Definitions
Polarization Background: is the amount of charge associated with the dipolar or free charge in a dielectric Pyroelectricity: when temperature increased, electric charges appear on the surface of the crystal (tourmaline the Ceylon magnet, 1703) Ferroelectrics: materials in which spontaneous polarization can be altered by electric field. Ferroelastics: materials in which mechanical stresses alter the spontaneous polarization. Piezoelectric: material in which application of stress generates electric charges on its surfaces; implies direct piezoelectric effect Electrostriction is a secondary coupling in which the strain is proportional to square of the electric field; frequently implies the inverse piezoelectric effect. Direct piezoelectric effect: convert mechanical energy into electrical (Pierre Currie in 1880) Inverse effect: convert electrical energy into mechanical (Lippman from thermodynamic principles; Currie experimentally in 1881)
Background: Piezoelectric Effect
Electric field E =
V d
Electrostatic Elastic
Di = ij E j
sij = S ijkl kl
Dielectric displacement q D= (flux) A Constitutive equations
E sij = Sijkl kl +d ijk E k
Equilibrium ij , j = f i
Di ,i =
Displacement s 1 sij = (ui , j + u j ,i ) 2 Ei = ,i
= stored electrical energy input mechanical energy
Di =d ijk s jk + ij E j
Electro-mechanical coupling: K2 = stored mechanical energy input electrical energy
Background: First Piezoelectrics
Quartz:
+
great physical and chemical stability small coupling coefficient applications: oscillators and resonators
Rochelle salt (NaKC4H4O6*4H2O):
+
great piezoelectric effect water soluble and had poor temperature characteristics applications: various transducers such as a phonograph pickups
Quarts crystal (from Cady, 1946)
Background: Barium Titanate
Perovskite structure: ABO3 The absence of center symmetry in crystal structure gives rise to spontaneous polarization Cubic above Curie temperature; tetragonal as it cools down. Barium Titanate (BaTiO3) the first material to be developed as a piezoceramic available in single crystal form Discovered independently United States (Waigner and Salomon 1942) Soviet Union (Wul and Goldman, 1945) Japan (Miyake and Ueda, 1946). Applications: detection of mechanical vibration, actuators, and for generation of acoustic and ultrasonic vibrations.
Crystal structure of Barium Titanate
Uchino, 1997
Background: PZT
PZT solid solution: PbTiO3 / PbZrO3 tetragonal system (PbTiO3): 6 poling directions Phase diagram (after Jaffe, 1971) rhombohedral system (PbZrO3): 8 poling Cubic O2Perovskite directions Pb2+
a
Discovered in 1955: Takagi, Shirane, Sawagachi, Japan. Jaffe, United States High coupling coefficient High Currie temperature Not available as single crystal Various compositions PZT-4, PZT-5, PZT-5A, PZT-5H (NAVY ) New devices such as ceramic filters and piezoelectric igniters
a PbZrO3 Rhombohedral a 350oC MPB
Zr4+/Ti4+
PbTiO3 Tetragonal
Ps Ps c a a a
Background: Polarization Reversal
180o polarization reversal:
D3 B -Ec A C a) A +Ec B E3 -Ec B b) C C s33 A c A B E3 a Ps a C E c Ps
90o
polarization reversal:
E1 c Ps a
Ps a Ps a s33 c
OR c
c/a = 1.01
s11 Ferroelectric 33
E1
Background: Domains
Ferroelectric domain: region with constant polarization direction Lower energy state 180o and non-180o (90o and 71o/109o) domains Literature : Mathias et al (1948): existence of domains in BaTiO3 Merz, 1952: observed antiparallel 180o; studied nucleation and growth; the 180o wall is only one or few lattice constants thick; wall energy ~10egr/cm2 Forsbergh (1949): (101) twin planes; respond to stress Little, 1955: domain wall dynamics and interaction Berlincourt and Krueger: 1959: switching is predominantly non-180o domain reversal
Jaffe, 1971
Background: Ferroelectric Domains
Literature : Uchida and Ikeda, 1967 Gerthsen and Kruger, 1976 Kruger, 1976
Electric fields both 180o and non-180o domain walls motion Mechanical stresses only non-180o domain wall motion
Intrinsic: due to deformation of a unit cell Extrinsic: due to domain wall motion
Merz, 1952
Polarization motion of both 180o and non-180o domain wall Strain motion of only non-180o domain wall
Background: Effect of Mechanical Prestress
Krueger and Berlincourt (1961); Krueger (1967, 1968)
the first extensive study; PZT-4, PZT-5, BaTiO3, PZT-5A, PZT-5H exposure to stress, temperature, or electric field was to found to begin a new aging cycle in the ceramic hard ceramics show better property recovery than soft ceramics; hard ceramics are superior for high-power high stress application permittivity generally increases with stress applied parallel poling direction, and decreases with stress perpendicular to the poling direction
Meeks and Timme (1975)
comprehensive comparative study (Navy I, II, III) d33 peaks at 60 and 120 MPa for type I and III but not for type II dielectric constant peaks for all three ceramic compositions dielectric loss tangent showed peaks for types I and III at 80 and 150 MPa which coincided with the peaks in dielectric constant. attributed peaks to a phase transition from the ferroelectric tetragonal to the ferroelectric rhombohedral
Butler et al (1994):
extensive literatures review Navy I and III high mechanical stress and electrical drive conditions 0.390.59 MV/m and 69103 MPa (10-15 kpsi)
Background: Effect of Mechanical Prestress
Lynch (1996):
PLZT ceramic; full polarization reversal at constant prestress values up to 60 MPa compressive stresses reduce the remnant polarization, change the piezoelectric coefficients, and decrease the coercive field
Hackenberger et al. (1999)
PZT-5H ceramics a quasi-linear regime (i.e., below coercive field); prestress up to 100 MPa observed peak in strain and polarization output; attributed to non-180o domain wall motion
Prestress: about 30 references, only 3-4 relevant--depends how you count
descriptive technical reports comparison of different materials rather than physical phenomena dielectric performance rather than actuator point of view low field operating conditions there are no analytical models that predict peaks in the response have not found comprehensive study of PZT-5H under combined loading
There is little stress/temperature/electric field data for the PZT compositions that have been around for over forty years
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