modern ceramic engineering 2nd richerson

This results in a state of residual tensile stress just below the extra plane of atoms balanced by compressive stress in the region above the dislocation.. The presence of the dislocatio

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Properties, Processing, and Use in Design

Contents

Prel." to the Second Edilion

Preface to the First Edition

Introd.dion

1 Atomic: Bonding, and Crystal Structure

• vii

xi

I

3

2 Crystal Chemistry and Speci6c Crystal Structures 32

3 Phase EguUibria and Phue Equilibrium Diagrams 71

1 Dieledrict Magnetic and Optical Behavior 1S1

8 Time, Temperature, and Environmental Elred!

EWed:ive Ionic Radii (or CalioD' aod AniOBS

periodic Table of the Elements

lode x

374

418

519 5% 6ZO

4 Chapter 1

The second shell h as eight e lectron s two in s orbital s and six in p orb ital s All h ave higher energy than th e two e lectr o n s in th e first s h e ll and are in

o rbit a l s farth e r f rom the nucleus (For in s tance the s o rbital s of th e seco nd

shell of lithium have a spherical probability distribution at about 3 A radius.) The p orbitals are not spherical but have dumbbell-shaped probability dis-

tributi o n s along the orthogonal axes, as s hown in Fi g 1.1 Th ese p electrons

have slightly higher energy than s electrons of the same shell and are in pairs

with opposite spins along each axis when the shell is full

The third quantum shell has d orbitals in addition to sand p orbitals A

full d orbital contains 10 electrons The fourth and fifth shells contain f orbitals

in addition to s p and d orbitals A full f orbital contains 14 electrons

A s imple notation i s u sed to show the electron confi g uration s within s hell s

t o s h ow the relative energy of the electrons, and thus to s how the o rd e r in which th e electrons ca n be added to or removed from a n a tom during bond ing This notation can best be illust r ated by a few examples

Example 1.1 Oxygen has eight e l ectrons and has the electron notation

I s'2s'2p' The I and 2 preceding the sand p designate the quantum shell the sa nd p designate the subshell within each quantum shell and the su-

perscripts designate the t o tal number of e lectron s in each s ub s h e ll For oxyge n

the Is and 2s subshells are both full but the 2p subshell is two electrons short

of being full

Example 1.2 As the a tomi c number and th e number of electrons increase the energy difference between electro n s and be tw ee n s hell s decreases and ove r l< lp between quantum gro up s occurs For example the 4 5 s ub s hell of iron

lills before the 3d subshell is full This is shown in the electron notation by

Figure 1.1 E l ec tr o n probability distributions f o r p o rbital s The hi g es t pr obab ility

e l ectron pos iti ons are a l o g t h e ort h ogo n al axes Two electrons each with oppos ite

s pin a r e associated with eac h axis resulting in a to tal o six p e l ect r ons if all th e

p orbitals in th e s hell a r e filled

dia-The different polymorphs are usually designated by letters of the greek

alphabet Figure 3.20b is a schematic of a binary eutectic diagram with

three A polymorphs each with partial solid solution of B

Figure 3.21 illustrates a real binary system with polymorphs

Poly-morphic transformations are also present in Fig 3.19

Three-Component Systems

A three-component system is referred to as a tertiary sysfem The addition

of a third component increases the complexity of the system and of the

phase equilibrium diagram The phase rule becomes F = 3 - P + 2 =

5 - P As with binary ceramic systems diagrams are usually drawn with

pressure as a constant (condensed system) The phase rule for the

con-174 Chapter 5

Figure 5.S Scanning electron photomicrographs of fracture surfaces of

reaction-bonded silicon nitride containing nearly spherical pores resulting from air ment during processing Arrows outline flaw dimensions used to calculate fracture stress

entrap-178 Chapter 5

)<", 1- - - ~

Figure 5.7 Typical ceramic tensile test specimen configuration

Another method of obtaining tensile strength of a ceramic material is known as the theta test [18] The configuration is shown in Fig 5.6c Applicaton of a compressive load to the two arches produces a uniaxial tensile stress in the crossbeam Very little testing has been conducted with this configuration owing largely to difficulty in specimen fabrication

Compressive Strength

Compressive strength is the crushing strength of a material, as shown in Fig 5.6f It is rarely measured for metals but is commonly measured for ceramics especially those that must support structural loads such as re-fractory brick or building brick Because the compressive strength of a ceramic material is usually much higher than the tensile strength, it is often beneficial to design a ceramic component so that it supports heavy loads

in compression rather than tension In fact in some applications the ramic material is prestressed in a state of compression to give it increased

ce-resistance to tensile loads that will be imposed during service The residual compressive stresses must first be overcome by tensile stresses before ad-ditional tensile stress can build up to break the ceramic, Concrete pre-stressed with steel bars is one example Safety glass is another example

is distorted so as to fill in the space of the missing half-plane of atoms This results in a state of residual tensile stress just below the extra plane

of atoms balanced by compressive stress in the region above the dislocation The presence of the dislocations and the associated residual stress allows slip to occur along atom planes at a fraction of the £ / 20 value that

Zone of compressive stress ~

Zone of tensile stress €E>

Figure 5.17 Sc h ematic of the residual st r ess state showing compressive s tr ess above the dislocation and tensile stre s s below the dislocation ( CI ASM In te rna· tional )

Figure 5.23 Crystal structure of AI~o.\ showing complex paths O !- and Alh ions must follow to allow slip to occur unde r an

applied stress (From W D Kingery et al lntroduction co Ceramics 2nd ed Wiley New York 1976 p 732.)

"

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• o·

Electrical Behavior 243

Figure 6.23 Example of the Meissner effect s howing the levitation of a magnet

at liquid nitrogen temperature by YBa ! Cu t01., ceramic superconductor (Courtesy Ceramatec Inc )

The response of the s uperconductive material to the amount of current

being carried or to an applied magnetic field is also very important Too

high a current density or magnetic field can destroy the superconductive behavior Each material has a different response

Evolution of Superconductor Materials

Figure 6.24 shows th e historical progression in discovery of superconductive

materials with higher T, Progress was extremely slow up to 1986, averaging about 4 K per decade Initial materials identified to be superconductive were elemental metals (Hg, Pb, Nb), followed primarily by solid solutions (NbTi) and intermetallics (Nb,Sn, V,Si, Nb,Ge) Until the early 1960's,

relatively few materials had been identified with superconductive behavior Superconductivity was thought to be an anomalous property Since 1960, techniqu es have been avai l able to achieve temperatures closer to absolute

zero (on the order of 0.0002 K) and to simultaneously apply high pressure

Under these conditions many more elements, so lid solutions, lics, and ceramics have been demonstrated to have superconductivity Several ceramic compositions were identified to be superconductive These included tungsten, molybdenum, and rhenium "bronze" composi-

intermetal-tions A,WO" A,MoO and A,RhO" where A was Na, K, Rb, Cs, NH"

Ca, Sr, Ba, etc.; oxygen-deficient SrTiO J and LiTi0 3 ; and BaPb, _ Bi.O J

Dieleclric Magnelic, Optical Behavior 275

equal probability of s hifting in s ix directions toward one of the corners of the octahedron As a result the tetragonal crystal contain s so me dipoles

in one portion of the crystal pointing in one direction, whereas others in

another portion may point in a direction 90 0

or 180 0

away from the first

A region of the crystal in which the dipoles are aligned in a common direction is called a domain An example of BaTiO 1 with a ferroelectric

domain with aligned dipoles is illustrated in Fig 7.18

Let us return now to Fig 7.16 and describe what happens in a lectric crystal such as tetragonal BaTiO, when an electric field is applied

ferroe-The f e rroelectric domains are randomly oriented prior to application of

the electric field, that is, at E = 0, the net polarization equals zero (P,,, = 0)

As we apply an electric field and increase the electric field, the domains begin to move in the BaTiO.\ and align parallel to the applied field This

results in an increase in net polarization along line OA The polarization reache s a saturation value (8) when all the domains are aligned in the direction of the field If we now redu ce the electric field to zero, many of the domains will remain aligned such that a remanent polarization (P,)

exists Interpolation of the line 8e until it intersects the polarization axis gives a value P J which is referred to as the spontaneous polarization If

we now reverse the electric field, we force domains to begin to switch direction When enough domains switch, the domains in one direction balance the domains in the opposite direction and result in zero net po-

Figure 7.18 TEM image of 180 0

ferroelectric domain s in a single grain of

BaTiO, (Courtesy of W E Lee, University of Sheffield.)

Dielectric, Magnetic , Oplical Behavior 285

Another import a nt wave-generation application i s the so nic delay line

A d e lay lin e consists of a so lid bar or rod of a sound-transmitting material

(glass, ceramic, metal) with a transducer attached to each end An electric

signal that is to be delayed is input to the first transducer The signal is

convert ed to a so nic wave impul se that travels a long the so und-tran s mitting

"waveg uid e." The so nic impul se i s th e n converted b ack to an e l ect rical

impulse by the second tr a n sducer The delay re s ults bec a u se a so ni c wave travels much mor e s l ow ly than e l ec tron s passing throu g h a wire The time

of delay is controlled by the length of the waveguide Delay lines are used

ex ten s iv ely in milit ary electronic s gear a nd in color t e levi s ion se t s One exa mpl e is r adar syste m s to co mp a re inf or m a ti o n from o ne echo with the

next echo and for range calibration

The wave-generation applic a tions di sc u sse d so far invol ve aco u s tic

waves transmitted through bulk media Additional freedom exists in the

Figure 7.25 Piezoelectric ceramics and assembli es for a variety of applicatio ns (Courtesy EDO Corporat i o n.)

324 Chapler 8

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-Figure 8.7 Hot-pressed Si l N~ specimen deformed by creep under a load of 276

MPa (40.000 psi) at llOOOC (-2200'F) for 50 hr

mechanisms available for crack growth Crack growth is relatively easy if the grain boundaries of the material are coated with a g l ass phase At high temperature, l ocalized creep of this glass can occur, resulting in grain

boundary sliding Figure 8.8(a) shows the fracture surface of an NC-132

hot-pressed Si J N 4 specimen that fractured after 2.2 min under a static

bending load of 276 MPa (40,000 psi) al - llOO'C ( 2000'F) The initial flaw was probably a shallow (20 10 40 pm) machining crack It linked up

with cracks formed by grain boundary sliding and separation and pores

formed by triple-point cavitation to produce the new Haw or structurally weakened region seen in Fig 8.8 as the large semicircular area extending

inward from the tensile surface This was the effective flaw size at fracture

Time, Temperature, Environmental Effects on Properties 325

Figure 8.8 Comparison of a s l ow crack growth fracture versus a normal bend fracture for hot-pre sse d Si N • (From Ref 9.)

-~ ~ .:.:.:.;.:; :

(b )

(a)

(d ) (e )

Figur e 8 11 Surfaces o f h ot-press e d S i N befo re and afte r ox i dation (a) As _ mac h ined surface, 32O-gri l diamon d; (b) oxi d ize d

in ai r for 50 h r al 98O"C (l 8OO" F); (c) oxidiz e d in air fo r 24 hr at 1 2()(rC (22OO"F); and (d) oxid ized in air for 24 hr at 137O"C (25OO"F) ( C ASM I nternation a l.)

348

Figure 8.23 Reaction-bonded SilN~

after exposure in a combustion rig with

5 ppm sea sa lt addition for 25 cycles of

1.5 hr at 900°C, 0.5 hr at 1120°C, and a

5-min air-blast quench (a), (b), and (c)

show the fracture surface at increasing

magnification and illustrate the g l assy

buildup in the region of combustion gas

impingement (From Ref 9.)

Chapter 8

as fouling, A thin buildup can protect th e surface from corrosion and

All three of these factors can increase the life of a component especially

a metal However, a thick buildup reduces the airflow through the engine and decreases efficiency

Fouling is an inherent problem in the direct burning of coal A variety

L Intermittent removal of buildup by thermal shock, melt-off, or

passing abrasive material (such as nutshells) through the system

388 Chapter 9

Figure 9.4 S i ,N J grinding m e dia s h owi ng one of the common configurations

Sp her es a r e also commo nl y u sed (Co urt esy K e m aNord.)

wear-resistant linings a nd h ave been u sed s u ccessf ull y with dry millin g a nd with water as a milling fluid However so m e millin g i s cond u c t e d with organic fluid s that may a tt ac k ru bbe r or p l y urethane Very hard gr inding media can reduce contamination beca u se th ey wear m o r e s l ow l y we i s goo d for some cases because it s hi g h hardness reduces wear a nd it s high

s pecific g ravity minimi zes millin g tim e If contamination from the media

i s a n especially critica l consideration, millin g ca n b e conducted with medi a mad e of th e sa m e compos iti o n as th e powder being mill ed Another a p- proach is to mill wit h s t eel media a nd remove th e contamination by a cid leaching

Milling can be conduc t ed either dry o r wet The advantages a nd adva nta ges are li sted in Table 9.5 Dry millin g has the adva nt age that the resulting p owde r d oes not have t o be separa t e d from a liquid The major concern in dry milling i s that th e p owde r d oes not p ack in th e corners of