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 www.thermocalc.com
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.
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;21:948-958. [2] Wagner R, Kampmann R. Homogeneous Second Phase Precptaton. In: Haasen P, edtor. Materals Scence and Technology: A Comprehensve Treatment. Wenhem: Wley-VCH, 1991. p. 213.
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
Introducton: Example of results All above smulatons made under sothermal condtons.
Non-Isothermal Condtons g/g Mcrostructure n U720 L Contnuous coolng at 0.0167 K/s R. Rads et al., Acta Materala, 57(2009)5739-5747
N-8Al-8Cr and N-10Al-10Cr
N-8Al-8Cr and N-10Al-10Cr Exp Contnuous coolng from 1150 to 380 C wth a coolng rate of 14 C/mn.
N-8Al-8Cr and N-10Al-10Cr s = 0.023 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.
N-8Al-8Cr and N-10Al-10Cr Vertcal Secton N-xAl-xCr Thermodynamc drvng force
N-8Al-8Cr and N-10Al-10Cr Thermodynamc drvng force Nucleaton rate
U720L Precptaton Knetcs durng Contnuous Coolng wt.% 1* 2** Al 2.53 2.46 B 0.014 C 0.014 0.025 Co 14.43 14.75 Cr 15.92 16.35 Fe 0.09 0.06 Mo 2.96 3.02 T 4.96 4.99 W 1.26 1.3 Zr 0.035 N Bal Bal g g Databases: TTNI8+MOBNI1 * Rads et al., Superalloys 2008 ** Mao et al., Metall. Mater. Trans. A, 32A(10) 2441(2001)
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+19 78 o C/s 1.625 o C/s 0.217 o C/s 1e+18 0.1 1 10 100 Partcle Radus (nm) Alloy 1 Partcle Sze (nm) 1000 100 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 10 0.1 1 10 100 1000 Coolng Rate ( o C/s) Alloy 1 & 2 s = 0.025 J/m 2
* 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 0.014 C 0.011 Co 14.66 g g Cr 16.14 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
U720L Secondary g Sze After Coolng + Agng 500 Average Sze of Secondary ' (nm) 400 300 200 100 Jackson and Reed Calculated s = 0.025 J/m 2 0 0 50 100 150 200 250 300 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.
1999Noble, Mater Sc Engr, A266, 80-85 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
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
Some example results System Phases Estmaton (J/m 2 ) Lterature (J/m 2 ) Al-L a/d 0.011 0.004 to 0.115 Cu-T Cu/Cu4T 0.035 0.067, 0.031 N-Al-Cr g/g 0.022 0.023 Co-W-C Co/WC 0.68 0.44 to 1.09 Used n Current Calculatons System Phases Estmaton (J/m 2 ) Used (J/m 2 ) N-Al-Cr g/g 0.022 0.023 N-Superalloys(Bulk) g/g 0.03~ 0.06 0.025 N-Superalloys(GB) g/g ~ 0.06 0.06 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
Alloy 282 Mean Partcle Sze (Bulk) CCT Startng Temperature 240 Mean ' Sze (nm) 220 200 180 160 140 120 100 80 constant (0.025 J/m 2 ) model expermental data Temperature ( o C) 1000 980 960 940 920 900 60 40 20 880 860 constant (0.025 J/m2) model expermental data 0 0 400 800 1200 1600 2000 2400 Coolng Rate ( o F/mn ) 840 0 400 800 1200 1600 2000 2400 Coolng Rate ( o F/mn) Al Co Cr Fe Mo T N wt.% 1.5 10.0 19.0 1.5 8.5 2.1 Bal. Databases: TCNI5+MOBNI2 * Expermental data from B. Alexandrov et al., Contnuous heatng and coolng transformaton dagram n N-base superalloy 282, TMS 2011
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
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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
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 * 2 2 1 b Z *2 * 4 4 r a b ) 1 1 / 2 / / n D X X X b a b a a b 2 2 3 * 3 16 m m G V G s Interfacal energy Volume Classc Nucleaton Theory Gran sze, dslocaton densty, etc
Q. Chen, J. Jeppsson, J. Ågren, Acta Mater. 56(2008)1890-1896 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