Acta metall, mater. Vol. 42, No. 12, pp. 4155~4163, 1994 Copyright © 1994 Elsevier Science Ltd

Pergamon 0956-7151(94)00181-2 Printed in Great Britain. All rights reserved 0956-7151/94 $7.00 + 0.00

THE EFFECT OF PORE SIZE ON THE INFILTRATION KINETICS OF ALUMINUM IN TITANIUM CARBIDE

PREFORMS

D. MUSCAT, R. L. HARRIS and R. A. L. DREW Department of Mining and Metallurgical Engineering, McGill University, 3450 University St, Montreal,

PQ, Canada H3A 2A7

(Received 18 November 1993; received for publication 3 May 1994)

A~traet--Capillaric melt infiltration is a simple and attractive way of fabricating metal/ceramic composites. In this work, four different TiC preforms of ~ 58% theoretical density, but different pore sizes ranging from about 1 to 30/am, were produced. These were suspended from a Thermo-Gravimetric Analyzer (TGA) and infiltrated with molten A1 under flowing Ar. Infiltration profiles were obtained by continuously monitoring the weight change of the preform. These tests were performed for temperatures ranging from 860 to 1300°C. Kinetic analysis on these infiltration profiles yielded activation energies ranging from 105 to 450 kJ/mol, depending on the pore size. It is suggested that the driving mechanism for the system changes from a diffusion controlled process for smaller pore sizes, to one which is driven by a surface reaction occurring at the interface for larger pores.

R6sum6---L'infiltration capillaire est une m&hode simple et r6pandue pour la fabrication des composites m6tal-c6ramique. Dans le pr6sent travail, quatre pr6formes de TiC pr6frit6es de porosit6 ~42% avec la taille de pores variante entre 1 et 30/~m, ont 6t6 infiltr6 par l'aluminium pur, sous argon, fi diff6rentes temp6ratures de 860 ~. 1300°C. Des profiles d'infiltration ont 6t6 6tablis par enregistrement continu du changement du poids des ces pr6formes. Les 6nergies d'activation de ces profiles ont vari6 de I05 ~t 450 kJ/mol, d6pendant de la taille de pore, mettant ainsi en 6vidence la transition entre deux modes d'infiltration; l'un contr616 par diffusion; l'autre, dans le cas d'une grande taille de pores, induit par une r6action de surface.

INTRODUCTION phases, 0, and the viscosity of the molten metal, q, such that

A popular technique of fabricating metal/ceramic composites is Melt Infiltration, whereby molten metal ( r ~ c o s 0 ) penetrates the pore channels of a ceramic preform K = c • ~ . (2) either by the assistance of an external force, such as in squeeze casting [1-3], or through the action c being a constant which describes a tortuosity of a capillary pressure which is created when the factor introduced by some authors in their analysis

molten metal wets the ceramic surface. Capillaric [7, 10]. melt infiltration has been used on various occasions The effect of temperature on the infiltration kin- to produce a wide spectrum of metal/ceramic corn- etics of molten metals in porous preforms has been posites [4-6]. investigated in very few systems. By performing

The rate of infiltration of molten metal in porous Arrhenius analysis on the infiltration rate as a func- preforms has been studied by a number of authors, tion of temperature, Semlak and Rhines [7] found the investigating systems such as Au, Pb or Cu in Fe, Cu, activation energy for the system Pb in porous Cu Ni, etc. [7, 8], or AI in AIN [9] or TiC [10] or SiC [11]. to be very similar to that of viscous flow and self- Generally the infiltration follows a parabolic rate diffusion of liquid Pb. Elsewhere, the activation [7, 12] such that energies for the systems Pb and In infiltrating porous

Ti were found to be an order of magnitude larger l 2 = K t (1) than their respective values of viscous flow, and was

therefore concluded that the increase in infiltration where l is the length of infiltration, t is the time, rate at higher temperatures cannot be due to the and K is the parabolic constant which is a function decrease in melt viscosity alone [13]. Toy and Scott [9] of the average pore radius, r, the liquid surface studied the infiltration of AI in two different AIN tension, 7, the contact angle between the two compacts of sub-micron pore size, and observed

4155

4156 MUSCAT et al.: EFFECT OF PORE SIZE ON INFILTRATION

linear infiltration profiles. From these, they estab- out on polished infiltrated sections. A Tracor North- lished activation energies of 330 and 460 kJ/mol ern TN-5700 image analyzer interfaced with the SEM respectively, suggesting that some chemical reaction through the IPA 57 program, was used to isolate and or surface desorption must be controlling the statistically characterise the pore phase, containing infiltration. AI, at high magnification ( × 4000). Depending on the

Recently, the infiltration of AI in porous TiC TiC content, 200-500 pores were measured for each preforms of sub-micron pore size has been studied sample. over a range of temperatures [10]. An average acti- The preforms were infiltrated with molten AI in vation energy of about 90 kJ/mol was established for a furnace specially designed for kinetic studies of four different preform densities having similar pore infiltration. A more comprehensive description of the size. Furthermore, wettability studies showed that a experimental equipment used for these tests has been stable contact angle between the two materials is published elsewhere [10, 14]. In brief, a custom-built never reached, indicating that some surface reaction vertical tube furnace, was fitted with a Thermo- occurs between the two phases. This could be playing Gravimetric Analyzer, or TGA (Cahn D-100). The an important role in controlling the infiltration mech- whole system was gas tight, and reached a vacuum of anism. In order to investigate this further, infiltration < 4 Pa. Argon gas flow was controlled through a kinetics for A1 in TiC preforms of different pore sizes flowmeter at a rate of 0.3 L/min. A TiC preform was were studied, the results of which will be presented suspended from the TGA arm, using a refractory here. metal wire. A bath of molten A1 contained in a

graphite crucible lay just below the preform. The bath EXPERIMENTAL PROCEDURE was sitting on a movable alumina rod, which exited

Mater ia ls the bottom of the furnace through a gas-tight seal. When the desired temperature was reached, the

Two TiC powders were used: the first having an crucible was pushed upwards in order to partially average particle size of 0.8/~m (H.C. Starck, grade immerse the end of the preform: typically, 5 mm of c.a.s.) and the other being less than 325 mesh the preform would lie below the surface of the AI. The (Kennametal, Inc.). The latter was further processed weight change experienced by the TiC body as the A1 to produce three powders of different average particle intruded the preform was monitored through the size; the as-received powder was separated through a TGA, which collected weight readings each second 400 mesh (38 ttm sieve), to give one powder with an and stored them in a personal computer. These were average size of approx. 10#m, and the other approx, later converted into an equivalent depth of pen- 40 #m. The 10 #m powder was then attrition milled etration of the A1 front. Infiltration rate curves were using Si3N 4 media of about 7 mm diameter, in re- thus obtained for the different preforms, at tempera- agent grade iso-propyl alcohol for 1 h. The particle tures ranging from 860 to 1300°C. size was thus reduced to approx. 3/~m. The 40/~m powder was further mixed with 10 wt% of fine c.a.s. RESULTS AND DISCUSSION powder (0.8 #m particle size) for reasons which will be explained later. To avoid confusion, the powders Due to their different particle size and their packing have each been designated as follows: A being the behaviour, the four powders had to be sintered at sub-micron, B the 3/~m, C the 10/~m and D the different temperatures. For convenience, a targeted 40/~m. The aluminum used in this work had a purity preform density of 58% of theoretical was selected. of 99.99% (Alcoa). Table 1 lists the sintering cycles used for each powder.

It should be noted that for powder D, some sub- Procedure micron c.a.s, powder had to be added to assist in

The TiC preforms were prepared by pressing about the sintering of the particles, since they were too large 16-18g of powder uniaxially at about 8MPa, in to produce necking, even after 2h of sintering at

1800°C. a rectangular die to form green bodies of approx. 6 x 1 × 1 cm 3. These were then partially sintered Table 2 compares the pore diameters of the pre- in a graphite element, resistance furnace. Sintering forms measured by both porosimetry and image was carried out under pre-purified argon at 1 atm analysis. It is clear that the values obtained by of pressure, and at temperatures ranging from porosimetry are always lower than those estimated

1200--1800°C for 30q50 min. The sintered density of the preforms were Table 1. Sintering cycles for the various starting powders

measured using the Archimedean method. The pores Average Final were characterised using two methods: porosimetry particle sintered Sintering Sintering and image analysis. Porosimetry was carried out Powder size density temperature time

type (#m) (% theor.) (°C) (rain) using a single-chamber, mercury porosimeter (Porous a 0.8 58 1200 30 Material Inc., model PMI 60K-A-I) on samples ~ 4 57-59 1600 60 of approx. 1 cm 3. Image analysis using Scanning C 10 56-58 1650 60 Electron Microscopy (Jeol JMS-840A) was carried D 40/0.8 5840 1800 60

MUSCAT et al.: EFFECT OF PORE SIZE ON INFILTRATION 4157

Table 2. Pore diameters of the preforms made with powders A, B, that image analysis gives a more realistic average c and D

pore size, whereas porosimetry will provide a better Powder type Porosimetry Image analysis value for estimating the capillary pressure created A 0.56±0.03/~m 1.16 _+ 0.87 ttm within the preform. SEM micrographs of polished B 2.38 + 0.04/tm 3.7 _+ 2.6 pm C 7.23 ±_0.05#m 9.15+ 5.4#m sections of the composites prepared with powders D 11.7+0.051~m 24.7 ___12.5 /~m A, B, C and D, all containing approx. 58%

TiC, are shown in Fig. l(a-d). From the micro- structure shown in Fig. l(d), the fine particles be-

through image analysis. This is probably due to tween the contact points of the larger ones can clearly the irregular nature of the pore channels. If one be seen. considers the pores to consist of a continuous net- The infiltration profiles for these preforms are work of necks and chambers, porosimetry would be presented in Fig. 2(a~t). Notice that for powder A, the measure of the pore necks through which mercury much lower temperatures were used for infiltration. is being forced, and image analysis would give Furthermore, at low temperatures the curves are not the average diameter of the channel. This implies completely parabolic, particularly in the initial phase

Fig. 1. SEM micrographs comparing pore sizes for different TiC powders.

4158 MUSCAT et al.: EFFECT OF PORE SIZE ON INFILTRATION

6 1010~ f 960° 910°C

....... 4 ? ~ s6°°c

r'- 3

t-- I1)

"-J 2

1

0 I F I

0 100 200 300 400 500 600 700 800 900 1000

Time (sec) Fig. 2. (a) Infiltration profiles for a pore size of 1 pm.

of infiltration, where an incubation period appears to and since no bulk reaction was detected in the exist. This aspect of the infiltration profiles has been as-fabricated material, it can only be the effect of dealt with in more detail elsewhere [10] and was some surface reaction occurring at the interface. attributed to the superimposed effect of wetting kin- Further insight into this can be seen by analyzing the etics between the molten A1 and TiC. The changing effect of temperature on the rate of infiltration. contact angle between the two phases is shown in Arrhenius analysis was carried out on each Fig. 3, which are the results of dynamic Sessile Drop series of curves by comparing the parabolic portion tests performed under vacuum [10]. The fact that the of the curves. The parabolic constant, K, was first contact angle never stabilizes over a long period of estimated and the slope of 50% infiltration was time indicates that the system is far from equilibrium, established. The Arrhenius plots are shown in Fig. 4.

6

"-'E 4 - j

t - 3 -

c

2-

1 -

0 I r I I I I I I I

0 100 200 300 400 500 600 700 800 900 1000

Time (sec) Fig. 2. (b) Infiltration profiles for a pore size of 3 pm.

M U S C A T et al.: EFFECT OF PORE SIZE O N I N F I L T R A T I O N 4159

5 1 I # / j 11100C

i '

(c) 0 T I I I I [ I l L I

0 100 200 300 400 500 600 700 aoo 900 1000

Time (see) Fig. 2. (c) Infiltration profiles for a pore size o f 9 #m.

The gradient of the lines will give the activation is the presence of a bi-modal particle size distribution energy according to in the starting powder, yielding a combination of a

( E a ) small number of fine capillaries along with the large In K0 5 = A exp --~--~ . (3) ones, as portrayed in Fig. 2(d). The fine capillaries

may have contributed to the early infiltration due to The computed values are shown in Table 3. It is the higher capillary pressure present in these pores. clear that the activation energy is increasing with However, the infiltration mechanism would be more increasing pore size. Another interesting feature from dependent on the larger pores since they constitute the graph in Fig. 4 is the fact that the plot for the the greater pore volume in the preform. preforms made with powder D appears to be shifted It has been seen elsewhere [10] that the infiltration somewhat to the right. One possible reason for this of sub-micron pores must have been activated by

6

(.ooc//- 1110 C 1060 C 5 ° °

~I, e -

l -

0 ~ I I I I I I I I

0 100 200 300 400 500 600 700 800 900 1000

Time ( s e c )

Fig. 2. (d) Infiltration profiles for a pore size of 25 #m.

4160 MUSCAT et al.: EFFECT OF PORE SIZE ON INFILTRATION

1 5 0 -

- 1oo ¢-

,< 8 6 0 ~

.E

5 0 - -

~ ° C

0 I I I I I I I I I I

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000

T i m e ( s e c )

Fig. 3. Contact angles for A1 on TiC using the sessile drop technique.

some additional driving force, such as a surface as pore sizes increase, the surface area of capillaries reaction between the A1 and the oxide layer on the decreases. TiC. This possible reaction was responsible for the Figure 5 shows a schematic of the contact line of changing contact angle as seen through the Sessile the molten front with the ceramic surface. Consider Drop tests as well as in the initial part of the the following model. Let the oxide layer be consumed infiltration profiles, also shown in Fig. 2(a). If a by the Al such that the reaction can be written as surface reaction is responsible for driving the infiltra- tion, then clearly the amount of surface available for AI(I ) + TiOx --* Al0) + Ti(sot) + x O~g). (4) reaction must play a crucial role in the system, since

This is conceivable since the oxide layer is of the order of nanometers in thickness and therefore only small

-1 f V amounts of the products result from the reaction. 1 n2~ai_ron Furthermore, as can be seen from the AI rich portion

of the A1-Ti equilibrium diagram [15] shown in -~ ~X~ ~ \ 'n2~ -r°n Fig. 6, molten A1 dissolves Ti, especially at higher

1 ~ ~ \ 9=_~ron temperatures. Therefore, the small quantity of Ti that [ ~ ~ ~ ZS/l..~¢raa is rejected into the A1 melt would probably not be

.a sufficient to form any TiA13. This was shown else- ~, where through X-ray diffractometry confirming that

no intermetallic was detected in the microstructure [10]. Assuming rutile (TiO2) occurs on the surface, the value of x in the reaction will be taken to be two.

.4 • The oxygen path could have two alternatives. Since oxygen is not soluble in molten A1, then it can react

i with AI to form AI203 . Alternatively, the oxygen can

Table 3. Activation energies computed from Fig. 5

Pore s i z e Activation energy (gm) (kJ/mol)

-7 1 105 0.0006 0.00065 0.0007 0.00075 0.0008 0,00085 0.0009 3 167 I/T (lfK) 9 224

Fig. 4. Arrhenius plots of different pore sizes. 25/1 445

MUSCAT e t al.: EFFECT OF PORE SIZE ON INFILTRATION 4161

~ ~ / ~ Table 4. Gibbs' free energyandOf(7)reaction for equations (6)

A I . AG for AG for Temperature equation (6) equation (7)

(K) (J/mol) (J/mol)

T i O× 900 744853.2 396834.9 950 725967.1 378986.4 / / / / S 1000 707119.5 361187.4

1050 688304.8 343435.0 1100 669521.8 325728.0

T i C 1150 650767.6 308065.2 1200 631568.5 290289.6 1250 612370.7 272547.6

Fig. 5. Reaction model at the contact line between molten 1300 593226.1 254857.1 A1 and TiC. 1350 574132.4 237217.3

1400 555086.3 219623.9 1450 536086.7 202077.5 1500 517132.2 184576.6

combine with carbon to form CO gas which will eventually escape through the pore channels ahead of the moving front. The carbon can either come from the TiC itself, through the reaction and

AI(~) + TiC(~) = AI(]} + Ti(so~ ) + C~s ) (5) 2Ct~) + TiO2(s) = Ti~so~ ) + 2CO(g). (7)

or can be present in the microstructure as free C, since The Gibbs' free energies of reaction for equations the as-received TiC powder always contains about (6) and (7) have been estimated using the F , A , C , T 0.1% free C.

Both the oxidation of AI and C are plausible and (Facility for the Analysis of Chemical Thermo- it would be difficult to predict which one is preferen- dynamics) database [16], and are shown in Table 4 for tially occurring since this would be highly dependent a range of temperatures. Note that the AG values are on factors such as the activity of the C and A1 or all positive. However, as Ti is being rejected into the partial pressures of the O or CO gases. The solution, its activity would be less than unity, depen- A1203 phase was not visible anywhere in the micro- dent on its concentration in the AI. Therefore, from structure. But this does not necessarily imply that the equilibrium constant, one can estimate the limit-

ing partial pressure of the CO gas being produced, it did not form. It could very well be present on a such that the reaction will have a negative free energy, scale too small to detect, especially when one con- siders the limited supply of oxygen present in the hence making it feasible. Figure 7 shows a plot of the system. CO partial pressures for the reactions in equations (6)

and (7), for decreasing Ti concentration (the calcu- If the oxidation of carbon occurred, however, then

lations for this reaction mechanism are shown in the following two reactions will take place, namely the Appendix). The oxygen will combine with either

2TiC~s) + Ti02(~) = 3Ti(~o~ ) + 2CO(g) (6) the A1 as previously discussed or C depending on the

1100

1 ooo L

(O o

tU 900 nr

rr W 800 n

U.I I.--

700

665°C L 9 9 . ~ 660'45°C

600 ~ F ~ ~ ~ , ~ ,

95 96 97 98 99 100

ATOMIC PERCENT ALUMINUM

Fig. 6. The AI rich portion of the AI-Ti phase diagram (after [16]).

4162 MUSCAT e t a L : EFFECT OF PORE SIZE ON INFILTRATION

~E+O3 / / ~ . / / molten AI can dissolve much greater quantities of Ti ~E+02 ri = 0.0005 at high temperatures). Once the pore size increases,

~ ~ diffusion of Ti becomes easier since the A1 sink grows, 1E+Ol- hence creating a larger concentration gradient. When E //~

~,~ 1E+O0 . . . . . . . . . . . . . . . . . . . . . . the diffusion of Ti is not the rate controlling mechan- ism in the system, then the consumption of TiO2

-~ m-01 becomes the driving force behind the infiltration o)

process. This reaction will contribute to the drop in 1E-02-

0. surface tension which in turn will lower the contact

.~IE-O3~+TtT.oi:L~~I0111) ang l e s u c h t h a t t he re is a n inc rease in the c o m p o n e n t 1=: of the liquid surface tension acting in the direction t~ a. 1E-04 of flow [Fig. 8(b)]. Furthermore, as the pore size 0 increases, the surface area of the ceramic phase O 1E-05. (o) decreases which implies that the oxygen content in

1E-OS the system will also decrease. Therefore, the reaction becomes even more critical in activating the system.

1 E-07 ~ , r P

900 1000 1100 1200 1300 1400 1500 T h i s c a n explain why t he a c t i v a t i o n energies o b t a i n e d in the Arrhenius plot of Fig. 1 increase to a value of

Temperature (K) 450 kJ/mol. Such a high value is typical of reaction Fig. 7. Limiting partial pressure of CO for surface reaction driven mechanisms, and strengthens the argument

not to proceed, that at such high pore diameters it is only the reaction that activates the infiltration process. From this, one

partial pressure of the CO gas, as this will decide can infer that at even higher pore diameters, infiltra- which is the favourable reaction, tion will become increasingly difficult to proceed, due

The model for the surface reaction can now allow to the extremely high activation energy necessary to further insight into the infiltration process, which has initiate the process. Naturally, this aspect cannot be already been considered as a system driven by some separated from the fact that the upward force due to form of reaction. The preforms with fine capillaries capillarity will have to be even larger, and only a resulted in an activation energy of 105 kJ/mol small wetting angle can provide this, which in turn (Table 1), which is indicative of a system controlled could result through a reaction according to the by a mass transfer mechanism through a liquid phase, model by Aksay [17] for spontaneous wetting. At this A possible rate controlling mechanism could be that stage, though, the weight of AI in the capillary may of the diffusion of Ti away from the reaction zone start to play a role in the system, and the case may into the A1 melt in the capillary. Since the capillaries arise where, the metal wets the ceramic but cannot have a very small diameter (about 1 gm), a high proceed into the preform. transient concentration of Ti could build up around the contact line, saturating the molten AI and there- CONCLUSIONS fore limiting the rejection of new Ti to the rate at which the Ti can diffuse away from the reaction zone Porous titanium carbide preforms, having pore [see Fig. 8(a)]. This is also supported by the fact that sizes ranging from about 1 to 25/~m, were infiltrated the increasing concentration of Ti at the contact line by liquid aluminum at temperatures as low as 860°C will make the reaction less likely to proceed, as can in an argon atmosphere. The rate of infiltration was be deduced from Fig. 7 (it should be noted that studied using a specially designed furnace equipped

TiC

TiC / / / / / / / / / / / / / / / /

conceotr.ior co o, ,ration \ gradient for 1 'P~ ~Y i¢~ gradient for di~sion ot TJO~ diHusio, o~ TiO~ 77 is small ] J,/,/./'~JZ.._ Ti is large ] /

11111111111111111 ,t TiC / / / / / / / / / / / TiC

(a) Fine Pore Size (b) Large Pore Size

Fig. 8. Rate determining factors in the surface reaction of two different pore sizes, (a) mass transfer control, and (b) reaction control.

MUSCAT et al.: EFFECT OF PORE SIZE ON INFILTRATION 4163

wi th a T G A . Inf i l t ra t ion inc reased wi th increasing Table 5. The activity of Ti in A1 as a function of temperature

t e m p e r a t u r e , y ie ld ing ac t iva t ion energies r ang ing Temperature a for a for f r o m 105 to 445 kJ /mol . T h e ac t iva t ion energy in- (K) -~ Ti =0.0005 Ti =0.001 c reased wi th po re size a n d the h igher ac t iva t ion 900 1.5E~)8 7.3E-12 1.5E-I1

950 3.8E~08 1.9E-11 3.8E-I 1 energies can be assoc ia ted wi th a surface r eac t ion 1000 8.9E~)8 4.5E 11 8.9E-I1 occur r ing be tw e e n the two phases . As the p o r e s size 1050 1.9E-07 9.7E-11 1.9E-10

1100 3.9E-07 2.0E-10 3.9E-10 increases , the r eac t ion be tween the m o l t e n AI a n d the 1150 7.4E-07 3.7E-10 7.4E-10 surface oxide b e c o m e s m o r e i m p o r t a n t in d r iv ing the 1200 1.3E-06 6.7E-10 1.3E-09 inf i l t ra t ion, especial ly since the surface area o f 1250 2.3E~)6 1.1E 09 2.3E--09

1300 3.8E4)6 1.9E-09 3.8E-09 the p r e f o r m decreases . 1350 6.0E-06 3.0Eq)9 6.0E-09

1400 9.2E-06 4.6E4)9 9.2E-09 1450 1.4E~05 6.9E-09 1.4E-08

REFERENCES 1500 2.0E~)5 1.0E~)8 2.0E-08 1. T. W. Clyne, M. G. Bader, G. R. Cappleman and P. A.

Hubert, J. Mater. Sci. 20, 85 (1985). 2. H. Fukunaga and K. Goda, Bull. Japan Soc. Mech. Eng. However, Koq is also equivalent to:

27, 1245 (1984). i 2 3 [ p (CO,l. a (Ti) 1 3. H. Westengen, D. L. Albright and A. Nygard, SAE Keq = P [c° ) ' a f f ° ] 2 3 (9) 2 ~ " Trans. 99 n Sect. 5, 606 (1990). a(xic)' a(rio2)]

4. K. Shanker, L. T. Mavropoulos, R. A. L. Drew and For activities of Ti lower then 1, the equilibrium partial P. G. Tsantrizos, Composites 23, 47 (1992). pressure of the CO gas can be deduced. If the solubility of

5. D. Muscat, K. Shanker and R. A. L. Drew, Mater. Sci. Technol. 8, 971 (1992). Ti in A1 is known, one can estimate the activity of Ti in the

6. L. T. Summers, J. R. Miller, M. J. Strum, R. J. Weimer A1 from the relationship and D. E. Kizer, Adv. Cryogenic Eng. 34, 835 (1988). a = X7 (10)

7. K. A. Semlak and F. N. Rhines, Am. Inst. Min. Engrs Trans. 212, 324 (1958). where X i s the atomic fraction of Ti in the AI, and 7 is the

8. W. N. Jeremienko and N. D. Lesnik, Izv. Akad. Nauk activity coefficient for Ti in AI. UkSSR Kijew, p. 155 (1961). The amount of Ti in solution must be quite small. As can

9. C. Toy and W. D. Scott, J. Am. Ceram. Soc. 73, 97 be seen from the phase diagram shown in Fig. 8, the limit (1990). of Ti solubility at the liquidus line, just above the solidifica-

10. D. Muscat and R. A. L. Drew, Metall. Trans. A. In tion temperature of AI, is 0.1 a t . l%, and below the solidus press, is also 0.1 at,% at say 500°C. Since no TiA13 was detected

11. G, P. Martins, D. L. Olson and G. R. Edwards, Metall. in the microstructure, it is assumed that the Ti content will Trans. 19B, 95 (1988). be even less than 0.I at.%.

12. E. W. Washburn, PHys. Rev. 17, 273 (1921). The activity coefficient is also a function of temperature. 13. A. A. Kurilko, G. A. Kurshev, V. A. Rudyuk and Due to lack of experimental data, one can only attempt to

Y. V. Naidich, Poroshk. Metall. 9, 35 (1984). predict how ~t changes with temperature, If the solution 14. D. Muscat and R. A. L. Drew, J. Mater. Sci. Lett. 12, is assumed to be regular [18], then it can be shown that

1567 (1993). the excess Gibbs' free energy, AG x~, is described by the 15. J. L. Murray, in Phase Diagrams of Binary Titanium relationship [19]

Alloys, p. 12. ASMInternational, Ohio(1987). ()ln__~ 16. C, W. Bale, A. D. Pelton and W. T. Thompson, Ecole GXS=RT v ~ (11)

Polytechnique, CRCT, Montreal. XAI )(Al~'Xi 17. I. A. Aksay, C. E. Hoge and J. A. Pask, J. Phys. Chem. where R is the universal gas constant, T is temperature, 7 is

78, 1178 (1974). the activity coefficient, and 2"is the atomic fraction of the 18. D. R. Gaskell, in Introduction to Metallurgical Thermo- elements, A1 and Ti, respectively. Furthermore, since the

dynamics, 2nd edn, p. 374. Hemisphere, N.Y. (1981). solution is regular, then AG x~ does not change with tempera- 19. ibid. [18], p. 362. ture. The value of the activity coefficient for Ti in A1 20. R. Li and R. Harris, in EDP Congress '91 (edited by available from literature is 1.49 × l0 -7 at 1033 K [20]. From

D. R. Gaskell), p. 387. TMS, Pa (1991). this the AG x~ can be computed for various Ti concen- trations. Consider the Ti concentration to be 0.I and 0.05 at.%. Table 5 shows the values of activity of Ti in AI

A P P E N D I X for these two concentration. By using these activities and the Thermodynamic analysis of equations (6) and (7), per- equilibrium constant, Keq, estimated through equation (8) formed using the F*A*C.T database [16], gives a Gibbs' and the data in Table 4, one can calculate the CO partial free energy of reaction as shown in Table 4. Consider pressure from equation (9). The change of CO partial equation (6); the equilibrium constant, K~q, for these reac- pressure over a range of temperatures is shown in Fig. 7, for tions can be calculated from two different Ti concentrations in A1, for the two possible

reactions proposed in equations (6) and (7). It appears that [ Keq = exp - ~ . (8) the latter reaction is more limiting making the first one more likely to proceed.