MICROSCOPIC PHASE FIELD METHOD SIMULATION FOR THE IN SITU TRANSFORMATION OF L1 0 PHASE AND L1 2 PHASE STRUCTURE

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1 d 45 z d 5 H Vol.45 No ; 5 % d x ACTA METALLURGICA SINICA May 2009 pp L1 0 ffi L1 2 ffiff!ß%v οξffiz~ *-( 1) & 4 1,2).2/ 1) 0 ' 1) ), 1) 3+1 1) 1) >ffρykg#ßg!, > ) >ffρykg>ψk±&nvgrs~, > " ψ } Ni 80Al 13Cr 7 2k.mswR, %ff, P h3lχe23 pr0πrp;.ff<,$j*, msν Al 0 Cr χe( (100) 0 (200) (e χe23 ;μpu*i Ni 3(Al, Cr) ffip;br!a. ms., (pul:bt, Al 0 Cr χe( (100) 0 (200) (e 2Φc'ffοfi~k ;, Xz(»(e -5c'ffJ_ο przw/l, }_2Φ c; w~kezdχ3`, 2a cq L1 0 ffiß<<j. T cq/lwzlgp, Al0 Cr χe 2Φc'ff 0-5c'ff( (100) (ej /L, z( (200) (e-j [a, Jffi~ke Dχ3`, L1 0 ffizwp L1 2 ffi`;. Ψ,$J*, χ3`, Ni 80Al 13Cr 7 2k, ß<<J $ } fl± TG111 ρfiw»ffl A ρ#u± (2009) MICROSCOPIC PHASE FIELD METHOD SIMULATION FOR THE IN SITU TRANSFORMATION OF L1 0 PHASE AND L1 2 PHASE STRUCTURE MIAO Shufang 1),CHENZheng 1,2), WANG Yongxin 1),XUCong 1),MARui 1), ZHANG Mingyi 1) 1) School of Materials Science and Engineering, Northwestern Polytechnical University, Xi an ) State Key Laboratory of Solidification Processing, Northwestern Polytechnical University, Xi an Correspondent: MIAO Shufang, Tel: (029) , msf1983@yahoo.cn Supported by National Natural Science Foundation of China (Nos and ) and China Postdoctoral Science Foundation (No ) Manuscript received , in revised form ABSTRACT As a Ni 3 Al precipitation strengthening alloy, Ni Cr Al alloy is one of typical structural materials applied in high temperatures. Much work has been done concerning its structure transformation from fcc to L1 2 during the process of ordering and phase separation. However, the study so far we know on the phase transformation in very early precipitation stage, especially on the phase transformation of unstable pre precipitation phase, was not yet sufficient. Microscopic phase filed method is used for describing the temporal and spatial evolution of atomic site in lattice. This method is employed to study the pre precipitation during the structure transformation from fcc to L1 2 in Ni 80 Al 13 Cr 7 alloy in this paper. The relationship between the occupation probability changes in Al and Cr atoms on (100) and (200) planes respectively and structure evolution of Ni 3 (Al, Cr) will be inveatigated. The simulation results demonstrate that at in very early aging stage, the composition order parameters of Al and Cr atoms keep unchange on both (100) and (200) planes. However their long range order parameters are equal in these two planes and gradually increase with aging time until the first in situ transformation by congruent ordering at that time the L1 0 pre precipitation phase with low long range order is formed. By prolonging aging time, their long range order parameters continue increase once they attain to the respective certain values, the composition order parameters and the long range order parameters of Al and Cr atoms on (100) plane become increasing rapidly but those on (200) plane decreasing quickly, The second in situ transformation occurs and the L1 0 is gradually transformed into L1 2. KEY WORDS microscopic phase field method, in situ transformation, Ni 80 Al 13 Cr 7 alloy, pre precipitation phase * 'OgX hckm }Gff 7 hckm d] W: ]I : , W`ffl ]I : p7ti : 1983 <k, ffl

2 d 5 H *ΨΞ^ :L1 0 I/ L1 2 Ieffffi2_ffl[+#I) lK +JA H_ G6]fl&B%, )K *6Q, 3K**fl8Faa /hffl8mb]7m= =K, }Da /offigfl1<i3ψν3kfl_an, hffl8fl3khbrfl7mk»" ]l7ρ==k (» `ol7k *sk). lπ$ρq]byl7]ρ== Koy 7mKν$ ]-%gfl1_8 [1 3], ΞCK ]3Ha ) m6rfφlc$ρ]keh_8. μc $ρ i]flv 1, ρ==k]]3 a H_8]n t#ω# X &]"^ [4 6]. Ni Al Cr 3l} Uj[]=D3lffiB, ο]- %gfl~ Ni 3 Al [/k]=f/fi=, 5O:xffiff3l d<hkψfi*6q fcc X L1 2 ]a m^οmμ ]nt [7 10], R}x Ni Cr Al 3l;JK, ffik} xkql7ρ==ka gam!nt. )K ]ntq, ψ4a I]})ψΩl7KB* sk]d@f l3ψ <1i;Wfl, ]3ßP7m] K, }fiω-φ}eρ<;] Ua ±x [11]. }Eρ <;]a ±xλ~ψ/ψ4a 1fi4a, KQψ4 a }I)ψρ<;D@f l3ψ <1i;Wfl, ] 3ß7m]ρ<;; fi4a }Iψρ<;@^X3KQ, X] ß7m]ρ<;)Kο"4WX]..M. -%K+ } UWm_K+±, )Afl3l/k *6Q] r H_ r G6bßn i±)y p fifl, ΛAZ3l/k*6Qψf]nßZ@, y fl q_1f%_, )ntkgfl]ψ4a ±)Λ~νst K:±@. fi6&fi-%k+, "*1: Ni 80 Al 13 Cr 7 3lqV*6Q Al 1 Cr ψf) (100) 1 (200) )f] 34RΦΩm!nt Ni 3 (Al,Cr) Kgfl]q<*6. 1 νλfly χ fic»i]x]-%k+1[ffl Khachaturyan [12] BY, Poduri 1 Chen [13,14] qο 1. ο}~ψf3x o»4m]j!/+ μ, ~ψf!$πmψf34j! </Z@, Ω-ΦψfGw d<`ψfψc*6. / U<L», Zb0±S&Φ)}0±S, 9qψf34J!ν z r 9". xbfl3lb%, i p A ( r, t), p B ( r, t) 1 p C ( r, t) Ψ / A, B 1 C ψf) t qξ3x r 4M ]J!, ffl p A ( r, t)+p B ( r, t)+p C ( r, t)=1, ν~%μ»ifj 2 μp ±6. /-Φ].*6, avψpμ E,jN ξ( r, t) Ω1:ZMfi. Qi~ A 1 B ψf] 34J!/ 2 μp μ, ZX-% Langevin ±6 [14] : dp A( r,t) dt = 1 k BT [L AA ( r ) L AB ( r F ) ]+ξ( r, t) dp B( r,t) dt = 1 k BT p B(,t) [L BA ( r ) L BB ( r F ) ]+ξ( r, t) p B(,t) F + p A(,t) F + p A(,t) (1) xq, k B / Boltzmann,fi; L αβ ( r ) }νq4q S7, x α 1 β ψf)»i4m r 1 f]]>j! "],fi [13], α, β=a, B B C; F /ffib]ihffl 8, )G +n CfflCxWm [12] : F = 1 [V AB ( r r )p A ( r)p B ( )+ 2 r V BC ( r )p B ( r)p C ( )+V AC ( r )p A ( r)p C ( )]+ xq, k B T r [p A ( r)ln(p A ( r)) + p B ( r)ln(p B ( r))+ p C ( r)ln(p C ( r))] (2) V αβ ( r )=V αβ ( r ) ch + V αβ ( r ) el (3) V αβ ( r ) ch = W αα ( r )+W ββ ( r ) 2W αβ ( r ) (4) xq, V αβ ( r ) /ψfs Vqfi8, V αβ ( r ) ch /<ik:qfi8, V αβ ( r ) el /S_K:qfi8, W αβ ( r ) /ψfsk:qfi8. ψbflffibq 3 Uψf]$N~HΛ8]Aχ, & fi nfiψfsk:qfin. i V 1 αβ, V 2 αβ, V 3 αβ, V 4 αβ Ψ }f 1, 2, 3, 4 nfiψfsk:qfi8, L»EQ ` ]ψfqfi8&fi6g [13, 15] Q]fix. οx-%s_k:qfi, Π+ψfΨχ]νkß " ]S_K:qfi E el / [16] E el = 1 2 r Fourier >8/ E el = 1 2N V αβ ( r r ) ch + V αβ ( r ) el (5) k V ( k) el p( k) 2 (6) xq, N /»iifi; ffl F 8)i k=0 A4LΛ _, S1ff- f^]e-»z)s1*6qva>ffii; V ( k) el /S_8'r,fi, } V ( r) el ] Fourier >, ).ρn C»z/ V αβ ( k) el M( n) =M el n 2 x n2 y ε2 0 (7) xq, n = k/k, /V ±SQ k ±Q]Q4tμ; n x 1 n y Ψ / n o x 1 y X]Ψμ; ε 0 =da c /(a 0 dc), /ffl 3Ψ ΠM]o»D5Bfi (KQ, a c /^O]o», fi, a 0 /Dffi]o»,fi, c /^O]ψfΨfi).»=S O1o»nC] 8(fi/ 4(C 11 +2C 12 ) 2 M el = C 11 (C 11 + C 12 +2C 44 ) ζ (8) xq, ζ = C 11 C 12 2C 44, }»zb%/s_νqλ _],fi; C i,j }Dffi]S_,fi, L»qufi6G [17] Q]fiH.

3 632 j Λ f Φ d 45 z Zx (4) 1 (5) N`x (2), Y8ZZX]x (2) N `x (1) ßm^ Fourier >, Y8)}0G)f&Φ8 &fi Euler ±6Sh, ZXfl$qΞ]ψf34J!, F Z=qV*6-%kE]q<(O. /οnt7mk]3]].en8fl, Π`Λ6 L1 2 gfll»] dk7].6d(fi. /Q?c-Φ L1 2 gfl dk]3*6qkgfl]a *6, Π`).6d (fiω»=)fim])7ψf dψχ]rφ. 2U.6 d(fi]»jx]x K, RK fl$, K»Jx/ η(i, j) = p(i, j) C(i, j) C(i, j)cos[(i + j)π] (9) x dk7].6d(fi, η(i, j)»z)2 μ dk 7 (i, j) A] dr, p(i, j) /) dk7^oψf) K?4]34J!, C(i, j) / dk7]g?r. x )7.6d(fi, η(i, j)»z dk72fim)7 (i, j) A] dr, p(i, j) /)fim)7^oψf)k?4] 34J!, C(i, j) /^Oψf)fim])7]G?r. οx).6d(fi]l»±, Jv) dk]2 ^B 2 fffλffψf]i=f, uλ~dfiλψffi)7] dr. )fi6q F, )7m]==K]3COD=F] dky L1 0 gfl]fi=, RK dr5b, xcg1v ΩY, fi6qzk1/b dr] L1 0 ρ==k. 2 ΩΠΦ ff ( 1 }x Ni 80 Al 13 Cr 7 3l) 873 K Cm^qV* 61:ZX]ψfq<(. (O&fi »i, q S!. Δt / 0.001, 1:*6νP]ZMfi/ 200!, ψ f34j!~?r»z, οxνh]?rfl$, 4d»i O» Ni ψf,?d»io» Cr ψf, Ξd»iO» Al ψf. /ο8ßq?cef=ρ==k]]3*6, 0M ο(o]xflr. ffl( 1 ΛV, ) t=1200!q, ;v9d] Ni 80 Al 7 - Cr 13 3lffiB]v"Uο l Eψ4a, }v=f _( 1a QνVz] dk, RCqK dr=5b. ο x dk]}0&φ(, Λ~Bv9Uρ==Ky L1 0 gfl, I]3ο Ub dr] L1 0 gflρ==k. μ cqs!fi]0m, 9Uρ==K]fi5[X0y, 9H [X0M, J9χ#ο>μffiB (( 1b), $q dk] drw[x0m. 0MqS!fi, Fψfq<(Λ~~ = (( 1b, c), )ρ==kq'e lgflwfl, I l ο}eψ4a, L1 0 gflρ==k[xq L1 2 gfla, M") t=3000!n, ffibq}v=f <ilμ fl] L1 2 gfl, _( 1c QνVz. μcqs!fi]0 M, <ilμfl] L1 2 dk[xq<ilμfla<, mt]3οmμ]<ilμfl] L1 2 νz. dk, _( 1d μ 1 Ni 80 Al 13 Cr 7 2k( 873 K pu)5 jdffip;' Fig.1 Temporal evolution of the microstructure of Ni 80 Al 13 Cr 7 alloy at 873 K aging for t=1200 step (a), t=2000 step (b), t=3000 step (c) and t=4000 step (d)

4 d 5 H *ΨΞ^ :L1 0 I/ L1 2 Ieffffi2_ffl[+#I) C)ZF].EN±)m!Ψ=3lqV*6Q Kgfl]a. ( 2 / Ni 80 Al 13 Cr 7 3l)qV*6Q Ni 3 (Al, Cr) K73Ψd(fiH.6d(firQΨχμq S] <. ffl(λv, ) t=1200!co, 3Ψd(fiß 1 l <,.6d(fi.=FοMfi, Ccux `3Ψ d<cu. ffl( 1 ΛA, Cq lf Eψ4a, ffl9d] fcc gfla / L1 0 gfl, ]3οb dr ] L1 0 gflρ==k. )CC8, μcqs!fi]0m, 3Ψd(fi=FM]ρn,.6d(fi[X0M, P0 M]!5. M") t=3000!q, dkqya]. 6d(fi panm H, 3Ψd(fi=);v3Ψf Cρn, ß1JXG6H, 9ffi/ d<] r ψf Gw] r, ßP)ψ l7ρ==k]4m lο3ψ ]ρn1i;]wfl, Ccux Kgfl]f}Eψ4 a. 0MqS!fi, 3Ψd(fiMe0M, [X]3< ilμfl] L1 2 gfl dk,.6d(fiw[xfflqyq ffiψ1, m8)>μ dk 7JXG6. ( 3 / Ni 80 Al 13 Cr 7 3lqV*6 Ni 3 (Al, Cr) K Q Al ψf) (100) 1 (200) )f]3ψd(fi1.6 d(fiμqs] <. ffl(λv, M") t=1200!co, Ni 3 (Al,Cr) KQ Al ψf) (100) 1 (200) )f]3ψd (fi/;v3ψ,.6d(fi/ 0(Iψfß1)o)f] I=F), CqB%A ;v]9dbß. )CC8, M" ) t=2500!co, 3Ψd(fi±7fl, μ)7].6 d(fiμqs0m[x0m (Iψf)o)f=F]IA ff]fs, ßP#Ω#/E), I"*`3Ψ d< lk gfl]f Eψ4a, ffl( 1a c ΛA)Ccu]3b dr] L1 0 gflρ==k. U (100) 1 (200) )7]. 6d(fiM"$q0MX 0.8 8, (200) )f].6d( fi}vk b (ψf]iaff]fs[xa<), (100) )f].6d( fi.me0m lf} Eψ4a, m T μ)7]d(fijx G6H, ]37m] L1 2 dk. ( 4 / Ni 80 Al 13 Cr 7 3lqV*6 Ni 3 (Al, Cr) K Q Cr ψf) (100) 1 (200) )f]3ψd(fi1.6d (fiμqs] <. ν( 3 Kfl, Crψf3ΨH dr ] <T ν Al ψfdfi K, R} <]Ωr/ET Al ψf (fi6q8=ntο Ni 80 AL1 0 Cr 10 3l, Z X$u]g(), ffi/)7m] L1 2 gfl] Ni 3 (Al, Cr) KQ β 4M vffl Al ψf3x,cr ψfj}q/ Uχ Oψf. ( 5 z ο Ni 80 Al 13 Cr 7 3lqV*6Kgfl]q Fig.2 μ 2 fi#prψffp Ni 80 Al 13 Cr 7 2k( 873 K pu)5p Ni 3 (Al,Cr) J6c'ff qpφffi Radial distribution of the composition order parameter (a) and long range order parameter (b) in Ni 3 (Al,Cr) phase of Ni 80 Al 13 Cr 7 alloy at 873 K aging for different time steps (t) μ 3 Ni 80 Al 13 Cr 7 2k( 873 K pu)5p Ni 3 (Al,Cr) J6 Al χe( (100) 0 (200) (e c'ff ; Fig.3 Temporal evolution of the composition order parameter (a) and long range order parameter (b) of Al in (100) and (200) of Ni 3 (Al, Cr) phase of Ni 80 Al 13 Cr 7 alloy with time steps at 873 K aging

5 634 j Λ f Φ d 45 z <*6. Dffl fcc 9dK (( 5a) "*`3Ψ d< lf Eψ4a, a /l7] L1 0 gflρ==k (( μ 4 Ni 80 Al 13 Cr 7 2k( 873 K pu)5p Ni 3 (Al,Cr) J6 Cr χe( (100) 0 (200) (e c'ff pr ; Fig.4 Temporal evolution of the composition order parameter (a) and long range order parameter (b) of Cr in (100) and (200) of Ni 3 (Al, Cr) phase of Ni 80 Al 13 Cr 7 alloy with time step at 873 K aging μ 5 fcc ffip L1 2 ffi`; y ' Fig.5 Structure evolution scheme from fcc to L1 2 (a) 3D lattice of the fcc disorder phase (b) 3D lattice of the L1 0 structure order phase (c) 3D lattice of the L1 2 structure order phase (d f) the projection of the fcc disorder, L1 0 and L1 2 structure order phase on [010], respectively 5b), Y8'pm!8ff, lf}eψ4a, a / 7m] L1 2 gfl (( 5c). ( 5d f Ψ /~f 3 μgfl ) [010] ±Qf]}0&Φ(. 3 Ωffi (1) ) Ni 3 (Al, Cr) Kffl fcc gflq L1 2 gfla< ]*6Q, l 2 Eψ4a. (2) )qv]m;cu, (100) 1 (200) )f] d rk`ßμqs[x0m, R3Ψfl, ß~`3Ψ d <]]x lf Eψ4a, ]3 drb] L1 0 g flρ==k. U dr0mx mhq, Al1 Cr ψf] 3Ψd(fi1.6d(fi) (100) )f k 0M, ) (200) )f. k b, lf}eψ4a, L1 0 g fl[xq L1 2 gfla<. (3) )>μqv*6q, Crψf]d(fivTT Al ψf] <Ωr, ffi/y 7m L1 2 gfl] Ni 3 (Al, Cr) KQ β 4M vffl Al ψf3x, CrψfJ}q/ UχOψf. xfiρfi [1] Chen L Q, Khachaturyan A G. Phys Rev, 1991; 44B: 4681 [2] Reinhard L, Turchi P E A. Phys Rev Lett, 1994; 72: 120 [3] ShiZL,LiuJY,GuMY,ZhangD,WuRJ.Acta Metall Sin, 1999; 35: 430 (or, ffi, χ.fi, 4 s, :[d. kξhψ, 1999; 35: 430) [4] ShiHT, NiJ. Phys Rev, 2002; 65B: [5] NiJ,GuBL.JChemPhys, 2000; 113: [6] NiJ,GuBL,AshinoT,IwataS.Phys Rev Lett, 1997; 79: 3922 [7] Pareige C, Soisson F, Martin G, Blavette D. Acta Mater, 1999; 47: 1889 [8] Saito Y, Harada H. Mater Sci Eng, 1997; A223: 1 [9] Menand A, Cadel E, Pareige C, Blavette D. Ultramicroscoy, 1999; 78: 63 [10] Lu Y L, Chen Z, Li Y S, Wang Y X. Acta Metall Sin, 2007; 43: 291 (χrffl, 0 t, ffiωm, )ΩW. kξhψ, 2007; 43: 291) [11] Ling B, Zhong P, Zhong B W, Gu B Z. Acta Metall Sin, 1995; 31: 209 (fl μ, S F, Sν5, ffi Y. kξhψ, 1995; 31: 209) [12] Khachaturyan A G. Theory of Structural Transformations in Solids. New York: Wiley, 1983: 129 [13] Poduri R, Chen L Q. Acta Mater, 1998; 46: 1719 [14] Chen L Q. Scr Metall Mater, 1993; 29: 683 [15] Caudron R, Barrachin M, Finel Y. Phsica, 1992; 180B: 822 [16] Li Y C, Chen Z, Lu Y L, Wang Y X. Acta Metall Sin, 2006; 42: 239 (ffiωm, 0 t, χrffl, )ΩW. kξhψ, 2006; 42: 239 [17] Prikhodko S V, Carnes J D, Isaak D G, Ardell A J. Scr Mater, 1998; 38: 67