipole density defines spontaneous polarization.2
Figure 1. The Perovskite structure with the general formula ABO3.
[Use sentence capitalization for figure descriptions (Capital letter to start, period to end). Figure
descriptions are usually indented. Note: After inserting the figure caption, put a period and tab, so titles
will line up in List of Figures.]
One of the main problems associated with using piezoelectric materials is their
time dependent properties. Piezoelectricity must be induced in a ferroelectric ceramic by
applying a high electric field at elevated temperatures. This poling process partially
realigns the polar axes of the domains to create a macroscopic polarization in the crystal.5
Over time, material properties like d33, k33, etc. slowly degrade a few per cent per decade
time. Depending on the application of the material, this can shift the instrument out of
specification.
Relaxor ferroelectrics of type ABIBIIO3, such as Lead Magnesium Niobate
(PMN), possess a non-linear electromechanical coupling, which is temperature and stress
dependent.1,6 They are characterized by a diffuse phase transition where a mixture of
polar and nonpolar regions exists at a microscopic scale.7 In other words, the phase
transformation in different parts of the sample occurs not at one definite temperature but
at various temperatures which together form a Curie Range.8 Cross,9 Nomura,10 and
3
Uchino11 explained this phenomena as follows: The composition fluctuations on the Bsite sublattice (the random arrangement of Mg and Nb) lead to a distribution of
microvolumes within the material that has widely different Curie temperatures. It is
theorized that the Mg+2 and Nb+5 ions also tend to order in a 1:1 ratio on the B-site of
PMN because of mechanical considerations.12
B.
Instrumentation Background
Critical instrumentation used in this thesis which is less commonly used in
electronic ceramic characterization is described in this section. These descriptions are
confined to the measurement of strain and acoustic velocity.
1. MTI Fotonic Sensor
The MTI Fotonic Sensor 2000 was used in this experiment to ensure the
accuracy of the strain gauge measurements. It utilizes the concept of an optical lever
where the power of a light beam striking a vibrational surface is modulated in such a way
that the power of the reflected beam is proportional to the displacement of the surface.15
One form of this concept, called step-index fiber optics, was used in this experiment. The
probes are composed of transmission fibers that illuminate the surface and receiving
fibers that transmit the reflected light to a photocell. The displacement sensitivity of this
technique is a result of the differential relationship between the distance separating the
sample and the fibers, and the amount of light received and transmitted to a photocell.15
Calibration of the sensor is performed by placing the sample under the probe.
Using a micrometer, the probe is adjusted to find the optimal distance between the
sample and the probe in which a receiving fiber is completely illuminated by reflected
light from a transmitting fiber.
2. Pulse-Echo Instrumentation
The pulse-echo method is one of the most important in ultrasonic imaging. In
many areas, including medical applications and nondestructive evaluation, it constitutes
one of the fundamental principles for acquiring information about the examined object.
4
EXPERIMENTAL PROCEDURE
A. Sample Sizes
B. Material Constant Calculations
1. PZT Calculations
C.
Archimedes’ Principle
D.
Analyses
1. X-ray Diffraction
2. SEM/EDS
3. Direct Measurement of Strain
4. Pulse-Echo Measurements
5
Table I. Calculated Values of d33 for Comparison with Berlincourt Measured Values
[Use title capitalization. Table titles are usually centered, but you can left justify as long as you are
consistent. Note: If you use a tab between the number and the title, the table titles will line up in the List
of Tables.]
6
RESULTS AND DISCUSSION
A. Results and Discussion for PZT
Figure 2.
Maximum dielectric constant for PZT P8 at various frequencies during
heating.
E.
Results and Discussion for PMN-15
7
SUMMARY AND CONCLUSIONS
8
FUTURE WORK
9
REFERENCES
[References are examples and do not match thesis text above]
1.
B. Jaffe, W.R. Cook, and H. Jaffe, Piezoelectric Ceramics; pp. 92-5. Academic
Press, New York, 1971.
2.
“IEEE Standard on Piezoelectricity,” ANSI/IEEE Std. 176-1987. American
National Standards Institute, New York, 1988.
3.
D.W. Richerson, Modern Ceramic Engineering; Ch. 7. Marcel Dekker, New York,
1992.
4.
S. Nomura and K. Uchino, “Electrostrictive Effect in Pb(Mg1/3Nb2/3)O3-Type
Materials,” Ferroelectrics, 41 [1-4] 117-132 (1982).
5.
S.A. Brown, C.L. Hom, M. Massuda, J.D. Prodey, K. Bridger, N. Shankar, and
S.R. Winzer, “Electromechanical Testing and Modeling of a Pb(Mg1/3Nb2/3)O3PbTiO3-BaTiO3 Relaxor Ferroelectric,”J. Am. Ceram. Soc., 79 [9] 2271-82
(1996).
6.
W.D. Kingery, “Grain Boundary Phenomena in Electronic Ceramics,” pp. 1-37 in
Grain Boundary Phenomena in Electronic Ceramics. Edited by L.M. Levinson.
American Ceramic Society, Westerville, OH, 1981.
7.
J.T. Dawley, G. Teowee, B.J.J. Zelinski, and D.R. Uhlmann, “Piezoelectric
Characterization of Bulk and Thin Film Ferroelectric Materials Using Fiber
Optics,” (1998) Mechanical Technomics. Accessed on July, 1999. Available at
<http://www.mechtech.com/appnotes/piezo/piezo.htm>
8.
S.P. Leary, “Methods for Quantifying the Nonlinear Electromechanical Response
of Pb(Mg1/3Nb2/3)O3-Based Relaxor Ferroelectrics”; Ph.D. Thesis, Alfred
University, Alfred, NY, 1998.
9.
C. Elissade, J. Ravez, and P. Gaucher, “The Low and High Frequency Dielectric
Relaxations in Lead Magnesium Niobate Ceramics,” Mater. Sci. Eng., B, B20
[3] 318-23 (1993).
10.
"Test Methods for Apparent Porosity, Liquid Adsorption, Apparent Specific
Gravity, and Bulk Density of Refractory Shapes by Vacuum Pressure", ASTM
Standard C 830-88. 1998 Annual book of ASTEM Standards, Vol. 15.01.
American Society for Testing and Materials, Philadelphia, PA, 1998.
11.
W. Schulze, Alfred University, January, 1998, Private Communication.
10
12.
J.G. Fagan, Jr. and V.R.W. Amarakoon, "Process for Preparing a Bulk Textured
Superconductive Material," U.S. Pat. 5,523,284, June, 1996.
13.
D.R. Clarke, "Direct Observations of Lattice Planes at Grain Boundaries in Silicon
Nitride," in Nitrogen Ceramics. Edited by F. Riley. Noordhoff Press, Groningen,
The Netherlands, 1998 (in press).
14.
Encyclopedia of Materials Characterization; pp. 120-121. Edited by C.R. Brundle,
C.A. Evans, Jr., and S. Wilson. Butterworth-Heinemann, Boston, 1992.
15.
W.M. Carty, L. Bergstrom, B.R. Sundlof, and W.A. Schulze, "Ink-Jet Printing
National Science Foundation Proposal," Alfred University, Alfred, NY, 2000
(unpublished).
11
APPENDIX
SEM, Samples, and Stress Rig Pictures, and XRD Graphs
12