CHANNELINDUSTRIES, INC.

Piezoelectric Ceramics

Applications Assistance

These same engineers have contributed to the develop-ment of many state-of-the-art piezoelectric devices inuse today. Drawing from their extensive knowledge ofpiezoelectric physics, they are available to assist withthe design of your product.

Production

Channel’s piezoelectric plant in Santa Barbara, Califor-nia is designed to produce large orders quickly. Channelhas the capability to produce millions of identical parts,as well as the flexibility to handle small orders. Manystandard parts are available from stock and can bedelivered in approximately two weeks. Normal lead-time for non-standard parts, depending on specifica-tions, is eight to 12 weeks. Whatever your requirement,Channel’s large plant capacity—in tooling, automatedmachinery, and experienced people—provides the ca-pability to match your specific needs.

Channel Industries, Inc., has been manufacturing highquality piezoelectric ceramic since 1959 and is proud tobe at the vanguard of the industry. Channel Industriesengineers are the industry leaders in the design and manu-facture of piezoelectric ceramics. We are proud of ourproducts and expertise and pleased to make these avail-able to you.

Development

At the core of Channel Industries is an internationallyrecognized group of piezoelectric ceramic engineers. OurPresident, Robert Callahan, heads up the team at ChannelIndustries. The team also includes Don Berlincourt, Presi-dent of Channel Products, Carmen Germano and MelKullin, each of whom is an expert in his field. This teamhas developed a family of very active materials—Channelite ceramics. These materials are used in a varietyof applications, including transducers, hydrophones, andultrasonic devices. Channel’s engineering and manu-facturing capability provide the technology necessary tomeet new applications as they arise.

2

Channel Industries, Inc.

Piezoelectricity

The piezoelectric effect is exhibited in a certain groupof crystalline solid materials whose unit cells do notpossess a center of symmetry. These materials, whenmechanically stressed, will produce an electricalcharge, and conversely, when an electric field is ap-plied, a mechanical strain will occur, changing thedimensional shape of the material.

Currently the most widely-used piezoelectric trans-ducer materials are poly-crystalline ceramics basedon lead zirconate titanate and barium titanate compo-sitions. Specific additives are included to give eachcomposition unique dielectric, piezoelectric and physi-cal properties.

In their original state, ceramic materials are composedof a multitude of crystalites with random domain ori-entation. Consequently, they are isotropic and pos-sess no piezoelectric properties. By the applicationof a temporary high-static electric field, the ceramicmaterial will become anisotropic, retain a remnantpolarization and become piezoelectric. This is re-ferred to as the poling operation, and the poling direc-tion, by convention, defines the Z axis of a three-dimensional orthogonal axis system. The X, Y, andZ axes are represented in the piezoelectric constantsubscripts as 1, 2 and 3. The subscripts 4, 5 and 6

Piezoelectric Ceramicrefer to shear distortions about the 1, 2 and 3 axesrespectively. Polar symmetry exists, and even thoughthe 1 and 2 axes are designated, they may be arbitrar-ily located but must be at right angles to each other.The 1 and 2 axes are identical, so for simplicity, ref-erence is usually made only to the 3 and 1 directions.The piezoelectric constants are generally written withtwo subscripts. The first subscript is the electricaldirection, and the second is the mechanical direction.

Polarity of Piezoelectric Effect

Subsequent to polarization, an electric field appliedin the 3 direction and of the same polarity as thepoling field will cause elongation along the 3 axisand contraction in all perpendicular directions. Areverse field will cause contraction along the 3 axisand expansion in all transverse directions. Thesestrains remain as long as the field is maintained.

A piezoelectrically-generated voltage of the same po-larity as the poling field occurs, due to a compressiveforce applied parallel to, or a tensile force appliedperpendicular to, the polar axis. Reversing the direc-tion of the applied forces reverses the polarity of thegenerated voltage. The positive electrode on the fin-ished ceramic shape is usually identified by a polaritymark. This is the electrode to which the positivevoltage is applied during the poling operation.

Piezoelectric Ceramic Materials

Channel Industries manufactures lead zirconate titanateand barium titanate compositions as listed on page14, as well as other specialized compositions.

Lead Zirconate Titanate

Characterized by high coupling factors and high pie-zoelectric and dielectric constants over extended tem-perature ranges and stress amplitudes, lead zirconatetitanates are the most extensively used material forelectro-mechanical and electro-acoustic transducers.

Barium Titanate

Modified barium titanates are widely used in transduc-ers requiring moderate power level and receiving sen-sitivity. Special characteristics have made barium ti-tanate a proven material for use in devices such asdepth sounders and expendable hydrophones.

Projector & Sensor Materials

Piezoelectric ceramic materials are compounded tohave advantageous properties depending upon theirend use. Two broad categories include:

1) High coercivity power ceramics that are capableof accepting high continuous input power and operat-ing at high mechanical stress levels. Important prop-erties of this group of materials are low dielectric andmechanical losses, even at large displacement ampli-tudes or acoustic intensities.

2) Sensor materials characterized by high charge andvoltage sensitivity with high dielectric constants andresistivity, as well as low aging of their propertieswith time. Most of these materials are capable oflarge displacements with positive applied static elec-tric fields, but are limited in their use as dynamictransducers to very low power projectors, due to die-lectric dissipation at high amplitude.

3

CHANNEL MATERIAL C300 C600 C1300 C5400 C5500 C5600 C5700 C5804NAVY MATERIAL TYPE* IV I II V VI IIILow Power Sonar X X X X XHigh Power Sonar X X XUltrasonic Cleaners X X XDepth Sounders X X XUltrasonic Welders X XHydrophones, Shallow X X X XHydrophones, Deep X XVibration Pickups X X X XAccelerometers X X XReceiver Transducers X X X XHigh Static Motion Transducers X X XHigh Dynamic Motion Transducers X XNon-Destructive Testing X X X X XHigh Voltage Generators X X XAudible Alarms X X X

Note: The units used to express the electrical, me-chanical, and electromechanical properties of piezoe-lectric ceramics are in the MKS system of units.

Dielectric (K) Constant

Values shown are for the relative dielectric con-stant—the ratio of the dielectric permitivity of thematerial to the dielectric permitivity of a vacuum(∈

0). Example: K

3 = ∈

3 / ∈

0. The subscript refer-

ences the direction of the electric field and chargedensity. The superscript T describes the condition ofconstant stress—no mechanical constraint. Super-script S would denote a condition of constant strain—material completely restrained to prevent any me-chanical deformation.

The values of K in the tables are for the mechanicallyfree, constant stress, low field, low frequency (wellbelow the first resonance) condition and are normallymeasured at 1 KHz.

Stress

Applied force per cross-sectional area.

Table I: Typical Uses Channel materials for common applications

Strain

The ratio of the change in a dimension to that dimen-sion itself.

Curie Point

The temperature at which a ceramic becomes com-pletely depolarized.

Dissipation Factor (tan δδδδδ)

The dielectric loss factor in the material is expressedas the tangent of the loss angle, i.e., the ratio of theeffective series resistance to the effective series reac-tance.

Electric Field

The ratio of the voltage applied or developed to thedistance between the electrodes.

Piezoelectric (d) Constant

This property relates the mechanical strain developedto the applied electric field.

T T

*All Navy type materials refer to DOD-STD-1376 (ships).

Definition of Material Properties

4

piezoelectric material to transduce electrical energy tomechanical energy and vice-versa.

k2 = electrical energy stored input mechanical energy

Conversely,k2 = mechanical energy stored

input electrical energyFor a given mode and material, these relationshipshold and the coupling coefficient is numerically iden-tical.

Elastic (s) Constant

Referred to as the compliance constant, s defines thestrain due to an applied stress.

s = strain = meters/meter stress Newton/meter2

Two numerical subscripts are added to indicate thedirections of stress and of strain. Because of theinterchange of mechanical and electrical energy in apiezoelectric material, the elastic properties of a pie-zoelectric body depend upon the electrical termina-tion. If the electrodes are shorted together, the bodywill be more compliant than when the electrodes areopen-circuited. The superscript E is added to thesymbol to indicate the condition of constant electricfield. Constant dielectric displacement (open circuit)is designated by the superscript D.

d = strain = meters/meter field volts/meter

This action is often referred to as the “motor effect.”Conversely, the d constant expresses the ratio of shortcircuit charge density to the stress applied.

d = charge density = coulombs/meter2

stress Newton/meter2

This is the direct piezoelectric effect or “generator”action. The values for d are numerically the same ineach action.

Piezoelectric (g) Constant

This material property expresses the ratio of the opencircuit electric field developed to the applied me-chanical stress.

g = field = volts/meter stress Newton/meter2

The g constant also describes the electrical to me-chanical relationship.

g = strain developed = meters/meter charge density input coulombs/meter2

Coupling (k)

The electro-mechanical coupling coefficient (k) is anumber less than unity that expresses the ability of a

*All stresses, other than the stress involved in second subscript, are constant.

g31

g15

FieldApplied stress

=Strain

Applied charge/electrode area*

StrainApplied field

=Short circuit charge/electrode area

Applied stress*

d33

kpElectromechanical

Coupling

k31

1st Subscript 2nd SubscriptBase LetterSymbol

Table II: Definition of Symbols

Indicates that electrodes areperpendicular to 3 axis

Indicates electrodes perpendicular to3 axis and stress or strain equal in all

directions perpendicular to 3 axis.Refers to the planar mode.

Indicates that electrodes areperpendicular to 3 axis

Indicates that electrodes areperpendicular to 3 axis

Indicates that electrodes areperpendicular to 1 axis

Indicates that the piezoelectrically-induced strain, or the applied stress,

is in shear form around 2 axis

Indicates that the piezoelectrically-induced strain, or the applied stress,

is in 1 direction

Indicates that the piezoelectrically-induced strain, or the applied stress,

is in 3 direction

Indicates that stress or strain is in 1 direction

ElectromechanicalCoupling

FieldApplied stress

=Strain

Applied charge/electrode area*

5

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0

0 0.1 0.2 0.3 0.4

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0

0 0.1 0.2 0.3 0.4

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0

0 0.1 0.2

0.7

0.6

0.5

0.9

0.8

0.4

0.3

0.2

0.1

0

0 0.1 0.2 0.3 0.4

Coupling Factor vs. (fn - fm) / fm for modes 1 through 10Use only where an isolated mode exists. See table for geometrical considerations.

k

keff

(fn - fm) / fm(fn - fm) / fm

k31

(fn - fm) / fm (fn - fm) / fm

kp

k

k k

k33

6

Symbol Description UnitsC Capacitance faraddij Piezoelectric constant m / V ≡ coul / Ndi Inner diameter meter (inch)

dia Diameter meter (inch)

dm Mean diameter (do + di) / 2 meter (inch)do Outer diameter meter (inch)E Electric field V / m

∈0 Permittivity of space (8.85 x 10-12) farad / meterF Force Newtonfm Frequency of minimum impedance Hzfn Frequency of maximum impedance Hzgij Piezoelectric constant Vm/ N ≡ m2 / coulh Height meter (inch)kij Electromechanical coupling coefficientK Relative dielectric constantl Length meter (inch)N Frequency constant Hz•m (kHz•inch)n Numberρ Density kg / m3

P Pressure N / m2

Qm Mechanical Qtan δ Dielectric loss factor

S Strain m / ms Elastic compliance coefficient m2 / NT Stress N / m2

t Thickness meter (inch)V Voltage voltw Width meter (inch)Y Modulus of elasticity N / m2

Zm Impedance at fm ohms

Table III: Symbols

Fundamental Piezoelectric Action Modesfor Common Ceramic Shapes

Table IV on pages 8–9 shows the basic electrome-chanical actions resulting from an applied voltage andalso the voltage generated when an appropriate forceis applied. These are the fundamental modes and con-sider only the stresses pertaining to that mode, withall other stresses equal to zero.

The equations are useful to approximate the displace-ments and generated voltages at low frequencies andcan extend to the static case.

All shapes shown are polarized along the 3 axis.

Caution is suggested in the direct rigorous applicationof the equations as they are somewhat simplified.Therefore, the results, including capacitance and reso-nance frequency, are geometry-dependent.

The symbols used are defined in the table above. Thevalues for the piezoelectric parameters d and g andthe relative dielectric constant K for each material areshown in Table VII. The values must be in the MKSsystem of units.

The frequency constants N are listed in Table VIII.

7

1. Parallellongitudinal mode

2. a. Transverselength mode

b. Transversewidth mode

10. Hollow Sphere

k33

keff=

k31

do > 3h > 3t3. Transverse

ring mode

4. Parallelwidth mode

k31

do > 8t k33

do > 8t kp

do > 8tkeff=kp

kGeometryTypical GeometryPrimary Mode of Motion

or Applied ForceAction/Shape

5. a. Planar mode

b. Thicknessextensional mode

6. Thicknessshear,

parallel E

7. Thin wallhollow

cylinder

8. Stripedhollow

cylinder

9. Hemisphere

t < .2d

kpd > 5t

l > 3d

t < .2wt < .2l

do > 8tl > .5t

w < .3l w > 3t

w < .3lw > 3t

l > 3w > 3t

8

l

k31l

k31w

k33w

k33t

k15t

t

2w

l3

1

3

dt

a. b.

tx

a. 1b.

do

23

1

t

a.

or1

2

3

b.

1

3

2

do

t

h

t

w

l

3

SHEARING FACE

1

t l3

w

do

1

2

3

t

1

3

2

l

do

do

1

2

3

l

a. b.

3d

l

CapacitanceFrequency Generated Voltage Displacement

N / A

a.

b.

a.

b.

a.

b.

b.

a.

N1

l

N3l

l

1 06 1. Nw

Vgw

F= 31

V

gF= 31

l

Nd

C

m

CK d d

h

To i=

∈ −( )π4

3 02 2

V gd

Po= 31 2

V g hdt

Po= 12 31

∆dd d

tVm

m= 31

∆dd d

hVm

m= 31

NW

w3

V g

wt

F= 33 l

∆w d V= 33

Nd

r

o

Nt

t Vt

dg F= 4

2 33π

∆dd d

tV= 31

Nt

s

C K

wt

T= ∈1 0 l

Vgw

F= 15 ∆x d V= 15

Nd

C

m

N1

l

V g d Po= 12 31

Vgd

Fm

= 31

π

∆dd d

tVm

m= 31

∆ l

l=

dt

V31

Nd

c

m

3

1 24. N

dsp

mC K

dt

T m= ∈π2 3 0

2

Vg d

Po= 31

2 ∆d

d dt

Vmm= 31

N

dsp

m

C Kdt

T m= ∈π 3 0

2

Vg d

Po= 31

2 ∆d

d dt

Vmm= 31

∆dd n

Vm = 33

π

C K

dT= ∈π4 3 0

2

l V

dg F= 4

2 33π

l ∆ l = d V33

C

K wt

T

=∈3 0 l

∆ l

l=

dt

V31

∆ wd w

tV= 31

C K

tw

T= ∈3 0 l

C Kdt

T= ∈π4 3 0

2

∆t d V= 33

C

KT

dd

oi

=∈

( )2 3 0π l

ln

C

K t nd

T

m

≈∈3 0

2l

πV

dn

gP

dd

oi

= ( )π 0 33

ln

9

CK hT

dd

oi

=∈

( )2 3 0π

ln

1950

−40 −20 0 20 40 60 80 100 120

2000

2050

2100

2150

2200

2250

2300

2350

0.5

−40 −20 0 20 40 60 80 100 120

0.52

0.54

0.56

0.58

0.6

0.62

0.64

1000

−40 −20 0 20 40 60 80 100 120

1500

2000

2500

3000

3500

4000

4500

Temperature Dependence

Temperature °CTemperature °C

Temperature °C

KT

3

Thermal Effects1) A pyroelectric charge is generated by most piezoe-lectric ceramic when subjected to a temperature change.The magnitude of this charge in lead zirconate titanatesis about 2 x 10−4 coulombs/m2 °C.

2) Thermal expansion coefficient (in parts/million/°C).

C5400 C5500Along (3) axis +1.7 +4

Along (1) axis +3.8 +1.4

3) Heat capacity of C5400 and C5500 approximately420 joules/kg °C.

4) Thermal conductivity C5400 and C5500 approxi-mately 1.8 watts/meter °C.

Frequency Constant Np vs. Temperature

5500

5700

5400

5804

Planar Coupling kp vs. TemperatureDielectric Constant vs. Temperature

Np

Hz•M

5500

5700

kp5400

5804

5500

5700

5804

5400

10

0

0 1 2 3 4 5 6

0.01

0.02

0.03

0.04

0.05

0

0 1 2 3 4 5 6

5

10

15

20

25

onto the electrode. Keep the duration of soldering timeto a minimum (<5 seconds) to prevent excessive alloy-ing of the silver electrode into the solder.

Nickel Electrodes

Also available are nickel electrodes that are applied bya low temperature electroless chemical deposition pro-cedure. These nickel electrodes are much thinner thansilver electrodes and have higher resistivity. They havespecific advantages and are nearly always used on thefaces of shear elements. They are applied to the facesperpendicular to the 1 axis of a plate that has beenprepoled. This prevents depolarization that wouldotherwise occur with high temperature electrode appli-cation.

Aging

After polarization, most of the properties of piezoelec-tric ceramics begin a gradual change with time. Thesechanges are very nearly logarithmic with time so it isconvenient to express aging as a percentage change pertime decade. The longer the period after polarization, orother event such as high temperature or stress exposure,the more stable the material becomes.

Piezoelectric ceramics are commonly supplied withsilver electrodes that are fused onto the surface at hightemperature. Electrode thickness is .0006" to .001" andthe adhesion strength is typically 3500 psi. The elec-trodes normally cover the full surfaces to the edge of theceramic but may be specified with margins, wrap-arounds, special patterns or stripes.

Leads can be attached by soldering, and the followingprocedure is recommended:

1) Clean the electrode surface to be soldered by lightabrasion with a common pencil eraser to remove silveroxides.

2) Tin the lead with Sn-62 solder (62% tin, 36% lead,and 2% silver).

3) Dip the pre-tinned lead into a mild non-corrosiveflux.

4) Melt a small quantity of the Sn-62 solder on the smalltip of a soldering iron of approximately 30 watts.

5) Position the lead on the electrode area and pressdown with the soldering iron tip until the solder flows

Electrodes

AC Field KV/cm (RMS)

Volts/Mil (RMS)0 2.5 5.1 7.6 10.2 12.7 15.2

Loss Tangent vs. AC Field

5804

5800

5400

Volts/Mil (RMS)

Loss

Tan

gent

AC Field KV/cm (RMS)

0 2.5 5.1 7.6 10.2 12.7 15.2

Change in DielectricConstant with AC Field

5400

5800

5804

High Field Dielectric PropertiesD

Œ

- perc

ent

3T

11

Static and Low Frequencies

The free displacement of a piezoelectric element atstatic or low frequencies is illustrated by the followinglinear equations:

Parallel mode ∆ t = d33

V

Transverse mode ∆ l = d31

(l / t) · V

At high electric fields, the strain/field relationship (ef-fective d) becomes non-linear in a positive direction.This gives larger free displacements (100% in somematerials) than the displacement calculated from lowfield d coefficients. Non-linearity leads to hysteresis,mechanical creep, and high power dissipation.

It is generally recommended that static fields be appliedonly in the direction of the original poling field (+E). Anegative field (−E) may be applied, but the magnitudemust be controlled, or partial to full depoling will result.Similarly, a low frequency dynamic field can causedepolarization due to the negative half cycles.

It is not possible to provide absolute values on permis-sible E, but TableV below lists some estimated maxi-mum guidelines.

At the full free displacement, the developed force goesto zero. To determine the actual displacement whenworking against a mechanical force, a linear interpola-tion can be made between the zero displacement force(F

B) and the full displacement zero force.

Displacement actual = DispF ( F

B − F

act ) / F

B

The blocked force:in the parallel mode F

B = d

33 Y

33 (A / t) · V

in the transverse mode FB = d

31 Y

11 w · V

The electromechanical characteristics of a piezoelectri-cal ceramic element can be represented in the simplestform by the equivalent circuit:

The series branch L, C, and R represents the convertedmechanical properties—effective mass, compliance andmechanical loss. Co is the clamped electrical capaci-tance. This basic circuit is applicable at frequenciesonly near the first fundamental resonance, well-re-moved from any other resonant modes.

If the electrical impedance of an appropriately shapedpiezoelectric ceramic element is measured as a functionof frequency, a characteristic plot is obtained.

From this impedance information and a knowledge ofthe dimensions, mass, capacitance and dissipation fac-tor, nearly all of the material properties can be deter-mined.

Channel Industries uses a modern automated system tomeasure and evaluate the piezoelectric resonator. Thissystem is comprised of a Hewlett-Packard computerand impedance analyzer with provision for printing outtabular data and impedance plots.

At frequencies well below the lowest frequency funda-mental resonance of a ceramic element, the piezoelec-tric, dielectric, and elastic properties are interrelated.

∈3 = K

3 ∈

0k

31 = d

31 / √ s

11 ∈

3

d31

= K3 ∈

0 g

31k

33 = d

33 / √ s

33 ∈

3

d33

= K3 ∈

0 g

33d

h = d

33 + 2d

31

For a definitive treatment of the piezoelectric relations,refer to “IRE Standards on Piezoelectric Crystals, 61IRE 14.S1.”

Electromechanical Relations

Material +E Static −E Static E Peak 60 Hz Kv/cm v/mil Kv/cm v/mil Kv/cm v/mil

C-5400 20 50 5 13 6 15C-5500 15 38 1.5 4 2 5C-5700 10 25 .5 2 1 3C-5804 30 75 7 18 8 20

T T

T

T

E

E

TE

TE

12

Co

L

C

R

DispF

FB

Force

Dis

plac

emen

t

Fm

Frequency

Log

| Z|

Fn

13

Level CAs Fired (±)

INCH MILLIMETER0.020 0.500.030 0.760.050 1.270.060 1.520.090 2.290.125 3.18

Wall0.005 0.130.010 0.250.015 0.380.020 0.510.030 0.760.040 1.020.050 1.27

Length0.010 0.250.015 0.380.020 0.51

Level BMinimal Machining (±)

INCH MILLIMETER0.010 0.250.015 0.380.025 0.640.030 0.760.050 1.270.060 1.52

Wall0.005 0.130.005 0.130.010 0.250.015 0.380.020 0.510.030 0.760.035 0.89

Length0.005 0.130.010 0.250.015 0.38

Level AFully Machined (±)

INCH MILLIMETER0.002 0.050.003 0.080.003 0.080.005 0.130.010 0.250.015 0.38

Wall0.002 0.050.002 0.050.003 0.080.003 0.080.004 0.100.004 0.100.005 0.13

Length0.002 0.050.005 0.130.10 0.25

Cylinder/Tube/RingOutside diameter—do

INCH MILLIMETER0.250-0.0500 6.35-12.70.500-1.000 12.7-25.41.000-2.000 25.4-50.82.000-3.000 50.8-76.23.000-4.000 76.2-101.64.000-6.000 101.6-152.4

Wall0.020-0.031 0.51-0.790.031-0.063 0.79-1.600.063-0.100 1.60-2.540.100-0.125 2.54-3.120.125-0.250 3.17-6.350.250-0.350 6.35-8.890.350-0.500 8.89-12.70

Length0.125-0.250 3.17-6.350.250-2.000 6.35-50.82.000-4.000 50.8-101.6

Squareness within: 0.5 degree 1.5 degrees 2.5 degrees

Level CAs Fired (±)

INCH MILLIMETER0.015 0.380.020 0.500.025 0.640.040 1.020.050 1.27

Within thickness tolerance upto 1-in. diameter and 0.080-in.thick. Within 0.005-in. above0.080-in. thick.

Disc (dia)Plates (l &w)

INCH MILLIMETER0.125-1.500 3.2-38.11.500-2.500 38.1-63.52.500-3.500 63.5-88.93.500-4.500 88.9-114.34.500-6.000 114.3-152.4

Disc & Plate(thickness) (t)

0.010-0.015 0.25-0.380.015-0.035 0.38-0.890.035-0.080 0.89-2.030.080-0.200 2.03-5.080.200-0.500 5.08-12.700.500-1.000 12.70-25.40Parallel within:Squareness within:Flatness:(maximum diameter for 2-inchdisc or maximum l or wdimensions for 2-inch plate)

Level AFully Machined (±)

INCH MILLIMETER0.003 0.080.005 0.130.005 0.130.010 0.250.010 0.25

Disc & Plate(thickness) (t)

0.001 0.030.001 0.030.002 0.050.003 0.080.004 0.100.005 0.130.001 0.030.75 degrees0.001 0.03per 1 per 26 mmin dia. dia.

Level BMinimal Machining (±)

INCH MILLIMETER0.010 0.250.015 0.380.020 0.500.025 0.640.030 0.76

Disc & Plate(thickness) (t)

0.002 0.050.002 0.050.003 0.080.008 0.200.010 0.250.020 0.500.003 0.081.5 degrees0.003 0.08per 1 per 26 mmin. dia. dia.

Note: The flatness of ceramic elements with large diameter-to-thickness ratio is difficult to maintain. When discs or plates with dimensionslarger than 50.8 mm(2.0 in.) are required, Channel Industries should be consulted on the tolerance that can be maintained on productionquantities. These tables can be used as a guide in preparing specifications; however, Channel Industries should be consulted to determinethe most cost-effective tolerances consistent with the application.

Table VI: Mechanical Tolerance Levels

Typical Mechanical ToleranceLevels for Plates and Discs

Typical Mechanical Tolerance Levels for Cylinders, Tubes, and Rings

do

Wall

l

l

twt

do

E

Material Reference Numbers 1300 5400 5500 5600 5700 5800 5804Channel Industries, Inc. 300 600 Navy Navy Navy Navy Navy Navy U.S. Navy IV I II V VI III

Coupling Coefficients k33 .46 .39 .45 .71 .73 .73 .72 .67 .66

k31 −.19 −.16 −.18 −.36 −.37 −.36 −.37 −.32 −.32

k15 .46 .39 .45 .72 .71 .68 .65 .60 .59

kp −.32 −.27 −.30 −.60 −.62 −.62 −.62 −.55 −.54

Piezoelectric Constants

d33 10−12 m/V 145 82 145 300 400 505 550 245 240

d31 " −58 −33 −56 −135 −185 −225 −250 −107 −105

d15 " 245 150 245 525 625 670 690 390 382

g33 10−3 Vm/N 13.1 16.8 12.2 26.1 25.8 22.0 19.4 25.2 25.8

g31 " −5.2 −6.8 −4.7 −11.7 −11.9 −9.8 −8.8 −11.0 −11.3

g15 " 20.5 29.8 19.1 40.5 40.0 31.5 26.4 31.5 32.2

Free Dielectric Constants

K3 1250 625 1350 1300 1750 2600 3200 1100 1050

K1 1350 570 1450 1475 1775 2400 2950 1400 1340

Elastic Constants

1 / s11

= Y11

1010 N/m2 11.7 11.6 11.9 8.2 6.4 6.2 6.2 8.6 8.6

1 / s33

= Y33

" 11.1 11.0 11.3 6.5 5.2 5.1 4.8 7.1 7.1

c44

" 4.2 4.2 4.3 2.5 2.0 2.2 2.3 2.9 2.9

Density (min.) 103 kg/m3 5.5 5.4 5.55 7.55 7.6 7.5 7.4 7.55 7.55

Mechanical Q 450 1200 600 500 75 70 65 1100 1050

Curie Point, °C >115 >140 >115 >300 >350 >240 >190 >300 >300

Dielectric Loss Tangent (Max)

Low field .008 .003 .008 .004 .02 .02 .02 .004 .004

2KV/cm RMS NA .01 .015* .02 NA NA NA .007 .005

4KV/cm RMS NA .025 .03* .04 NA NA NA .01 .01

Change in K3 (%) (Max)

2KV/cm RMS NA 3 6* 5 NA NA NA 2.5 2.0

4KV/cm RMS NA 8 12* 18 NA NA NA 6.5 4.0

Static Tensile Strength psi 7500 8500 7500 11000 11000 11000 11000 12000 12000

Rated Dynamic Tensile Strength psi 3000 3500 3000 6000 4000 4000 4000 7000 7000

Change in N1 / Time Decade % 0.5 0.4 0.4 1.5 0.2 0.25 0.25 1.0 1.0

Change in kp / Time Decade % −1.8 −0.7 −1.9 −2.3 −0.2 −0.35 −0.35 −2.0 −1.8

Change in K3 / Time Decade % −0.8 −2.9 −1.3 −5.5 −1.0 −1.5 −1.5 −5.0 −4.0

E

TABLE VII: PROPERTIES OF PIEZOELECTRIC CERAMICS

LEAD ZIRCONATE TITANATEBARIUM TITANATE

(Values are averaged and a consistent set)

*Values for 1300 are at 1.5 and 3KV/cm RMS NA—not applicable

T

T

E

E E

14

T

T

TABLE VIII: FREQUENCY CONSTANTS

Material Reference Numbers 1300 5400 5500 5600 5700 5800 5804Channel Industries, Inc. 300 600 Navy Navy Navy Navy Navy NavyU.S. Navy IV I II V VI III

Frequency Constant Hz m 2310 2310 2310 1650 1470 1450 1450 1680 1700

N 1

Transverse kHz in 91 91 91 65 58 57 57 66 67

N t

Thickness Hz m 2690 2640 2690 2030 1980 1900 1980 2110 2110

kHz in 106 104 106 80 78 75 78 83 83

N r

Radial Hz m 3150 3150 3150 2210 1980 1980 1980 2260 2310

kHz in 124 124 124 87 78 78 78 89 91

N c

Circumferential Hz m 1470 1470 1470 1040 910 940 910 1070 1070

(mean dia.) kHz in 58 58 58 41 36 37 36 42 42

N 3C

Circumferential Hz m 1370 1400 1370 970 910 910 890 1010 1010

(mean dia.) kHz in 54 55 54 38 36 36 35 40 40

N 3l

Parallel longitudinal Hz m 2290 2290 2290 1500 1400 1420 1400 1570 1570

KHz in 90 90 90 59 55 56 55 62 62

N s

Thickness shear Hz m 1420 1450 1420 940 890 890 890 960 960

kHz in 56 57 56 37 35 35 35 38 38

N sp

Hollow sphere Hz m 2410 2440 2410 1730 1550 1520 1520 1800 1830

kHz in 95 96 95 68 61 60 60 71 72

N 3w

Parallel width Hz m 2490 2490 2490 1650 1550 1520 1550 1700 1700

kHz in 98 98 98 65 61 60 61 67 67

LEAD ZIRCONATE TITANATEBARIUM TITANATE

are prepaid and added to the invoice prior to shipping.

We typically ship via UPS. However, we will be happyto ship via the carrier of your choice.

RETURNS

Channel Industries will credit any part not meetingspecifications agreed upon in writing at the time theorder was placed, providing:

1. All parts be set aside after inspection andtested as to the cause of rejection.2. Notification of the rejected parts be made toChannel Industries and test results given.3. A “Return Authorization Number” beissued by Channel Industries.4. Authorized return goods be packaged in amanner similar to that in which they werereceived.5. Return shipments be freight-prepaid.

Chipped or broken parts will not be credited. ChannelIndustries’ products are carefully inspected before ship-ping and packed according to freight and postal regula-tions. The carrier bears responsibility for any breakagein shipment, and any claims for damage in shipmentmust be made directly to the carrier.

When ordering from Channel Industries, Inc., please besure to provide the following information.

1. Material TypeOptions: Barium Titanate: Channel C-300, C-600, orC-1300. Lead ZirconateTitanate: C-5400, C-5500,C-5600, C-5700, C-5800 or C-5804 (refer to page 14for specific properties of each material).2. ShapeOptions: Hollow Cylinder, Striped Cylinder, Disc,Disc with Hole, Sphere, Hemisphere, Bar, Ring, Unique.3. Part or Drawing Number (if applicable)4. Mechanical TolerancesPlease include these, if known.5. DimensionsPlease specify requirements for applicable dimensions:Diameter (D), Outer Diameter (OD), Inner Diameter(ID), Thickness (TK), Length (L), Width (W), WallThickness (W TK).6. SpecificationsPlease include other information pertaining to yourindividual requirements.

SHIPPING INFORMATION

All shipments are FOB Santa Barbara. Shipping charges

Ordering Information

15

(805) 967-0171 FAX: (805) 683-3420

839 Ward Drive, Santa Barbara, CA 93111

ciisales@channeltech.com

CHANNEL INDUSTRIES, INC.