Kutz M. Handbook of materials selection

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422 OVERVIEW OF CERAMIC MATERIALS

encountered in a simply shaped billet of material. This is an important point of

which a design engineer specifying a ceramic component needs to be constantly

mindful.

3 BRITTLENESS AND BRITTLE MATERIALS DESIGN

Even when ceramics are selected for other than mechanical applications, in most

cases some level of strength and structural integrity are required. It is therefore

necessary to brieﬂy discuss the issue of brittleness and how one designs with

brittle materials before proceeding to discuss applications and the various ce-

ramic and glass materials families and their properties.

The main issues in designing with a brittle material are that a very large

scatter in strength (under tensile stress), a lack of capacity for mitigating stress

concentrations via plastic ﬂow, and relatively low energy absorption prior to

failure dominate the mechanical behavior. Each of these issues is a result of the

presence of one or more ﬂaw distribution within or at the surface of the ceramic

material and/or the general lack of plastic ﬂow available in ceramics. As a

consequence, ceramic and glass components that are subjected to tensile stresses

are not designed using a single valued strength (deterministic design) as com-

monly done with metals. Rather, ceramic components are designed to a speciﬁed

probability of failure (probabilistic design) that is set at acceptably low values.

The statistics of failure of brittle materials whose strength is determined by a

population of varying sized ﬂaws is similar to modeling the statistics of a chain

failing via its weakest link. The statistics utilized are known as Weibull statistics.

A Weibull probability of failure distribution is characterized by two parameters,

the characteristic stress and the Weibull modulus.

Computer programs for in-

corporating Weibull statistical distributions into ﬁnite-element design codes have

been developed that facilitate the design of ceramic components optimized for

low probabilities of failure.

The effectiveness of such probabilistic design meth-

odology has been demonstrated by the reliable performance of ceramics in many

highly stressed structural applications, such as bearings, cutting tools, turbo-

charger rotors, missile guidance domes, and hip prosthesis.

Flaws (strength-limiting features) can be intrinsic or extrinsic to the material

and processing route by which a test specimen or a component is made. Intrinsic

strength-limiting ﬂaws are generally a consequence of the processing route and

may include features such as pores, aggregations of pores, large grains, agglom-

erates, and shrinkage cracks. While best processing practices will eliminate or

reduce the size and frequency of many of these ﬂaws, it is inevitable that some

will still persist. Extrinsic ﬂaws can arise from unintended foreign material en-

tering the process stream, i.e., small pieces of debris from the grinding media

or damage (cracks) introduced in machining a part to ﬁnal dimensions. Exposure

to a service environment may bring new ﬂaw populations into existence, i.e.,

oxidation pits on the surface of nonoxide ceramics exposed to high temperatures

or may cause existing ﬂaws to grow larger as in the case of static fatigue of

glass. In general, one can have several ﬂaw populations present in a component

at any time, and the characteristics of each population may change with time.

As a consequence of these constantly changing ﬂaw populations, at the present

time the state of the art in life prediction of ceramic components for use in

extreme environments signiﬁcantly lags the state of the art in component design.

4 APPLICATIONS 423

As in most ﬁelds of engineering, there are some rules of thumb that one can

apply to ceramic design.

While these are not substitutes for a carefully executed

probabilistic ﬁnite-element design analysis, they are very useful in spotting pit-

falls and problems when a full-ﬂedged design cannot be executed due to ﬁnancial

or time constraints.

Rules of Thumb for Design with Brittle Materials

1. Point loads should be avoided to minimize stress where loads are trans-

ferred. It is best to use areal loading (spherical surfaces are particularly

good); line loading is next best.

2. Structural compliance should be maintained by using compliant layers,

springs or radiusing of mating parts (to avoid lockup).

3. Stress concentrators—sharp corners, rapid changes in section size, un-

dercuts and holes—should be avoided or minimized. Generous radiuses

and chamfers should be used.

4. The impact of thermal stresses should be minimized by using the smallest

section size consistent with other design constraints. The higher the sym-

metry the better (a cylinder will resist thermal shock better than a prism),

and breaking up complex components into subcomponents with higher

symmetry may help.

5. Components should be kept as small as possible—the strength and prob-

ability of failure at a given stress level are dependent on size; thus min-

imizing component size increases reliability.

6. The severity of impact should be minimized. Where impact (i.e., partic-

ulate erosion) cannot be avoided, low angle impacts (20

⬚–30⬚) should be

designed for. Note this is very different than the case of metals, where

minimum erosion is at 90

⬚.

7. Avoid surface and subsurface damage. Grinding should be done so that

any residual grinding marks are parallel, not perpendicular, to the direc-

tion of principal tensile stress during use. Machining induced ﬂaws are

often identiﬁed to be the strength-limiting defect.

4 APPLICATIONS

The combinations of properties available in many advanced ceramics and glasses

provide the designers of mechanical, electronic, optical, and magnetic systems

a variety of options for signiﬁcantly increasing systems performance. Indeed, in

some cases the increase in systems performance is so great that the use of

ceramic materials is considered an enabling technology. In the applications ex-

amples provided below the key properties and combinations of properties re-

quired will be discussed, as well as the resultant systems beneﬁts.

4.1 Ceramics in Wear Applications

In the largest number of applications where modern ceramics are used in highly

stressed mechanical applications, they perform a wear resistance function. This

is true of silicon nitride used as balls in rolling element bearings, silicon carbide

journal bearings or water pump seals, alumina washers in faucets and beverage

424 OVERVIEW OF CERAMIC MATERIALS

Table 1 Key Properties for Wear-Resistant Ceramics

Material K

(MPa 䡠 m

1/2

) H (kg/mm

) E (GPa) MOR (MPa)

␳

(g/cm

)

99% 3.9–4.5 1900 360–395 350–560 3.9

C — 3000 445 300–480 2.5

Diamond 6–10 8000 800–925 800–1400 3.5

SiC 2.6–4.6 2800 380–445 390–550 3.2

4.2–7 1600 260–320 450–1200 3.3

TiB

5–6.5 2600 550 240–400 4.6

ZrO

(Y-TZP) 7–12 1000 200–210 800–1400 5.9

dispensing equipment, silicon nitride and alumina-based metal cutting tools, zir-

conia fuel injector components, or boron carbide sand blast nozzles, to cite some

typical applications and materials.

Wear is a systems property rather than a simple materials property. As a

systems property, wear depends upon what material is rubbing, sliding, or rolling

over what material, upon whether the system is lubricated or not, upon what the

lubricant is, and so forth. To the extent that the wear performance of a material

can be predicted, the wear resistance is usually found to be a complex function

of several parameters. Wear of ceramic materials is often modeled using an

abrasive wear model where the material removed per length of contact with the

abrasive is calculated. A wide variety of such models exist, most of which are

of the form:

0.8

⫺

0.75

⫺

0.5

V ⬀ PK H N (1)

where V is the volume of material worn away, P is the applied load, K

is the

fracture toughness, H is the indentation hardness, and N is the number of ab-

rasive particles contacting the wear surface per unit length. Even if there are no

external abrasives particles present, the wear debris of the ceramics themselves

act as abrasive particles. Therefore, the functional relationships that predict that

wear resistance should increase as fracture toughness and hardness increase are,

in fact, frequently observed in practice.

Even though the point contacts that occur in abrasive wear produce primarily

hertzian compressive stresses, in regions away from the hertzian stress ﬁeld

tensile stresses will be present and strength is, thus, a secondary design property.

In cases where inertial loading or weight is a design consideration, density may

also be a design consideration. Accordingly, Table 1, lists the fracture toughness,

hardness, Young’s modulus, four-point modulus of rupture (MOR) in tension,

and the density for a variety of advanced ceramic wear materials. Several suc-

cessful applications of ceramics to challenging wear applications are described

below.

Bearings

Rolling element bearings, for use at very high speeds or in extreme environ-

ments, are limited in performance by the density, compressive strength, corrosion

resistance, and wear resistance of traditional high-performance bearing steels.

The key screening test to assess a material’s potential as a bearing element is

4 APPLICATIONS 425

Table 2 Commercial Applications of Si

Hybrid Bearings

Machine tool spindles The ﬁrst and largest application, its main beneﬁts are higher

speed and stiffness, hence greater throughput and tighter toler-

ances

Turbomolecular pump shaft Presently the industry standard, the main beneﬁts are improved

pump reliability and marginal lubrication capability, which

provides increased ﬂexibility in pump mounting orientation

Dental drill shaft The main beneﬁt is sterilization by autoclaving

Aircraft wing ﬂap actuators Wear and corrosion resistance are the main beneﬁts

In-line skates / mountain bikes Wear and corrosion resistance are the main beneﬁts

Space Shuttle main engine

oxygen fuel pump

Here, the bearing is lubricated by liquid oxygen. Steel bearings

are rated for one ﬂight; Si

hybrid bearings are rated for

ﬁve.

rolling contact fatigue (RCF). RCF tests on a variety of alumina, SiC, Si

and zirconia materials, at loads representative of high-performance bearings,

demonstrated that only fully dense silicon nitride (Si

) could out-perform bear-

ing steels.

This behavior has been linked to the high fracture toughness of

silicon nitride, which results from a unique ‘‘self-reinforced’’ microstructure,

combined with a high hardness. Additionally, the low density of silicon nitride

creates a reduced centrifugal stress on the outer races at high speeds. Fully dense

bearing materials have demonstrated RCF lives 10 times that of high-

performance bearing steel. This improved RCF behavior translates into DN

(DN

⫽ bearing bore diameter in millimeters ⫻ shaft rpm) ratings for hybrid

ceramic bearings (Si

balls running in steel races, the most common ceramic

bearing conﬁguration), about 50% higher than the DN rating of steel bearings.

Other beneﬁts of silicon nitride hybrid bearings include an order of magnitude

less wear of the inner race, excellent performance under marginal lubrication,

survival under lubrication starvation conditions, lower heat generation than com-

parable steel bearings, and reduced noise and vibration.

Another important plus for Si

is its failure mechanism. When Si

rolling

elements fail, they do not fail catastrophically; instead they spall—just like bear-

ing steel elements (though by a different microstructural mechanism). Thus, the

design community only had to adapt their existing practices, instead of devel-

oping entirely new practices to accommodate new failure modes. The main com-

mercial applications of silicon nitride bearing elements are listed in Table 2.

Cutting Tool Inserts

While ceramic cutting tools have been in use for over 60 years, it is only within

the past two decades that they have found major application, principally in turn-

ing and milling cast-iron and nickel-based superalloys and ﬁnishing of hardened

steels. In these areas ceramics based on aluminum oxide and silicon nitride

signiﬁcantly outperform cemented carbides and coated carbides. High-speed cut-

ting tool tips can encounter temperatures of 1000

⬚C or higher. Thus, a key prop-

erty for an efﬁcient cutting tool is hot hardness. Both the alumina and Si

families of materials retain a higher hardness at temperatures between 600 and

1000

⬚C than either tool steels or cobalt-bonded WC cermets. The ceramics are

also more chemically inert. The combination of hot hardness and chemical in-

ertness means that the ceramics can run hotter and longer with less wear than

426 OVERVIEW OF CERAMIC MATERIALS

the competing materials. Historic concerns with ceramic cutting tools have

focused on low toughness, susceptibility to thermal shock, and unpredictable

failure times. Improvements in processing, together with microstructural modi-

ﬁcations to increase fracture toughness have greatly increased the reliability of

the ceramics in recent years

Alumina-based inserts are reinforced (toughened) with zirconia, TiC, or TiN

particles or SiC whiskers. The thermal shock resistance of alumina–SiC

sufﬁciently high, so that cooling ﬂuids can be used when cutting Ni-based alloys.

Silicon-nitride-based inserts include fully dense Si

and SiAlON’s, which are

solid solutions of alumina in Si

. Fully dense Si

can have a fracture tough-

ness of 6–7 MPa

䡠 m

1/2

, almost as high as cemented carbides (⬃9MPa䡠 m

1/2

a high strength (greater than 1000 MPa) and a low thermal expansion that yields

excellent thermal shock behavior. Silicon nitride is the most efﬁcient insert for

the turning of gray cast iron and is also used for milling and other interrupted

cut operations on gray iron. Because of its thermal shock resistance, coolant

may be used with silicon nitride for turning applications. SiAlON’s are typically

more chemically stable than the Si

’s but not quite as tough or thermal shock

resistant. They are mainly used in rough turning of Ni-based superalloys.

Ceramic inserts are generally more costly than carbides (1.5–2 times more),

but their metal removal rates are

⬃3–4 times greater. However, that is not the

entire story. Ceramic inserts also demonstrate reduced wear rates. The combi-

nation of lower wear and faster metal removal means many more parts can be

produced before tools have to be indexed or replaced. In some cases this en-

hanced productivity is truly astonishing. In the interrupted single-point turning

of the outer diameter counterweights on a gray cast-iron crankshaft a SiAlON

tool was substituted for a coated carbide tool. This change resulted in the metal

removal rate increasing 150% and the tool life increasing by a factor of 10. Each

tool now produced 10 times as many parts and in much less time. A gas turbine

manufacturer performing a machining operation on a Ni-based alloy using a

SiAlON tool for roughing and a tungsten carbide tool for ﬁnishing required a

total of 5 h. Changing to SiC-whisker-reinforced alumina inserts for both op-

erations reduced the total machining time to only 20 min. This yielded a direct

savings of $250,000 per year, freed up 3000 h of machine time per year, and

avoided the need to purchase a second machine tool.

Ceramic Wear Components in Automotive and Light-Truck Engines

Several engineering ceramics have combinations of properties that make them

attractive materials for a variety of specialized wear applications in automotive

engines.

The use of structural ceramics as wear components in commercial engines

began in Japan in the early 1980s. Table 3, lists many of the components that

have been manufactured, the engine company that ﬁrst introduced the compo-

nent, the material, and the year of introduction. In some of these applications

several companies have introduced a version of the component into one or more

of their engines.

Many of these applications are driven by the need to control the emissions

of heavy-duty diesels. Meeting current emissions requirements creates conditions

within the engine fuel delivery system that increase wear of lubricated steel

4 APPLICATIONS 427

Table 3 Ceramic Wear Components in Automotive and Light-Truck Engines

Component

Engine

Manufacturer

Engine

Type Ceramic

Year of

Introduction

Rocker arm insert Mitsubishi SI Si

1984

Tappet Nissan Diesel Si

1993

Fuel injector link Cummins Diesel Si

1989

Injector shim Yanmar Diesel Si

1991

Cam roller Detroit Diesel Diesel Si

1992

Fuel injector timing plunger Cummins Diesel ZrO

1995

Fuel pump roller Cummins Diesel Si

1996

SI ⫽ spark-ignited engine.

against steel. One of these conditions is increased injection pressure, another is

an increase in the soot content of engine lubricating oils. Strategic utilization of

ceramic components within the fuel delivery systems of many heavy-duty truck

engines has enabled the engines to maintain required performance for warranties

of 500,000 miles and more. The fuel injector link introduced by Cummins in

1989 is still in production. Well over a million of these components have been

manufactured. And many of these have accumulated more than a million miles

of service with so little wear that they can be reused in engine rebuilds. In a

newer model electronic fuel injector, Cummins introduced a zirconia timing

plunger. The part has proved so successful that a second zirconia component

was added to the timing plunger assembly several years later. Increasingly strin-

gent emissions requirements for heavy diesels has increased the market for ce-

ramic components in fuel injectors and valve train components. Many of these

heavy-duty engine parts are manufactured at rates of 20,000 up to 40,000 per

month.

Perhaps the largest remaining problem for this set of applications is cost.

Ceramic parts are still more expensive than generally acceptable for the auto-

motive industry. Reluctance of designers to try ceramic solutions still exists, but

it is greatly diminishing thanks to the growing list of reliable and successful

application of structural ceramic engine components.

4.2 Thermostructural Applications

Due to the nature of their chemical bond, many ceramics maintain their strength

and hardness to higher temperatures than metals. For example, at temperatures

above 1200

⬚C, silicon carbide and silicon nitride ceramics are considerably

stronger than any superalloy. As a consequence, structural ceramics have been

considered and utilized in a number of demanding applications where both me-

chanically imposed tensile stresses and thermally imposed tensile stresses are

present. One dramatic example is the ceramic (silicon nitride) turbocharger that

has been in commercial production for automobiles in Japan since 1985. Over

one million of these have been manufactured and driven with no recorded failure.

This is a very demanding application, as the service temperature can reach

900

⬚C, stresses at ⬃700⬚C can reach 325 MPa, and the rotor must also endure

oxidative and corrosive exhaust gases that may contain erosion inducing rust

and soot particles. Silicon nitride gas turbine nozzle vanes have been ﬂying for

428 OVERVIEW OF CERAMIC MATERIALS

200

100

0.1 1 10 100 1000

Time, h

Stress, ksi

Hot-Pressed Si

(High-Time Dependence)

Sintered SiC (Low-Time Dependence)

2000°F

2100°F

Hi-Perf

Ceramics at

2200°F

Hi-Perf-NiCo

Superalloys

(i.e. , René-80,

B-1900)

Fig. 2 Stress rupture performance of nonoxide structural ceramics compared to superalloys

(oxidizing atmosphere).

several years in aircraft auxiliary power units. Other applications include heat

exchangers, and hot gas valving. Recently, ceramic matrix composites have been

introduced as disks for disk breaks in production sports cars by two European

manufacturers. A major future market for structural ceramics may be high-

performance automotive valves. Such valves are currently undergoing extensive,

multiyear ﬂeet tests in Germany.

This class of applications requires a focus on the strength, Weibull modulus,

m (the higher the m , the narrower the distribution of observed strength values),

thermal shock resistance, and often the stress rupture (strength decrease over

time at temperature) and/or creep (deformation with time at temperature) be-

havior of the materials. Indeed, as shown in Fig. 2, the stress rupture perform-

ance of current structural ceramics represents a signiﬁcant jump in materials

performance over superalloys.

The thermal shock resistance of a ceramic is a systems property rather than

a fundamental materials property. Thermal shock resistance is given by the max-

imum temperature change a component can sustain,

⌬T.

␴

(1 ⫺

␮

) k

⌬T ⫽ S (2)

␣

Erh

where

␴

is strength,

␮

is Poisson’s ratio,

␣

is the coefﬁcient of thermal expansion

(CTE), E is Young’s modulus, k is thermal conductivity, r

is the half-thickness

for heat ﬂow, h is the heat transfer coefﬁcient, and S is a shape factor totally

dependent on component geometry.

Thus it can be seen that thermal shock

resistance,

⌬T, is made up of terms wholly dependent on materials properties,

dependent on heat transfer conditions, and on geometry. It is the role of the

ceramic engineer to maximize the former and of the design engineer to maximize

the later two terms. It has become usual practice to report the materials-related

thermal shock resistance as the instantaneous thermal shock parameter, R, which

is equal to

4 APPLICATIONS 429

Table 4 Calculated Thermal Shock Resistance of Various Ceramics

Material

␴

(MPa)

␮

CTE (cm / cm K) E (GPa) R (K)

(99%) 345 0.22 7.4 ⫻ 10

-6

375 97

AlN 350 0.24 4.4

⫻ 10

⫺

350 173

SiC (sintered) 490 0.16 4.2

⫻ 10

⫺

390 251

PSZ 1000 0.3 10.5

⫻ 10

⫺

205 325

(sintered) 830 0.3 2.7 ⫻ 10

⫺

290 742

LAS (glass CERAMIC) 96 0.27 0.5

⫻ 10

⫺

68 2061

Al-titanate 41 0.24 1.0

⫻ 10

⫺

11 2819

Table 5 Weight Loss of Fully Dense SiC in Acids and Bases

Reagent (wt %) Test Temperature (⬚C) Weight Loss (mg/ cm

yr)

98% H

100 1.5

50% NaOH 100 2.5

53% HF 100

⬍0.2

85% H

100 ⬍0.2

45% KOH 100

⬍0.2

25% HCl 100

⬍0.2

10% HF

⫹ 57% HNO

25 ⬍0.2

Specimens submerged 125 to 300 h, continuously stirred.

Data Courtesy of ESK-Wacker, Adrian, MI.

␴

(1 ⫺

␮

)

R ⫽ (3)

␣

The value of R for selected ceramics is presented in Table 4. Another frequently

used parameter is R

⬘, the thermal shock resistance where some heat ﬂow occurs:

⬘ is simply R multiplied by the thermal conductivity, k. For cases where heat

transfer environments are complex, Ref. 12 lists 22 ﬁgures of merit for selecting

ceramics to resist thermal stress.

4.3 Corrosion Resistance

Many advanced structural ceramics such as alumina, silicon nitride, or SiC have

strong atomic bonding that yields materials that are highly resistant to corrosion

by acidic or basic solutions at room temperature (the notable exception being

glass or glass-bonded ceramics attacked by HF). This corrosion resistance has

led to many applications. Carbonated soft drinks are acidic, and alumina valves

are used to meter and dispense these beverages at refreshment stands. The chem-

ical industry utilizes a wide variety of ceramic components in pumps and valves

for handling corrosive materials. For example, the outstanding corrosion resis-

tance of fully dense SiC immersed in a variety of hostile environments is given

in Table 5. There are many cases where corrosion and particulate wear are

superimposed, as in the handling of pulp in papermaking or transporting slurries

in mineral processing operations, and ceramics ﬁnd frequent application in such

uses.

430 OVERVIEW OF CERAMIC MATERIALS

Table 6 Key Properties for Electronic Substrates and Packages

Material CTE (10

⫺6

/K)

Therm. Cond.

(W/ mK) Resistivity

Dielectric

Const.

(96%) 6.8 26 ⬎10

9.5

(99%) 6.7 35 ⬎10

AlN 4.5 140–240

⬎10

BeO 6.4 250

⬎10

6.5

Diamond 2 2000

⬎10

5.5

Silicon 2.8 150

Note: CTE and thermal conductivity are at room temperature, and the dielectric constant is at 1

MHz.

4.4 Passive Electronics

The role of passive electronics is to provide insulation (prevent the ﬂow of

electrons) either on a continuous basis (as in the case of substrates or packages

for microelectronics) or on an intermittent basis as is the case for ceramic ca-

pacitors (which store electric charge and hence need a high polarizability). These

two applications constitute two of the largest current markets for advanced ce-

ramics. For electronic substrates and packages key issues include the minimi-

zation of thermal mismatch stresses between the Si (or GaAS) chip and the

package material (so the CTE will be important) and dissipation of the heat

generated as electrons ﬂow through the millions of transistors and resistors that

comprise modern microelectronic chips; hence the thermal conductivity is a key

property. All other things being equal, the delay time for electrons to ﬂow in

the circuit is proportional to the square root of the dielectric constant of the

substrate (or package) material. Additionally, the chip or package must maintain

its insulating function, so resistivities of

⬎10

are required. Most high-

performance packages for computer chips are alumina. With the advent of mi-

crowave integrated circuits (e.g., cell phones) aluminum nitride substrates are

beginning to be utilized for high thermal conductivity. The environmental draw-

backs to machining BeO has tended to favor the use of AlN to replace or avoid

the use of BeO. Synthetic diamond is an emerging substrate material for special

applications. Isotopically ‘‘pure’’ synthetic, single-crystal diamond has values of

thermal conductivity approaching 10,000 W/mK. Typical values of the above

properties for each of these materials is given in Table 6, along with selected

properties of silicon for comparison. For design purposes exact values for spe-

ciﬁc formulations of the materials should be obtained from the manufacturers.

Over a billion ceramic capacitors or multilayer ceramic capacitors (MLCC)

are made every day.

Since electrons do not ﬂow through capacitors, they are

considered passive electronic components. However, the insulators from which

ceramic capacitors are made polarize thereby separating electric charge. This

separated charge can be released and ﬂow as electrons, but the electrons do not

ﬂow through the dielectric material of which the capacitor is composed. Thus,

the materials parameter, which determines the amount of charge that can be

stored, the dielectric constant, k, is the key parameter for design and application.

Table 7 lists the approximate dielectric constant at room temperature for several

families of ceramics used in capacitor technology. The dielectric constant varies

4 APPLICATIONS 431

Table 7 Dielectric Constants for Various Ceramic

Capacitor Materials

Material Dielectric Constant at RT

Tantalum oxide (Ta

) ⬃25

Barium titinate

⬃5,000

Barium–zirconium titinate

⬃20,000

Lead–zirconium titinate (PZT)

⬃2,000

PZT with W or Mg additives

⬃9,000

Lead magnesiun niobate (PMN)

⬃20,000

Lead zinc niobate (PZN)

⬃20,000

with both temperature and frequency. Thus, for actual design precise curves of

materials performance over a relevant range of temperatures and frequencies are

often utilized. Many ceramics utilized as capacitors are ferroelectrics, and the

dielectric constant of these materials is usually a maximum at or near the Curie

temperature.

4.5 Piezoceramics

Piezoceramics are a multi-billion dollar market.

Piezoceramics are an enabling

material for sonar systems, medical ultrasonic imaging, micromotors and micro-

positioning devices, the timing crystals in our electronic watches, and numerous

other applications. A piezoelectric material will produce a charge (or a current)

if subjected to pressure (the direct piezoelectric effect) or, if a voltage is applied,

the material will produce a strain (the converse piezoelectric effect). Upon the

application of a stress, a polarization charge, P, per unit area is created that

equals d

␴

, where

␴

is the applied stress and d is the piezoelectric modulus. This

modulus, which determines piezoelectric behavior, is a third-rank tensor

that

is thus highly dependant on directions along which the crystal is stressed. For

example, a quartz crystal stressed in the [100] direction will produce a voltage,

but one stressed in the [001] direction will not. In a polycrystalline ceramic the

random orientation of the grains in an as-ﬁred piezoceramic will tend to mini-

mize or zero out any net piezoelectric effects. Thus, polycrystalline piezocer-

amics have to undergo a postsintering process to align the electrically charged

dipoles within the polycrystalline component. This process is known as poling

and it requires the application of a very high electric ﬁeld. If the piezoceramic

is taken above a temperature, known as the Curie temperature, a phase trans-

formation occurs and piezoelectricity will disappear. The piezoelectric modulus

and the Curie temperature are thus two key materials selection parameters for

piezoceramics.

The ability of piezoceramics to almost instantaneously convert electrical cur-

rent to mechanical displacement, and vice versa, makes them highly usefull as

transducers. The efﬁciency of conversion between mechanical and electrical en-

ergy (or the converse) is measured by a parameter known as the coupling co-

efﬁcient. This is a third key parameter that guides the selection of piezoelectric

materials.

Although piezoelectricity was discovered by Pierre and Jacques Curie in

1880, piezoceramics were not widely utilized until the development of poly-