Interdffuson n multphase, ---- dffuson couples T. Gómez-Acebo*, B. Navarcorena, F. Castro CEIT and Unversty of Navarra Manuel Lardzabal 15, E-218 San Sebastan, SPAIN *: rrespondng author s e-mal: tgacebo@cet.es Paper presented at Calphad XXXII, La Malbae, Québec, Canada, May 25-3, 23 Journal of Phase Equlbra and Dffuson Vol. 25 No. 3 pp. 237-251 (24) Abstract The nterdffuson n matrx/ partcle alloys and /-based substrates was studed usng electron probe mcroanalyss and smulated wth the software DICTRA. loys were prepared by mxng elemental powders and furnace meltng under an nert atmosphere. The phases nvolved n the study were γ (-based or -based), β-, and γ. The alloys were sngle phase (γ), as well as two-phase (γ+β and γ+γ ). Several equlbrum ponts n the -- system were measured and compared to the calculated dagram at 11 C. The dffuson couples were prepared to produce combnatons of selected alloys and were subjected to annealng at 11 C for tmes up to 72 h. The dffuson calculatons made wth DICTRA were performed usng the TCNI1 thermodynamc database together wth moblty data collected from dfferent lterature sources. A lterature survey on dffuson data of ths system was performed, and comparsons wth avalable data were made. The valdty of the selected moblty data was checked wth the composton profles measured on some sngle phase γ/γ dffuson couples. In the γ+β/γ and γ/γ+γ dffuson couples a regresson of the dspersed phase (β or γ ) was observed due to the nterdffuson of. From combned expermental and theoretcal results, the effects of temperature and coatng thckness were determned as an nput for a coatng lfetme predcton model. 1. Introducton Overlay coatngs are generally appled to land-based combuston turbne blades to mprove oxdaton and corroson resstance. Typcal overlay coatngs are so-called MY, where M s ron, nckel and/or cobalt. The effcency of these coatngs dmnshes wth tme after exposure to hgh temperatures. Lfetme estmatons of overlay coatngs n -based superalloys requre a careful modelng of the coatng degradaton. Several models have been publshed [1-4] that consder degradaton due to the followng three dfferent phenomena: oxdaton; nterdffuson; and oxde spallaton. Spallaton occurs n materals experencng thermomechancal fatgue due to cyclc operaton of the turbne. Oxdaton of the coatng forms a protectve layer, provded that the content n the coatng surface s hgher than a crtcal value. [5] The oxde layer grows n conformty wth a parabolc law. Interdffuson between the coatng and the substrate s enhanced at hgh temperatures. In the absence of spallaton (.e., n
turbnes operated n the steady state) the followng two crtera have been proposed for defnng the onset of coatng falure: (a) a crtcal content [5] ; and (b) the volume fracton of the β phase. [4] Interdffuson s the man factor of loss n the coatng, whch s hgher than that produced by oxdaton. mputer smulatons of multphase materals can be used as an ad to estmate the lfetme of coatngs, provded that the thermodynamc and knetc descrptons of the alloy system are well known. For -base superalloys, there are good recent thermodynamc [6] and knetc [7] descrptons. However, wth as one of the man components of several MY coatngs, the necessary modfcatons of the thermodynamc and knetc descrptons of the - - system are not fully known. Morral et al. [8] have analyzed the dfferent types of planar boundares n multphase dffuson couples. Three types of planar boundares can exst. These are boundares across whch there are changes of zero phases (Type ), one phase (Type 1), or two phases (Type 2). Dependng on the movement of the boundary, a shorthand notaton for the couples was proposed. In ths work, nterdffuson experments have been done at 11 C for several alloys n the ---- system. The results have been compared wth calculatons performed wth Thermo-Calc [9] and DICTRA. [1] It has been shown that composton profles are well reproduced, but the agreement s not so good for other elements such as. Fnally, a lfe estmaton s done as a functon of some operatng parameters. 2. Materals and Expermental procedure Several alloys were prepared from elemental metals by mxng 2 g of the metallc powders n a Turbula shaker-mxer (model T2C, Wlly A. Bachofen AG Maschnenfabrk, Basel, Swtzerland) for 3 mn. Characterstcs of the metallc powders are shown n Table 1. Nomnal and measured compostons for the mxtures are gven n Table 2. The powder mxtures were unaxally pressed at 4 MPa. mpacts were ntroduced n 2 O 3 crucbles and were melted n a furnace wth graphte heatng elements under Ar at a temperature 2 C hgher than the lqudus temperature of the mxture. The alloys were then homogenzed at 11 C for 3 h n Ar and were quenched n water. Sheets of 2 mm thckness were cut from the samples and polshed wth 3 µm damond paste. These samples were studed usng a scannng electron mcroscope (SEM) (model XL3, Phlps, Amsterdam, The Netherlands) operatng at 2 kv acceleraton voltage and ftted wth an energy dspersve X-ray mcroanalyss (EDS) system from EDAX (Mahwah, NJ). The samples also were studed by X-ray dffracton wth an X-ray dffractometer (model PW17, Phlps). Table 1. Characterstcs of the Elemental Powders Element Purty Partcle Sze Suppler Impurtes (ppm) (%) 99.5 4 µm maxmum Goodfellow Cu<2, Fe<35, Mn<2, S<25 99 2 µm maxmum Goodfellow 16, Cu 3, Fe 25, S 5, C 2, S 8 99.7 1 µm mean OMG Amercas, Inc. O 28, C 76, S<1, 2, Fe 23, Cu 1, Zn<1, Mn 4, Na<1, Mg 3, Ca 2, S<1 99.5 25 µm maxmum Goodfellow <5, Cu<9, Fe<15, C<6, S<5, oxdes 16 99.5 15 µm maxmum Goodfellow C<1, Cl 17, Fe 2, N<1, O 1
Table 2. loy mpostons loy System - - -- -- loy number mposton (wt.%) mposton (at.%) Used n uple A1-4. -8.3 C1, C2 A2-8.3-16.5 C3 A3-9. -17.8 C4 A4-1. -19.5 C5 A5.1-8.9-9.9 C1 A5.2-11. -12.3 C3 A6.1-14. -15.6 C2 A6.2-17. -18.8 C4 A7-3. -32.7 C5 A8-5.-25.7-1.-26.6 C9 A9-6.-27.9-11.8-28.5 C1 A1-6.6-28.7-12.9-29.1 C13 A11-7.7-32. -14.8-32. C11 A12-5.-28.9-1.5-27.2 C6, C7 A13.1-5.3-38.4-1.9-36.1 C8, C1, C11 A13.2-6.5-4.8-13.2-37.8 C9 A14-7.7-25.8-15.4-23.6 C6 A15-1.-21.6-19.5-19.3 C7 A16-1.8-2. -2.9-17.7 C8 --- A18-1.4-5.5-8.9-2.9-5.9-1.5 C13 Table 3. Temperature and me for the Dffuson Anneal n the Dfferent uples loy System -- -- --- uple No. mposton of alloys used (wt.%) (a) Phases T ( C) me (h) C1-4. (A1) / -8.9 (A5.1) γ/γ 11 72 C2-4. (A1) / -14. (A6.1) γ/γ 11 72 C3-8.3 (A2) / -11. (A5.2) γ+β/γ 11 72 C4-9. (A3) / -17. (A6.2) γ+β/γ 11 72 C5-1. (A4) / -3. (A7) γ+β/γ 11 72 C6-5.-28.9 (A12) / -7.7-25.8 (A14) γ/γ 11 24 C7-5.-28.9 (A12) / -1.-21.6 (A15) γ/γ+γ 11 48 C8-5.3-38.4 (A13.1) / -1.8-2. (A16) γ/γ+γ 11 72 C9-5.-25.7 (A8) / -6.5-4.8 (A13.2) γ+β/γ 11 48 C1-6.-27.9 (A9) / -5.3-38.4 (A13.1) γ+β/γ 11 48 C11-7.7-32. (A11) / -5.3-38.4 (A13.1) γ+β/γ 11 48 ---- C13-6.6-28.7 (A1) / -1.4-5.5-8.9 (A18) γ+β/γ 11 72 (a) loy number s n parentheses. The samples were then placed 2 by 2 facng each other and were joned n a hot-press furnace at 11 C and 35 MPa for 5 mn under an Ar protectve atmosphere. The nterdffuson due to ths process was found to be neglgble. These dffuson couples were consequently gven a dffuson anneal n Ar at 11 C for dfferent tmes, followed by water quenchng. The dffuson couples produced are lsted n Table 3. The dffuson couples were cut nto two halves and were prepared metalographcally. The fnal polshng was done wth 3 µm damond paste. Sem-quanttatve EDS analyss was performed along a lne parallel to the dffuson nterface, wth manual spacng of 1 µm between the analyzed ponts. Measurements were performed as sngle lne measurements for obtanng
averaged compostonal data n weght percent (wt.%). The termnal composton of the dffuson couples was measured at a dstance far enough from the nterface, where the composton dd not change any longer. Some oxde partcles that were present at the polshed surface of the alloys were used as markers of the Krkendall nterface. The mpurtes of the startng alloys dd not form any compound wth alumnum (), cobalt (), chromum (), nckel (), and ttanum (); no nfluence of these mpurtes was found n the dffuson profles. Fg. 1. Isothermal sectons of the -- system calculated wth the TCNI1 database, [6] together wth expermental data from Ishkawa et al. [11] at several temperatures. 3. Calculaton Procedure 3.1 Thermodynamc Descrpton The thermodynamc calculatons have been performed wth the TCNI1 database, [6] whch ncludes an assessed descrpton of all the bnary systems nvolved n ths work. It also ncludes completely assessed descrptons for the ternares: --; --; --; --; and
--. There s no assessment for the remanng ternares: --; --; --; --; and --. l of these ternary systems contan n ther composton. Of the non-assessed ternares, the -- s of great mportance for the study of the stablty of hgh-temperature MY overlay coatngs. There has been some expermental nformaton about the phase relatons n ths system publshed by Ishkawa et al. [11] The reported expermental data are presented n Fg. 1, together wth the calculated sothermal sectons of the system. The calculaton was done as an extrapolaton from the three bnares, wthout any ternary nteracton parameter. There s a reasonable agreement between the calculated dagram and the expermental data, except for the composton of the β- (B2) phase. It can be seen n Fg. 1 that the composton trend towards the - sde of the trangles seems to be at too hgh an content n the B2 phase. Notng that the bnary - s well-characterzed, [12,13] those expermental data n the ternary were regarded as naccurate, and the thermodynamc modelng of the ternary was accepted as an deal system. 3.2 Knetc Descrpton 3.2.1 Modelng of the Dffuson effcents From the absolute reacton rate the moblty of an arbtrary speces may be expressed as M = M RT Q exp RT (1) where M represents the frequency factor and Q represents the actvaton enthalpy. Ths expresson can be wrtten as M 1 = RT Q exp RT * (2) * where Q Q RT ln( M ). The tracer dffuson coeffcent moblty as * D = RTM * D s related drectly to the (3) The chemcal dffusvty s gven by a more complex relaton n whch the concentraton of one n element n has been chosen as dependent on the others. The chemcal dffusvty D ~ j can be expressed as [14] ~ D n j = n 1 k= 1 µ k µ k ( δ ) k x xkm k (4) x j xn where the Kronecker delta δ k = 1 when k = and otherwse, and x k s the mole fracton of the element k. Usng the chemcal dffusvty, the flux of element k n the number-fxed frame of reference J k can be calculated as
J k = ~ c n n j Dkj j= 1 z (5) where c j / z s the concentraton gradent of element j n the z drecton. The nteractons n a multcomponent system can be modeled by means of the Redlch- Kster polynomals: where the j Q and the j> p * j k pj Q = x Q + x x A ( x x ) j j p p j k k pj A are lnear functons of temperature, and are gven n the Appendx. pj Only k A parameters wth k = are used for ths system. For example, n the ternary system - * - the term Q n eq. (2) s calculated as p j k (6) *, x Q = x Q + x Q + x Q + x x A + x A + x x A (7),, 3.2.2 Avalable Dffusvty Data There are publshed assessments of the mobltes n the fcc phase for the followng bnary and ternary systems: - [15] ; - [15] ; - [16] ; - [7] ; - [17] ; - [16] ; -- [15] ; and --. [16] l of these data were ncluded n the moblty database publshed by Campbell et al. [7] For the followng bnary systems there are no publshed assessed moblty data: -; -; -; and -. Engström and Ågren [18] have suggested the followng approxmatons for the mobltes n the fcc phase: Q = Q ; Q = Q ; Q = Q ; Q = Q ; Q = Q = Q = Q ; Q = Q. so, Campbell et al. [7] suggested the approach approxmatons have been accepted. Q = Q. l of these For the mobltes n the bnary -, no assessment has been publshed. Impurty dffuson of n fcc- was measured by Peterson and Rothman. [19] The mpurty dffuson of n fcc- has not been drectly measured. We have accepted the data suggested n the MOB2 database [2] (.e., 5 tmes the self-dffusvty of fcc-fe). The followng ternares have been regarded as deal: --; --; --; - -; --; --; --; and --. l the moblty parameters used n ths work are ncluded n the Appendx. 3.2.3 Dffuson n Dspersed Phases Engström [21] has suggested the use of the Hashn-Shtrkman [22] (H-S) bounds for the study of dffuson n dspersed systems. When there s a bg dfference n the dffusvty of an element n two phases, say D γ > D β, the effectve dffusvty n the 2-phase γ+β s reduced due to the presence of the β-phase. Upper and lower bounds to the effectve dffusvty can be establshed.
Hashn and Shtrkman [22] used a varatonal prncple to obtan bounds for the effectve magnetc permeablty of macroscopcally homogeneous and sotropc mxtures of several phases. These bounds hold for any transport property such as the dffuson coeffcent. For two phase materals (D 1 > D 2 ), the upper D u and lower D l bounds are gven by: f 2 D u = D1 + (8) /( D D ) + f /(3D ) 1 2 1 1 1 f1 D l = D2 + (9) /( D D ) + f /(3D ) 1 1 2 2 2 where f are the volume fractons, and D s the dffusvty wthn each phase. These bounds are wdely accepted as the most restrctve ones, dependng only on the volume fracton, and otherwse ndependent of mcrogeometry. They are llustrated n Fg. 2 for the case when D 1 = 1 D 2, together wth the Wener bounds (drect and nverse rules of mxtures). Fg. 2. Upper and lower bounds for the effectve dffusvty n a two-phase system when D 1 = 1 D 2 : sold lnes are upper (D eff = f 1 D 1 + f 2 D 2 ) and lower (D eff = 1/(f 1 /D 1 + f 2 /D 2 )) Wener bounds. Dashed lnes are upper and lower H-S [22] bounds gven by eqs. (8) and (9), respectvely. Dotted lnes are the approxmatons gven by eqs. (1) and (11). When D 1 >> D 2 and f 1 > f 2, the H-S upper bound (eq. (8)) can be smplfed to: 2 f 1 D u = D 1 (1) 3 f1 When D 1 >> D 2 and f 1 < f 2, the H-S lower bound (eq. (9)) smplfes to: f = + 1 D l D 2 1 3 (11) f 2
The terms n brackets n eqs. (1) and (11) are the so-called labyrnth factors n the calculatons. In ths work, we have used the upper bound (eq. (1)) for a correcton of the dffusvty n the γ- phase due to the presence of the β-phase: D eff 2 f γ / Dγ = (12) 3 f γ It has to be understood that ths approach s an underestmate of the reducton of the dffusvty n the γ-phase, but, as a frst approxmaton, t should be satsfactory. 4. Results and Dscusson 4.1 Thermodynamcs of the -- System Several ternary alloys n the -- were produced, all of them beng two-phase γ+β, wth dfferent volume fractons of the β-phase. The compostons of the alloys A8, A9, A1, and A11 are gven n Table 2. SEM mcrographs of these alloys are shown n Fg. 3. The matrx phase n all cases s the fcc γ-phase, whle the β-phase (shown n dark contrast n the mcrographs) s a dspersed phase. The measured and calculated volume fracton of the β-phase n three of these alloys s shown n Table 4. The agreement s good. Table 4. Measured and Calculated Volume Fracton of the B2 Phase n the -- Ternary loys loy Number mposton (wt.%) Measured Volume Fracton of the B2 Phase Calculated Mole Fracton of the B2 Phase A8-5.-25.7.6.3 A9-6.-27.9.24.23 A11-7.7-32..59.51 The compostons of the two phases are represented n Fg. 4, together wth the calculated sothermal ternary secton at 11 C. The agreement s also satsfactory, even though the calculaton has been made drectly from the three bnary systems. mpared to the expermental data reported by Ishkawa et al. [11] (Fg. 1), we have not measured the hgh content n the β- phase that they report. Our measurements agree better wth the thermodynamc calculatons. Ths supports the use of the current thermodynamc descrpton of the ternary -- system, wth no ternary nteracton parameter, at least for the γ+β regon.
(a) (b) (c) Fg. 3. SEM photomcrographs of the two-phase -- alloys represented n Fg. 4. Chemcal compostons n wt.%: (a) A8 (-5.-25.7); (b) A9 (-6.-27.9); and (c) A11 (-7.732.).
Fg. 4. Secton of the calculated -- system at 11 C, together wth the measured compostons of the phases n ths ternary system and n the bnary -. The chemcal composton of the GT29 overlay coatng s also shown (chemcal composton n wt.%: -6-29-.3Y, wthout Y). 4.2 Dffuson uples The composton of the dffuson couples studed s presented n Table 3. The calculated dffuson profles, together wth the measured chemcal analyses usng EDS, are shown n each secton for several dffuson couples, dstrbuted nto the dfferent chemcal systems. so the mcrostructure of some couples s shown. 4.2.1 Dffuson uples n the -- System g/g Dffuson uples. As a frst check of the avalable moblty data, sngle-phase - γ alloys were subjected to dffuson wth sngle-phase γ - alloys. The and dffuson profles for dffuson couples C1 and C2 are shown n Fg. 5, together wth the calculated profles. The agreement for s very good, although for t can be seen that the calculated mobltes are slghtly underestmated. g+b/g Dffuson uples. - alloys wth hgher content are two-phase (γ+β) systems. Three dfferent - alloys (γ+β) wth ncreasng content were subjected to dffuson anneal wth - alloys (sngle-phase γ). The ntal volume fracton of the β-phase n the - alloys vared from.22-.42. Measured and calculated composton profles for the dffuson couples are represented n Fg. 6. The calculatons were made consderng a reduced dffusvty n the γ+β-phase by the use of the labyrnth factor gven n eq. (12). The calculated profles shown n Fg. 6 nclude the followng three dfferent curves: the calculated average composton (ntermedate lne); and the phase composton n γ (fcc) and β (B2). These lnes are drawn n the whole dstance profle, although they are an extrapolaton n the areas where the materal s γ sngle phase. As n the γ/γ dffuson couples, the profles are very well predcted, but the profle s agan underestmated. The measured profles, although they are from sem-quanttatve EDS analyss, suggest a slght peak n composton n the two-phase sde (left sde) of the dffuson couples, however, the smulatons wth DICTRA dd not predct ths peak.
(a) Fg. 5. Expermental and calculated composton profles for and of the dffuson couples (a) C1 and (b) C2, both annealed at 11 C for 72 h. (b) (a) (b) (c) Fg. 6. Expermental and calculated composton profles for and of the dffuson couples (a) C3, (b) C4 and (c) C5, all annealed at 11 C for 72 h.
In Fg. 7, the mcrostructure of one of these dffuson couples s shown. It can be clearly seen that, due to nterdffuson, there s a regresson n the β-phase. For the couple shown n the mcrograph (C4), the regresson s about 11 µm. The calculated mole fracton of ths β- phase s shown n Fg. 8 for the three dffuson couples studed. These dffuson couples can be expressed n shorthand notaton proposed by Morral et al. [8] as γ + β < γ n whch < ndcates the drecton of moton of the boundary between the two regons relatve to the ntal nterface. They are boundares of Type 1, n whch one phase s added or subtracted on crossng the boundary. The dffuson paths for the fve couples are shown n Fg. 9, wth the calculated phase dagram of the -- system at 11 C. Fg. 7. SEM mcrograph of the dffuson couple C4 annealed at 11 C for 72 h. Fg. 8. Calculated regresson of the β-phase n the dffuson couples C3, C4, and C5, all annealed at 11 C for 72 h.
Fg. 9. Expermental and calculated dffuson paths of the -- dffuson couples, together wth the calculated sothermal secton of the ternary phase dagram at 11 C. 4.2.2 Dffuson uples n the -- System Several alloys n the ternary system --, both sngle-phase and two-phase (γ+γ ), were prepared. The content n the γ+γ alloys was vared to change the volume fracton of the γ -phase. The dffuson couples prepared were γ/γ (C6) and γ/γ+γ (C7 and C8). In Fg. 1, a mcrograph of the C7 dffuson couple after annealng treatment s shown. The expermental dffuson profles of and are shown n Fg. 11, together wth the calculated profles. The dffuson couples tested n the -- system are of Type 1: γ > γ + γ As n the γ+β/γ dffuson couples, there s a regresson of the two-phase regon due to nterdffuson. It s shown n Fg. 12 for the couples C7 (at around 7 µm) and C8 (35 µm). The dffuson paths for these three couples are shown n Fg. 13, wth the calculated phase dagram of the -- system at 11 C. Fg. 1. SEM mcrograph of the dffuson couple C7, annealed at 11 C for 48 h.
(a) (b) (c) Fg. 11. Expermental and calculated composton profles for and of the dffuson couples (a) C6, (b) C7, and (c) C8, all annealed at 11 C for 24, 48 and 72 h, respectvely. Fg. 12. Calculated regresson of the γ -phase n the dffuson couples C7 (11 C, 48 h) and C8 (1 C, 72 h).
Fg. 13. Expermental and calculated dffuson paths of the -- dffuson couples, together wth the calculated sothermal secton of the ternary phase dagram at 11 C. 4.2.3 Dffuson uples n the --- System The dffuson couples C9, C1, and C11 were prepared by dffuson anneal of γ+β - - alloys and γ -- alloys. The -- alloys were selected wth compostons smlar to a typcal commercal overlay coatng (GT29: -6-29-.5Y, nomnal composton n wt.%), but wthout yttrum addtons. The compostons of these alloys are represented n the ternary -- phase dagram (Fg. 4) together wth that of the GT29 alloy. The mcrostructure of these alloys s shown n Fg. 3. The mcrostructure of the dffuson couples after the dffuson anneal s shown n Fg. 14. The dark phase s the ntermetallc β-phase. In all cases, a regresson of the β-phase s observed due to nterdffuson: about 2 µm n dffuson couple C9, 4 µm n C1 and 6 µm n C11. The measured dffuson profles are shown n Fg. 15 (for ) and Fg. 16 (for,, and ), together wth the calculated profles. For and, a good ft s observed n all cases, and also for and n the sngle phase regon. However, the dffuson profles of these elements are overestmated n the two-phase regon. The calculated regresson of the β-phase after 48 h of dffuson annealng at 11 C s shown n Fg. 17. For the dffuson couple C9 (wth the lowest β-phase volume fracton), the calculaton predcts the formaton of a small regon of β wthn the -- alloy, wth a type nterface. However, ths could not be confrmed expermentally. 4.2.4 Dffuson uples n the ---- System Fnally, a two-phase γ+β -- alloy of composton smlar to the overlay coatng GT29 was subjected to dffuson annealng wth a sngle-phase -- alloy (dffuson couple C13). The mcrostructure of ths dffuson couple s shown n Fg. 18. As n all the couples prevously studed, there s a regresson of the β-phase due to nterdffuson. The composton profles are shown n Fg. 19 together wth the calculated profles. For and, the followng three lnes are represented: average calculated composton; and calculated composton of the two phases γ-fcc and β-bcc. though there s some scatter n the measured compostons, the agreement wth calculatons s reasonably good, especally for. The dffuson of s overestmated n the calculatons. The calculated regresson of the β-phase s shown n Fg. 2.
(a) (b) (c) Fg. 14. SEM mcrograph of the dffuson couples (a) C9, (b) C1, and (c) C11, all annealed at 11 C for 48 h. The cast mcrostructure of the left-hand alloys of the couples s shown n Fg. 3.
(a) (b) (c) Fg. 15. Expermental and calculated composton profles for of the dffuson couples (a) C9, (b) C1, and (c) C11, all annealed at 11 C for 48 h.
(a) (b) (c) Fg. 16. Expermental and calculated composton profles for, and of the dffuson couples (a) C9, (b) C1, and (c) C11, all annealed at 11 C for 48 h. Fg. 17. Calculated regresson of the β-phase n the dffuson couples C9, C1, and C11, annealed at 11 C for 48 h.
Fg. 18. SEM mcrograph of the dffuson couple C13, annealed at 11 C for 72 h. Fg. 19. Expermental and calculated composton profles of the dffuson couple C13, annealed at 11 C for 72 h. Fg. 2. Calculated regresson of the β-phase n the dffuson couple C13, annealed at 11 C for 72 h.
4.3 Lfe Assessment of MY atngs In land-operated gas turbnes, nterdffuson between the coatng and the substrate s more ntensve at hgh temperatures. In the absence of spallaton (.e., n turbnes operated n the steady state) the followng two crtera have been proposed for defnng the onset of coatng falure: 1) a crtcal content n the surface [5] ; and 2) depleton of the β phase. [4] Interdffuson s the man factor of loss n the coatng, hgher than that produced by oxdaton. Whle recognzng that dffuson of and n the dffuson couples that were examned s n some cases mscalculated wth the current knetc descrpton, both the dffuson of and the regresson of the β-phase are very well-predcted. Ths gves an opportunty for obtanng, at least, an estmate for the lfetme of the overlay coatngs. Lfetme estmatons have been done usng the crtera of the β-phase depleton n the coatng. Oxdaton has not been consdered n ths model, but t could be easly taken nto consderaton to refne the model. As a reference, the substrate studed has been the -based superalloy GTD111 (chemcal composton n wt.%: -9.5-14-3.-3.8W-1.5Mo-4.9-.1C), but smplfed accordng to the avalable thermodynamc data n the TCNI1 database, [6] n whch there s currently no nformaton for Mo and C. Ths s a two-phase alloy (γ+γ ). The selected reference coatng has been the GT29 overlay coatng (chemcal composton n wt.%: -29-6-.5Y), but t has been smplfed by takng away yttrum from the calculatons. Ths s a two-phase alloy (γ+β). The calculatons have been done supposng sothermal nterdffuson between an overlay coatng of varyng thckness (1-2 µm) wth a substrate of 1 mm thckness. The onset of the coatng has been supposed to be the tme for depleton of the β-phase n the coatng. Results are shown n Fg. 21. Such a fgure can be used as an ad to the determnaton of the lfetme of a selected coatng. Fg. 21. Lfetme estmaton of a GT29 overlay coatng over a 1 mm -based superalloy GTD111. Two dfferent coatng thcknesses are shown. atng lfetme s calculated as the tme for depleton of the B2 phase n the coatng. 5. nclusons Several dffuson couples n the ---- system have been studed theoretcally and expermentally at 11 C. Recently developed thermodynamc and knetc databases of
these systems have been used for the smulatons. The system -- has been especally revewed, showng that the current thermodynamc descrpton behaves reasonably well, at least for the γ+β regon. The predcted dffuson profles for show a very good ft to the expermentally measured compostons. For other elements such as and, the tendency s clearly predcted, although the current knetc descrpton cannot ft the expermental profles. Ths suggests that a revson of these mobltes should be carred out. Acknowledgements The authors are grateful for fundng of ths work to the electrcal company Iberdrola S.A. One of the authors (B.N.) also acknowledges the Asocacón de Amgos de la Unversdad de Navarra for a research grant. References 1. K. S. Chan, N. S. Cheruvu, and G. R. Leverant: atng lfe predcton for combuston turbne blades, J. Eng. Gas Turbnes Power (Trans. ASME), 1999, 121(3), pp. 484-488. 2. Y. Itoh and M. Tamura: Reacton dffuson behavors for nterface between -based super alloys and vacuum plasma sprayed MY coatngs, J. Eng. Gas Turbnes Power (Trans. ASME), 1999, 121(3), pp. 476-483. 3. D. F. Susan and A. R. Marder: - composte coatngs: dffuson analyss and coatng lfetme estmaton, Acta Mater., 21, 49(7), pp. 1153-1163. 4. E. Y. Lee, D. M. Charter, R. R. Bederman, and R. D. J. Ssson: Modellng the mcrostructural evoluton and degradaton of M---Y coatngs durng hgh temperature oxdaton, Surf. at. Technol., 1987, 32, pp. 19-39. 5. J. A. Nesbtt and C. A. Barrett: Predctng the oxdaton-lmted lfetme of beta-, n Proceedngs of the Frst Internatonal Symposum on Structural Intermetallcs, R. Darola, ed., Champon, PA, USA, 1993, pp. 61-69. 6. N. Dupn and B. Sundman: A thermodynamc database for -base superalloys, Scand. J. Metall., 21, 3(3), pp. 184-192. 7. C. E. Campbell, W. J. Boettnger, and U. R. Kattner: Development of a dffuson moblty database for -base superalloys, Acta Mater., 22, 5(4), pp. 775-792. 8. J. E. Morral, J. Cheng, A. Engström, and J. Ågren: Three types of planar boundares n multphase dffuson couples, Scr. Mater., 1996, 34(11), pp. 1661-1666. 9. B. Sundman, B. Jansson, and J.-O. Andersson: Thermo-Calc Databank System, Calphad, 1985, 9(2), pp. 153-19. 1. A. Borgenstam, A. Engström, L. Höglund, and J. Ågren: DICTRA, a Tool for Smulaton of Dffusonal Transformatons n loys, J. Phase Equlbra, 2, 21(3), pp. 269-28. 11. K. Ishkawa, M. Ise, I. Ohnuma, R. Kanuma, and K. Ishda: Phase equlbra and stablty of the BCC alumnde n the -- system, Ber. Buns./Phys. Chem., 1998, 12(9), pp. 126-121. 12. N. Dupn: ntrbuton à l'évaluaton thermodynamque des allages polyconsttués à base de nckel, Ph.D. Thess, Insttut Natonale Polytechnque de Grenoble, France, 1995.
13. N. Dupn and I. Ansara: Thermodynamc assessment of the - system, Rev. Metal., 1998, 95(9), pp. 1121-1129. 14. J.-O. Andersson and J. Ågren: Models for numercal treatment of multcomponent dffuson n smple phases, J. Appl. Phys., 1992, 72(4), pp. 135-1355. 15. A. Engström and J. Ågren: Assessment of dffusonal mobltes n face-centered cubc - - alloys, Z. Metallkd., 1996, 87(2), pp. 92-97. 16. N. Matan, H. M. A. Wnand, P. Carter, M. Karunaratne, P. D. Bogdanoff, and R. C. Reed: A coupled thermodynamc/knetc model for dffusonal processes n superalloys, Acta Mater., 1998, 46(13), pp. 4587-46. 17. B. Jönsson: Assessment of the mobltes of, Fe and n bnary fcc -Fe and - alloys, Scand. J. Metall., 1995, 24(1), pp. 21-27. 18. A. Engström and J. Ågren: Smulaton of Dffuson n Multcomponent and Multphase Systems, Defect and Dffuson Forum, 1997, 143-147, pp. 677-682. 19. N. L. Peterson and S. J. Rothman: Impurty dffuson n umnum, Phys. Rev. B, 197, 1, pp. 3264-3273. 2. A. Engström: MOB2 loy Moblty Database, Thermo-Calc Software, Stockholm, Sweden, 1999. 21. A. Engström: Interdffuson n multphase, Fe-- dffuson couples, Scand. J. Metall., 1995, 24(1), pp. 12-2. 22. Z. Hashn and S. Shtrkman: A varatonal approach to the theory of the effectve magnetc permeablty of multphase materals, J. Appl. Phys., 1962, 33(1), pp. 3125-3131. Appendx: Knetc Parameters for the fcc Phase l parameters are gven n J mol 1. Moblty of 4 Q = 142 + RT ln(1.71 1 ) [15] 4 Q = 286 + RT ln( 3.5 1 ) [2] Q = 235 82 T [15] 4 Q = 284 + RT ln( 7.5 1 ) [15] Q = Q [18], A = 335 [15], A = 413 91. 2 T [15] A, = 335 [16] A, = 532 [15], A = 532 [16] Moblty of 2 Q = 1748 + RT ln( 4.64 1 ) [19] Q = 286175 76. T [7] Q = Q [18] Q = 284169 67. 6 T [7] Q = Q [18], A = 1787 11. 5 T [7] Moblty of Q = 2617 + RT ln(.64) [15] Q = 24694 11 T [7] Q = 235 82. T [17] Q = 287 64. 4 T [17]
Q = Q [18], A = 487 [15], A = 118 [15] A, = 68 [17] Moblty of 4 Q = 1459 + RT ln( 4.4 1 ) [15] Q = 27348 87. 3 T [7] Q = 235 82. T [17] Q = 287 69. 8 T [17] Q = Q [7], A = 211 [15], A = 113 + 65. 5 T [15], A = 7866 + 7. 65 T [7] A, = 81 [17], A = 81 [16] Moblty of Q = Q [18] Q = Q [18] Q = Q [18] 5 Q = 2569 + RT ln( 8.6 1 ) [18] Q = Q [18], A = 118 [16], A = 487 [16], A = 68 [16], A = 211 [16]