Transcript งานนำเสนอ PowerPoint

What is Ferroelectric?
Ferroelectrics are materials which possess a “spontaneous”
electric polarization Ps which can be reversed by applying a
suitable electric field E.
This process is known as “switching”, and is followed by “hysteresis”.
Ferroelectrics are electrical analogues of “ferromagnetics” (P-E and M-H
relations).
Ferroelectric Characteristics
Three important characteristics of ferroelectrics:
• Reversible polarization
• “Anomalous” properties (i.e. ferroelectric disappears
above a temperature Tc known as “Curie Point”
• Non-linearities
Ferroelectric Characteristics
• “Anomalous” properties (i.e. ferroelectric disappears
above a temperature Tc known as “Curie Point”
• Above Tc, the anomaly is frequently of the “ Curie-Weiss”
form: (Curie-Weiss Relation)
e = C / (T-T0)
C ~ Curie-Weiss constant
T0 is called “Curie-Weiss Temperature”
T0 < Tc in materials with first-order transitions
T0 = Tc in materials with second-order transitions
!! Some materials do not follow Curie-Weiss Relation !!
Ferroelectric Characteristics
• Dielectric non-linearities
Measured dielectric permittivity changes with
change of applied (bias field)
What is Piezoelectricity?
Piezoelectrics are
 materials which acquire electric polarization under
external mechanical stresses (Direct Effect),
OR
 materials that change size or shape when subject to
external electric field E (Converse Effect).
! (Piezo ~ Pressure or Stress) !
 Many piezoelectric materials are NOT ferroelectric
 All ferroelectrics are piezoelectric
Above T0, some ferroelectrics are STILL piezoelectric
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• ที่จุดเตาแก๊ ส
• นาฬิ กา
• ไมโครโฟน
• ลาโพง
• อุปกรณ์ วดั ความดัน
• แอกทัวเอเทอร์
การประยุกต์ ใช้ งาน
การประยุกต์ ใช้ งาน
การประยุกต์ ใช้ งานในหม้ อแปลงไฟฟ้าเซรามิก
ตัวอย่ างได้ รับการเอือ้ เฟื้ อจาก Prof. Kenji Uchino, Penn State University, USA
การประยุกต์ ใช้ งานในหม้ อแปลงไฟฟ้าเซรามิกแผ่ นกลม
ตัวอย่ างได้ รับการเอือ้ เฟื้ อจาก Prof. Kenji Uchino, Penn State University, USA
การประยุกต์ ใช้ งานในอัลตร้ าโซนิกมอเตอร์ แบบท่ อ
ตัวอย่ างได้ รับการเอือ้ เฟื้ อจาก Prof. Kenji Uchino, Penn State University, USA
Structural Symmetry
Crystals in Nature
7 Crystal Systems
Triclinic, Monoclinic, Orthorhombic,
Tetragonal, Trigonal, Hexagonal, Cubic
Symmetry Elements
1,1,2, 2,3, 3,4, 4,6, 6, m, translation
230 Space Groups (Microscopic)
IF Translation Symmetry Removed
32 Point Groups (Macroscopic)
14 Bravais Unit Cells
Structural Symmetry
Crystal
Structure
Point Groups
Triclinic
1, 1
Monoclinic
Centro
Symmetry
Non-Centrosymmetry
Piezoelectric
Pyroelectric
1
1
1
2, m, 2/m
2/m
2, m
2, m
Orthorhombic
222, mm2, mmm
mmm
222, mm2
mm2
Tetragonal
4, 4, 4/m, 422, 4mm,
42m, (4/m)mm
4/m, (4/m)mm
4, 4, 422, 4mm,
42m
4, 4mm
Trigonal
3, 3, 32, 3m, 3m
3, 3m
3, 32, 3m
3, 3m
Hexagonal
6, 6, 6/m, 622, 6mm,
6m2, (6/m)mm
6/m, (6/m)mm
6, 6, 622, 6mm,
6m2
6, 6mm
Cubic
23, m3, 432, 43m,
m3m
m3, m3m
23, 43m
None
Point Groups for Seven Crystal Systems
Note that: underlined numbers represent inversion symmetry
Structural Symmetry
32 Crystal Classes
(all crystalline materials are electrostrictive)
11 Classes
Centro-Symmetric
21 Classes
Non-Centrosymmetric
1 Class
Non-Piezoelectric
20 Classes
Piezoelectric
10 Classes
Unique Polar Axis
(Pyroelectric)
10 Classes
NO Unique Polar Axis
1, 2, m, 2mm, 4, 4mm, 3, 3m, 6, 6mm
Pyroelectrics: Spontaneous polarization upon heating or cooling
Ferroelectrics: Reversible or re-orientable spontaneous polarization
Ferroelectrics are a subgroup of the polar materials and
are BOTH pyroelectric and piezoelectric
Polarization (P)
Polarization (P) = Values of the dipole moment per unit volume
= Values of the charge per unit surface area
P = Nm / V = Nqd/Ad = Nq/A
N = number of dipole moment per unit volume
m = dipole moment = qd
q = charge
d = distance between positive and negative charges
V = volume
AND
A = surface area
Spontaneous Polarization (Ps)
Spontaneous polarization (Ps) exists in 10 classes of polar crystals
with a unique polar axis (out of 20 piezoelectric classes)
BaTiO3 Single Crystal
Cubic (T > Tc)
Ps = 0
Tetragonal (T < Tc)
Ps  0
Pyroelectric Effect
BaTiO3
Triglycine Sulfate (TGS)
Pyroelectric Effect = Change of spontaneous polarization
(Ps) with temperature (T) (Discovered in Tourmaline by
Teophrast (314 B.C.) and named by Brewster in 1824);
p = pyroelectric coefficient = Ps/T
Notice that BaTiO3 and TGS (and most crystals) has a negative
pyroelectric coefficient
Spontaneous Polarization (Ps) Re-Orientation
Ceramics  a large number of randomly oriented crystallites 
 polarization re-orientation “Poling Process”
E
Unpoled
Poled
Changes in Ps-directions require small ionic movements
 Larger number of possible directions of polar axes 
 Closer to poling direction  Easily poled
Tetragonal 4mm  6 possible polar axes
Rhombohedral 3m  8 possible polar axes
 better alignment (poled)
Ferroelectric Domains
Ferroelectric Domains = A region with uniform alignment (same direction)
of spontaneous polarization (Ps)
Domain Walls = The interface between the two domains
 very thin ( < a few lattice cells)
A ferroelectric single crystal, when grown, has multiple ferroelectric domains

Applying appropriate electric field

Possible single domain through domain wall motion

Too large electric field

Reversal of the polarization in the domain “domain switching”

Hysteresis Loop
Ferroelectric Hysteresis Loop
D
Hysteresis Loop
Starting from very small E-field  Linear P-E relationship (OA)
E  leads to domain re-alignment in the positive direction along E
rapid increase in P (OB) until it reaches the saturation value (Psat)
E  results in  P, but NOT all to Zero P as E = 0 (BD) because some domains remain aligned in positive direction
 Remnant OR Remanent Polarization (Pr) 
Certain opposite E is needed to completely depolarize the domain  Coercive Field (Ec)
As E  in negative direction  direction of domains flip
 Hysteresis Loop 
 Spontaneous Polarization (Ps) is obtained through extrapolation 
 Hysteresis Loop is observed by a Sawyer-Tower Circuit 
Ferroelectric Curie Point and Phase Transitions
Curie Point (Tc) = Phase transition temperature between
non-ferroelectric and ferroelectric phases
T < Tc = Ferroelectric Phase
T > Tc = Paraelectric (Non-ferroelectric) Phase
Transition Temperature = Other phase transition temperature
between one ferroelectric phase to another
Ferroelectric Curie Point and Phase Transitions
Near Curie Point (Tc)  Thermodynamic properties
(dielectric, elastic, optical, thermal)
show “ anomalies” and structural changes
Ferroelectric Curie Point and Phase Transitions
In most ferroelectrics, er above Curie Point (Tc) obeys
Curie-Weiss Relation
e = e0 + C/(T-T0)
C = Curie-Weiss constant
T0 = Curie-Weiss Temperature
(different from Curie Point Tc)
T0 < Tc for first-order phase transition
T0 = Tc for second-order phase transition
Tc = actual temperature when crystal structure changes
T0 = formula constant obtained by extrapolation
(Usually e0 term is neglected because e0 << e near T0)
Ferroelectric Curie Point and Phase Transitions
In relaxor ferroelectrics, such
as Pb(Mg1/3Nb2/3)O3 (PMN),
and Tungsten-Bronze type
compounds,
such as (Sr1-xBax)Nb2O6,
er does NOT obey
Curie-Weiss Relation
(1/e) – (1/em) = C’/(T-Tm)n
C’ = constant
Tm = Temperature with em
em = Maximum dielectric constant
1<n<2
Equilibrium Properties of Crystals
Heckmann’s Diagram
(1)
(1)
(2)
(2)
(0)
(0)
Relations Between Thermal, Electrical, and Mechanical Properties of Crystals
(Rank of Tensors in Parenthesis)
Equilibrium Properties of Crystals
Heckmann’s Diagram
Three Outer Corners: Temperature (T), Electric Field (Ei), and Stress (ij)  “Forces”
Three Inner Corners: Entropy (S), Electric Displacement (Di), and Strain (ij)  “Results”
Lines Joining These Corner Pairs

“Principal Effects”
Relations Between Thermal, Electrical, and Mechanical Properties of Crystals
Equilibrium Properties of Crystals
I.
An increase of temperature produces a change of entropy dS:
dS = (C/T)dT
where
C ( a scalar) is the “heat capacity per unit volume”
T is the absolute temperature
II. A small change of electric field dEi produces a change of electric
displacement dDi
dDi = ijdEj
where
ij is the “permittivity” tensor
III. A small change of stress dkl produces a change of strain dxij
dxij = sijkl dkl
where
sijkl is the “elastic compliance”
Equilibrium Properties of Crystals
Coupled Effects : Lines joining pairs not on the same corner
Bottom : Thermoelastic Effects
Right : Electrothermal Effects (Pyroelectric Effects)
Left : Electromechanical Effects (Piezoelectric Effects)
Direct and Converse Piezoelectric Effects
(Third-Rank Tensors)
dDi = dijkdjk  “Direct Effect”
dxij = dijkdEk  “Converse Effect”
where dijk is the “piezoelectric coefficient ”
Thermoelastic Effects : dxij = jjdT
Pyroelectric Effects : dDi = pidT