INFLUENCE OF RUTHENIUM ON TOPOLOGICALLY CLOSE PACKED PHASE PRECIPITATION IN SINGLE-CRYSTAL NI-BASED SUPERALLOYS: NUMERICAL EXPERIMENTS AND VALIDATION

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1 INFLUENCE OF RUTHENIUM ON TOPOLOGICALLY CLOSE PACKED PHASE PRECIPITATION IN SINGLE-CRYSTAL NI-BASED SUPERALLOYS: NUMERICAL EXPERIMENTS AND VALIDATION R. Rettg and R.F. Snger Insttute of Scence and Technology of Metals; Unversty of Erlangen; Martensstr. 5; D-9158 Erlangen, Germany Keywords: precptaton, modelng, CALPHAD, TCP-phases, ruthenum Abstract The suppresson of topologcally close-packed phases (TCP) n nckel-based sngle-crystal superalloys by the addton of ruthenum s modeled wth a fully multcomponent mesoscale precptaton model based on the numercal Kampmann-Wagnermethod usng thermodynamc CALPHAD-calculatons. For the applcaton of the model n ruthenum-contanng superalloys, moblty assessments of the bnary systems nckel-ruthenum (- Ru) and nckel-rhenum (-Re) were performed to create a new moblty database. It s postulated that the domnatng effect of ruthenum regardng more sluggsh TCP-phase precptaton s a change of nterface energy reducng the number of precptates nucleatng. The precptaton sequences occurrng durng TCPphase precptaton can be explaned usng CALPHAD thermodynamcs. Introducton Rhenum-contanng sngle crystal superalloys have ganed great nterest n the last two decades due to ther ncreased creep strength [1]. Ths leads to a consderable ncrease of the turbne blade operaton temperature n statonary and aeroengne gas turbne applcatons. As effcency s drectly related to the turbne nlet temperature, the turbne effcency s rased and emssons are decreased [2]. Besdes the postve effects of Re on the deformaton rate, t has been frequently reported that Re strongly decreases the alloy stablty and promotes precptaton of brttle topologcally close packed (TCP) phases [3-8]. TCP precptaton s hghly undesrable and eventually lmts the amount of Re that can be added to advantage: On the one hand Re, whch preferentally enters the TCP-phases, s removed from the matrx [9, 1] lowerng the soluton strengthenng effect, whle on the other hand the brttle and needle-lke precptates may grow to consderable sze where they act as crack ntaton stes [6, 7, 1]. One promsng soluton s the addton of ruthenum to the alloy. It s now wdely accepted that ths element strongly decreases the susceptblty to TCP-phase precptaton after Re addton. Alloys contanng rhenum and ruthenum show superor creep propertes [11, 12]. Heckl et al. [13] concluded that wth addton of 1 at-% Re the maxmum applcaton temperature can be ncreased by 87 K. Even an addton of 1 at-% Ru rases the lmt by 38 K n low Re-contanng alloys. Nevertheless concerns are rsng due to the very hgh prce of both elements, whch requres careful optmzaton of the alloy composton [14]. The detaled mechansms of the Ru-effect are stll under dspute [9, 11, 15-19], because the expermental nvestgaton of the retarded precptaton process s dffcult and the alloy system s very complex. In the followng, numercal smulaton wll be employed to shed some lght on the Ru effect. Thermodynamc modelng Numercal smulaton The CALPHAD-method (Calculaton of Phase Dagram) allows not only the calculaton of phase dagrams, but the dervaton of thermodynamc propertes n general, lke drvng forces or phase compostons. The basc dea of the CALPHAD-method s the numercal determnaton of the phase compostons wth mnmum total Gbbs enthalpy n the system.e. the equlbrum state. For ths purpose, the Gbbs free enthalpy of the dfferent phases s modeled as the sum of the Gbbs free enthalpes of the chemcal elements, the deal and the non-deal mxng enthalpy. Due to the latter term, the relaton must be ftted to expermental results and those parameters are stored n thermodynamc databases. For further detals on the CALPHAD-method, the reader s redrected to standard textbooks. In the present work, the ThermoCalc (verson R) software nterface TC-API (verson 4, ThermoCalc, Stockholm, Sweden) was used together wth the commercal thermodynamc database TT7 (ThermoTech Ltd, Surrey, UK) [2] for all CALPHAD-calculatons. Dffuson modelng The dffuson n multcomponent systems (n elements ncludng ) s descrbed by the extended Fck s law, where j k s the dffuson flux of element k, c j s the concentraton of the element j n and D the matrx of the nterdffuson coeffcents [21]. The kj dstance s defned as x. The non-dagonal elements of ths matrx are the so-called cross-dffuson coeffcents. n1 c n j jk D (1) kj j1 x The multcomponent extenson consders not only the gradent of the dffusng element k but of all elements. It s more convenent to express dffuson wth the dffuson mobltes M, as rather than (n-1)x(n-1) dffuson coeffcents, only (n-1) mobltes have to be assessed. The ntrnsc dffuson coeffcent and the moblty are connected by a thermodynamc factor / x, where x j j s the molar fracton of element j. V Therefore, the ntrnsc dffuson coeffcent D can be kj expressed as: n V Dkj k xk xm (2) x 1 j 25

2 Ths descrbes the dffuson n the volume-fxed frame of reference and can be converted to the nterdffuson coeffcent n D, whch s obtaned from dffuson experments, as follows: kj n V V D D D (3) kj kj kn k n eq. 2 s the Kronecker symbol. The mobltes M have to be assessed wth respect to the dependency on composton and temperature and are stored n moblty databases. The moblty can be descrbed by a Boltzmann-approach wth the actvaton energy Q and the frequency factor, whch depends on the lattce parameter a and the jump frequency of the atoms: Q M exp (4) RT RT a 2 (5) Followng other work, s set to 1 because the absolute values of the parameters are of no mportance. In ths case the assessment of the mobltes can be reduced to the temperature and concentraton dependency of Q. In analogy to the classcal CALPHADapproach, ths dependency s successfully modeled wth a Redlch-Kster-polynomal. Ths allows assessng the model j parameters Q and k pj A wth the same optmzaton software as used for thermodynamc database development: j k pj Q x Q x x A x x k (6) j p j p j j p j p k In analogy to [22], pj j A s assumed to be constant and Q s modeled wth a lnear dependency on temperature: j j j Q V V T (7), A, B The parameters V and, A V have to be consstent wth, B exstng data n other bnary systems -X n order to ntegrate them nto one database. For all assessments, the software code DICTRA verson 24 (ThermoCalc, Stockholm, Sweden) was used and the results were ntegrated nto the exstng database from [22]. In the smulatons, the mobltes were agan obtaned from the database wth the programmng nterface TC-API. Precptaton knetcs modelng Due to the avalablty of the CALPHAD-method wth sgnfcant thermodynamc models, meanngful precptaton models can be developed even for complex multcomponent systems. The man challenge of these systems s that the composton at the nterface between matrx and precptate depends on a complex set of equatons descrbng flux balances and thermodynamc equlbrum. In the present work the fully multcomponent precptaton model developed n [23] was appled, whch s based on the numercal Kampmann-Wagner-method. In general, use of the numercal Kampmann-Wagner method s an alternatve to the phase-feld method. Here, the Kampmann-Wagner method s chosen because long-term smulatons wth phase feld over thousands of smulaton hours n multcomponent systems are stll very challengng due to the long computaton tmes. In the followng, only a short overvew of the multcomponent numercal Kampmann-Wagner method shall be presented; detals on theory and mplementaton can be found n [23]. It was mplemented usng MATLAB 27b (MathWorks, Ismanng, Germany). The basc dea s to group the precptates nto a number of classes; each contans all partcles nucleated n a certan tme step. All these partcles share the same concentraton and sze. In each tme step, nucleaton and growth are consdered separately (see fgure 1). Based on the regularly updated nucleaton rate, t s decded f a new precptate class s formed n the tme step. After ths step, the current growth rate of the already exstng precptate classes s calculated wth a fully multcomponent growth law. Next the matrx concentraton s adapted, because the matrx s depleted due to the precptaton. Ths depleton causes a steady change of precptaton drvng force as the system approaches equlbrum. start nucleaton growth matrx concentraton change tmesteps Fgure 1. Basc algorthm of the mesoscale Kampmann- Wagner precptaton model. The major model parameters are the energy of the nterface between matrx and precptate and the number densty of avalable nucleaton stes. The model s very senstve to both. Number densty can be estmated from metallographc analyss of the precptates, but t must be consdered that t s also dependng on the drvng force for precptaton [23]. The second parameter, the nterface energy, cannot be determned drectly by expermental methods. It s therefore most often ganed from fttng expermental results to the precptaton model. Examples can be found n [24, 25] as well as n ths work. As an alternatve, calculatons wth ab-nto methods are emergng but these methods can stll not be appled to complex multcomponent alloy systems wthout dffcultes. The precptaton model from [23] allows the tme-dependent calculaton of TTT-dagrams, drvng forces, precptate and matrx concentratons and the length of precptates n complex alloy systems for sngle precptate phases as well precptaton sequences. Experments new precptate class? exstng partcles In the followng, the results from the calculatons wll be compared to experments, mostly taken from the work of our own research group, e.g. [1, 16, 26]. Typcally, precptaton of needle-lke TCP-phases wth lengths of up to 5 µm or more s observed n the bulk. However, so called TCP-phase cell colones wth a comparatvely coarse mcrostructure also can be found at large-angle gran boundares. 26

3 The mechansm of formaton s smlar to the secondary reacton zone (SRZ) whch s often observed beneath thermal barrer coatngs [26]. Oversaturaton of the -matrx as well as nterface stresses cause a dscontnuous transformaton of the two-phase / -mcrostructure nto a cellular 3-phase structure wth a - matrx and lamellar - and TCP-phase precptates. The reacton can be descrbed as [26]: (matrx) + (precp.) (matrx) + (precp.) + TCP (8) The cell colony s growng away from the orgnal gran boundary wth a contnuous reacton front. Ths type of phase transformaton was mostly found n 3 rd generaton superalloys contanng 6 wt-% Re. An nterestng aspect of the dscontnuous transformaton s that t allows for a relable determnaton of TCP-phase fracton as well as phase composton n equlbrum, as t obvously represents the fnal stage of the phase transformaton [26]. Ths s smlar to eutectod transformatons n steels. Due to the large dmensons, the phase compostons can be easly measured wth the mcroprobe (EPMA) method transmsson electron mcroscopy (TEM) s not requred. Another advantage s the shorter tme requred for the reacton to occur compared to bulk dscontnuous transformaton. As such, n the present study cell colones were used for obtanng the TCP-phase fracton as a functon of the Rucontent of the alloy. The measured TCP-phase fractons were evaluated by mage analyss from SEM-mages. Results In ths study all requred propertes and parameters for understandng the nfluence of Ru on TCP-phase precptaton usng a fully multcomponent model are derved and verfed systematcally. At frst knetc and thermodynamc databases are developed, then the major parameters of precptaton (nterface energy and nucleate densty) are analyzed n a parameter study and the nfluence of ruthenum on the TCP-phase precptaton s nvestgated usng the developed parameters. Fnally the thermodynamcs of the TCP-phase precptaton sequences are examned. Moblty database for ruthenum-contanng superalloys An approprate moblty database s requred for precptaton modelng. In the feld of nckel-based superalloys, a publshed database from [22] for the elements Al Co Cr Hf Mo Re Ta T W exsts. It has been wdely appled, but a relable assessment of the mobltes n the system -Ru s stll mssng. Thus an assessment of the bnary system -Ru was performed, and due to the mportance of rhenum n the presented model, the system -Re was reassessed. The work of [22] and others proved that already by ntegratng moblty descrptons of the bnary subsystems, t s possble to develop a relable dffuson database. Both bnary models were desgned for ncorporaton nto the exstng database by choosng the model parameters for pure dentcal to those of [22]. The assessments were performed wth the expermental data gven n table I and were based on the moblty model descrbed n a prevous secton. Data at temperatures lower than 9 C was not consdered, because [22] rased concerns about gran boundary dffuson below that temperature. All requred thermodynamc data was taken from the database [2]. a) b) lg(d Ru,Ru ) / lg(m2 s -1 ) lg(d Re,Re ) / lg(m2 s -1 ) Hobbs et al. Mabrur et al. Karunaratne et al. 13 C 125 C 12 C 11 C 1 C 9 C Ru / wt-% -13 Hobbs et al. Mabrur et al. Karunaratne et al C 125 C C C C Re / wt-% 8 1 Fgure 2. Assessment of the dffuson coeffcents n the bnary systems (a) -Ru and (b) -Re. The DICTRA-model (sold lnes) s compared to the expermental data from [17, 27-29]. The datasets descrbe well all experments. The results of the assessments n the system -Ru are presented n fgure 2a and the assessed parameters are gven n table II. Ths dataset s consstent and fts well to lterature data from [17, 28, 29]. The derved model can reasonably be extended far nto the metastable regon wth hgh ruthenum contents. Ths s a prerequste for the applcaton of the model n a multcomponent database. The assessed dataset for the system -Re also fts well to the expermental data (see fgure 2b and table II). It fully confrms the assessment from [22]. 27

4 Table I: Expermental data used for the assessment of the bnary systems -Re and -Ru wth estmated errors. source coeff. error conc. temp. / C error [3] [17] [27] [29] [17] [28] [29] D ±1% n * D Re,Re ±1% D Re,Re ±1% D Re,Re ±2% D ±1% Ru,Ru D Ru,Ru ±1% D Ru,Ru ±2% 8 wt-% 1 wt-% 5 at-% 8 wt-% 1 wt-% 5 at-% ±5 C ±5 C ±5 C 125 ±5 C ±5 C ±5 C 125 ±5 C Table II: Assessed parameters for dffuson moblty n the bnary systems -Re and -Ru above 9 C. DICTRA-nomenclature param. value rhenum MQ(FCC_A1&Re,:VA) Q T MQ(FCC_A1&Re,Re:VA) MQ(FCC_A1&Re,,Re:VA;) MQ(FCC_A1&,Re:VA) MQ(FCC_A1&,,Re:VA;) ruthenum MQ(FCC_A1&Ru,:VA) MQ(FCC_A1&Ru,Ru:VA) MQ(FCC_A1&Ru,,Ru:VA;) MQ(FCC_A1&,Ru:VA) MQ(FCC_A1&,,Ru:VA;) Modelng TCP-phase thermodynamcs Re Re Re Re, Re Re Re, Q T A Q T A Q T Q T Ru Ru Ru Ru, Ru Ru Ru, A -177 Q T A In ths secton, the results of the thermodynamc calculatons are verfed and the nfluence of Ru s nvestgated. In a later secton the study s extended towards the ntegrated modelng of precptaton knetcs and thermodynamcs. Equlbrum TCP phase fracton n a varety of alloys. At frst, the thermodynamc modelng capabltes are evaluated n a general way. Results from the CALPHAD-calculaton (database TT7 [2]) are compared wth expermental observatons n a large number of expermental alloys (EROS-alloys) reported prevously by ths research group (Volek et al. [1]). The composton range of the alloys nvestgated s gven n Table III. Fgure 3 shows the probablty of fndng expermentally TCP-phases versus a certan calculated TCP-phase fracton. The probablty s defned as the rato of alloys wth TCP-phases detected compared to the total number of alloys nvestgated. For the evaluaton, the alloys were grouped n dependence of the CALPHAD-calculated TCP-phase fracton. For example all alloys wth 5 6 molar percent of TCPphases are represented by the 6% data pont. It s very clear from the dagram that there s a good correlaton between a large TCPphase fracton calculated wth CALPHAD and the expermental observaton of TCP-phases. Ths emphaszes the valdty of the thermodynamc calculaton approach. However, as wll be shown below, knetcs must be consdered, too. exp. probablty of TCP phases / % smulated TCP-phase fracton / mol-% Fgure 3. Correlaton of the CALPHAD-smulated TCP-phase fracton and the probablty of expermental observaton of TCP-phases from Volek et al. [1] (exposure temperatures C and exposure tmes 5 5 h). There s a clear correlaton between smulated phase fracton and TCP-phase occurrence n the experments. Effect of Ru on TCP-phase fracton n equlbrum. The equlbrum TCP-phase fractons were taken from work publshed prevously by our group [26]. The TCP-phase fracton n cell colones was measured for dfferent expermental ASTRA1-2x superalloys (x =, 1, 2 at-% Ru) as descrbed above. The alloy compostons can be found n table III. TCP-phase fracton / vol-% experment smulaton Ru / at-% Fgure 4. Measured equlbrum phase fracton of the TCPphases n the ASTRA1-2x alloys (x =, 1, 2 at-% Ru) at 95 C (expermental data: [26]) n comparson to calculatons wth CALPHAD (database: TT7). The phase fractons have been estmated from fast growng TCP-phase colones at the gran boundares. The equlbrum phase fracton s strongly reduced by addton of ruthenum. 28

5 The measured values are compared to thermodynamc equlbrum CALPHAD-predctons usng the database TT7 (see fgure 4). The experments ndcate a strong reducton of TCP-phase fracton wth ncreasng Ru-content. In contrast to the experments, the CALPHAD-calculatons do not show any sgnfcant dependency. A further fndng n [26] was that the addton of 1 at-% Ru ncreased the average TCP-nucle dstance n the cell colony from 3.2 µm to 15.6 µm. Ths corresponds to a reducton of the nucle densty from m -3 to m -3. Modelng precptaton knetcs: Senstvty study for nterface energy and nucle densty The senstvty of the precptaton model [23] regardng ts two major parameters s examned n order to prepare the calbraton of the model. Interface energy and nucle densty are almost mpossble to be determned expermentally. In fgure 5 the nfluence of the nucle densty on the precptaton knetcs (a) and the nterface energy on the TTT-dagram (b) s demonstrated. a) b) temperature / C P-phase fracton / vol-% tme / h Jm m m m Jm Jm tme / h Fgure 5. Senstvty study on the nfluence of the major model parameters: (a) Nucle densty (phase fracton at 11 C) and (b) nterface energy (TTT-dagram wth 1 vol-% P-phase). Both calculatons were performed for ASTRA1-2. All other parameters remaned unchanged and are documented n table IV. Both parameters nvestgated obvously have a strong mpact. The nucle densty mostly nfluences the precptate phase fracton at a certan tme, whle the nterface energy has a strong nfluence on the temperature of maxmum transformaton rate ( nose temperature ). Comparng two alloys wth dfferent nucleate denstes assumng otherwse unchanged growth condtons, the alloy wth the larger nucleate densty has a larger precptate fracton after a certan tme. The effect of nterface energy can be explaned n the followng way: A larger value of nterface energy ncreases the actvaton energy for nucleaton thus requrng longer undercoolng resultng n a lower nose temperature. The nucleate denstes N and nterface energes chosen n fgure 5 are n a range whch s typcal for TCP-phase precptates. The nterface energes are n between those for coherent and semcoherent nterfaces. The mean dstance of the precptates s gven by 3 1/ N, whch means that nucleate denstes of 1 16 m -3 and 1 14 m -3 correspond to 4.6 µm and 21 µm, respectvely. Modelng precptaton knetcs: Ru-nfluence on the TCP-phase precptaton The precptaton process s controlled by the thermodynamc drvng force, by nterface energy and dffuson rate. Ruthenum may nfluence all of them. The alloys TMS-121 ( wt-% Ru), TMS-138 (2 wt-% Ru) and TMS-138+ (2.5 wt-% Ru, see table III) were chosen for the calculatons because for them the TCPphase precptaton ncludng nucleaton was already thoroughly nvestgated expermentally by Sato et al. [18, 19]. In these alloys, P-phase precptaton domnates. Sato et al. showed that Ruaddtons have a strong mpact on TCP-phase formaton. Table III. Composton of the alloys used n the present study. All values are gven n wt-%. For the EROS-alloy seres the mnmum / maxmum compostons are noted. The TMSalloys contan addtonally.1% Hf. alloy Al Co Cr Mo Re Ru Ta W EROS * ASTRA ASTRA ASTRA TMS TMS TMS * addtonally.8 wt-% C,.8 wt-% Zr Fgure 6 presents the drvng force of P-phase precptaton calculated wth the CALPHAD-method (database TT7). These results are later on used n the precptaton model. It s apparent that the drvng force s decreasng wth ncreasng temperature. There s only a small dfference n the drvng force for TCPphase precptaton between the Ru-free and the Ru-contanng 29

6 alloy. The dfference s much too small to explan the strong reducton n TCP-precptaton wth Ru-addton. Ths result s smlar to the calculaton of equlbrum phase fractons n the pror secton (see fgure 4). It s not clear at ths pont how to explan the dscrepancy wth the experments. Ether the CALPHAD-smulaton underestmates the effect of Ru on the thermodynamc drvng force or there s some other mportant effect of Ru. drvng force / kj/mol wt-% Ru wt-% Ru temperature / C Fgure 6. Thermodynamc (chemcal) drvng force of P-phase precptaton calculated wth CALPHAD (database: TT7) n the alloys TMS-121 ( wt-% Ru) and TMS-138+ (2.5 wt-% Ru) wth dfferng ruthenum contents. The smulatons ndcate only a small dfference, whch cannot be confrmed by experments. precptate length / µm 3 experments 25 smulatons % Ru 2. % Ru tme / h Fgure 7. Calculated precptate length as a functon of annealng tme at 11 C. The smulatons are compared to expermental results from [19]. The precptates n the alloy TMS-121 ( wt-% Ru) are represented by closed ponts and a contnuous lne, whle those n TMS-138 (2. wt-% Ru) are ndcated by open ponts and the dashed lne. The precptates n the Ru-contanng alloy have much larger nterface energy. Fgure 7 shows the results for the fnal smulaton of TCP-phase precptaton n alloys wth dfferent Ru-contents applyng the model from [23]. They are compared to measurements from Sato et al. [18, 19]. The ntal matrx concentraton n the smulaton s set to the estmated dendrte core composton (see table IV), because the TCP-phases occur mostly n ths regon, where the drvng force s hgher even after heat treatment due to resdual segregaton of Re and W. The segregaton of all other elements can be neglected. Good agreement wth Sato s results can be acheved wth the nucleate denstes and the nterface energes gven n table IV. All other requred parameters are also noted there. The nucleate denstes are consstent wth the values whch can be derved from the expermental work of Sato et al. ( m -3 wthout Ru and m -3 wth Ru). The experments could only be matched reasonably f much larger nterface energy s assumed for the Ru-contanng alloy. Modelng thermodynamcs of precptaton sequence Prevously we assumed the type of TCP-phase precptaton to be known n advance. However, there are a multtude of phases and t s n general not smple to predct whch TCP-phase wll form. Addtonally, complex precptaton sequences are common because metastable phases nucleate frst due to coherent,.e. low energy nterfaces. The stepwse precptaton process then progresses towards energetcally more stable phases wth sem- or ncoherent nterfaces nucleatng at the nterface of the prevously formed coherent phases. a) b) Gbbs free enthalpy / J mol -1 actvaton energy / ev step 2. step temperature / C P drect P ndrect temperature / C Fgure 8. (a) Calculated Gbbs free enthalpy of the phases n the precptaton sequence of the TCP-phases and (b) actvaton energes for nucleaton n the alloy ASTRA1-2. The ndrect precptaton wth the sgma phase as a metastable phase s energetcally favorable. P 21

7 The focus of the followng s to show whether t s possble to predct precptaton sequences from CALPHADthermodynamcs. Fgure 8a shows thermodynamc calculatons of the Gbbs free enthalpy of the - and the P-phase n the alloy ASTRA1-2. The results clearly prove that the -phase has a sgnfcantly smaller Gbbs enthalpy and s therefore metastable compared to the P- phase. Ths means that from a thermodynamc pont of vew, the exstence of precptaton sequences for TCP-phases can be ratonalzed and the -phase s expected to be the frst phase to form (provded t features sutable low energy nterfaces). Ths s n accordance wth the expermental observatons [5]. Addtonally, the actvaton energy G * for - and P-phase nucleaton n ASTRA1-2 has been calculated (see fgure 8b) accordng to the relatonshp below, wth beng the nterface energy, G v the CALPHAD-drvng force, G s the msft stran and f het a factor consderng heterogeneous nucleaton: 3 * 16 (9) G 2 3 Gv Gs fhet All requred drvng forces were taken from CALPHADcalculatons; the other parameters are noted n table IV. For smplcty the energy of a coherent nterface s assumed to be.5 Jm -2 and.5 Jm -2 for an ncoherent one. In accordance wth the prevously mentoned smple model of precptaton sequences and expermental observatons from the work of Rae et al. [5], t s assumed that the -phase s coherent and the P-phase s ncoherent n the case of nucleaton n the bulk (drect precptaton). It s further assumed that the P-phase becomes coherent n case of nucleaton at the nterface of the exstng - phase precptates (ndrect precptaton). Fgure 8b shows that based on these smple assumptons dramatc dfferences n the calculated actvaton energy are obtaned. Obvously the probablty for the ncoherent P phase to form drectly n the bulk wll be very low. Table IV. Physcal parameters of the precptaton model. Further detals on the model parameters can be found n [23]. The other parameters are the actvaton energy of selfdffuson n the lattce G t = 255 kj/mol, the strans due to lattce msmatch = 3.6% and the shear modulus G = 7 GPa. The heterogenety factor s set to f het =.2. fgure nucleate densty N / m -3 nterface energy / Jm -2 form factor Φ alloy fg. 5a (P) 2 ASTRA1-2 fg. 5a (P) 2 ASTRA1-2 fg. 5a (P) 2 ASTRA1-2 fg. 5b (P) 2 ASTRA1-2 fg. 5b (P) 2 ASTRA1-2 fg. 5b (P) 2 ASTRA1-2 fg (P) 5 TMS-121* fg (P) 5 TMS-138* fg. 8b -.5 (σ) - ASTRA1-2 fg. 8b -.5(σ, P) - ASTRA1-2 *The concentratons of Re and W are ncreased n the smulaton by a factor of 1.5 respectvely 1.5 compared to the nomnal composton n order to model the ncomplete homogenzaton n the dendrte core of the alloy. The calculatons are thus representatve for the dendrte core. Dscusson Mechansm of suppresson of TCP-phases by ruthenum Precptaton can be separated nto two processes, nucleaton and growth. Ruthenum mght affect both steps. The rate of transformaton and resultng sze dstrbuton of the TCP-phase at a gven tme and temperature s controlled by: 1. nucleaton rate (nucle densty, controlled by dffuson rate and actvaton energy barrer) 2. growth rate (speed of phase nterface, controlled by dffuson rate and drvng force) Extendng the deas from Hobbs et al. [9], the nfluences of ruthenum regardng precptaton mght be due to: 1. change n -phase fracton 2. change n parttonng between - and -phase (reverse parttonng) 3. change n nterface energy between matrx and precptate 4. change of dffusvty The effect of Ru on the -phase plays a major role because many TCP-phase formng elements lke Re and W are hardly soluble n ths phase and the matrx concentraton of these elements depends on the -phase composton and volume fracton. Consequences of Ru addton -phase fracton and reverse parttonng. In the lterature t s controversal as to whether Ru changes the -phase fracton and the parttonng rato of Re between - and -phase. On the one hand, Hobbs et al. [9] observed a reduced -fracton n the alloy SRR3D wth 3 wt-% ruthenum addton compared to the same alloy wthout Ru. On the other hand Neumeer et al. [15] dd not fnd a sgnfcant change n another expermental alloy. There s probably a dependence on the general alloy composton, explanng such dfferent fndngs. Further, the error n the - phase fracton measurements s comparatvely large. The nfluence of the ruthenum concentraton on the / - parttonng rato has been debated for a long tme and reverse parttonng, whch descrbes the ntensfed parttonng of rhenum nto the -phase upon addton of ruthenum, s often gven as the only explanaton for the ruthenum effect [15, 16, 31-34]. The many dfferent results n lterature for a large range of superalloy compostons let us conclude that the reverse parttonng effect s probably strongly dependent on the overall alloy composton. Carroll et al. [35] support ths expermentally as well as our prevous numercal study [36]. There s evdence that reverse parttonng only occurs f the chromum content s rather low. The fundamental queston s how a change of alloy characterstcs may lead to decelerated TCP-phase precptaton. In earler work of the same authors [36], the multcomponent model as used n the present study was appled n a numercal experment addressng ths queston. In that study the -phase fracton was reduced by 5 mol-% (approxmately 5 vol-%) wthout changng any other features n the alloy. In a second experment the parttonng rato 211

8 of Re was reduced by one thrd keepng everythng else constant. Both assumed changes n the alloy are very large and can be taken as upper lmts for what seems lkely. The numercal experments showed that precptaton wll be reduced, but the effect s very small compared to the Ru-effect observed n realty. Thus we conclude that a change of -phase fracton and / -parttonng rato by addton of Ru are not the only reasons for the mportant Ru effect on TCP-phase precptaton. Interface energy. The nterface energy between matrx and TCPphases can be estmated based on the calculatons presented above (see fgure 7 and table IV). The results ndcate a large ncrease of the nterface energy between matrx and precptate wth addton of Ru from.5 to.27 Jm -2. It s very dffcult to compare the values quanttatvely wth lterature results because there s lttle relevant research. Robson et al. and Sourmal et al. found for example Jm -2 for TCP- and Laves-phases n austentc stanless steels [24, 37]. A reason for a change of nterface energy wth addton of Ru mght be the segregaton of Ru nto the matrx / TCP-nterface and thus a local change of the chemstry. Further hgh resoluton observatons have to be conducted n order to prove ths hypothess. Dffuson rate. Hobbs et al. [17] and Mabrur et al. [29] have measured the dependence of the rhenum dffuson coeffcent on the ruthenum content. They found that t s not at all nfluenced by ruthenum. As rhenum s the most mportant TCP-phase former, t seems that the growth rate, whch s dependent on the dffuson coeffcent, s not altered by ruthenum. In accordance wth ths, fgure 7 shows only a moderate nfluence of ruthenum on the growth rate. expermentally prove that the -phase s the frst metastable phase to be formed and later on the equlbrum TCP-phase, whch can be µ- or P-phase dependng on the alloy composton, s nucleated at the -nterface rather than n the bulk n order to save surface energy. Our thermodynamc calculatons support ths nterpretaton because the -phase s a metastable phase n the nvestgated alloy. Addtonally, t became evdent that the stable P-phases (assumng hgh nterface energy) have very large actvaton energy and can hardly nucleate drectly. Conclusons 1. A new moblty database for ruthenum contanng superalloys was developed whch descrbes the -Ru system consstently. 2. Ruthenum affects the TCP-phase precptaton mostly by retardng nucleaton. It s postulated that ths s domnated by an ncrease of nterface energy between matrx and TCPphase on Ru-addton. The nfluence on reverse parttonng and -phase fracton seems to be smaller. 3. The number of nucle s strongly reduced by Ru due to larger actvaton energes, whle the growth rate of the precptates s essentally unchanged. 4. Accordng to expermental results, Ru mght ncrease the thermodynamc stablty of the alloy regardng TCP-phase formaton. 5. The σ-phase s metastable and therefore precptaton sequences of the TCP-phases are allowed by thermodynamcs. Influence of Ru on speed of transformaton The results n the present study are ambguous as far as an nfluence of Ru on the thermodynamcs s concerned,.e. the drvng force for precptaton of TCP-phases seems to be hardly affected. Ths suggests that the explanaton for the reduced rate of TCP formaton mght be a change n nucleaton rate caused by changes n nterface energy. The actvaton energy for nucleaton s controlled by drvng force and nterface energy. Accordng to the dscusson n the prevous secton, the addton of ruthenum probably ncreases the actvaton energy va an ncrease of nterface energy. As such, n the ruthenum contanng alloy, there are less actve nucleaton stes avalable, whch means that less precptates are formed and that the tme to the dentcal precptate fracton s longer, because ndvdual precptates have to grow larger. 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