8
Surface and Coatings Technology 179 (2004) 257–264 0257-8972/04/$ - see front matter 2003 Elsevier B.V. All rights reserved. doi:10.1016/S0257-8972(03)00819-3 Improvement in the oxidation resistance of a -Ti Al by sputtering Al 2 3 film and subsequent interdiffusion treatment M.S. Chu, S.K. Wu* Department of Materials Science and Engineering, National Taiwan University, Taipei 106, Taiwan, ROC Received 10 February 2003; accepted in revised form 10 June 2003 Abstract Sputtering Al film on a -Ti Al alloy and subsequent interdiffusion treatment at 600 8C for 24 h in high vacuum can effectively 2 3 improve its oxidation resistance, due to a good adhesive TiAl layer formed on the surface. The thicker the Al film, the thicker 3 the TiAl layer that can be formed. Cyclic and isothermal oxidation tests at 800 8C in air show that the a -Ti Al with 3–5 mm 3 2 3 Al film can dramatically reduce its oxidation rate, and the parabolic oxidation rate constant K of specimen with 5 mm Al film p is only approximately 1y5000 of that of bare a -Ti Al. The X-ray diffractometer and scanning electron microscopic results 2 3 indicate that the TiAl layer has formed a protective and continuous a-Al O scale on the outer surface, and inter-reacted with 3 2 3 a -Ti Al to form g-TiAl phase at 800 8C after 80 h of oxidation, i.e. there are layers of a-Al O yg-TiAlya -Ti Al formed on 2 3 2 3 2 3 specimens. 2003 Elsevier B.V. All rights reserved. Keywords: a -Ti3Al intermetallic; Sputtering; Diffusion; Oxidation 2 1. Introduction Titanium aluminides are being considered as promis- ing structural materials for high temperature applications in aircraft and automotive industries, because of their high strength and low density at elevated temperature w1–5x. The major concern for structural applications of Ti Al-based alloys is the insufficient oxidation resistance 3 at high temperature and the lack of ductility at room temperature. It was demonstrated for these alloys that, the room temperature ductility could be effectively improved by the addition of b-phase stabilized elements, such as Nb, Mo and V w3,6–8x. Two main approaches, viz., alloying design and surface modification have been used to improve the oxidation resistance at high tem- perature w6–17x. However, many reported studies indi- cate that, the improvement in oxidation resistance for Ti Al-based alloys favors the methods of surface modi- 3 fication rather than those of alloying design, due to the addition of alloying elements can induce the degradation of ductility w10–17x. *Corresponding author. Tel.: q886-2-2363-7846; fax: q886-2- 2363-4562. E-mail address: [email protected] (S.K. Wu). It has been reported that the high temperature oxida- tion resistance limit of a -Ti Al alloys is 650 8C w3x, 2 3 because it could not form a protective Al O layer on 2 3 the surface at high temperatures, instead, a mixed TiO y 2 Al O oxide scale w19–21x is formed. TiAl , another 2 3 3 intermetallic phase formed in the Ti–Al binary phase diagram, is known as an alumina former with good oxidation resistance at high temperature due to its higher aluminum content w22,23x. Therefore, a layer of TiAl 3 coating deposited on Ti Al-based alloys should improve 3 their high temperature oxidation resistance. Many meth- ods such as pack cementation aluminizing w13–16x, electro-spark deposition w17x and aluminum cladding w18x have been investigated regarding the formation of TiAl layer on g-TiAl as well as Ti Al-based alloys. 3 3 However, the poor adhesion of TiAl coating to the 3 substrate resulted from the inherent microcracks and the intrinsic brittleness of the coatings prevents the improve- ment of oxidation resistance significantly. To overcome these drawbacks, use of the magnetron sputtering dep- osition technology seems to be a feasible method, which has reported to offer very good mechanical properties of TiAl coatings on g-TiAl alloy w12,25x. 3 In this study, we aim to modify the surface of a - 2

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Page 1: Improvement in the oxidation resistance of a -Ti Al by ...ntur.lib.ntu.edu.tw/bitstream/246246/86875/1/110.pdfintermetallic phase formed in the Ti–Al binary phase diagram, is known

Surface and Coatings Technology 179(2004) 257–264

0257-8972/04/$ - see front matter� 2003 Elsevier B.V. All rights reserved.doi:10.1016/S0257-8972(03)00819-3

Improvement in the oxidation resistance ofa -Ti Al by sputtering Al2 3

film and subsequent interdiffusion treatment

M.S. Chu, S.K. Wu*

Department of Materials Science and Engineering, National Taiwan University, Taipei 106, Taiwan, ROC

Received 10 February 2003; accepted in revised form 10 June 2003

Abstract

Sputtering Al film ona -Ti Al alloy and subsequent interdiffusion treatment at 6008C for 24 h in high vacuum can effectively2 3

improve its oxidation resistance, due to a good adhesive TiAl layer formed on the surface. The thicker the Al film, the thicker3

the TiAl layer that can be formed. Cyclic and isothermal oxidation tests at 8008C in air show that thea -Ti Al with 3–5 mm3 2 3

Al film can dramatically reduce its oxidation rate, and the parabolic oxidation rate constantK of specimen with 5mm Al filmp

is only approximately 1y5000 of that of barea -Ti Al. The X-ray diffractometer and scanning electron microscopic results2 3

indicate that the TiAl layer has formed a protective and continuousa-Al O scale on the outer surface, and inter-reacted with3 2 3

a -Ti Al to form g-TiAl phase at 8008C after 80 h of oxidation, i.e. there are layers ofa-Al O yg-TiAl ya -Ti Al formed on2 3 2 3 2 3

specimens.� 2003 Elsevier B.V. All rights reserved.

Keywords: a -Ti3Al intermetallic; Sputtering; Diffusion; Oxidation2

1. Introduction

Titanium aluminides are being considered as promis-ing structural materials for high temperature applicationsin aircraft and automotive industries, because of theirhigh strength and low density at elevated temperaturew1–5x. The major concern for structural applications ofTi Al-based alloys is the insufficient oxidation resistance3

at high temperature and the lack of ductility at roomtemperature. It was demonstrated for these alloys that,the room temperature ductility could be effectivelyimproved by the addition ofb-phase stabilized elements,such as Nb, Mo and Vw3,6–8x. Two main approaches,viz., alloying design and surface modification have beenused to improve the oxidation resistance at high tem-peraturew6–17x. However, many reported studies indi-cate that, the improvement in oxidation resistance forTi Al-based alloys favors the methods of surface modi-3

fication rather than those of alloying design, due to theaddition of alloying elements can induce the degradationof ductility w10–17x.

*Corresponding author. Tel.:q886-2-2363-7846; fax:q886-2-2363-4562.

E-mail address: [email protected](S.K. Wu).

It has been reported that the high temperature oxida-tion resistance limit ofa -Ti Al alloys is 650 8C w3x,2 3

because it could not form a protective Al O layer on2 3

the surface at high temperatures, instead, a mixed TiOy2Al O oxide scalew19–21x is formed. TiAl , another2 3 3

intermetallic phase formed in the Ti–Al binary phasediagram, is known as an alumina former with goodoxidation resistance at high temperature due to its higheraluminum contentw22,23x. Therefore, a layer of TiAl3coating deposited on Ti Al-based alloys should improve3

their high temperature oxidation resistance. Many meth-ods such as pack cementation aluminizingw13–16x,electro-spark depositionw17x and aluminum claddingw18x have been investigated regarding the formation ofTiAl layer on g-TiAl as well as Ti Al-based alloys.3 3

However, the poor adhesion of TiAl coating to the3

substrate resulted from the inherent microcracks and theintrinsic brittleness of the coatings prevents the improve-ment of oxidation resistance significantly. To overcomethese drawbacks, use of the magnetron sputtering dep-osition technology seems to be a feasible method, whichhas reported to offer very good mechanical propertiesof TiAl coatings ong-TiAl alloy w12,25x.3

In this study, we aim to modify the surface ofa -2

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258 M.S. Chu, S.K. Wu / Surface and Coatings Technology 179 (2004) 257–264

Table 1Sputtering conditions used in this study

System base Sputtering RF power Sputtering Distance Al filmpressure pressure (W) time between target and substrate thickness(Torr) (Torr) (min) (mm) (mm)

-6=10y7 5=10y3 100 24–240 80 0.5–5

Fig. 1. The SEM morphologies ofa -Ti Al specimen with 3mm Al2 3

film after interdiffusion treatment at 6008C for 24 h in high vacuum.(a) Surface morphology and(b) cross-sectional morphology.

Ti Al alloy by sputtering various thicknesses of pure Al3

films with a subsequent interdiffusion treatment in highvacuum. Thereafter, a TiAl layer is formed on the3

surface with rather good adhesion to thea -Ti Al2 3

substrate. Specimens treated by the aforementioned pro-cesses are cyclically oxidized at 8008C in static air andtheir weight gains are measured. Based on the measureddata and the microstructural observations, the oxidationresistance improvement ofa -Ti Al alloy is discussed.2 3

2. Experimental procedures

The ingots ofa -Ti Al alloy used in this study were2 3

prepared from the raw materials of titanium(99.7%)and aluminum(99.98%) by a vacuum arc remelterunder high-purity argon atmosphere. The ingots werere-melted at least six times to ensure the homogeneityof the as-cast structure. After homogenization of theingots at 10008C for 100 h in vacuum, specimens forsputtering were cut by a diamond-saw into the size of10=10=1 mm . Before the sputtering, all surfaces of3

the specimens were mechanically polished by a standardmetallographic procedure to a final polishing of 0.3-mmalumina, then ultrasonically cleaned with acetone andethanol, and then blown dry. The pure aluminum targetfor sputtering was also prepared by the same procedure,but the Al ingot was finally sectioned into a disk shapeof 50 mm in diameter and 5 mm in thickness.The Al film was deposited on all the surfaces of the

a -Ti Al specimens using an r.f. magnetron sputtering2 3

apparatus. The sputtering conditions are given in Table1. Aluminum films in the thickness range of 0.5–5mmwere deposited, as measured bya-step(Veeco Dektak3

ST). After the sputtering deposition, a subsequent inter-diffusion treatment was processed at 6008C for 24 h ina high vacuum of approximately 3=10 torr. Isother-y7

mal oxidation tests at 8008C in static air were performedusing a thermogravimetric analysis(TGA, TA ModuleTGA-DTA 1500). Cyclic oxidation tests were conductedto evaluate the oxidation resistance ofa -Ti Al. The2 3

specimens were exposed in a muffle furnace at 8008Cand regularly removed from the furnace at time intervalsof 5–10 h, air cooled, weighed and returned to the 8008C furnace. The weight gains were measured on ananalytical balance within an accuracy of"0.001 mg(Model: Mettler MT5).

An X-ray diffractometer (XRD, Philips PW1729)with Cu Ka radiation at 30 kV, 20 mA and 48 2uyminscanning rate was used to identify the phases of sput-tered-films formed by the interdiffusion treatment andthe oxidation tests. The surface morphologies and cross-sectional microstructures of specimens were observedby a Leo 1530 scanning electron microscope(SEM)equipped with energy dispersive spectrometry(EDS).Electron probe microanalyzer(EPMA, JEOL JXA-8600SX) was used for measuring the chemical composition

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259M.S. Chu, S.K. Wu / Surface and Coatings Technology 179 (2004) 257–264

Fig. 2. The XRD spectra ofa -Ti Al specimens with various thicknesses of Al films(from 0.5 to 5 m) after interdiffusion treatment at 6008C2 3

for 24 h in high vacuum.

of phases formed by sputtering, interdiffusion treatmentand oxidation tests.

3. Results and discussion

3.1. Interdiffusion of a -Ti Al with sputtered Al films2 3

Aluminum films with different thicknesses of 0.5–5mm were sputtered on thea -Ti Al substrate. To control2 3

the thickness of Al film accurately, the sputtering rateof Al film should be determined. According to thesputtering conditions of Table 1 and the thicknessmeasurement ofa-step, the sputtering rate of Al film iscalculated to be 3.5 Ays w25x. Consequently, the appro-˚priate thickness of Al film can be obtained by controllingthe sputtering time. However, the intrinsic stress in thefilm increases with increasing film thickness, resultingin poor adhesion of coating to the substrate. Once thethickness of Al film is over 5mm, small parts of thefilm spall out from the a -Ti Al substrate after the2 3

interdiffusion treatment. Hence, in this study the thick-nesses of the as-sputtered Al films are all less than 5mm. The as-sputtered Al film is crystalline with apartially amorphous structure in terms of the result ofXRD patternw25x.In order to form a TiAl layer on thea -Ti Al surface3 2 3

and to increase the adhesion between the thin film and

a -Ti Al substrate, an interdiffusion treatment is con-2 3

ducted for each specimen sputtered with Al film. Fig.1a and b show the SEM images of top-viewed andcross-sectional morphologies, respectively, ofa -Ti Al2 3

with a 3mm thick as-sputtered Al film via interdiffusiontreatment at 6008C for 24 h in vacuum. From Fig. 1a,the microstructure was found to be relatively dense,with extremely small grain and no visible crack. TheXRD diffraction patterns of the surface indicate that themain product of Fig. 1b is TiAl phase, as shown in3

Fig. 2. From Fig. 1b, the TiAl layer formed on the3

outer surface has a uniform thickness with no crack orvoid introduced at the interface. Thus, the aforemen-tioned interdiffusion procedure is beneficial to the bond-ing between thin film and substrate. From the results ofEPMA and EDS analyses, this layer has a Al:Ti at.%ratio of 3:1, which again confirms that the diffusionlayer consists of TiAl phase. The present observation3

coincides with the XRD patterns shown in Fig. 2.The first phase formation in the diffusion system of

a -Ti Al and Al thin film is the TiAl layer, according2 3 3

to the solid-state diffusion theoryw26,27x and an effec-tive heat of formation modelw28x. This is due to theformation of TiAl intermetallic, which has more nega-3

tive formation energy than the other titanium aluminides.The formation of TiAl phase finishes until all the3

sputtered Al atoms are exhausted during the interdiffu-

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260 M.S. Chu, S.K. Wu / Surface and Coatings Technology 179 (2004) 257–264

Fig. 3. Cyclic oxidation tests in static air at 8008C for a -Ti Al specimens with various thicknesses of Al films which have been interdiffusion2 3

treated at 6008C for 24 h in high vacuum.

Fig. 4. Effect of the thickness of Al film on the cyclic oxidation resistance(parabolic rate constantK ) of a -Ti Al specimens oxidized at 800p 2 3

8C in air. TheK values are calculated from Fig. 3.p

sion treatment. This means that the thickness of TiAl3

layer formed by interdiffusion treatment is highlydependent on the thickness of as-sputtered Al film. Itwas found that, for a 3-mm thick Al film, the thicknessof TiAl layer can be extended to approximately 4mm3

by the interdiffusion ofa -Ti Al and Al film, as shown2 3

in Fig. 1b.

3.2. Cyclic and isothermal oxidation

The cyclic oxidation tests were evaluated at 8008Cin static air for 80 h. The weight gainDw of the

oxidation was measured from the weight change oftested specimens, including the remaining and exfoliatedscales. Fig. 3 compares the weight gain of sputteredspecimens with that of the unsputtered(bare) one. Allspecimens with sputtered Al film were subjected to theinterdiffusion treatment at 6008C for 24 h in vacuum.Fig. 3 indicates that the thickness of Al film is a majorfactor for the improvement of oxidation resistance ofa -Ti Al alloy. For barea -Ti Al alloy which has the2 3 2 3

highest oxidation rate, severe weight gain and scalespallation can be observed clearly within 80 h of

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261M.S. Chu, S.K. Wu / Surface and Coatings Technology 179 (2004) 257–264

Fig. 5. The TGA isothermal oxidation tests in static air at 8008C for a -Ti Al specimens with various thicknesses of Al films.2 3

Fig. 6. The XRD diffraction spectra of Al-sputtereda -Ti Al specimens after interdiffusion treatment and then oxidation at 8008C for 80 h in2 3

air. The thickness of Al film ranges from 0mm (barea -Ti Al ) to 5 mm.2 3

exposure in static air at 8008C. Obviously,a -Ti Al2 3

specimens with Al films of certain thickness in the 3–5 mm range have excellent oxidation resistance at 8008C. This comes from the fact that they have a TiAl3

layer with sufficient thickness, which can form anadhesive and continuousa-Al O layer on the surface2 3

during the cyclic oxidation tests. At the same time, no

scale spallation occurs during the cyclic oxidation forspecimens with 3–5mm Al film, even at the corners oralong the edges of the specimens.The parabolic oxidation rate constant,K , which wasp

calculated from the relation(DwyA) sK t can be esti-2p

mated from the curve fitting of Fig. 3, and this constantcan be used as a convenient index for comparing the

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262 M.S. Chu, S.K. Wu / Surface and Coatings Technology 179 (2004) 257–264

Fig. 7. The SEM surface morphologies of the oxidation scale afteroxidation at 8008C for 80 h for(a) a -Ti Al; (b) 3 mm Al film and2 3

(c) 5-mm Al film. The specimens were interdiffusion treated in highvacuum before the oxidation.

improvement of oxidation resistance. Here,A is thesurface area of tested specimens andt is the time. Fig.4 shows the relation between calculatedK value andp

the thickness of Al films. TheK value for the cyclicp

oxidation of 3-mm thick Al film at 800 8C is 1.15Ey3mg ycm h, in comparison with 2.294 mgycm h for2 4 2 4

the barea -Ti Al. The K value for the former is2 3 p

approximately 1y2000 of the latter. Furthermore, theK value for the cyclic oxidation of 5-mm thick Al filmp

at 800 8C can be further reduced to 4.28Ey4 mg y2

cm h, which is approximately 1y5000 of theK value4p

for the barea -Ti Al. In other words, theK value is2 3 p

found to decrease upon increasing the TiAl layer3

thickness, indicating that the oxidation resistance ofa -2Ti Al alloy with 3–5mm thick Al films can be improved3

dramatically, to the extend of above three orders ofmagnitude, as compared to the barea -Ti Al alloy. Figs.2 3

3 and 4 indicate that, in the thickness range of 3–5mmAl film, the improvement in the oxidation resistance ofa -Ti Al is mainly dependent on the TiAl thickness.2 3 3

The thicker the TiAl layer, the higher the oxidation3

resistance obtained, since the thicker TiAl layer can3

form a thicker protective and continuousa-Al O layer2 3

on the substrate for long-term oxidation at 8008C.Isothermal oxidation tests were carried out by TGA

at 8008C up to 70 h to compare the oxidation propertiesof a -Ti Al with and without Al film, as shown in Fig.2 3

5. From Fig. 5, the sputtered Al film and subsequentinterdiffusion treatment can substantially reduce theoxidation rate ofa -Ti Al. This result is in agreement2 3

with the cyclic oxidation results as shown in Fig. 3.

3.3. Surface and cross-sectional morphologies of speci-mens after 800 8C cyclic oxidation

Fig. 6 shows the XRD spectra ofa -Ti Al specimens2 3

with and without Al film, which have been interdiffu-sion-treated at 6008C for 24 h and then cyclicallyoxidized at 8008C in air. The XRD pattern of bareTi Al specimen shown in Fig. 6 has strong peaks3

corresponding to TiO (rutile) with a few weak a-2

Al O peaks, indicating that the oxides formed consist2 3

of a mixture of Al O and TiO . Also from Fig. 6, for2 3 2

specimens with 3–5mm Al film, the a-Al O layer is2 3

formed exclusively on the outer surface. At the sametime, TiAl has reacted witha -Ti Al to form the g-3 2 3

TiAl phase after oxidation at 8008C for 80-h oxidationw24x, as the XRD spectra ofg-TiAl shown in Fig. 6.The results of Figs. 3 and 6 indicate that, when thethickness of Al films is over 3mm, a protectivea-Al O scale, instead of a fragile TiO one, is formed on2 3 2

the outer surface of the specimen.Fig. 7 shows the SEM surface morphologies(top-

view) of the oxidation scale after oxidation at 8008Cfor 80 h for: (a) barea -Ti Al, (b) 3 mm Al film and2 3

(c) 5 mm Al film. The sputtered specimens in Fig. 7b

and c were interdiffusion-treated at 6008C for 24 h inhigh vacuum before the cyclic oxidation. Fig. 7a revealsthat, for the barea -Ti Al specimen, only large quanti-2 3

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263M.S. Chu, S.K. Wu / Surface and Coatings Technology 179 (2004) 257–264

Fig. 8. The SEM cross-sectional images of the specimens of Fig. 7 for(a) a -Ti Al; (b) 3 mm Al film; (c) 5 mm Al film; and (d) EDS2 3

composition analyses of points 1–5 shown in(c).

ties of crystalline TiO oxide were formed on the2

surface, which is consistent with the reported investi-gations w19–21,29x. In contrast, for the 3-mm Al filmspecimen, a dense and stablea-Al O layer without2 3

brittle rutile has formed on the oxide scale, as shown inFig. 7b. Additionally, a very small amount of needle-like a-Al O is also found at some areas. In general,2 3

the needle-likea-Al O is formed at the early oxidation2 3

stage andyor at relatively low temperatures. After a longexposure at higher temperatures, a densea-Al O tran-2 3

sited from the cluster of needle-likea-Al O could be2 3

observed w17x. This a-Al O layer exhibits a good2 3

barrier against inward oxygen diffusion, resulting in animproved oxidation resistance ofa -Ti Al at 800 8C in2 3

air. In the case of 5mm Al film specimen, the needle-like a-Al O increases in number on the surface, as2 3

shown in Fig. 7c.The SEM cross-sectional microstructures of the same

specimens of Fig. 7 are shown in Fig. 8. Fig. 8a revealsthat the microstructure of the oxide layer ofa -Ti Al is2 3

similar to that ofg-TiAl, but there is no continuousAl O barrier, and a discontinuous Al O -rich sublayer2 3 2 3

exists above the TiOyAl O mixture w19x. From Fig.2 2 3

8b and c, the microstructure of specimens with 3 or 5mm Al film is not complicated: only two layers coexist,as indicated by XRD results of Fig. 6 and EDS com-

position analyses of points 1–5 shown in Fig. 8d. TheXRD and EDS results show that the outer thin layer isdue toa-Al O , the inner thick layer is due tog-TiAl2 3

and the substrate is due toa -Ti Al. An adhereda-2 3

Al O scale formed on the surface ofg-TiAl layer can2 3

provide excellent protection against the oxidation attack.From Fig. 8b and c, one can find that the thicker the Alfilm, the thicker thea-Al O layer on the outer surface.2 3

As to the g-TiAl formation, it appears to be reactedfrom TiAl and a -Ti Al, as confirmed by the XRD3 2 3

spectra shown in Fig. 6. This phenomenon can beunderstood from the phase formation sequence of Ti Al–3

Al thin film system, as further discussed in anotherpaperw24x. The thickness ofg-TiAl layer increases uponincreasing the Al film thickness, as shown in Fig. 8band c. In this study, we find that the alumina scale canmaintain its integrity with no microcrack and spallationafter 80-h cyclic oxidation.

4. Conclusions

The oxidation resistance ofa -Ti Al alloy can be2 3

improved by sputtering Al film followed by the inter-diffusion treatment at 6008C for 24 h in high vacuum.The Al film has its thickness accurately controlled bymagnetron sputtering process, but this thickness cannot

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264 M.S. Chu, S.K. Wu / Surface and Coatings Technology 179 (2004) 257–264

exceed 5mm because the intrinsic stress in the film canspall it out from the substrate via the interdiffusiontreatment. After the interdiffusion treatment, the Al-sputtereda -Ti Al alloy forms a TiAl layer on the2 3 3

surface due to the first phase formation of the interactionbetweena -Ti Al and Al thin film. This TiAl layer2 3 3

exhibits good adhesion with the substrate and plays animportant role in the long-term oxidation resistance.Experimental results show that the thickness of TiAl3

layer is strongly dependent on Al film and the thickerthe Al film, the thicker the TiAl layer that can be3

formed. Cyclic and isothermal oxidation tests at 8008Cin air indicate that thea -Ti Al alloy with TiAl layer2 3 3

on the surface can dramatically reduce the oxidationrate if the sputtering thickness of Al film can reach 3–5 mm. The parabolic rate constantK of cyclic-oxidizedp

specimens with 3 and 5-mm Al film thickness can bereduced to approximately 1y2000 and 1y5000, respec-tively, as compared to that of specimens without sput-tering Al film. From the XRD and SEMqEDS resultsof cyclic-oxidized specimens at 8008C, the TiAl layer3

not only result in the formation of a continuousa-Al O scale on the outer surface, but also inter-react2 3

with a -Ti Al substrate to formg-TiAl layer during the2 3

oxidation. After the cyclic oxidation at 8008C for 80 hin air, the cross-sectional microstructures of specimenswith Al film show that there are layers ofa-Al O yg-2 3

TiAl ya -Ti Al, in which the a-Al O layer maintains2 3 2 3

its integrity with no microcracks and spallation.

Acknowledgments

The authors would like to acknowledge the financialsupport of this research by the National Science Council(NSC), Taiwan, Republic of China, under Grant Nos.NSC90-CS-7-082-001 and NSC91-CS-7-002-002.

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