Chapter 7- Ceramics Phase Equilibrium Diagrams Kingery
28
264 6.2 D with Increasing pressurecfor 6.3. If diffusion anneal times re 6.4. 6 5 From data on ZnS d f n temperature to the meI Uil difus lon coemcient of 3 × IO• ’ Z/ l USlO imcieIIIs were measured At • the basis 6.6 pIot ? (d) What is the to? (;) Would quenchlng the the state of ' the -- ..... energy ‘ experlmental) for Na+ diff · 1: 11 r i OF MICRO 'S' TR UCTURES .I, N CERAMICS ‘ ‘ The propertie s of ceramics are determined by the properties of each phase present and by .the way in which these phases , including ...Q___ orosity and in many cases the are arranged. ln Part 11 we have discussed the structure of crystalline materials , the structures of glasses , imperfections in these structures , the characteristics of interfaces , and how moþility of to structural propertie s of each phase present in more complex ceramics. ln Part 111 we want to develop an understanding of the factors which determine the phase distribution and how they in ceramic systems. The development of microstructure proceed s on two fronts . First there a tenden-c y to form an concentra- tion of phases such as to minimize thé Phase-equilibrium diagrams are an economical method for de s'cribing the final state tùwards which the phase composition tends . ln our discussion of phase diagrams we have limited ourselves to a maximum of three and have developed the underlying thermodynamics only to the minimum level necessary . In many actual more than three components are important , but the of our treatment to this mòre complicated case uses the sam'e principles which have been described and discussed. The primary difficulty with including a greater number of components is not so much conceptual as in the easy representation of a large body of data in conci se diagrammatic form,. For 265
Transcript of Chapter 7- Ceramics Phase Equilibrium Diagrams Kingery
264
6.2 싫 i§§§뚫 짧:§탤찮웰;잖Eg:혔§풍g?4S;품옆;찮隨띔뿔뿔$짧C쯤 ;뚫:￡:」? D with Increasing pressurecfor (aT?隱뽑i認j혈짧뽑i짧평
6.3. If diffusion anneal times re
6.4. 繼뭘탤탤짧gF 현E렐 찮 J혔r:tt 『$t빼 6 5 From mX짧tering data on ZnS d f n 震。?m temperature to the meIUil
difuslon coemcient of 3 × IO• ’Z/ l USlO imcieIIIs were measured At 563℃， •
뚫짧@魔i뿔繼隱싫짧e탠혔?魔e혔 鍵l露;윈많選J￡? 繼뽑廳5tZ양; ;;↓앞 the basis 穩關at;nrtv많鋼몇￡짧않짧h魔핑띔t$RZ
6.6 짧§뚫혔EQgs웰줬3f:Ei§Z:쏠;;:?J: t;넓o;af? ZZ3델總;옆;$?성;:um ;::麗tpIot? (d) What is the activ짧ZZZe to? (;) HO꺼 Would quenchlng the g싫 cha뺨 the state of' the glas~. --..... 04~UV~llun energy ‘experlmental) for Na+ diff ·
Pl홉，rt， 1:11 r
i
D~EVELO'PMENT OF MICRO'S'TR UCTURES
.I,N CERAMICS ‘ ‘
The properties of ceramics are determined by the properties of each phase present and by .the way in which these phases, including ...Q___orosity and in many cases the interfa으잃， are arranged. ln Part 11 we have discussed the structure of crystalline materials , the structures of glasses , imperfections in these structures, the characteristics of interfaces, and how ~he moþility of atofl1호is r반핫ed to the낭e structural char원teristics . 캔품끊다꿇표옮dj論ζ닮효닮짧jig-닮표앓패견릎죠짧딛.E뚫짧휠i§‘표T효e properties of each phase present in more complex ceramics. ln Part 111 we want to develop an understanding of the factors which determine the phase distribution and how they oper~te in ceramic systems.
The development of microstructure proceeds on two fronts . First there are탤탤홉냐없꿇앓and a tenden-cy to form an εquilibrium concentration of phases such as to minimize thé ‘f뚫흘탤앉gy-_.오I aThRrX￥~，1~Jll. Phase-equilibrium diagrams are an economical method for des'cribing the final state tùwards which the phase composition tends. ln our discussion of phase diagrams we have limited ourselves to a maximum of three compoIl:~nts and have developed the underlying thermodynamics only to the minimum level necessary. In many actual syst~Ins more than three components are important, but the εxtension of our treatment to this mòre complicated case uses the sam'e principles which have been described and discussed. The primary difficulty with including a greater number of components is not so much conceptual as in the easy representation of a large body of data in concise diagrammatic form,. For
265
266 INTRODUCTION TO CERAMICS
ceramic students we have found that the most useful introductory discussion to multicomponent systems is that given by A. Muan and E . F. Osborn , Phase Equilibria in and among Oxides in Steelmaking. *
In addition to changes in the chemical constitution and amounts of phases present physical factors are also important in determining the direction in which changes proceed during the development of microstructure. A꾀칸단친뚝떤단뾰으단쁘효뀔뜨!!!.k achieved with .Q뜨똥월웰 surface and interface are~ ， which occurs during the processes of ~~~펀; 교즙뀐팬E한i잃파돼윷값 grow맨 In addition there are strain.:eï바rgy terms and surfàce-energy terms associated with the formation of a new phase which affec~ both its morphology and its tendency to appear. These aspects of the driving forces toward minimizing the system’ s free energy during microstructural development are discussed in Chap~er 8 in relationship to phase transformations and in Chapter 10 in relationship to grain growth and sintering. The physical changes occurring, such as the decrease in porosity , the distribution in porosity , and the morphology of the phases present, are equally as important as the chemical processes related to phase equiIibria discussed in Chapter 7 and chemical equilibria discussed in Chapter 9.
Only a small percèntage of real ceramic systems are treated under conditions such that equilibrium is achieved. Particularly with regard to the small driving forces associated with surface and interface energy and for systems in which the mobiIity of atoms is small, including many silicate systems and almost all systems at moderate and low temperatures, the way in whtch equilibrium is approached and the rate at which it Is approached 없e equally as important as the equilibrium being approached. In the conden~￥d phase systems with which we are mostly concerned, material tninsfe~ processes may take place by 댄띤ε φ맺맺필 or 앨때똥핀땐떤Ef 양법~￥윌앓!‘ or 힐‘Z훌IWJ:-tr효ns{?으!1.요~트~S혹~ . The rate and kinetics by W1tich these processes are important in affecting the development of microst대야ure are discussed in Chapter 8 with regárd to phase transformations, in Cfià함~r 9 with regard to solid-state reactions, and in Chapter 10 with regard to gfãin_용 owth and sinterìng. A thorough understanding òf the way in which systemsÎnodify their microstructure in the approach toward equilibrium is absolutely essential for understanding the microstructurè and therefore the properties of ceramic products.
In Chapter 11 some characteristic measurements necessary to describe microstrúcture together with typical examples of ceramic microstructur e in a variety of real systems are discussed and described. In addition to the specific systems described in Chapter t 1 we have been implicitly or
*Addison-Wesley Pu\ilishlna Cgmpany; 매C. ， Readlns, Mass .. 1965.
MICROSTRUCTURES IN CERAMICS 267
zza;?itlf鍵짧yWi임1뜸$;?3원짧rZ않SZ:zr파t:; t.많u魔n많3 throughout Indeed, the development of microstructure, ltS InjlCnce on the properties of ceramics, and its control by compositlqn and processIng
changes are a ζentral theme.
7
Ceramic PhaseEquilibrium
Diagrams At equilibrium a system is in its lowest free energy state for the
composition, te'm_Qe잭샌않ι.Pl응옆파싫짧.other iml?.Q..\>S일Q않i!jgas - Wheh a given set of system parameters is fixed , there is only one mixture of phases that can be present, and the composítion of each of these phases is determined. Phase-equilibrium diagrams provide a ciepr and concise method of graphically representing this equilibrium situation and are an invaluable tool for characterizing ceramic systems. They record the composition of each phase present, the number of phases present, and the
、 amounts of each phase present at equilibrium. The time that it takes to reach this equilibrium state from any arbitrary
starting point is highly variable and dependson factors other than the finaJ equilibrium state. Particularly for systems rich in silica the high viscosity of the liquid phase leads to slow reaction rates and very long times before equilibrium is established ; equilibrium is rarely achieved. For these systems and for others, metastable equilibrium , in which the system tends to a lower but not the lowest free energy state, becomes particularJy Important.
It is obvious that the phases present and their composition are an essentiaJ element in analysing, controlling, improving, and deveJoping ceramic materials. Phase diagrams are used for determining phase and composition change occurring when the partial pressure of oxygen or other gases is changed , for evaluating the effects of heat treatments on crystallizatiop and precipitation processes , for planning new compositions. and for many other purposes. We have already seen the importance of thermodynamic equilibrium in our discussions of single-phase systems: crystalJine sQlid solutions (Chapter 2), crystalline imperfections (Chapter 4), structure of glasses (Chapter 3), and surfaces and interfaces (Chapter 5). In this chapter we concentrate our attention on equilibria invoJving two or morξ phases.
269
270 INTRODUCTlON .TO CERAMICS
7.1 Gibbs’s Phase Rule
When a system is in equilibrium, it is necessary that the temperature and pressure be uniform throughout and that the chemical potential or vapor pressure of each constituent be the same in every phase. Otherwise there would be a tendenζy for heat or material to be transferred from ooe part of the system to some other part. ln 1874 J . Willard Gibbs* showed that these equilibrium conditioos cao occur ooly if the relatiooship
P+V=C+2
is satished- This is known as the phase rule, with P being the number of phases preseot at equilibrium, V the variaoce or oumber of degrees of freedom , aod C the number of compooents. This relationship is the basis for prepariog aod usiog phase-equilibrium diagrams.
A phase is defioed as aoy part of the system which is physicaIIy homogeneous and bouoded by å surface so that it is mechaoicaIIy separable from other parts of the system. It oeed not be cootiouous; that is, two ice cubes in a driok are ooe phase. The number of degrees .of freedom or the variaoce is the number of ioteosive variables (pressure, temperature, composition) that can be altered independently and arbitrarily without bringiog about the disappearance of a phase or the appearance of a new phase. The oumber of componeots is the smaIIest oumber of independeotly variable chemical coostitueots oecessary and sufficient to express the compositioo of each phase presen t. The meaniog of these terms wiII become clearer as they are applied to specific systems in the foIIowiog sectioos.
Deductioo of the phase rule foIIows directly from the requirement that the chemical potential μ; of each constituent i be the same in every phase preseot at equilibrium. The chemical potential is equal to the partial molar free energy G;,
ã; = (짧) T. P. n , . n
which is the change in free energy of a system at constant temperature and pressure resulting from the addition of one mole of constituent i to such a large quaotity of the system that there is no appreciable change in the conceotratioo. In a system with C components we have ao indepen. dent equation for each component represen t"ing the equality of chemical potentials: For a system containing P phases, we have
a b c P μ ， = μ ， = μI = ... = μl (7.2)
*Collec led Wq rks. Vo l. 1, Löngmons. Green & Co .. Lld .. LQndon" 1928.
CERAMIC PHASE.EQUILIBRíUM DIAGRAMS
P μ2a = μr = μ2‘ :: ". = μ:
etc .
271
(7 .3)
whiζh constitute C(P - l) independent equatlons which serve to hx
람l-;4혔겹CZns:2:￡;p:;魔lCl$짜i關앓:ag짧댔뽑f뿔 phases requires P (C - 1) ιon‘;entration
terms , v ·vp
imposed conditions of temperature and pressure gIve
Total nùmber of variables == P (C - 1) + 2
Variables fixed by equalityof chemical póteotials == C (P - 1)
Variables remainiog to be fixed == P (C - 1) + 2 - C (P - 1)
V==C-P+2
(7.4)
(7.5)
(7.6)
(7 .7)
캡E3했뚫rE생;원뚫Ei렀$ 짧RE33t。E:lZq업鋼tw짧많경cZ?Ea:z Z23iJE:룹옆@?￡gg: :zz1?1따%R§:@t댐eR3짧:$많파옆껍n뜰SX?vFC that equilibrium does not exist), the reverse is not always true- That ls,
conformation with the phase rule is not a demonstration of equllibrillm .
• 7.2 One.Componeot Pbase Diagrams
3훨혈뿔편3뚫뒀짧뒀짧줬짧願$뚫隨줬 짧폈월앓뭘3g짧r$평$;많$￥;쩔3￥E줬평젊짧짧 뚫隨隨짧蠻평짧:짧뿔폈$뿔뚫 Rnd different Phase distributions correspond to Fig. 7·2a to c. In actual
mctice measurements in which the vapor phase is unimportant are
ugually made at constant atmospheric pressure In a way similar to Fig.
7.Zd· Although this is not an ideal closed system, it closely approximaFs
歸뽑r많 織앓짧업n$않S$;tn협잃빠$:3$￡램p껍잃 Z땀Xetxr;;
꿇:갱겁S찮l짧랬랬 Z뽑 j:싫?FJ많§e% uz;Z경않?g협l*3qLA1영E캅Z!
편껄tr171캡認찮원랬4찌델:맏u鋼캡뽑짧앓:블L『엽뽑많 p꺼않빨鋼:펴않져캉 u ’ -, (:>) (q) (lJ)
TL 'S!d
1"0 1「m@@특m (엉크)
Z"Z S3IIWH33 Ol NOIl3tMORiNI
-q!I!nb::l lj:>e::l1 01 p::lJ!nb::lJ ::IJV-::1띠!1 JO SPO!J잉d 8uo( 1941 OS ‘4S!원9n(s 3Jll
UMOqS SUO!IBWJOJSUB11 J::Iq10 ::Ilj1.. '::I(q!SJ::IA::I1 pUB p!dUJ 51 oEL!; 113 UO!I!SUlIJI
ZlJBnb-잉-zlJenb-;o ::Il.p ‘0['<: uO!l:>::IS U! pdssn:>S!p sy 'UMOljS SB 3JB S3JI11
-lUddW::I1 UOmSUBJl dql ::lJnss::lJd 띠lB [ lV 'B:>
275
rium. The vapor pressure shown in the diagram is a measure of the chemical potential of silica in the .different phases . and this same ,kind of diagram can be extended to include . the metastable forms of silica which may occur (Fig. ,7.5). The phase with the싶않효묘뾰와Q많옳않싫the heavy lines in the diagram) 따표모값윤닮패닮; ~띤l2.erat!l~ the equilibrium phase. However, once formed , the transition between cristobalite arid quaπz is so slu,ggish that ß -cristobalite commonly transforms on cooling into a -cristobalite. Similarly, β2-tridymite commonly transforms into aand ß -tridymite rather than into the equilibrium quartz forms. These are the forms present in the refractory silica brick, for example. Similarly , when cooled, the liquid forms silica glass, which can remain indefinitely in this state at room temperature.
At any constant temperature there is always a tendency to transform into another phase of lower free energy (lower vapor pressure), and ,the reverse transition is thermodynamically impossible. It is not necessary , however, to transform into the lowest energy form shown. For example , at llOOo silica glass could transform into ß -cristobalite, ß -quartz, or ß2-tridymite. Which of these transformations actually takes place is
∞ 」그 이 이 @
』” ι
i> \'!;' Tempe대lure !
1)1애ram InQludlnll~πIItiuable phaSé8 occurrina in the system SiG, .
’--y 흔 ;…*?
←←S→서
tμ y’
CERAMIC PHASE-EQtJlLIBRIUM DIAGRAMS
LiqUld
I Graphite ’ ‘ 3000
'F ( ' Kl
Efg꾀i￡ ;1:f魔s;;r꽤ie?효;?Perature phase eq삐ibrium diagram for carbon. From C
5000
1000
200
0
870' 1470. 1713'
Vapor
573.
1 atm
a-Quartz
@ ‘ 『} 이 이 @ ‘ ι
" "
Figo 7.4.
, !
Temperature Equilibrium diagram for SiO, .
r ‘ i
’ JFτ낀 꽉 ~-，j; ~i
214
l t
276 INTRODUCTION TO CERAMICS
determined by the kinetics of these changes. In practice, when silica glass is heated for a long time at this temperature, it crystallizes, or devitrifies , to form cristobalite, which is not the lowest energy form but is structurally the most similar to silica glass. On cooling, β-cristobalite transforms into α-cristobalite.
The silica system illustrates that the phase-equilibrium diagram graphically represents the conditions for minimum free energy in a system; extension to include metastable forms also allows certain deductions about possible nonequilibrium behavior. Almost always, however, a number of alternative nonequilibrium courses are possible, but there is only one equilibrium possibility.
7.3 Techniques for Determining Phase-Equilibrium Diagrams
The phase-equilibrium diagrams discussed in the last section and in the rest of this chapter are the product of experimental studies of the phases present under various conditions of temperature and pressure. In using phase-equilibrium diagrams it is important to remember this experimental basis. In critical cases, for example, diagrams should not be used without referring directly to the original experimenter’s description of exactly how the diagram was determined and with what detail the measurements were made. As additional measurements are carried out, diagrams are subject to constant revision.
There is a large body of literature describing methods of determining phase equilibrium. In general, any physical or chemical difference between phases or effect occurring on the appearance or disappearance of a phase can be used in determining phase equilibrium. Two general methods are used: dynamic methods use the change in properties of a system when phases appear or disappear, and static methods use a sample held under constant conditions until equilibrium is reached , when the number and composition of the phases present are determined.
Dynamic Methods. The most common dynamic method is thermal analysis, in which the temperature of a phase change is determined from changes in the rate of cooling or heating brought about by the heat of reaction. Other properties such as electrical conductivity, thermal expansion, and visζosity have also been used. Under the experimental conditions used, the phase change must take place rapidly and reversibly at the equilibrium temperature without undercooIing, segregation , or other nonequilibrium effects . .In silicate systems the rate of approach toward equilibrium is slow; as a result thermal-analysis methods are 1088 useful for silicates than they are for metL\ls, for oxampl톨.
CERAMIC PHASE-EQUlLlBRIUM DlAGRAMS 277
Dynamlc methods are suitable for determining the temperature Of
總뿔;學f&§댈:靈뚫웰뭘§뿔:f짧trf§웰§gg?뒀 뿔짧펴;」;t펌:성?;짧많F;:gr앓앓§많:?녔t않밍2강X;@C;ztF옐ragi structure , and mICroscoplc examination of phase amounts and phase
di§I$;많thods. In때l ments따ts 0아따fte태n consist of three steps- Eqmlibrim c.onditions are held at
짧뚫t짧騙웰댐y짧StZ핍짧;CZt 풍ig잃:Aar$풍밀파tggt:。;z;$ and then the specimen is examined to determine the phases present- By
鐵魔隱S앓S때t歸짧魔e앓많魔魔魔: 패풍nCi짧앓앓뜸많t씁뽑쩍엎 감앓따밸며點r&따뚫:;?g;? ￡Z￡피g
z;E§5E3원E뚫짧짧-;앓 3#앓sg3b4￡FrZ￡:;r:앓r3 J3u;$歸밍2§ 1t1e difRcult-- in ensuring that equllibrillm has actually been reached. For most …st싸s this means that statlc measurements are necessary A
c야omm rat“io to g밍ive t얀the뼈e뼈fin빼뼈na뻐1뼈때a떠l“c∞om매lpO빼n des잉iηred . These are held at a consta법 lemPerature in platinum fml ; after rapid cooling, the mixture lS regrollL in a mortar and pestle and then heatcd for a second time and q뼈C뼈
짧 S3za:kgS영앓밝혔때피Eggt앓鋼l; 잉상u:Ze뒀믿;;짧 I§I$얹5나 th얻댐eJCZZZsC때e짧i임uC솥 t?짧 양:zn짧ort ; since several thωsand individual experiments, such as those just described, may be nece쉰ary for one ternary dlagram, we can understand why only a few systems “ave
be뚫鋼끓t하YIa앓v룹$$u댄뿔생합di않 general , the original experi
menter investigating a partiClllar phase diagram is usually QOncerncd with some limited region of composition, temperature, and pressure- His effort is concentrated in that area, and the other parts of the ph렐 diagram are d@termined with much less precision and detail. As reported ln summarlz-
냈짧짧앓O$ $;앓 $$:?r풍￡X::ti?」?꽤짧:es)파많lEl歸u잃 ?;:
'íme떼 cor뼈u비따r빼-l냄efi1 þefa따l때ure원s and compositions of individual lines or points on …e
279
indicated by lines on the diagram. (ln binary diagrams two-phase regions will often be shaded , single-phase regions not.) The intersection of a constant-temperature “ tie line" with the phase boundaries gives the compositions of the phases in equilibrium at temperature T. With two phases present, P + V = C + 2, 2 + V = 2 + 2, V = 2. At an arbitrarily .. fixed pressure , any arbitrary change in éither temperature or composition of one of the phases present requires a corresponding change in the other variable. The maximum number of phases that can be present where pressure is arbitrarily fixed (V = 1) is
CERAMIC PHASE.EQUlLIBRIUM DIAGRAMS
P + V = C + 2, P + 1 = 2 + 2, P = 3.
When three phases are present , the composition of each phase and the temperature are fixed , as indicated by the solid horizontal line at C.
Systems in Which a Gas Phase Is Not Important , Systems containing only stable oxides in which the valence of the cations is fixed comprise a large fraction of the systems of interest for ceramics and can adequately be represented at a constant total pressure of 1 atm. At equilibrium the chemical potential of each constituent must be equal in each phase present. As a result the variation of chemical potential with composition is the underlying thermodynamic consideration which determines phase stability. If we consider a simple mechanical mixture of two pure components, the free energy of the mixture G μ is
GM = XAGA +XBGB
[l nd under all conditions the free energy of the solution is less than that of n mechanical mixture; the free energy curves for the solid and liquid olutions and the resulting phase-equilibrium diagram are similar to those
nlready illustrated in Fig. 4.2. Since very dilute solu.tions approach ideal bchayior, Eq. 7.10 requires that there is always at least some minute ol \J bility on the addition of any solute t'o any pure substance.
Most concentrated solutions are not ideal , but many can be well rcpresented as regular solutions in which the excess entropy of the 뼈lutlon 1s negligible, but the excess enthalpy or heat of mixing ð. H xs is Ii J맡nltl can t. Jn this case the free energy of the regular solution is
(7.10) G id•S = G M
- T ð. Sm
(7.11) T~S’” ~H1t1 ‘a ’‘~ IIIJ
INTRODUCTION TO CERAMICS
g;a§r&TJrz밸e?파X1&F:z:ELt3JZ;tg;3밍폐Zrey represent 빠esu . These cautIOns are particularly appl.lcable to regions of llrnltcd crystal
Jine s빠lon at high temperatures sm for many systems exsolutlok
鐵隱總t앓s??감慮ngi임.鍵짧靈認i랩Sa?옆鐵re “ low te띠Peraturc s often results ln submicroscopic phases which arc
i풍5뽑5월경魔;밍e꾀s;양 5짧r임￡;;r鍵밟 빨 강Z:i짧;git뎌댐
278
(7.9)
For the simplest case , an ideal solution in which the heat of mixing and changes in vibrational entropy terms are zero , random mixing gives rise to [1 configurational entropy of mixing ð. Sm which has been derived in Eq. 4, 14 ; the free energy of the solution is
Two-Component Systems
1n two-component systems one add피onaJ variable , the composition , is Introduced so that if only onc phase IS present, the variance is three:
￡싫r짧깅 2h4 J우g4Jik g길휴 않 않g따4ZiG않앓말;lE$$멍E3:zr$ :rrS짧;얀양SI;Z렘lZ풍경T때뀔jpC§X않s갚?않VZ;at양웅$tZt ;ge:ea;많Z ;3g;ETegl책Fgk:hZt t%암Z$;t 엽r웰풍;회밍@ssr￡￡; 3:tES생￡넓띔승 and composltlOn gs variables A dlagram of this kind is shown in Fig 7.6
If one pha야 IS prFsent, both temperature and compositlOn can be a얀때ily va뼈， as 뼈rated for point A In the areas In which two p”ases are present at equilibrIum, the composition of each phase is
7.4
φ 」그 } m」φ a E φ 」〔 7
/
:;;~\I?， Q‘I?,-'
B
Sìmplc blrlßry diollf Îln1 ,
CompoSltiOl1 FiS. 7,6.
281
situation is illustrated in Fig. 7.7 d, in which the minimum system free energy again consists of a mixture of the two solutions a and β.
When , for any temperature and composition, free-energy curves such as shown in Fig. 7.7 are known for each phase which may exist , these phases actually occur at equilibrium which give the lowest system free energy consistent with equal chemical potentials for the components in each phase. This has been illustrated for an ideal solution in Fig. 4.2 , compound formation in Fig. 4.3, and phase separation in Fig. 3.10 and is iIlustrated for a series of temperatures in a euteζtic system in Fig. 7.8.
Systems in Which a Gas Phase Is Important. ln adjusting the oxygen pressure in an experimental system , it is often convenient to use the equilibria
CERAMIC PHASE-EQUILIBRIUM DIAGRAMS INTRODUCTION TO CERAMICS
The resulting form s of typical free-energy-composition curves for an ldeal sqmuon and for regular solutions with positive or negative excess enthalmes are shown iF Fig. 7-7 In Fig. 7.7c the Inmrnml the system at compositions intermediate between a and β consists of a míxture of a and β in which these two solution compositions have the same chemical potential for eaζñ component and a lower free energy than lntermediate single-phase compositions ; that is, phase separanon occursWhen differences of crystal struct ure occur (as discussed in Chapter 2), a complete series of solld solutions between two components is not possible, and the free energy of the solution increases sharply after an initial decrease required by the configurational entropy of mixing. This
280
(7.12) I CO+5oz=COz G B
(7 .13)
In this case , with no condensed phase present, P + V = C + 2, 1 + V = 2 + 2. V = 3, and it is necessary to fix the temperature , system total pressure, and the gas composition, that is, CO2/CO or H2/H20 ratio , in order to fix the oxygen partial pressure. If a condensed phase , that is, graphite , is in equilibrium with an oxygeri-containing vapor phase , P + v = C + 2, 2 + V = 2 + 2, V = 2, and fixing any two independent variables completely defines the system.
The most extensive experimenlal data available for a two-component system in which the gas phase is important is the Fe-O system, in which a number of condensed phases may be in equilibrium with the vapor phase. A useful diagram is shown in Fig. 7.9, in which the heavy lines are boundary curves separating the stability regions of the condensed phases und the dash-dot curves are oxygen isobars. ln a single condensed-phase region (such as wüstite) P + V = C + 2, 2 + V = 2 + 2, V = 2, and both the lemperature and oxygen pressure have to be fixed in order to define the omposition of the condensed phase. ln a region of two condensed phases
(such as wüstite plus magnetite) P + V = C + 2, 3 + V = 2 + 2, V = 1, and f1 xing either the temperature or oxygen pressure full y defines the system. Por this reason , the oxygen partial-pressure isobars are horizontal, that is , 뼈othermal ， in these regions , whereas they run diagonally across single ondensed-phase regions.
An alternative metbod of rep resenting the phases present at particular ox ygen pressures is shown in F ig. 7.9b. In this representation we do not
’ ‘ihow the O/Fe rfl lio, that is, the composition of the condensed phases, but önly the pressure- temperß ture nrnges for each stable phase.
H2+502 = H2O GA
B Composition (bl
~ ( 띠 」φ Z
띠
A B
GB
-Tð.Sm
GM + !;,.H %S
Composition (a l
~[
며」 @ Z
내
A
느」 훌낀 @ β B A Q
Composftion Compos비on (C)
‘d) Fig. 7.7. Free-energy-composition diagrams for (a ) ideal s이비 ion ， (b) Ilnd (c ) r08버ür solutions, and (d) incomplcte solld 5QlutiQn.
B β
-Tð.S m
~ ( 며」 ω t
버
A
T., AT--
‘(야」ω--
∞ ιφ」」
Te A세11
〉띠」ω=φφ
ω」」
l、- 7r 「a ---Îm------ --------펴-꺼 틸
a+ β \ .• n -4------~
__________ ， ~ 1.
。 -pT-I~1r ’ ‘ 1 ,.1
←~.~
~'; A
, 서서 I앙‘l B
’‘ f ’ ， ’감냉 X s 티g. 7.8. Free-energy• ompositioq curves and the tempefature·c。Ihpj펴써 ,'-.' dlagram for a eutectic syitem- From p . Gordon, PrinciPIes oI Phase Dtagrains trl Systems, McGrawSHill Book tCompany, New York, I%8. n E: ‘-J rf~ 호 주F.，;~ J 용f호
1→ "'""".f~초 →lτf- f;') r ~ ,'.:1
i; T,j 등 ':t~‘!효후τ 즙， 훌 Hè 칸i i'"1ß-J~-l 」등은듬길관 뭘좋쉴들 옹펴 .' , 응f노 J ' 션 응을'qfπ"! 든흐=; J l'., 1갚f 걷i감 1
\ ι ‘* \ /
'\. A ",U\ 、
ι
4 、 : '\ magnetite + liqu id
ι\ν μ낯뉴
l l O
6
-+10二-
- -+10다-
--i10괴 -wüsti te + magnetite
--+10다-
---L10파-- 「 - -i-lO피-----LiO피------}-1O링 -
- - - - ---!- IO _'::': '---'-- -- '-~10닥늑;
----.---.--10二츠_.-
- .- .- - ----10다，_ ._
a ~ i ron + magnet ite
\ liqu id
\
ι\ O\ ,
‘ 、
\ 、
wustlte + ilquid " \
)' -l(on +
wust ite
i}'
。
B
T
rF
l
o
X s
A
AT1
〉띠」@I@ω@」」
A|
@」긍@』@gEω
←
b
T 3
10 200 L_
l“ ",0 40 50 60 FeO.Fe20 380 Weight %
Fi8‘ 7.9. (a) Ph a,se relations in the FeO-Fe,O, system. Dash-dot lines.are oxygen isobars Alternate solidiflcation paths for composi~iori A are discussed in tex t. From A. Muan and E. F: Osborn . Phase Equilibria among Oxides in Stee/making, Addison-Wesley Publishing Company , Inc., Reading, Mass .. 1965 .
Fe20 :l
."
>,
, ,1
90 30
주 != !.i:ξ l석 염 :.= 1 .t • ,
1 ì t" ~ τr _~~i~승← 를ε . H j:j!"
213
!
20
11t흐h ~ . .. :-.:.=-= :.
흥::... t
X B
A
2.3
5 T
T,
‘ ,
A에||
〉띠」@rωω@」」
4l
|
〉야」@I@ωει
A|
〉쁜일@ ωω」
hi‘
j
;, ? '1
A
285 CERAMIC PHASE-EQUILIBRIUM DIAGRAMS INTRODUCTION TO CERA’ncs 284
Liquid
.A
‘ 、
‘ 、
、、
、
、、
\ 、、
、、
\ \ 、
、
‘ 、
\ 、、
、、
、、
、、
、、
、、、、
、、、‘
μq + BeO
1980。
2600
1700
QC 뼈
때 1200
1600
1500 Liquid oxide
Ltquid iron
δIron
7.0
i 'è.. 6.0 e‘ 、、
o
6.5
m
o o 빼
+
뻐
BeO + 3 BeO Al20 3 0
짧-」 3 앞댐3$;g:， A${ 짧.PFZfuSZE?빨됐;?r않)dIagram for the Fe-Fe2OI SYStem-
- 2 - 4 - 8 -6 log p02(atml
60 3:1
Weight % A1203 The binary system BeO-AIzOι
O BeO
、
lO be of limited extent, although this is uncertain, and are not shown in the diagram. The system can be divided into three simpler two-cqmponent ystems (BeO-BeAh04, BeAh04-BeAI60 IO, and BeAI60 ur-Ah03) in ~ach
0' which the freezing'point of the pure material is lowered by addition of the second component. The BeO-BeAhO. subsystem contains a compound , Be3Ah06, which melts incongruently, as discqssed in the next Icction. In the single.-phase regions there is only one phase present, its
mposition is obvious1y that of the entire system, and it comprises 100% f the system (point A in Fig. 7: 10). In two-phase regions the phases
prcsent are indicated in the diagram (point B in Fig. 7.10); the composit뼈n of . éach phase is represented by the intersection of i ,a constant tcmperature tie 1ine and the phase-boundary 1ines. The amounts oLeach phlll!e can aIso be determined from the fact that tbe sum ofι t,he.
ömposìtion times the amount of each phase present must equa1 the omposit ion òf the entire system. For examp1e, at point C in Fig .. 7 .. 10 ,the ntJre Ilystem ls compos흩d of 29% A120 3 and cQnsists of two phases, BeO ontlllnloi no Al~O~) ßnd，3BcO'; _̂bO~ (which contains 58% Ah0 3). There
Phase-equilibrium diagrams are grgphical representations of experimema! observanons The most extenSIVe collection of diagrams useful in
551a띠찮 §;껍 짧g;q짧Stt앓 $뚫껍?￡r따맏ef;?z:원?s원없S§Z QIagrams ca? be classi6ed Into several general types-Eutectic Diagra꾀s. When a second component is added to a pure mat맏ial ， the freezlng point is often lowered A complete binary sy강em consísts of lowered 1iq미dus curves for both end members, as illustrated in Flg. 7.8· The. eutectlC temperature is the temperature at which the liquidus curves lntFrsect and ?s tpe lowest temperature at Which liquid occurs- The eutectlC CompoF1tl?n IS the composition of the liquid at this temperature, the llquid coeXISUng with two solid phases. At the eutectic temperature three phases are present, so the variance is one- Since
S鍵뚫rf 6xed, the temperature cannot change unless qne phase
thg월찮R4cz::;;諾ee:R펴ERL않떻AZ;gc;Z따짧a옆h$f;XiZ앓t:iizg
「 .... 1:3 Al2Q3
Fill. 7.10 Two-Component Phase Diagrams 7.5
u amlï l .t, ·E· M· Levin, c. R· Robbins, llnd H F· MCMurdie, Phase Dtagrums for ican Ceramic Soclety, Colun뻐Y8 . 1964: SUpplf ml! l lI , 1969.
286 INTRODUCTION TO CERAMICS
must be 50% of each phase present for a mass balance to give the correct overall composition. This can be represented graphically in the diagram by the lever principle, in which the distance from one phase boundary to the overall system composition, divided by the distance from that boundary to the second phase boundary , is the fraction of the second phase present. That is, in Fig. 7.10,
OC ;::;:. (1 00) = Per cent 3BeO'Ab03 OD
A little consideration indicates that the ratio of phases is given as
DC BeO OC 3BeO' Ab03
This same method can be used for determining the amounts of phases present at any point in the diagram.
Consider the changes that occur in the phases present on heating a composition such as E , which is a mixture of BeAbO. and BeAI60 lO •
These phases remain the only ones present until a temperature of 18500 C is reached ; at this eutectic temperature there is a reaction, BeAbO. + BeAl6 0 lO = Liquid (85% Ab03), which continues at constant temperature to form the eutectic liquid until all the BeAl60 lO is consumed. On further heating more of the BeAbO. dissolves in the liquid , so that the liquid composition changes along GF until at about 18750 C all the BeAbO. has disappeared and the system is entirely liquid. On cooling this liquid , exactly the reverse occurs during equilibrium solidification.
As an exercise 'students should calculate the fraction of each phase present for different temperatures and different system compositions .
One of the main features of eutectic systems is the lowering of the temperature at which liquid is formed. In the BeO-Ab03 system, for example , the pure end members melt 'at temperatures of 25000 C and 20400 C, respectively. In contrast, in the two-component system a liquid is formed at temperatures as low as 1835 0 C. This may be an advantage or disadvantage for different applications. For maximum temperature use as a refractory we want no liquid to be formed . Addition of even a smalJ amount of BeO to Ab03 results in the formation of a substantial amount of a fluid liquid at 18900 C and makes it useless as a refractory above thi temperature\ ,However, if high-temperature applications are not of majQr importance , 'it may be desirable to form the liquid as an aid to firing ãl lower temperatures , since liquid increases the ease of densification. Thi is true , for example , in the system Ti02- U0 2, in which addition of 1% Ti02 form s a eutec tic liquid . wh ich is a great aid in obtain ing high densities al low tcmperatures. Thc st l'ucture of thi s system. shown il1 I’‘ ig.
CERAMIC PHASE-EQUlLIBRIUM D1AGRAMS 287
7.11 , consists of large grains of U02 surrounded by the eutectíc composl
t lOn. The effectiveness of eutectic systems in lowering the melting point is
made use of in the N a20-Si0 2 system, in which glass compositions can be melted at low temperatures (Fig. 7.12). The liquidus is lowered from 17100 C in pure Si02 to about 7900 for the eutectic compositíon' at approximately 75% Si02- 25% Na20 .
Formation of low-melting eutectics also leads to some severe limitations on the use of refractories . ln the system CaO-Ab03 the liquidus is strongly lowered by a series of eutectics. In general, strongly basic oxides such as CaO form low-melting eutectics with amphoteric or basic oxides, and these classes of materials cannot be used adjacent to each other, even though they are individually highly refractive.
Incongruent Melting. Sometimes a solid compound does not melt to form a liquid of its own composition but instead dissociates to form a new 이id phase and a liquid. This is true of enstatite (l4gSiO3) at I557。c (Fig.
7 l3); this compound forms solid Mg2S:04 plus a liquid containing about 61 % Si02. At this incongruent melting point or peritectic temperature there
1800
Tridymite + liquid
_----- .... “‘ Metastable 、、
two ,liquids ';
50 70 • 80 9O lQO Weight ?~ Siû"
짧s:따꾀많짧n때 sy5tem Na2SiO,-Si02. The dashed line shows metasta바eliq삐
2900
1900
1700
1500 L__.1 O • 1,0 20 30, 40 50 60 Mgo forsterite enstatlt!l
We1iht percent SiOa Fiì, 7.ìi ~'The blnary mtem M.ι.siOI r 펴 i 증펴，_ í홈
IJ 딩 잉 :1을'f'J-;- 풍 i ....
CERAMIC PHASE-EQUILIBRlUM DIAGRAMS 289
are three phases present (two solids aïid a lìquid) , so that the temperature remains fixed until the reaction is completed. Potash feldspar (Fig. 7.14) also melts in this way.
Phase Separation. When a liquid or crystalline solution is c。이ed ， it separates into two separate phases at the consolute temperature as long as the excess enthalpy is positive (see Fig. 7.7). This phenomenon is particularly important relative to the development of substructure in glasses, as discussed in Chapter 3 (Figs. 3.11 , 3.12, 3.14 to 3.19). Although it has been less fully investigated for crystalline oxide solid solutions, it is probably equally important for these systems when they are exposed to moderate temperatures for long periods of time , The system CoO-NiO is shown in Fig. 7.15.
1800
1600
Û 1400
。J
:::J
m
gi E q’ f- 1200
1000
Cristobalite + Liquid
o ' ' 20 40 60 80 100 Leucite ‘ Potash
K ~û . A1 2 Û3'4SiO ~ feldspar K2Û'AI 2Û3'ßSiû 2 1 .1 ‘ Weillht per ，~ent SìÛ2
P1I , 7,14, πle blnarý . y. tem K10 ' AI1Q) ,/JSi02 (Ieycite)- SiO., From J , F, Schairer and N. L. 8owl n, 8u /l , Soc, 0101: FlnL, 20. 74 (1947) , Two.pha8e reaion, are showI! shaded in this dlqrám, r"- •'" !.
1;:·r---‘_ Liquid --• •“-1 ‘ •‘-•--“ -‘-‘-
----」 -“ --‘-_------==-
r;... 1200
(Ni CoJ û 50lid 5olution
1000
800
.8 Coû Mole fraction
Fig. 7.15. The binary system NiO-CoO.
m 강
@
」3 @
」∞ g E ω 」
Mgû 55 + Caû 55
1800
1600ð
MgO 60
Weliht-" CøO FI, . 7.16. The blnary ìyllem M.O-C.O.
80
I응 ';,
I톨@
100 CIIO
'"
CERAMIC PHASE-EQUILIBRIUM DIAGRAMS 291
Solid Solutions. As discussed in Chapter 4 and in Section 7.4, a complete series of solid solutions occurs for some systems such as illustrated in Fig. 4.2 and Fig. 7.15, and some minute or significant limited solid solution occurs for all systems, as shown in Figs. 4.3, 7.13, and 7.15.
It has only been in the last decade or so that careful experimentation has revealed the wide extent of solid solubility, reaching several percent at high temperatures in many systems, as shown in Figs. 4.3, 7.13, and 7.15 and .for the MgO-CaO system in Fig. 7‘ 16 and the MgO-Cr203 system in Fig. 7.17. For steel-plant refractories directly , bonded magnesia-chromite brick is formed when these materials are heated together at temperatures above 16000 C as a res lJ.lt of the partial solubility of the constituents; exsolution ocζurs on cooling. Almost all open-hearth roofs are formed of either direct-bonded, rebonded fine-grain , or fusion-cast magnesiachromite refractories . In the basic oxygen-furnace process for steel making MgO-CaO refractories bonded with pitch are widely used , and the solid solubility at high temperatur.es forms a high-temperature bond. In magnesia refractories the lower solid solubility of Si02 as compared
3900
2800
2600
2400
암 2200
현q그eji 2om
얻E 1800
/ MgO 5.5. + MgCr2û. 5.5
: 1400 ."•
....... " 1200
MgCrzÜ4 40 60
Weight %‘Cr2~~
Ei •. 7.17. Tht blnll'Y IYltem M‘O-M，Cr~O> .
292 INTRODUCTION TO CERAMICS
with CaO in MgO re9uirFS that excess CaO be added to prevent the formation of low-melting intergranular silicates.
anrJF웅뿐?섣#얻;?gZ였SEa ;섣3L상많:얹c양앓s수꽤$z짧:상iE뜸:멈:뜸za젊§앓:많u맴gi:$않와E앓 $ so이씨l피u배b비il피IhihtyR뿌ecreasesι， an띠1띠d co야orur뼈lT (Fig. 7.18)
This same sort of limited solid solution is observed in the Ca0-ZrCL syste피 (Fig 7 19); in this system there are three diRerent 6elds of solid somuon, the tetrFgonal form , the cubic form , and the monoclinic form. Pure ZrO2 exhiblts a monodink tetragonal phase transition at 1000℃， which lrwolves a largF mIume change and makes the llSe of pure zirconia impoFsible as a CeramIC material. Addition of lime to form the cubic solid somuon, which has no phase transition, is one basis for stabilized zirconia, a valuable refractory.
d ‘ Complex Diagrams. AIl the basic parts of binary phase-equilibrium lagrams have been Ulustfated ; readers should be able to identify the
nur빼er of pha.sgs, compos1tl()n of phases, and amounts of phases present at any composItlOn and temperature fr。m any of these diagrams with ease and c?n5denge. If they cannot, thcy should consult one of the more extensive treatments listed in the references.
E찮J↓Lg RPTg랩맙n Qf AhOI from 에 plnel ’빼
。J
:J
(。
용 E Q’ f- 1000
CERAMIC PHASE-EQUILIBRlUM DlAGRAMS
Liquid
10 20
Mole per cent CaO
50 ZrCa03
293
Fig.7.19. The binary system CaO-ZrO,. From P. Duwez, F. Odell, and F. H. Brown, Jr. , J. Am. Ceram. Soc. , 35, 109 (1952). Two-phase regions are shown shaded in this figure.
Combinations of simple elements in one system sometimes appear frightening in their complexity but actually offer no new problems in interpretation. In the system Ba2Ti04- Ti02 (Fig. 7.20), for example, we find two eutectics, three incongruently melting compounds , polymorphic forms of BaTiO), and an area of limited solid solution. AIl of these have already been discussed. ’
Generally phase diagrams are constructed at a total pressure of 1 atm with temperature and composition as independent variables. Since the interesting equilibrium conditions fo r many ceramics involve low oxygen partlul pressures, phasc diogrums at a fixed lemperature but with oxygen
.IlJUJQl O-J:':>-:l.:::J 01.1‘L '''~(dwo:l QJOW QωO;):>q s띠\u8UfP ~l(1 ‘SI:.lu!ds SH 4:lI1S 'Spunödω0::1 :)l껴!P~WJ"llJ! 山JO]40!I.IM SlU"lsÁs uI '(f-V)IZ'L '~!d u! UMoqs S! tOd JO UO!l3unJ R se A1lA!l3e lg껴;)!U ;)4l ]0 1이d γ ('(OlJ;) 이끼MO이f7 7
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ue uo P:.ll;):.lf01d ~q ue;) S;)101tU~dW:.l1 :.l1.(1 UO!le1U:.lS:.l1d:.l1 IeUO!SU:.lW!P-OM1 lOd 'ZZ'L '융!d se tpOS We1~e!p :.lsel.(d e :.l^1융 01 ;)leU!p10 Ie;)!ll:.l^ e uo :.llOle1:.ldw:.l1 :.l1.(1 pue :.l[î!ue!11 le1:.llel!ob:.l ue uo P:.l1U:.lS:.l1d;)1 :.lq ue;) SUO!l -ISodwo;) ‘1Ue1SUO;) PI;)I.( S! :.llOSS:.lld :.l1.(1 ]! 10q ‘110;)파!P S! SW:.l1SÁS Á1eU1:.l1 JO uO!lelU:.lS:.l1d:.l1 le;)!l.(de1융 ~l:.lldω0;) V'띠:.llSÁS 1Ue!le^U1 ue 01 ~s!l S~^!î!
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JO UO!le11U;);)UO;) ;)q1 uo 융u!pu;)d;)p “Ol(l;)‘;)d) 10 '(Ol(l;)‘;)d) + .0((1;)‘;)d) ‘γ0'(1;)‘;)d) + O;)d ‘O;)d ;)q λew s;)seqd ;)(qe1S ;)q1 ‘띠1e 01_01 = 'od JÖ ;)lOSS;)ld U;)î!Áxo ue lV 'q 1 Z' L 'î!!d U! UMOI.(S S! )1。μÇl1e W:.l1SÁS
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297 CERAMIC PHASE-EQUILIBRIUM DIAGRAMS
z
… ‘ ‘ 긍 m a
g g ω 」{
x
Y
W W Space diagram of (a) ternary eutectic and (b) complete series of solid solutions
Y
dimensional representation is to take a constant-temperature cut through the diagram , indicating the phases at equilibrium at some fixed temperature.
lnterpretation of ternary diagrams is not fundamentally different from that of binary diagrams. The phases in equilibrium at any temperature and composition are shown; the composition of eaζh phase is given by the phase-boundary surfaces or intersections ; the relative amounts of each phase are determined by the principle that the sum of the individual phase compositions must equal the total composition of the entire system. ln Fig. 7.22 and Fig. 7.23 , for example , the composition A falls in the primary field of X. If we cool the liquid A , X begins to crystallize from the melt when the temperature reaches T ,. The composition of the liquid changes along AB because of the loss of X. Along this line the lever principle applies, so that at any point the percentage of X present is given by 100(BA/XB). When the temperature reaches T 2 and the crystallization path reaches the boundary representing equilibrium between the liquid and two solid phases X and Z , Z begins to crystallize also , and the liquid changes in composition along the path CD. At L , the phases in equilibrium are a liquid of composítion L and the solids X and Z, whereas the overall composition of the entire system is A. As shown in Fig. 7.23b , the only mix ture of L , X, and Z that gives a total corresponding to A is x A/x X ( 애0) = Per cent X , z A/zZ (100) = Per cent Z, IA /l L (1 00) = Per cent L Thât 1s. the smaller ;t riangle XZL is a ternary system in which the omposirion of A can be represen ted in terms of its three constituent s.
Fig.7 .22
INTRODUCTION TO CERAMICS 296
, ‘ ‘ 긍 애 」잉 g E ∞ 」{
J
Fe20 Spihel Wustite
T = 1573 0
K.
Fe30‘/ Fe20 3
• -4
￡ 。。
으 -6
‘
Alloy + spinel
-16
0.4 0.6
xc，~
(bJ
Fig. 7.2I (continued)· (b) Fe-Cr-O system-(I) Composition--p。z diagram and (2) oxygen isobars for equiIibrimn between two phases. From A. pelton and H. SchIrialzried, Met. Trans., 4, 1395 (1 973).
Cr 0.8 Fe
isotherms. The diagram is divided into areas repre&enting equiIibrillm between the liquid and a solid phase- Boundary curves represent equilib- ‘
rillm bttween two solids and the liquid, an# intersegtions tOf three bouri~ary_ψrves represen(þo첸t5 of four phases in, equilib뻐m< {inv없뻐lt points in ' fhe constant-pÌ'ess'ure system). _ AnQt빠I meth_og , of two-
x
z Z
Y x Composition
Fig.7.23. (a) Crystallization path il’ustrated in 'Fig. 7.22a and (b) application of center of gravity principle to a ternary system.
8i02 Cristobalite
20 Potash feldspar K 20'A1203' 68i02
30
40
30
. 20 L
10
K 20 Al.。톨 50 '60 70 • 굽o--9õ
Weiaht per cent; ’톨훌 z 헬 '+
많，짧'. I짧:;;빨y_Sj'Jlem I{..μlaO!-SIOj . FfDml. F요뼈빠JwtN . L ._Bow빼내숨l 」 구 , _It • T !~ 르 f! 드 등 츠 ';"'f-J.‘ 홀 f
21'
CERAMIC: PHASE-EQUILIBRIUM DIAGRAMS . 299
Many ternary systems are of interest in ceramic science and technology. Two of these , the K 20-Ab03-Si02 system and the Na20-CaO-SiO: system, are illQstrated in Figs . 7.,24 and 7.25. Another important system , the MgO-AbO칸Si02 system. is discussed in' Section 7.8. The K20-Ab03-Si02 system is important as the basis for many porcelain compositions. The eutectic in the subsystem potash-feldsparsilica-mullite determines the firing behavior in many compositions. As discussed in Chapter 10, porcelain compositions are adjusted mainly on the basis of (a) ease in forming and (b) firing behavior. Although. real systems are usually somewhat more complex , this 'terriary diagram provides a 'good. description of the compositions used. The Na20-CaOSi02 system forms the basis for much glass technology . Most compositions fall along the border between the primary phase of devitrite , Na20.3CaO.6Si02, a l)d silica ; the liquidus temperature is 900 to 1050oC.
To Caû
。‘
m tM
Aη
잉 ”• Ma
m o ιv
9i
a N
Two liquids
2Na2û'Caû '3Siû2
Na2SiOa
To Na2û SiÛ2 50 Na 2SiOS
40 10
1ξ
Weight per cent Na 2û Plli; 7.2'. The_Na.O- O- CaO-SiO. system. From G. W. Morey and N. L. Bowen. J. Soc. CJ/cfll r，eh패'-C9， 232 (192$). "투
300 INTRODUCTION TO CERAMICS
This is a compositional area of low melting temperature , but the glasses formed contain suf윈cient calcium oxide for reasonable resistance to chemical attack. When glasses are heated for extended times above the transition range, devitrite or cristobalite is the crystalline phase formed as the devitrification product.
Very often constant-temperature diagrams are usefu l. These are illustrated for subsolidus temperatures in Figs. 7.24 and 7.25 by lines between the forms that exist at equilibrium. These lines form composition triangles in which three phases are present at equilibrium, sometimes called compatibility triangles. Constant-temperature diagrams at higher temperatures are useful , as illustrated in Fig. 7.26, in which the 12000 isothermal
40
KS 2
Tridymite + Liquid
/ 50
To K 2 0
Liquid Leucite + KAS 2
Liquid L3
Si02
A1Z03 + Leucite + KAS z
To K 20
〔그 Single-phase region
툴클 Tw。때ase 대glO n s
F>. /:1 Three - phase regions
40
+ Tridymite + Liquid L 1
Mullite + Leucite + Liquid L 2
30 20 Weight per cent
Mullite + Leucite + AloO 2~3
10 AI 20 3
Fig. 7.26. )sothcrmal cut in the K，O-AhO.，-SiO~ úi [l~nllÎ1 111 1200"‘_.
CERAMIC PHASE-EQUILIBRIUM DlAGRAMS 301
plane is shown for the K20-AbO,-Si02 diagram. The Iiquids formed in this system are viscous; in order to obtain vitrifiιation ， a substantial amount of liquid must be present at the firing temperature ‘ From isothermal diagrams the composition of liquid and amount of liquid for different compositions can be easily determined at the temperaturc selected. Frequently it is sufficient to determine an isothermal planc rather than an entire diagram , and obviously it is much easier.
Altnough our discussion of three-component diagrams has been bri ef and we do not discuss phase-equilibrium behavior for four or more component systems ' at all , students would be well advised to becomc familiar with these as an extra project.
7.7 Phase Composition versus Temperature
One of the useful applications for phase equilibrium diagram s in ceramic systems is the determination of the phases present at different temperatures. This information is most readily used in the form of plot s of the amount of phases present versus temperature.
Consider, for example , the system MgO-Si02 (Fig. 7.13). For a compos. ition of 50 wt% MgO-50 wt% Si02 , the solid phases present at equilibrium are forsterite and enstatite. As they are heated , no new phases are forme니 until 15570 C. At this temperature the enstatite disappears and a composi . tion of about 40% liquid containing 61% Si02 is formed . On furthcr heating the amount of liquid present increases until the liquidu s is reache <J at some temperature near 1800oC. In contrast, for a 60% MgO-40o/r SiO: composition the solid phases present are forsterite , Mg2SiO., and periclase , MgO. No new phase is found on heating until 18500 C. wh en lhι composition becomes nearly aJl liquid , since this temperature is near thc eutectlζ ζomposition. The changes in phase occurring for these two compositions are iJlustrated in Fig. 7.27.
Several things are apparent from this graphical representation . One b the large difference in liquid content versus temperat비'e for a relatively small change in composition. For compositions containing greatcr th :.ll1
42% silica, the forsterite composition, liquids are formed at relatively low temperatures. For compositions with silica contents less than 42% no liquid is formed until 1 850oC. This fact is used in the treatment of chromite refractories. The most common impurity present is scrpcntinc, 3MgO.2Si02 '2H 20 , having a composition of about 50 wt% SiO~ . If su에cient MgO is added to put thi s in the MgO- forsterite fi e ld , it no longe r' ha s a dcletcriou s cffcct. Without this addition a liquid is form ed al low temperatures.
Another appliζE\ lìQ I'l of Ihi s di l\Brum ìs ìn lhe se l eιtìon of CQlllp t'lsitiðfls
302
1900
INTRODUCTION TO CERAMICS
20 40 60 80 100 ---- 0 20 40 60 80 100 Weight per cent 01 each phase present Weight per cent 01 each phase present
(e) 65% Si02 (f) 70% Si02 Phase composition versus temperature for sampJes in the MgO-SiO, system.
Û 1800
뻐 뼈
양」그-gigaEa
20 '40 60 80 100 Weight per cent 01 each phase present
(a) 40% Si02
1900
Û 18때
콩 1700 홍 엉 1600
20 40 60 80 100 Weight per cent 01 each phase present
(c) 55% Si02
1900
Û 1800
콩 1700 공
Fig. 7.27.
1900
P 18때 '" 응 1700 용 E ~ 1600
20 40 60 80 100 Weight per cent 01 each phase present
(b) 45% Si02
뼈 뼈
∞늠-∞」용
E@』
1500 o 20 40 60 80 100 Weight per cent 01 each phase present
(d) 60% Si02
1900
Û 1800
를 1700 훌 ~ 1600
that pave desirable Rring characteristics It is necessary to form a S뼈clent amount of liqu띠 for v끼i“tr뼈r s잉h씨umψps or warps during 6rlng. The Iimits of liquid required vary with th@ propFrties of the liqpid but are in the range of 20 to 5O wt%. To have sumclent range of hrlng temperature, it is desirable that the liquid conteM not change much with temperature- Forsterite compositions calm아 b 6red until very high temperatures if the composjtjon is exactly 42% SifL smce no liquid is formed below I 850@C Compositions in 뼈 fors ter1t흥l enstatite field whjç h are ma inJy fOf S1Crite f orm a Ii폐uid ílt 1 557.1lC, nnd
CERAMIC PHASE-EQUILlBRIUM DIAGRAMS 303
since the liquidus curve is steep , the amount of liquid present changes but slightly with temperature , as shown in Fig. 7.27. Consequently , these compositions have a good firing range and are easy to vitrify . In contras t.
compositions that are mostly enstatite (55 , 60 . 65 o/c SiOJ form large amounts of liquid at low temperature , and the amount of liquid present changes rapidly with temperature . These materials have a limited firing range and pose difficult control problems for economíc production .
For systems in which the gas phase is important the way in which condensed phases appear and their compositional changes on cooling depend on the conditions imposéd. Referring back to the Fe-O system i1Justrated in Fig. 7.9, if the total condensed-phase composition remains constant, as occurs in a closed nonreactive container with only a negligible amount of gas phase present , the composition A solidifies along the dotted line with a corresponding decrease in the system oxygen pressure. In contrast, if the system is cooled at constant oxygen pressure , the solidification path is along the dashed line . In one case the resulting product at room temperature is a mixture of iron and magnetite ; in the second case the resulting product is hematite. Obviously in such systems the control of oxygen pressure during cooling is essential for the control of the products formed.
For detai!ed discussions of ζrystallization paths in ternary systems the references should be consulted. The following summary* can serve as a revlew .
1. When a liquid is co이ed ， the first phase to appear is the primary phase for that part of the system in which the composition of the melt is represented.
2. The crystallization curve follows to the nea rest boundary th e extension of the straight line connecting the composition of the original liquid with that of the primary phase of that field . The composition of the Iiquid within the primary fields is represented b y points on the crystallization curve. This curve is the intersection of a plane (perpendicular to the base triangle and passing through the compositions of original melt and the primary phase) with the liquidus surface.
3. At the boundary line a new phase appears which is the primary phase of the adjacent field. The two phases separate together along this boundary as the temperature is lowered .
4. The ratio of the two solids crystallizing is given by the intersection () f the tangent to the boundary curve with a line connecting the composi-
' After E. M. Lçvin . H‘ F. McMurdie. and F. P. HaJJ . P!wse Diagrallls for Ceramist s. Amξrlι0'; C흥rnmìζ Söcicty. CleveJand. Ohio. 1956.
304 INTRODUCTION TO CERAMICS
tions of the two solid phases. Two things can occur. If this tangent line runs between the compositions of the two solid phases, the amount of each of these phases present increases . If the tangent line intersects an extension of the line between solid compositions, the first phase decreases in amount (is resorbed; Reaction A + Liquid = B) as crystallization proceeds. ln some systems the crystallization curve leaves the boundary curve if the first phase is completely resorbed, leaving only the second phase. Systems in which this occurs may be inferred from a study of the mean composition of the solid separating between successive points on the crystallization path. 씨
5. The crystallization curve always ends at the invariant point which represents equilibrium of liquid with the three solid phases of the three components within whose composition triangle the original liquid composition was found.
6. The mean composition of the solid Which is crystallizing at any point on a boundary line is shown by the intersection at that point of the tangent with a line joining the composition of the two solid phases which are crystallizing.
7. The mean composition of the total solid that has crystallized up to any point on the crystallization curve is found by extending the line connecting the given point with the originalliquid composition to the line connecting the compositions of the phases that have been separating.
8. The mean composition of the solid that has separated between two points on a boundary is found at the intersection of a line passing through these two points with a line connecting the compositions of the two solid phases separating along this boundary.
7.8 The System Ah03-SiO, As an example of the usefulness of phase diagrams for considering
high-temperature phenomena in ceramic systems , the Ab03-Si02 system illustrates many of the features and problems encountered. ln this system (Fig. 7.28), there is one compound present, mullite , which is shown as melting incongruently. (The melting behavior of mullite has been controversial; we show the metastable extensions of the phase boundaries in Fig. 7.28. For our purposes this is most important as indicative of the fact that experimental techniques are difficult and time consuming; the diagrams included here and in standard references are sllmmaries of experimental data. They usually include many interpolations and extrap이ãtions
and have been compiled with greater or lesser care, dependiog 00 the needs of the original investigator.) The èutectÌC between ITI ullìte and
CERAMIC PHASE-EQUILIBRIUM DIAGRAMS 30S
100
( n ) C
--- Stable equilibrium diagram - ._.- Metastable extension 01
liquidus and solidus lines
Liquid
뼈 m
ω‘그}m」φQE@뉴
/
녁
----_j_-------
I Alumina + i mullite (88)
1700 Mullite (88) + liquid
1600 158r :t 10。(@띠) @ξ=『}E
1500
1400 Si02 10 20 30 40 60 70 80 90 A1203 50
A1 203 (mole %)
Fig.7.28. The binary system AI,O,-Si02 • From Aksay and Pask, Science, 183,69 (1974).
cristobalite occurs at 15870C to form a liquid containing about 95 mole% Si02 • The solidus temperature between mullite and alumina is at 18280C.
Factors affecting the fabrication and use of several refractory products can be related to this diagram. They include refractory silica brick (0.2 to 1.0 wt% Ab03), clay products (35to 50 wt% Ab03), high-alumina brick(60 to 90 wt% Ab03), pure fused mullite (72 wt%' Ab03), and pure fused or sintered alumina (> 90 wt% Ab03). ‘
At one end of the composition range are silica bricks widely used for furnace roofs and similar structures requiring high strength at high temperatures. A major application was as roof brkk for open-hearth furnaces in which temperatures of 1625 to 16500C are commonly used. At this temperature a part of the brick is actually in the liquid state. In the development of silica brick ìt has be흥n found that small amounts of alumlnum oxldc are partic비arly dcletcriou8 to brick properties because
306 INTRODUCTION TO CERAMICS ~
쁘e eutectíc composítíon ís 디익e to the sílíca end of the díagram consequently, even small addltIOns of aluminum oxide mean that substantial amounts of liquid phase are present at temperatures above l600。c. For thlS reason supersilica brick, which has a lower alumina content through special raw-material selection or treatment, is used in structures that will be heated to high temperatures.
Fíre-clay brícks have a composítion rangíng from 35 to 55% alumínum oxide. For compositions without impurities the equilibrium phases present at temperatures below l587。C are mullite and silica (Fig. 729). The relatlve amounts of these phases present change with composition, and there are corresponding changes in the properties of the brick. At temperatures abo?e 1600℃ the amount of liquid phase present is sensitive to the alum띠a-silICa ratio, and for these high-temperature applications the higher-alumina brick is preferred.
rig; 짧ler서ullite crystals i씨
CERAMIC PHASE-EQUILIBRIUM DIAGRAMS 307
Refractory properties of bríck can be substantíally improved if sufficíent alumina is added to increase the fraction of mullite present until at greater than 72 wt% alumina the brick is entirely mullíte or a mixture of mullite plus alumina. Under these conditions no líquid is present until temperatures above 18280 C are reached. For some applicatíons fused mullite brick is used; it has superíor ability to resist corrosion and deformation at high temperatures. The highest refractoriness is obtained with pure alumina. Sintered Ab03 is used for laboratory ware, and fusion-cast AbO, is used as a glass tank refractory.
7.9 The System MgO-AI20 3-Si02
A ternary system important in understanding the behavior of a number of ceramic compositions is the MgO-AbOrSi02 system , iIlustrated in Fig. 7.30. This system is composed of several binary compounds which
Al20 3
PIι 7.30, The lcr…‘ry sys1cm Mlt!O- AI,O.-Sì01. Prom M. L. Keith and J. F. Schairer, J (1r끼l‘ . M’ . IR2 ( 1 ’) ~ 2 ) . R~l!i()nN or Nl1l1d sululion IIre nol shown ; sce Figs. 4.3 and 7.13 .
309
firing process, which is described in more detail in Chapter 12. On heating, clay decomposes' at 9800 C to form fine-grained mullite in a silica matrix . Talc decomposes and gives rise to a similar mixture of fine-grained protoenstatite crystals, MgSi03, in l). siliè:a matrix at about 1000oC. Further heating of clay gives rise to increased growth of mullite crystals, crystallization of the silica mat,rix as cristobalite , arid formation of a eutectic liquid at .1 595 0 C. Further heating of pure falc leads to crystal growth of the enstatite, and liquid is formed at a temperature of 15470 C. At this temperature almost all the composition melts , since talc (66.6% Si02, 33.4% MgO) is not far from the eutectic composition in the MgO-Si02 system (Fig. 7.13) .
The main feature which characterizes the melting behavior of cordierite, steatite porcelain, and low-loss steatite compositions is the limited firing range which results when pure materials are carried to partial fusion. ln g~neral ， for firing to form a vitreous densified ceramic about 20 to 35% of a viscous silicate liquid is required. For pure talc, however, as indicated in Fig. 7.32, no liquid is formed until 15470 C, when the entire composition liquifies. This can be substantially improved by using talcclay mixtures . For example, consider the composition A in Fig. 7.31 which is 90% talc-IO% clay, similar to many commercial steatite compositions. At this composition about 30% liquid is formed abruptly at the liquidus temperature , I345 0 C ; the amount of liquid increases quite rapidly with temperature (Fig. 7.32), making close control of firing temperature necessary , since the firing range is short for obtaining a dense vitreous
CERAMIC PHASE-EQUILIBRIUM DIAGRAMS
100
o 1200 1400 1500 1600
Temperature ("C)
Fla. 7.32. Amount of Iiquid present 111 different temperatures for compositions illustratcd InF애. 7.31.
1800 1300
INTRODUCTION TO CERAMICS
havF a!ready been described, together with two ternary compounds, cordlente, 2Mgp·2Al2O3 5SiOz, and sapphirine, 4MgO·5Al2O3·2SiOz, both of whiFh melt lncongruently. The lowest liquidu5 temperature is at the tridymlte-promFnstatite• cordierite eutectic at I345 0 C, but the cordieriteen한atit한forsteri‘te eutectic at 13600 C is l'!lmost as la'w-m~itin~~ - ---;
ceramlC compos띠ons that in large part appear on this diagram indlude magnesite retractorles, f야S댄따 ceramics, steatite ceramics, sa;;ial low-loss steames, and cordlente ceramics. The general composition areas of these products on thF ternary diagram are illustrated in Fig. 731. In all but magnesite refractorles, the use of clay and talc as raw materials is the basis for the compositional developments. These materials are valuabIe in large part because of their ease in forming; they are 6ne-grained and plat약 and are consequently plastic, nonabrasive, and easy to form. In àddition, the fine-grained nature of these materi~l~-i; ~;;~n;ial~f~;"tl~;
MgO ' (enstatite)
/ Low-Ios. Forster,te CeramlCS / st·-…" 감E42꽤iti5많mon compositions in the ternary system MaO- AI'OJ-S10.. See text ror
308
(앙) 는%Eg --릅-」
Periclase
8i0 2 17I3 %S.
310 INTRODUCTION TO CERAMICS
body (this composition would be fired at 1350 to 13700 C). ln actual fact , however, the raw materials used contain Na20 , K 20 , CaO ‘ BaO, Fe,O" and TiO, as minor impurities which both lower and widen the fusion range. Additions of more than 10% clay again so shorten the firing range that they are not feasible , and only Iirriited compositions are practicable. The addition of feldspar greatly increases the firing range and the ease of firing and has been used in the past for compositions intended as low-temperature insulators . However , the electrical properties ar~ not good.
For low-Ioss steatites , additional magnesia is added to combine with the free silica to bring the composition nearer the composition triangle for forsterite-cordierite-enstatite. This changes the melting behavior so that a composition such as B in Fig. 7.31 forms about 50% liquid over a temperature range of a few degrees , and control in firing is very difficult (Fig. 7.32). In order to fire these compositions in practice to form vitreous bodies , added flux is essential. Barium oxide , added as the carbonate , is the most widely used.
Cordierite ceramics are particularly useful , since they have a very low coefficient of thermal expansion and consequently good resistance to thermal shock. As far as firing behavior is concerned , compositions show a short firing range corresponding to a flat liquidus surface which leads to the development of large amounts of liquid over a short temperature interval. If a mixture consisting of talc and clay , with alumina added to bring it closer to the cordierite composition, is heated , an initialliquidus is formed at 13450 C , as for composition C in Fig. 7.3 1. The amount of liquid rapidly increases; because of this it is difficult to form vitreous bodies. Frequently when these compositions are not intended for electrical applications , feldspar (3 to 10%) is added as a fluxing medium to increase the firing range.
Magnesia and forsterite compositions are different in that a eutectic liquid is formed of a composition widely different from the major phase with a steep liquidus curve so that a broad firing range is easy to obtai n. This is ilIustrated for the forsterite ζomposition D in Fig. 7.31 and the corresponding curve in Fig. 7.32. The initialliquid is formed at the 13600 C eutectic , and the amount of liquid depends mainly on composition and does not change markedly with temperature . Consequently , in contrast to the steatite and cordierite bodies , forsterite ceramics present few problems in firing.
ln all these compositions there is normally prcscnt at thc fìring temperature an equilibrium mixture of crysta lline an l.l Jiqu itl phüscs. Thi ~
is illustrated for a forsterite composition in Pig. 7.33. Forst 당 rilι crystals are present in a matrix of lîquid si licate ço rre~ pondîng 10 the Jiqllidus
CERAMIC PHASE-EQUILlBRIUM DIAGRAMS 311
Fig. 7.33. Crystal-liquid structure of a forsterite composition (I 50x).
composition at the firing temperature. For other systems the crystalline phase at the firing temperature is protoenstatite, periclase, or ζordierite ， and the crystal size and morphology are usually diRerent as well The liquid phase frequently does not crystallize on cooling but forms a glass (or a partly glass mixture) so that the compa삐ity triangle cannot be us며 for fixing the phases present at room temperature, but they must be deduced instead from the firing conditions and subsequent heat treatment.
7.10 Nonequilibrium Phascs
The kinetics of phase transitions and solid-state reactions is considered in the next two chapters; however , from our discussion Qf glass structure in Chapter 3 and atom mobility in Chapter 6 it is already apparent that the lowest energy state of phase equilibria is not achieved in many practlcal systems- For any change to take place in a system it is necessary that the free energy be lowered. As a result the sort of free-energy curves illustrated in Figs. 3.10, 4.2, 4.3, 7.7, and 7.8 for each of the possible Dhases that might be present remain an important guide to metastable Lquilibrillm In FIg 7 8, for example, if 따 temperature T 2 the solid solution a were absent for any reason, the common tangent between the liQuid and solid solution ß would determine the cOn1position of those pGases ln which the CO빠it삐ltS have the same chemical potent때 pne ?f thc ιommon types of noncquilibrium behavior in silicale systems IS the slowneRR of cryslulliZHuon suQh that lhc liquid is supercooled. When thlS
energies required for their conversion into more stable phases cause a low rate of transition. The energy relationships among three phases of the same composition might be , represented as given in Fig. 7.34. Once any one of these phases is formed , its rate of transformation into another more stable phase is slow. In particular, the rate of transition to the lowest energy state is specially slow for this system.
The kinetics of transformation in systems such as those iIIustrated in Fig. 7.34 are discussed in Chapter 9 in terms of the driving force and energy barrier. Structural aspects of transformations of this kind have been discussed in Chapter 2. In general , there are two common ways in which metastable crystals are formed. First, if a stable crystal is brought into a new temperature or pressure range in which it does not transform into the more stable form , metastable crystals are formed . Second, a precipitate or transformation may form a new metastable phase. For example, if phase 1 in Fig. 7.34 is cooled into the region of stability of phase 3, it may transform into the intermediate phase 2, which remains present as a metastable crystal.
The most commonly observed metastable crystalline phases not undergoing transformation are the various forms of silica (Fig. 7.5). When a porcelain body containing quartz as an ingredient is fired at a temperature of 1200 to 14OOoC, tridymite is the stable form but it never is observed ; the quartz always remains as such. In refractory silica brick, quartz used as a raw material must have about 2% calcium oxide added to it in order to be transformed into the tridymite and cristobalite forms which are desirable . The lime provides a solution-precipitation mechanism which essentially eliminates the activation energy barrier, shown in ’ Fig. 7.34, and allows
313 CERAMIC PHASE-EQUILIBRIUM DI-AGRAMS INTRODUCTION TO CERAMICS
happens, metastable phase separation of the liquid is quite common, discussed in Chapter 3.
h G-lasses. OnF of the most common departures from equiIibrillIn be-aVIor In CeramlC Systems is the ease with which many silicates are cooled
from the liquid state to form n아lcrystalline products. This requires that the-dri?ing force for the liquid-crystal transformation be low and that thp actwatIOn energy for the process be high Both of these conditions ar; ful6lled for many sillcate systems- /
The rate of nucleation for a crystalline phase foriing from the nquid is proportional to the product of the energy difference between the crystal aFd liquid and the mobility ?f the constituents that form a crystal, as dlscussed in Chapter 8. In sUlcate systcms, both of these factors change so as to favor the formation of glasses as the silica content increases. Although data for the diffusion coemcient are not generally available, the !imiting mobility is that of the large network-forming anions and is
뉘r:짧tg$$3r$rgzL텀;t:￥암앓잎I잖;따양 깝않캅S:43링/J$l뭔웅 as shown in Table 7. 1.
312
Table 7.1.
B20 3
1 ~3
State 1
State 2
*|1|
굶」@Eω @@‘ι
Comments
Good glass fo rmel’
Good glass former
Good glass fo rmer
Poor glass former
Very difficult to form as glass ,
Not aglass former
Factors A~ecting Glass-Forming Ability
(ð.HtlT mp) X ( 1 /기)lIl P
1.5X lO - 4 2 X 10- 5
( 1 /η)mp (poise- ')
ð.HtlT mp
T mp( oC) (cal/molej OK)
7 .3 450
Composition
Si0 2 1 . 1 X 10- 6 1 X 10- 6 1. 1 1713
3. 7 X 10- 3
4 .5 X 10- 2
0.74
345
5 X 10• 4
5 X 10- 3
10-1
50
7 .4
9.2
7 .4
6.9
874
800 .5
1088
1544
Na2Si20 S
Na2Si0 3
CaSi0 3
NaCI
State 3 Rate 01 transition 1-<>-2> 2-3 > 1--->> 3
lllus!nuion of energy barricrs bNween threc di’Terenl SIßICS of 11 syslem Fill, 7,34.
li많짧혈많le￡Zyg컵폈tP껍$tsareFE댐ut따l폐짧點 엽i:;짧 짧stzz conditions ?f temperatuκ pressure, and composition of the system. These remam present m a metastable state becauge the hi훌h 8ctivati0 l1
314 INTRODUCTION TO CERAMICS
the stable phase to be formed . This is , in general , the effect of mineralizers such as fluorides , water, and alkalies in silicate systems. They provide a fluid phase through which reactions can proceed without the activation energy barrier present for the solid-state process.
Frequently , when high-temperature crystalline forms develop during firing of a ceramic body , they do not revert to the more stable forms on cooling. This is partic비arly true for tridymite and cristobalite , which never revert to the more stable quartz form. Similarly, in steatite bodies the main crystalline phase at the firing temperature is the protoenstatite form of MgSi03. 1n fine-grained samples this phase remains as a metastable phase dispersed in a glassy matrix after cooling. 1n large-grain samples or on grinding at low temperature, protoenstatite reverts to the equilibriurn fOrm , clinoenstatite.
A common type of nonequilibrium behavior is the formation of a metastable phase which has a lower energy than the mother phase but ~s not the lowest-energy equilibrium phase. This corresponds to the situ~
tion illustrated in Fig. 7.34 in which the transition from the highest-energy phase to an intermediate energy state occurs with a much lower activation energy than the transition to the most stable state. It is exemplified by the devitrification of silica glass , which occurs in the temperature range of 1200 to 1400oC , to form cristobalite as the crystalline product instead of the morè stable form , tridymite. The reasons for this are usually found in the structural relationships between the starting material and the final product. 1n general , high-temperature forms have a more open' stri.lcture. than low-temperature crystalline forms and consequently are more nearly like the structure of a glassy starting material. These factors tend to favor crystallization of the high-temperature form ffom a supercooled liquid or glass , even in the temperature range of stability of a lower-temperature modification.
This phenomenon has been observed in a number of systems. For example, J. B. Ferguson and H . E. Merwin* observed that when calciumsilicate glasses are cooled to temperatures below 11250 C , at which wollastonite (CaSi03) is the stable crystalline form , the high-temperature modification, pseudowollastonite, is found to crystallize first and then slowly transform into the more stable wollastonite. Similarly, on cooling compositions corresponding to N a20 . Ah03' 2Si02, the high-temperature crystalline form (carnegieite) is observed to form as the reaction product, even in the range in which nephelite is the stable phase ; transformation of carnegieite into nephelite occurs slowly.
1n order for any new phase to form, it must be lower in free energy than the starting material but need not be the lowest of all possible new phases.
*Am. J. Science, Series 4, 48. 16S (1 919).
CERAMIC PHASE-EQUILlBRIUM DlAGRAMS 315
Thi샌s re여qUlπre타ment me the phase equ비il피libr디ium diagram, the liquidus curves of other phases on the diagram must be extended to determine the conditions under whICh some other phase becomes more s빼le than the starting solution and a possible precipitate. This is illustrated for the potassium dlSilicate-silica system ln Fig 7 35. Here, the compound KzO·4SiO1 crystallizes only with-gregt difRculty so that the eutechI corresponding to this prCQIPltatlOn lS frequently not observed. Instead, the liquidus curves for sillCa and for notassillm disilicate intersect at a temperature about 200。 below the true Smectic temperature This nonequilibrium eutectic is the temperaturE at whichi bth notassium disil1Cate and silica have a lower free energy tuan the liquid COmposition corresponding to the false eutectic Actually, for this sYstem the situation is complicated somInI빼ha따t mor cristobalite commonly crystallizes from the melt in plaFe of the equ니i안 rillIn quartz phase. This gives additional possible behaVIors, as indicateu
by the dotted line in Fig. 7.35. Extension of equilibrium curves on phase diagrams, such as has been
1400
1300
1200
1100
ιJ
-; 100。그
"' ~ E @
•
500 l 56 60
K20.28i02
70 K20 .48i02
Liquid + Tridymite
Liquid + Quartz
Quartz + K8 4
Weight per cent 8102
100 8i02
111 (1 - 7.3' ‘ Equilibrlum und noncquilibrium liquidus curves in the pot!lssium disilicate- silica syMtcm’
316 ‘ INTRODUCTION TO CERAMICS
shown in Fig. 7.35 and a1so in Fig. 7.5 , provides a genera1 method of using equi1ibrium data to determine possib1e nonequilibrium behavior. It provides a highly useful guide to experimental observations. The actual behavior in any sys'tem' may 'follow any one of severa1 possible courses, so that an ana1ysis of the kinetics ofthese processes (or mòre εommon1y experimental observations) is a1so required.
Incomplete Reactions. Probably the most common source of nonequi1ibrium phases in ceramic systems are reactions that are not completed in:the time available during firing or heat treatment. Reaction ràtes in condensed ' phases are discussed in Chapter 9. The main kinds of incomp1ete reactions observed are incomp1ete solution, incomplete solidstate reactiOIl-S, and in.comp1ete resorption or solid-liquid reactions. All of these arise from the presence of re::iction products which act as‘ b~다er
layers and prevent further reaction. Perhaps the most striking examp1e of incòmp1ete reactiöns is the entire metallurgical industry, since a1most all meta1s are thermodynamically unstab1e in the atmosphere but oxidize.a:nd corrode on1y slowly.
A particu1ar example of incomp1ete solution is the existence of quartz grains which are undissolved in a porce1ain body, even after firing at temperatures of 1200 to 1400oC. For the highly siliceous.liquid in contact with the quartz grain, the diffusion coefficient is low, and there is no fluid flow to remove the boundary layer mechanically . The situation is simi1ar to diffusion into an infinite medium, illustrated in Fig. 6.5. To a first approximation, the diffusion coefficient for Si02 at the highly siliceous boundary may be of the order of 10-8 to 10-9 cm2/sec at 1400oC. With these data it is 1eft as an exercise to estimate the thickness of the diffusion layer after 1 hr of firing at this temperature.
The way in which incomp1ete solid reactions can lead to residual starting material being present as nonequi1ibrium phases will be clear from the discussion in Chapter 9. However, new products that arénot the final equi1ibrium composition can a1sò, be formed. For examp미lé타;시， ir띠n배1 eq민u비11피imo이1a없r mixtures.ofCaC03 and Si02 to form CaSi03, the first product formed and tþe one that remains the major phase through most of the reaction is the orthosilicate, Ca2Si04 • Similarly, when BaC03 and Ti02 are reacted to ~orm BaTi03, substantial amounts of Ba2Ti04 , BaTh07, and BaTi‘0 9 are formed durìng the reaction process, as might b<? expected from the phase-equilibrium diagram (Fig. 7.20). When a series of intermediate compounds is formed in a solid reaction, the rate at which each grows depends on the effectÎve diffusion coefficient through it. Those layers for which the diffusion rate is high form most ' rapidly , For the CaO- Si02 system this is the orthosilicate. For the BaO- Ti0 2 system the most rapidly fQrming compound is again the orthotitanate{ BatTiO •.
CERAMIC PHASE-EQUILIBRIUM DIAGRAMS 317
C
A AB B
Fig , 7.36. Nonequilibrium crystallization path with (1 ) Liquid • A, (2) A + liquid • AB , (3) Liquid • AB , (4) Liquid • AB + B, (5) Liquid • AB + B+ C.
A final example of nonequilibrium conditions important in interpreting phase숙quilibrium diagrams is the incomplete resorption that may occur whenever a reaction, A + Liquid = AB , takes place during crystallizatIonThis is the case , for example, when a primary phase reacts with a liquid to form a new compound during cooling. A layer tends to build up on the surface of the original parti이e ， formirtg a batrieÌ' to further reaction. As the temperature is low'ered, the final products are not those anticlpated from the equilibrium diagram. A nonequilibrium crystallization path for incomp1ete resorption is schematically illustrated in Fig. 7.36.
Suggested Readi",g
1. E. M. Levin, C. R. Robbins , and H. F. McMurdie, Phase Diagrams for Ceramists, American Ceramic Society, Columbus, Ohio, 1964.
2. E. M. LevÌn, C. R. Robbins, H. F. McMurdie, Phase Diagramsfor Ceramists, 1969 Supplement, American Ceramic Society , Columbus, Ohio, 1969.
3, A, M. AJper, Ed., Phase Diagram s: Materials Science and Tech_nology, Vol. 1, “ Theory , PrincipJes, and Techniques of Phase Diagrams," Academic Press, Inc .. New York, 1970; VoJ. ll. “ The U se of Phase Diagrams in Metal , Refractory , Ceramic , ánd Cement Technology." Academic Press , Inc ., New
318 INTRODUCTION TO CERAMICS
York , 1970; Vol. III , “ The U se of Phase Diagrams in Electronic Material s and Glass Technology," Academic Press , Inc ., New York . 1970
4 A Muan and E F Osborn, Phase Equilibria among Oxides in Steelmaking, Addison-Wesley , Publishing Company , Inc., Reading, Mass. , 1965 .
5. A. Reisman, Phase Equilibria, Academic Press, Inc., New York. 1970. 6. P. Gordon, Principles of Phase Diagrams in Af.aterials Systems , McGraw H iII
Book Company , New York , 1968.
7. A. M . Alper, Ed., High Temperature Oxides, Part 1, “ Magnesia, Lime and Chrome Refractories ," Academic Press , Inc. ‘ New York , 1970: Part 11. “ Oxides of Rare Earth, Titanium, Zirconium , Hafnium, Niobium, and Tantalum," Academic Press, Inζ. ， New York, 1970; Part III , “ Magnesia, Alumina, and Beryllia Ceramics: Fabricanon, Characterization and Properties,,J Academic Press, Inc., New York ; Part IV , “ Refractory Glasses , GlassCeramics , Ceramics," Academic Press , New York , lnc. , 197 1.
8. J. E. Ricci , The Phase Rule and Heterogeneous Equilibrium , Dover 빼o_ks ， New York , 1966. \
Problems
7.I. A power failure allowed a furnace used by a graduate student worklng in the K20-Ca0-Si.Oi System to cool down over night For the fun of lt, the Student analyzed the composition he was studying by X-ray ditrraction. To his horror, he found β-CaSiO" 2K20'CaO.3Si02, 2K20 'CaO .6SiOι K20.3CaO '6SiOμ and K20 .2CaO.6Si02 in his sample. (a ) How could he get more than three phases? (b) Can you tell him in which composition triangle his original composition was? (C ) Can you predict the minimum temperature above whlCh hIS furnace was
ope_rating before .power failure? (d) He thought at first he also had some questionable X-ray ditrraction evidence for
K20 .CaO.Si02, but after thinking it over he decided K20.CaO.Si02 shOliId not crystallize out of his sample. Why did he reach this concJusion?
7.2. According tO Alper, McNally, Ribbe, and DOman,* the maXlmum solubility of AlzOI m MgO is 18 wt% at 19950 C and of MgO in MgAI20 ‘ is 39% MgO, 51 % AI20 ,. Assuming the Ni0-Al2O3 binary-ls similar to the Mg0-AlzO3 blnary, construct a ternary. Make isothermal plots of this ternary at 2200oC, 1잊)()OC ， and 1700oC.
7.3. You have been assigned to ~tudy the electrical properties of calcium metasilicate by the director of the laboratory in which you work. If you were to make the materlal synthetically, give a batch COInPOSItion of materlals commonly obtainable in high purity. From a production standpoint, l0% liquid would increase the rate of sintering and reaction. Adjust your composition accordingly. What would be the expected firipg 샤mperature? Should the boss ask you to explore thç possibility òf lowering the 6rlng temperature and rnamain a white body, suggest the directIOn to procede- What polymorphic transformations would you be conscious of in working with the above systems?
*J. Am.• Ceram. Soc. 45(6), 263-268 (1 962).
CERAMIC PHASE-EQUlLlBRIUM DlAGRAMS 319
7.4. Discuss the importance of liquid-phase formation in the production and utilization of refractory bodies. Considering the phase diagram for the MgO-Si02 system , comment on the relative desirabiJity in use of compositions containing 50MgO-50Si02 by weight and 6OMg0 -40Si02 by weigh t. What other characteristics of refractory bodies are important in their use?
7.5 . A binary silicate of specified composition is melted from powders of the separate oxides and cooled in ditrerent ways , and the following observations are made:
Condition
(a) Cooled rapidly
(b) Melted for 1 hr , held 800 C below liquidus for 2 hr
(c ) Melted for 3 hr, held 800 C below liquidus for 2 hr
(d) Melted for 2 hr, cooled rapidly to 2000 C below liquidus, held for 1 hr, and then cooled rapidly
Observations
Single phase , no evidence of crystallization
Crystallized from surface with primary phases Si02 plus glass
Crystallized from surface with primary phases compound AO.Si02 plus glass
No evidence of crystaJlization but resulting glass is cloudy
Are all these observations self consistent? How do you explain them ?
7‘ 6. Triaxial porcelains (flint-feldspar-clay) in which the equilibrium phases at the firing temperature are mullite and a silicate liquid have a long firing range; steatite porcelains (mixtures of talc plus kaolin) in which the equilibrium phases at the firing temperature are enstiatite and a silicate liquid have a short firing range. Give plausible explanations for thís ditrerence in terms of phases present, properties of phases, and changes in phase composition and properties with temperature.
7.7. For the composition 40MgO-55Si02-5AJ,O" trace the equilibrium crystallization path in Fig. 7.30. Also, determine the crystallization path if incomplete resorption of forsterite 0ζcurs along the forsterite-protoenstatite boundary. How do the compositions and temperatures of the eutectics compare for the equilibrium and nonequilibrium cry,stallization paths? What are the compositions and amounts of each constituent in the final product for the two cases?
7. 11 . If a homogeneous glass having the composition I3Na20-13CaO-74Si02 were heated 10 1 0500C , 1 아)()OC ， 9OOoC, and 800oC, what would be the possible ζrystalline products that might form ? Explain.
7,9. The clay mineral kaolinite, AJ,Si,O,(OH)‘ , when heated above 6OO0 C decomposes to AhSi,O, and water vapor. If this composition is heated to 16000 C and left at that temperature until equilibrium is established , what phase(s) will be presen t. If more Ih!Iß Qne is present , what will be their weight percentages. Make the same calculations ror I ~85.C .
