Thermo-Calc Software. Modelling Multicomponent Precipitation Kinetics with CALPHAD-Based Tools. EUROMAT2013, September 8-13, 2013 Sevilla, Spain

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1 Modellng Multcomponent Precptaton Knetcs wth CALPHAD-Based Tools Kasheng Wu 1, Gustaf Sterner 2, Qng Chen 2, Åke Jansson 2, Paul Mason 1, Johan Bratberg 2 and Anders Engström 2 1 Inc., 2 AB EUROMAT2013, September 8-13, 2013 Sevlla, Span

2 Introducton: CALPHAD CALPHAD method and CALPHAD-based tools play a central role n materals desgn H or S Interfacal energy & Volume & Elastc constants Thermodynamcs: Gbbs energy CALPHAD Phase Feld Method Langer-Schwartz f(r) t Frst Prncples Calculaton r Dffuson: Moblty CALPHAD-type databases where each phase s descrbed separately usng models based on physcal prncples and model parameters assessed from expermental and ab nto data provde fundamental nputs for predctng mcrostructure evoluton and materals propertes.

3 Introducton: TC-PRISMA A general computatonal tool for smulatng knetcs of dffuson controlled mult-partcle precptaton process n mult-component and mult-phase alloy systems. TC-PRISMA s based on Langer-Schwartz theory [1], and t adopts Kampmann-Wagner numercal (KWN) method [2] to compute the concurrent nucleaton, growth, and coarsenng of dspersed phase(s). [1] Langer J, Schwartz A. Phys. Rev. A 1980;21: [2] Wagner R, Kampmann R. Homogeneous Second Phase Precptaton. In: Haasen P, edtor. Materals Scence and Technology: A Comprehensve Treatment. Wenhem: Wley-VCH, p. 213.

4 Introducton: In and Output Input Thermodynamc data Knetc data Alloy composton Temperature - Tme Smulaton tme Property data (Interfacal energy, volume, etc.) Nucleaton stes and related mcrostructure nformaton TC-PRISMA Output Partcle Sze Dstrbuton Number Densty Average Partcle Radus Volume Fracton Matrx composton Precptate composton Nucleaton rate Crtcal radus TTP

5 Introducton: Example of results All above smulatons made under sothermal condtons.

6 Non-Isothermal Condtons g/g Mcrostructure n U720 L Contnuous coolng at K/s R. Rads et al., Acta Materala, 57(2009)

7 N-8Al-8Cr and N-10Al-10Cr

8 N-8Al-8Cr and N-10Al-10Cr Exp Contnuous coolng from 1150 to 380 C wth a coolng rate of 14 C/mn.

9 N-8Al-8Cr and N-10Al-10Cr s = J/m 2 Exp N-8Al-8Cr have larger msft between g and g compared to N-10Al-10Cr. Ths wll gve an elastc energy contrbuton whch has not been consdered n the smulaton.

10 N-8Al-8Cr and N-10Al-10Cr Vertcal Secton N-xAl-xCr Thermodynamc drvng force

11 N-8Al-8Cr and N-10Al-10Cr Thermodynamc drvng force Nucleaton rate

12 U720L Precptaton Knetcs durng Contnuous Coolng wt.% 1* 2** Al B C Co Cr Fe Mo T W Zr N Bal Bal g g Databases: TTNI8+MOBNI1 * Rads et al., Superalloys 2008 ** Mao et al., Metall. Mater. Trans. A, 32A(10) 2441(2001)

13 U720L : Coolng Rate Effect Sze Dstrbuton Mean Partcle Sze 1e+34 Sze Dstrbuton (1/m 4 ) 1e+33 1e+32 1e+31 1e+30 1e+29 1e+28 1e+27 1e+26 1e+25 1e+24 1e+23 1e+22 1e+21 1e+20 1e o C/s o C/s o C/s 1e Partcle Radus (nm) Alloy 1 Partcle Sze (nm) Mao et al. Rads et al. Regresson lne for calculated results Calculated usng Rads et al.'s composton Calculated usng Mao et al.'s composton Coolng Rate ( o C/s) Alloy 1 & 2 s = J/m 2

14 * M.P.Jackson and R.C.Reed, Mater. Sc. Eng. A259(1999)85-97 U720L wt.%* Secondary/Tertary g durng Coolng + Agng Al 2.51 B C Co g g Cr Mo 2.98 S 0.05 T 5.08 W 1.23 N Bal Tme No prmary g s consdered, but g matrx concentraton s adjusted due to prmary g formaton at 1105 o C (based on equlbrum calculaton) Heat Treatment: coolng from 1105 o C to 400 o C, followed by agng at 700 o C for 24hrs

15 U720L Secondary g Sze After Coolng + Agng 500 Average Sze of Secondary ' (nm) Jackson and Reed Calculated s = J/m Coolng Rate ( o C/mn) Smulatons are good for large to ntermedate coolng rate ( > 1 o C/s) Future model mprovements nclude multple nucleaton stes, mean feld devaton, loss of coherency, nterfacal energy varaton, nterface moblty, morphology change.

16 1999Noble, Mater Sc Engr, A266, Estmaton of nterfacal energy Classc or non-classc thermodynamcs Dstrbuton of Al-L a/d nterfacal energy value found n lterature Atomstc modelng - molecular dynamcs and Monte Carlo method Frst prncples

17 Our frst approxmaton For a bnary matrx and precptate of the same structure that can be descrbed by a regular soluton model* s c NZ s N Z A s l E sol E X X ) 2 sol P M Mscblty gap of non-regular soluton phase Matrx and precptate of dfferent structure Multcomponent system E sol * Based on Becker R. Ann Phys 1938;424:128

18 Some example results System Phases Estmaton (J/m 2 ) Lterature (J/m 2 ) Al-L a/d to Cu-T Cu/Cu4T , N-Al-Cr g/g Co-W-C Co/WC to 1.09 Used n Current Calculatons System Phases Estmaton (J/m 2 ) Used (J/m 2 ) N-Al-Cr g/g N-Superalloys(Bulk) g/g 0.03~ N-Superalloys(GB) g/g ~ Interfacal energy shows composton and temperature ndependence Estmated value seems better for gran boundary precptaton n mult-component alloys Further developments nclude dffusveness of nterface, ncoherency, sze effect, gran boundary energy

19 Alloy 282 Mean Partcle Sze (Bulk) CCT Startng Temperature 240 Mean ' Sze (nm) constant (0.025 J/m 2 ) model expermental data Temperature ( o C) constant (0.025 J/m2) model expermental data Coolng Rate ( o F/mn ) Coolng Rate ( o F/mn) Al Co Cr Fe Mo T N wt.% Bal. Databases: TCNI5+MOBNI2 * Expermental data from B. Alexandrov et al., Contnuous heatng and coolng transformaton dagram n N-base superalloy 282, TMS 2011

20 Summary A non-sothermal model has been developed n TC-PRISMA and has been successfully appled to smulate mult-modal partcle sze dstrbuton of g precptates n N-base superalloys More GUI outputs have been provded to facltate separate analyses of partcle sze dstrbuton, mean sze, volume fracton, and number densty A model has been mplemented to estmate the nterfacal energy between matrx and precptate phases

21 Thank You! E-mal:

22 Theory: Conservaton laws T X B B A Lq a b LS (Langer-Schwartz) and KWN (Kampmann and Wagner Numercal) Approach ) ), ( ), ( ), (, t R j t R f t R R t t R f ) ) dr R t R f C C C C 3 0 0, 3 4 a b a a 0 ), ( dr t R f N 0 ), ( 1 RdR t R f N R 0 3 ), ( 3 4 dr R t R f Contnuty equaton Mass balance

23 Models: Multcomponent Nucleaton kt G N Z J s * * exp b ) t J t J S exp 2 1/ 2 2 * 2 1 n n n G kt Z * b Z *2 * 4 4 r a b ) 1 1 / 2 / / n D X X X b a b a a b * 3 16 m m G V G s Interfacal energy Volume Classc Nucleaton Theory Gran sze, dslocaton densty, etc

24 Q. Chen, J. Jeppsson, J. Ågren, Acta Mater. 56(2008) Models: Multcomponent Growth Rate a / b b/ a a/ b c c ) a/ b c M a a/ b )/ r b / a 2s r b V m Advanced Analytcal Flux-balance Approxmaton Smplfed Pseudo-steady state Approxmaton K Gm r 2sV m r Pseudo-bnary dlute soluton Approxmaton Cross dffuson hgh supersaturaton X X X X a a / b b a / b D r a/ b a b X 1 Xe 2sVm exp( ) a b a X X X RTr e e