Interdiffusion in Solid Solution of the Al-Cu-Mg-Ag System

Transcription

1 Materals Transactons, Vol. 44, No. 11 (2003) pp to 2257 #2003 The Japan Insttute of Metals Interdffuson n Sold Soluton of the Al-Cu-Mg-Ag System Tomosh Takahash 1, Koj Hsayuk 2, Toshm Yamane 2, Yortosh Mnamno 3 and Takanor Hno 1 1 Department of Materals Scence and Engneerng, Nhama Natonal College of Technology, Nhama , Japan 2 Department of Mechancal Engneerng, Hroshma Insttute of Technology, Hroshma , Japan 3 Department of Adaptve Machne systems, Graduate School of Engneerng, Osaka Unversty, Suta , Japan Quaternary and ternary nterdffuson experments of Al-rch Al-Cu-Mg-Ag alloys have been performed n the temperature range from 793 to 853 K. The concentraton profles ndcate that the dffuson dstance of Cu s shorter than those of Mg and Ag n the sold solutons. The drect and ndrect nterdffuson coeffcents are postve n the ternary and quaternary alloys. The rato of ndrect coeffcent to drect one suggests that repulsve nteractons exst between Cu and Mg atoms n the Al-Cu-Mg-Ag alloys. In addton, the rato values of converted nterdffuson coeffcents n the quaternary alloys suggest that the nteractons between Al(solvent) and Cu atoms are attractve n the present alloy. (Receved July 22, 2003; Accepted September 8, 2003) Keywords: alumnum-copper-magnesum-slver alloy, quaternary dffuson, dffuson couple, thermodynamc nteracton 1. Introducton Most mportant and practcal alloys are composed of mult-components. In partcular, extensve studes about the metallography and materals structure have been carred out n Al-Cu-Mg-Ag alloys, because these alloys orgnated from duralmn are the promsng structural materals. 1) In order to obtan ther superor mechancal propertes of such alumnum alloys, the alloys are heat-treated for recoverng, recrystallzaton, homogenzaton, agng, precptaton, etc. Dffuson s a basc and mportant factor for understandng and dscussng the phenomena and the heat treatments. Therefore, t s necessary to obtan the nformaton on the dffuson n such Al-base quaternary alloys. 2) Many expermental studes of dffuson n Al-base bnary alloys have been performed 2 4) n order to determne the only one nterdffuson coeffcent. On the other hand, some nvestgatons of dffuson have been made n Al-base ternary alloys 5 8) n whch the four coeffcents were requred to represent nterdffuson. Number of studes on dffuson n the ternary Al-Cu-Mg alloys as the practcal materals s small n spte of ts mportance, and the nterdffuson coeffcents n the ternary alloys have been reported only by the present authors. 5,6) In partcular, a study on the dffuson n the quaternary Al-Cu-Mg-Ag alloys has been not nvestgated yet 9) because the nne nterdffuson coeffcents should be evaluated. The purposes of the present work are (a) to determne the ternary nterdffuson coeffcents n the -phase regon of the ternary Al-Cu-Mg system n a temperature range from 793 to 853 K, (b) to determne the quaternary nterdffuson coeffcents n the quaternary Al-Cu-Mg-Ag system at 813 K, and (c) to dscuss the thermodynamc nteractons between solute atoms (solvent-solute atoms) n Al-Cu-Mg-Ag sold solutons. 2. Expermental Procedures The Al-Cu, Al-Mg, Al-Cu-Mg and Al-Cu-Mg- Ag alloys for dffuson couples were prepared from mass%al, mass%mg, mass%ag, and a Al mass%cu mother alloy by hgh frequency nducton meltng n an argon atmosphere. These alloy ngots were annealed at 773 K for 432 ks for homogenzaton and gran coarsenng. These alloys have a sngle phase of -phase sold soluton and the gran dameter more than about 0.7 mm. The alloy ngots were cut nto dffuson plates of mm 3 n sze. The surfaces of the alloy plates were metallographcally polshed by SC paper and 0.3 mm alumna powder. The polshed plates for dffuson couples were hold together by means of stanless steel clamps. The termnal compostons of dffuson couples are lsted n Table 1. The termnal compostons of ternary Al-Cu-Mg dffuson couples have been reported n elsewhere. 5) The assembled dffuson couples were placed n a Pyrex tube wth T powder enclosed an alumnum fol. They were evacuated, and then sealed. The dffuson couples were annealed n a temperature range from 793 to 853 K for 12.6 to 96.3 ks. After dffuson annealng, the couples were quenched n ce water and then mounted n synthetc resn. The dffuson couples were cut at ther center parallel to the dffuson drecton n order to expose sectons whch had no oxdaton and evaporaton of elements. The exposed secton of each couple was metallographcally polshed. Solute Table 1 Termnal compostons of dffuson couples n Al-Cu-Mg-Ag alloys. Couple name Compostons Equvalent concentraton J1 Al-2Cu-9Mg-1.74Ag/Al-1.88Cu-1.98Mg-1.48Ag Mg, Ag J2 Al-1.16Cu-0.95Mg-1.45Ag/Al-1.13Cu-3.12Mg-1.35Ag Cu, Ag J3 Al-1.31Cu-2.37Mg-2Ag/Al-1.20Cu-1.78Mg-3.25Ag Cu, Mg

2 Interdffuson n Sold Soluton of the Al-Cu-Mg-Ag System 2253 concentraton profles n these dffuson couples were measured by a JEOL JXA-8900 electron mcroanalyzer (EPMA). The characterstc X-ray ntenstes of Cu, Mg and Ag were corrected for atomc number, absorpton and fluorescence effects, and were converted nto concentraton values of Cu, Mg and Ag usng the bulk alloy compostons at the ends of the couples as standards. 10,11) The nterdffuson coeffcents n the Al-Cu-Mg alloys have been evaluated by usng the extended Matano-Krkaldy method to the ternary alloy system descrbed n elsewhere. 5,6) On the other hand, nne nterdffuson coeffcents n a 4-components alloy system can be obtaned from the dffuson profles by usng the extended Matano-Krkaldy method to the 4-component alloy system. 12,13) Z C C ð 1Þ xdc ¼ 2t X3 k¼1 ~D 4 k=@x ð ¼ 1; 2; 3Þ; ð1þ where C (=1, 2, 3) s the concentraton of solute, C ð 1Þ and C ðþ1þ : the termnal compostons at the ends of the dffuson couples, ~D 4 (=1,2,3) are the drect nterdffuson coeffcents, ~D 4 k: the ndrect nterdffuson coeffcents, t: the dffuson tme, and x: the dstance from the Matano nterface located at x ¼ 0, whch can be determned for dffuson profle from the relaton: Z C ðþ1þ C ð 1Þ xdc ¼ 0 ð ¼ 1; 2; 3Þ: ð2þ For the 4-component system, three ndependent dffuson couples are needed, n general, for determnaton of nne nterdffuson coeffcents at one common composton of ntersecton of the dffuson paths. In other words, the extended Matano-Krkaldy method for quaternary system requres us to prepare three ndependent dffuson couples whose dffuson paths ntersect at one common composton. It s qute dffcult to satsfy ths expermental condton. Recently, an elegant method for the determnaton of the dffuson coeffcents has been presented by Thompson and Morral 14) under the assumpton of constant dffusvty n the reacton zone of the multcomponent alloys. By defnton, the dffusvty matrx [ ~D] s related to ts square root dffusvty matrx [r] ½ ~DŠ ¼½rŠ½rŠ ð3þ The relaton between ~D 4 j and r j (, j=1, 2, 3) n quaternary alloys of ths experments s; 2 ~D 4 11 ~D 4 12 ~D r 11 r 12 r 13 r 11 r 12 r ~D 4 21 ~D 4 22 ~D ¼4 r 21 r 22 r r 21 r 22 r 23 5 ~D 4 31 ~D 4 32 ~D 4 r r 32 r 33 r 31 r 32 r 33 ð4þ The values of r 11 to r 33 can be obtaned expermentally from the followng eqs. (5) and (6). S ¼ ðt=þ 0:5 ðr 1 C 1 þ r 2 C 2 þ r 3 C 3 Þ C ¼ C ðþ1þ ð5þ C ð 1Þ ð ¼ 1; 2; 3Þ ð6þ The terms, S 1, S 2 and S 3, represent the amounts of solute whch have crossed the ntal nterface, and C s the (a) Concentraton, C (b) Concentraton, C (c) Concentraton, C K J2 dfference n the ntal concentratons on the rght and left sdes of the couples. 3. Results and Dscusson Dstance, X / µ m 3.1 Concentraton profles and dffuson paths Typcal concentraton profles of the J1, J2 and J3 couples annealed at 813 K for ks are shown n Fgs. 1(a), (b) and (c), respectvely. The dffuson dstance of Cu s shorter than those of Mg and Ag. The concentraton profles ndcate that the dffuson rate of Cu s smaller than those of Mg and Ag n the Al-Cu-Mg-Ag alloys. Snce the J1, J2 and J3 couples have nearly equal concentratons of the two solute elements n the termnal alloys as lsted n Table 1, the concentraton dstrbuton of such elements are almost constant over the entre dffuson zone. Fgures 2(a) and (b) show the projectons of the dffuson Mg Cu Ag 813 K J Dstance, X / µ m Dstance, X / µ m Mg Ag Cu 813 K J3 Fg. 1 Typcal concentraton profles n dffuson couples (a) J1, (b) J2 and (c) J3 annealed at 813 K for ks. Mg Cu Ag

3 2254 T. Takahash, K. Hsayuk, T. Yamane, Y. Mnamno and T. Hno Mg Concentraton, C Mg (a) 813 K J2 J3 J1 / m 2 s K (a) 853 K 833 K 813 K Ag Concentraton, C Ag (b) 813 K Cu Concentraton, C Cu J2 J3 Cu Concentraton, C Cu J1 MgMg / m 2 s Cu Concentraton, C Cu (b) 853 K 833 K 813 K 793 K Fg. 2 Projectons of dffuson paths for quaternary dffuson couples J1, J2 and J3 at 813 K for ks: (a) projectons onto the C Mg -C Cu plane and (b) projectons onto C Ag -C Cu plane. paths for the quaternary J1, J2 and J3 couples at 813 K onto the C Mg -C Cu plane and the C Ag -C Cu plane, respectvely. 3.2 Concentraton dependence of nterdffuson coeffcents By usng the extended Matano method to ternary dffuson (Matano-Krkaldy method), the nterdffuson coeffcents of ~ and ~ MgMg are evaluated at the ntersecton compostons of the dffuson paths 5) n the ternary Al-Cu- Mg alloys n the temperature range from 793 to 853 K. These coeffcents are shown n Fgs. 3(a) and (b). The nterdffuson coeffcents are not senstve to the solute concentratons n the Al-Cu-Mg sold solutons. Table 2(a) lsts the values of the nne nterdffuson coeffcents n the quaternary Al-Cu-Mg-Ag alloys evaluated from the concentraton profles of the dffuson couples (J1, J2, J3) at 813 K by the Thompson-Morral method. The drect nterdffuson coeffcents ~D 4, ~D 4 MgMg and ~D 4 AgAg are postve, and the other ndrect coeffcents are postve. The drect nterdffuson coeffcent ~D 4 s the smallest value among the drect ones. Table 2(b) shows the comparson of the values of the nterdffuson coeffcents n the bnary Al- Cu, Al-Ag alloys, 15,16) the ternary Al-Cu-Mg alloy and the quaternary Al-Cu-Mg-Ag alloy. The drect nterdffuson coeffcent ~D 4 MgMg n the quaternary alloy does not almost change n comparson wth the values of the bnary and ternary alloys, but the drect coeffcents ~D 4 AgAg and ~D 4 ncrease slghtly Mg Concentraton, C Mg Fg. 3 Concentraton dependence of drect nterdffuson coeffcents (a) ~ and (b) ~ MgMg of ternary Al-Cu-Mg system n a temperature range from 793 to 853 K. Table 2 (a) Interdffuson coeffcents of quaternary Al-Cu-Mg-Ag system at 813 K and (b) Comparson of bnary, ternary and quaternary nterdffuson coeffcents at 813 K. (a) 813 K (Thompson-Morral method) Unts 10 8 m/s 0:5 n j Cu Mg Ag ½r j Š Cu Mg :05 Ag Unts m 2 /s n j Cu Mg Ag [ ~D j ] Cu Mg Ag (b) 813 K (k=al or 4) (10 14 m 2 /s) Al-Cu Al-Mg Al-Ag Al-Cu-Mg Al-Cu-Mg-Ag ~D k 13.3 * * ~D k MgMg * 42.2 * ~D k AgAg * * 27.3 * 34.0 ~D k CuMg * * * ~D k MgCu * * * ~D k MgAg * * * * 5 ~D k AgMg * * * * 5.6

4 Interdffuson n Sold Soluton of the Al-Cu-Mg-Ag System Thermodynamc nteractons among the solute components Krkaldy et al. 17) have approxmately derved the relaton between ~D 3 j = ~D 3 (j) and Wagner s nteracton parameter, " for very dlute solutons n the ternary alloy systems. ~D 3 j = ~D 3 ¼f1þ " (j) gn : ð; j ¼ 1; 2Þ ð7þ The smlar equaton can be derved n the quaternary alloys. 18) From the phenomenologcal theory and Fck s 2nd law, the dffuson flux of component s gven by the followng equatons, 19) respectvely, J ¼ X3 k¼1 J ¼ X3 j¼1 L j X j ð8þ ~D 4 k=@x ð ¼ 1; 2; 3Þ: ð9þ where L j are the phenomenologcal coeffcents, X are the drvng force (thermodynamc force). The drvng force X j are gven by: X j ¼ X3 j¼1 ð j þ V C j =V 4 C 4 Þ@ =@x ð10þ where j s the Kronecker symbol, 0 when 6¼ j, 1 when =j, V s the partal molar volume of component, and j the chemcal potental of component. For example, the chemcal potental 1 of component 1 s expressed by 1 ¼ 0 1 þ RTfln N 1 þ ln 0 ð1þ 1 þ N 1 " 1 þ N 2 " 1 ð2þ þ N 3 " 1 ð3þ g ð11þ where N 1 s the mole fracton of component 1, 0 1 s the actvty coeffcent at nfnte dlute soluton. In eq. (8), we assume L j ¼ 0 ( 6¼ j) for very dlute solutons n the quaternary alloy systems. 13) Substtutng X j [eq. (10)] n eq. (8), and comparng factors k =@x n eq. (8) and eq. (9), we obtan eq. (12) relatng to the quaternary system. For solute atoms 1 and 2 ( = 1, j = 2), ~D 4 12 = ~D 4 11 ¼fN 1 ðn 1 þ N 4 Þ" ð2þ 1 þ N 1 ð1 þ N 2 " ð2þ 2 Þ þ N 1 N 3 " 3 ð2þ g=fðn 1 þ N 4 Þð1 þ N 1 " 1 ð1þ Þ þ N 1 N 2 " 2 ð1þ þ N 1 N 3 " 3 ð1þ g: ð12þ If eq. (12) s rearranged wth eq. (13); n dlute soluton N ¼ 0 (=1,2,3), N 1 N 2 ¼ 0; N 1 N 3 ¼ 0; N 2 N 3 ¼ 0; N 4 ¼ 1; ð13þ t becomes the followng equaton; ~D 4 12 = ~D 4 11 ¼f1þ " ð2þ 1 gn 1 =f1 þð1þ " ð1þ 1 ÞN 1 g: ð14þ In partcular, for hghly dlute soluton, t reduces the relaton, 17) ~D 12 4 = ~D 11 4 ¼f1 þ " 1 ð2þ gn 1 : ð15þ The equaton n the quaternary alloys s the same equaton as eq. (7) n ternary alloys derved by Krkaldy et al. 17) Also, Tanaka et al. 20,21) have derved a method for evaluaton of nteracton parameter n dlute lqud alloy n a ternary A-B-C alloy on the bass of the free volume theory by Shmoj and Nwa. 22) " B (C) ¼fð@G Ex =@N B Þ NB!0;N C!0g=kT ¼ð B (C) T B (C) Þ=kT ð16þ where G Ex s the excess Gbbs free energy, k the Boltzmann constant, B (C) and B (C) are the enthalpy and entropy nteracton parameters, respectvely. 20) The values of B (C) can be calculated by usng Medema s enthalpy 23) of soluton at nfnte dluton relatng the consttuent elements. In addton, the values of B (C) can be evaluated on the bass of molar volume 21,24) of the consttuent elements, the meltng pont, and the coeffcent () 25) to transfer the sold state frequency to that n the lqud at the meltng pont. In accordance wth eq. (7), the relaton between ~ MgCu= ~ MgMg and Mg concentraton n the Al-Cu-Mg system at 753, 793 and 813 K s plotted n Fgs. 4(a). Ths fgure also ncludes the rato of ~ MgCu= ~ MgMg at 813 K n the quaternary Al-Cu-Mg-Ag alloy. Fgure 4(b) shows the relaton between ~ CuMg= ~ and Cu concentraton at 813 K and also shows the smlar rato values at 813 and 832 K n the quaternary Al-Cu-Mg-Ag alloys. In addton, the ratos of ~ CuZn= ~ at 813 K n the ternary Al-Cu-Zn alloy 7) are plotted by the closed crcles n Fg. 4(b). The broken lnes are drawn by eq. (7) wth the values of " Mg (Cu) MgCu / MgMg D CuMg Al / (a) 813 K 793 K 753 K 813 K (Q) (Cu) ε Mg = Mg Concentraton, C Mg (b) 813 K CuMg / CuZn CuMg CuMg Al /D Al /D (813 K, Q) (832 K, Q) /D Al (Mg) ε Cu = Cu Concentraton, C Cu Fg. 4 (a) Relaton between ~ MgCu= ~ MgMg and Mg concentraton n Al-Cu-Mg system at 753, 793 and 813 K. (b) Relaton between ~ CuMg= ~ and Cu concentraton n Al-Cu-Mg system at 813 K. (Q: Quaternary Al-Cu-Mg-Ag system)

5 2256 T. Takahash, K. Hsayuk, T. Yamane, Y. Mnamno and T. Hno and " (Mg) Cu ¼þ9 n Al-Cu-Mg alloys, respectvely. The expermental values of ~ MgCu= ~ MgMg and ~ CuMg= ~ ncrease wth the Mg and Cu concentraton n the Al-Cu-Mg alloys, although they scatter around the lne of " (Mg) Cu ¼þ9. The (rato) values of ~ MgCu= ~ MgMg and ~ CuMg= ~ n the quaternary Al-Cu-Mg-Ag alloy exhbt the postve values. Whle eq. (16) s appled for the calculaton of nteracton parameters, one has " (Mg) Cu ¼þ2:2 and " (Zn) Cu ¼þ1:5 n the sold soluton of Al-Cu-Mg and Al-Cu-Zn alloys, respectvely. These postve " (Cu) Mg and " (Mg) Cu ndcate that repulsve nteractons exst between Cu and Mg atoms. Smlarly, the postve sgn of " (Cu) Mg [" (Mg) Cu ] n eq. (7) s n agreement wth that of value obtaned by eq. (16) (" (Mg) Cu ¼ 2:2). It s evdent that the repulsve nteractons between Mg and Cu atoms exst n the ternary system. In the quaternary system, the ~ MgCu= ~ MgMg and ~ CuMg= ~ have large postve values. These facts ndcate that the nteractons between Mg and Cu atoms have a repulsve force n the quaternary alloys as well as ternary ones, and that the slver element has a small nfluence on the nteracton between Cu and Mg elements. The converted equatons relatng to the ternary nterdffuson coeffcents have been reported by Sabater and Vgnes. 26) Ther equatons can be extended to the quaternary alloy system. When the component of solvent s 4 (=Al), for example, the dffuson flux of component 1 s expressed by the followng equaton, J 1 ¼ ~D 4 11@C 1 =@x ~D 4 12@C 2 =@x ~D 4 13@C 3 =@x: ð17þ In addton, the component 2 (=Mg) s consdered as the solvent, J 1 ¼ ~D 2 11@C 1 =@x ~D 2 13@C 3 =@x ~D 2 14@C 4 =@x: ð18þ X 4 ¼1 C V ¼ 1 ð19þ On the assumpton that the partal molar volumes V of 1, 2, 3 and 4 are constant, eq. (19) s dfferentated wth respect to x, and then s substtuted n eqs. (17) and (18). When both equatons are compared n the dffuson coeffcent terms, the quaternary converted equatons smlar to the ternary system can be obtaned as follows ~D 2 11 ¼ ~D 4 11 ðv 1 =V 2 Þ ~D 4 12; ð20þ and ~D 2 13 ¼ ~D 4 13 ðv 3 =V 4 Þ ~D 4 12; ð21þ ~D 2 14 ¼ ðv 4 =V 2 Þ ~D 4 12 ð22þ For nstance, by usng the equaton ~D 14 2 = ~D 11 2 ¼ f1 þ " 1 ð4þ gn 1, the effect of 4 (=Al) on 1 (=Cu) can be consdered. The nteracton parameter " Cu (Al) s found from the calculaton to be 2:0 by usng the quaternary nterdffuson coeffcents n Table 2(a). The values of V 1 (1=Cu), V 2 (2=Mg), V 3 (3=Ag) and V 4 (4=Al) calculated from the data of the lattce parameters are 7.1, 14.0, 10.3 and 1 (10 6 m 3 mol 1 ). From the value of " Cu (Al), t s thought that the nteractons between Al and Cu atoms have attractve force n the quaternary alloys. If the component 1 (=Cu) and 3(=Ag) are consdered as the solvent, the equatons smlar to eqs. (20) through (22) are derved, and the nteractons between Al and Mg (or Ag) can be dscussed. 27) However, the dscusson s beyond the scope of ths paper. 4. Summary Quaternary and ternary nterdffuson experments of Alrch Al-Cu-Mg-Ag alloys have been performed n the temperature range from 793 to 853 K. The results are summarzed as follows. (1) The drect and ndrect nterdffuson coeffcents are postve n the quaternary alloys. The drect coeffcent ~D 4 s the smallest value among the drect ones. The drect coeffcent ~D 4 MgMg n the quaternary alloy does not almost change n comparson wth the values of the bnary and ternary alloys, but the drect coeffcents ~D 4 AgAg and ~D 4 ncrease slghtly. (2) From the rato values of ndrect coeffcent to drect one, t s suggested that repulsve nteractons of Cu-Mg atoms exst n the Al-Zn-Mg-Cu alloys. In addton, from the converted equatons relatng to the nterdffuson coeffcents n the quaternary alloys, t s thought that the nteractons between Al and Cu atoms have attractve force n the present alloy. Acknowledgments Ths work was fnancally supported by the Lght Metal Educatonal Inc., Osaka , Japan. The authors are deeply ndebted to the support. Chemcal analyss of the alumnum alloys was performed by Showa Alumnum Co. Ltd., Oyama 323. The authors would lke to thank Mr. Satosh Hozum of the company for hs assstance of the chemcal analyss. REFERENCES 1) See, for example, T. Sato: The Structure and Property n Alumnum Alloys (Japanese), (Japan Inst. Lght Metals, Tokyo, 1991) pp ) K. Hrano: The Problems of Dffuson n Materals Development (Japanese), Semnar Text of The Japan Inst. Metals, Japan, (1991) pp ) K. Hrano: Fundamentals and Applcaton of Dffuson (Japanese), Semnar Text of The Japan Inst. Metals, Japan, (1984) pp ) Y. Mnamno and T. 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