Quaternary Diffusion in 7000 Aluminum Alloys

Transcription

1 Materals Transactons, Vol. 43, No. 2 (2002) pp. 232 to 238 c 2002 The Japan Insttute of Metals Quaternary Dffuson n 7000 Alumnum Alloys Tomosh Takahash 1, Yortosh Mnamno 2 and Toshm Yamane 3 1 Department of Materals Scence and Engneerng, Nhama Natonal College of Technology, Nhama , Japan 2 Department of Adaptve Machne Systems, Graduate School of Engneerng, Osaka Unversty, Suta , Japan 3 Department of Mechancal Engneerng, Hroshma Insttute of Technology, Hroshma , Japan Quaternary and ternary nterdffuson experments of 7000 alumnum alloys have been performed at 725 and 755 K. The concentraton profles ndcate that the dffuson dstance of s shorter than those of Zn and Mg n the sold solutons. The drect nterdffuson coeffcents ZnZn Al, MgMg Al are postve, and ndrect coeffcents ZnMg Al, MgZn Al are negatve n the ternary Al Zn Mg alloys. The effectve nterdffuson,c eff. When the concentraton dstrbuton of Zn and Mg are,c = 4 = coeffcents n 7000 alumnum alloys are n the order Zn,C eff > Mg,C eff > almost constant and the concentraton of approaches zero n the Al Zn Mg/Al Zn Mg couple, t s obvous that (Al Zn Mg). The rato values of ndrect to drect dffuson coeffcents suggest that attractve nteractons of Zn Mg and Mg exst n the Al Zn Mg alloys. (Receved September 7, 2001; Accepted December 10, 2001) Keywords: alumnum-znc-magnesum-copper alloy, quaternary dffuson, dffuson couple, nteracton 1. Introducton Most practcal alloys are composed of more than two elements. For example, the 7000 seres alumnum alloys have as many as 8 or more components. The 7000 seres alumnum alloys have been orgnated from Extra super duralmn, and are the promsng structural materals. 1, 2) In order to obtan superor mechancal propertes n 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 such phenomena and heat treatments. Therefore, t s necessary to obtan the nformaton for dffuson n such Al-base alloys wth multcomponents. 3) Many expermental studes of dffuson n Al-base bnary alloys have been performed 3 5) n order to determne only one nterdffuson coeffcent. On the other hand, a few nvestgatons of dffuson have been made n Al-base ternary alloys 6 8) n whch four coeffcents were requred to represent nterdffuson. Especally, the number of studes on dffuson n practcal ternary Al Zn Mg alloys s very small n spte of ts mportance; three reports on the mpurty dffuson coeffcents of Zn or Mg n ths Al Zn Mg alloy system 9 11) and two reports on the nterdffuson 12, 13) have been publshed. Recently, the authors have reported the nne nterdffuson coeffcents n the quaternary Al Zn Mg alloys. 13) The purposes of the present work are (a) to determne the ternary nterdffuson coeffcents by Matano-Krkaldy method 14, 15) n the α-phase regon of the ternary Al Zn Mg system at 725 K, (b) to determne the effectve nterdffuson coeffcents by Dayananda method 16, 17) n the 7000 alumnum alloys at 755 K, (c) to clarfy the relaton between the nterdffuson coeffcents and the effectve nterdffuson coeffcents on the bass of the results of quaternary nterdffuson coeffcents by Thompson-Morral Method 18) n the α Al Zn Mg sold solutons, and (d) to dscuss the thermodynamc nteractons between solute atoms n α Al Zn Mg sold solutons. 2. Expermental Procedures Commercal alloys used n the present work were 1050 pure alumnum, 7003 and 7075 alumnum alloys produced by Showa Alumnum Co. Ltd. In the 7003 and 7075 alumnum alloys, the man solute elements are Zn, Mg,, and small amounts of the other elements such as Mn, Cr, T etc. are added. Quaternary and ternary alloys wth compostons of 7050 alumnum alloys (laboratory alloys) were prepared from mass%al, mass%zn, mass%mg and a Al mass% mother alloy by hgh frequency nducton meltng n an argon atmosphere. The commercal and laboratory alloys were annealed at 773 K for 432 ks for homogenzaton and gran coarsenng. The These alloys have a sngle phase of α-phase sold soluton. The gran dameter of commercal alloys was about 0.3 mm, and that of laboratory alloys was about 0.7 mm. The alloy ngots were cut nto 5 mm 5 mm dffuson plates of about 3 mm n thckness. The surfaces of the alloy plates were metallographcally polshed wth SC paper, 0.3 µm alumna powder and damond paste. 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(a). The quaternary dffuson couples are desgnated P1-P3 and M1-M3 accordng to the combnaton of commercal and laboratory alloys, respectvely, as lsted n Table 1(b). The termnal compostons of ternary Al Zn Mg dffuson couples have been reported n elsewhere. 13) The assembled dffuson couples were vacuum-sealed nto a Pyrex tube. The quaternary and ternary dffuson couples were annealed at 755 K for ks and 725 K for ks, respectvely, and then quenched n ce water. The annealed 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, and then they were mounted n synthetc resn. The exposed secton of each couple was metallographcally polshed. In order to obtan dffuson profles n the dffuson couples, the characterstc X-

2 Quaternary Dffuson n 7000 Alumnum Alloys 233 Table 1 (a) Compostons of commercal 1050 and 7000 alumnum alloys (at%). Al S Fe Mn Mg Cr Zn T Zr Commercal 1050 al < <0.005 < Commercal 7003 al Commercal 7075 al Al Zn Mg Laboratory alloy 7050 al Laboratory alloy T1 al Laboratory alloy T2 al Laboratory alloy Q1 al (b) Quaternary A Zn Mg dffuson couples couple name Combnaton of alloys P1 Commercal 1050/Commercal 7003 P2 Commercal 1050/Commercal 7075 P3 Commercal 7003/Commercal 7075 M1 Al(99.99%)/Laboratory 7050 M2 Laboratory T1/Laboratory 7050 M3 Laboratory T2/Laboratory Q1 ray ntenstes of Zn, Mg and n these dffuson couples were measured by a JEOL JXA-8900 electron mcroanalyzer (EPMA), and then ther characterstc X-ray ntenstes were converted nto concentraton values of Zn, Mg and by the ZAF method usng the bulk alloy compostons at the ends of 19, 20) the couples as standards 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 14, 15) alloy system. C C ( ) xdc = 2t 3 k=1 4 k C k/ x ( = 1, 2, 3), (1) where C ( = 1, 2, 3) s the concentraton of solute, C ( ) and C (+ ) : the termnal compostons at the ends of the dffuson couples, t: the dffuson tme, and x: the dstance from the Matano nterface located at x = 0, whch can be determned for dffuson profle from the relaton: C (+ ) C ( ) xdc = 0 ( = 1, 2, 3). (2) 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 dffuson couples whose dffuson paths ntersect at one common composton. It s qute dffcult to satsfy ths expermental condton. Therefore, the nterdffuson coeffcents n the Al Zn Mg alloys have been evaluated 14, 15) by usng eqs. (1) and (2) to the ternary alloy system. The effectve nterdffuson coeffcents n a multcomponent alloy system can be evaluated by the followng 16, 17) equaton [ (+ ) ] C /(,R = 1/2t (x x 0 ) 2 dc C (+ ) C 0 C 0 where x 0 refers to the Matano plane, C 0 s the concentraton at x 0,,R eff s the effectve nterdffuson coeffcents of component over the concentraton range C (+ ) to C 0 on the rghthand sde of the Matano nterface. The effectve nterdffuson coeffcents on the left-hand sde of the Matano nterface,l eff are also expressed by a smlar equaton. The average nterdffuson coeffcents eff are gven by 17) ) (3) =,R Y +,L (1 Y ), (4) where Y = (C 0 ). The effectve nterdffuson coeffcents are related to the man nterdffuson coeffcents n, the cross coeffcents j n and the concentraton gradents of the elements n the n-component alloy: 17) (+ ) C )/(C (+ ) C ( ) n 1 = n + ( j n C j/ x)/( C / x), ( j = ) (5) j As shown n Fg. 1, a plot of C Zn vs (X Zn X 0 ) 2 s drawn by usng the concentraton profle of znc (755 K, M1) n Fg. 2(b), the ntegral n eq. (3) can be graphcally determned from the dotted area. 3. Results and Dscusson 3.1 Concentraton profles and Dffuson paths Fgures 2(a) and (b) show the concentraton profles of the P3 and M1 couples annealed at 755 K for ks, respectvely. The orgn of each abscssa n Fgs. 2(a) and (b) s the Matano nterface. The Mg and elements dffuse accordng to ther concentraton gradents, whle a pronounced up-hll dffuson of Zn s observed n Fg. 2(a). A mnmum or a max-

3 234 T. Takahash, Y. Mnamno and T. Yamane Fg. 1 A schematc plot of concentraton C Zn of znc vs. (X Zn X 0 ) 2 ; X Zn s dffuson dstance of Zn and X 0 the Matano nterface. The dotted areas correspond to the ntegral n eq. (3). Fg. 3 Dffuson paths of dffuson couples annealed at 725 K for ks. mum n the concentraton profles due to the up-hll dffuson can occur n an alloy of three or more components. Durng annealng of the P3 couple (7003/7075), the dffusng znc s redstrbuted n the neghborhood of the jont to gve local equlbrum, that s, to elmnate the gradents n the chemcal potental of znc. It suggests that the addton of magnesum to Al Zn alloys ( ) decreases the chemcal potental (or actvty) of znc. As shown n n Fg. 2(b), the dffuson dstance of s shorter than those of Zn and Mg. Ths ndcates that the dffuson rate of s smaller than those of Zn and Mg n the 7000 alumnum alloys. Ths result agrees wth the tendency of mpurty dffuson of, Mg or Zn n alumnum. 21) Fgure 3 shows the dffuson paths of the ternary Al Zn Mg alloys couples at 725 K. The dffuson paths show the S-shaped curve n the Al Zn/Al Mg couples (D4, D5), whch have comparatvely large solute concentratons. Such S-shaped dffuson paths have been also observed n the Al Mg 6, 7) and Al Zn 8) systems. Fg. 2 Typcal concentraton profles n dffuson couples (a) P3 and (b) M1 annealed at 755 K for ks. 3.2 Dffuson coeffcents of ternary and quaternary alloy systems Interdffuson coeffcents n ternary Al Zn Mg alloys Four nterdffuson coeffcents of Al ZnZn, ZnMg Al, Al MgMg and MgZn Al n the ternary Al Zn Mg alloys at 725 K were evaluated at the ntersecton compostons of the dffuson paths by usng the extended Matano method, 14, 15) and they are shown n Fgs. 4(a) to (d). All of drect coeffcents Al Al MgMg ZnZn and are postve, whle the great majorty of ndrect coeffcents ZnMg Al and MgZn Al are negatve. Some postve MgZn Al coeffcents were evaluated n the vcnty of the termnal compostons, where the error n evaluaton of the coeffcents becomes larger, because the [ C k / x] and [ C xdc C ( ) ] fac- tors n eq. (1) become smaller when the common compostons of ntersecton of the dffuson paths approach to the termnal compostons. 22, 23) As shown n Fg. 4, the nterdffuson coeffcents are not senstve to the solute concentratons n the α Al Zn Mg sold solutons. The average nterdffu-

4 Quaternary Dffuson n 7000 Alumnum Alloys 235 Fg. 4 Drect and ndrect nterdffusn coeffcents (a) ZnZn Al (b) ZnMg Al (c) MgMg Al and (d) MgZn Al of ternary Al Zn Mg system at 725 K. son coeffcents are as follows: ZnZn Al = m 2 /s, MgMg Al = m 2 /s, Al ZnMg = m 2 /s, Al MgZn = m 2 /s. (6) where the postve values of MgZn Al were excepted from the calculaton of the average values of Al The value of MgZn. ZnZn Al s slghtly larger than that of Al value of the ndrect coeffcents ZnMg Al MgMg. The absolute s larger than that of MgZn Al Interdffuson coeffcents and effectve nterdffuson coeffcents n quaternary alloys Nne nterdffuson coeffcents n the quaternary alloys can be determned by Thompson-Morral method. 18) However, by applyng Matano-Krkaldy method for the bnary system, the three drect nterdffuson coeffcents can be easly evaluated from the dffuson profles of Darken-type couples. 24) In ths case, the ndrect coeffcents cannot be obtaned (see Fg. 1 n Ref. 13)). The obtaned three drect dffuson coeffcents at 755 K are; ZnZn 4 = m 2 /s, MgMg 4 = m 2 /s, 4 = m 2 /s (7) n the quaternary Al Zn Mg alloys. The effectve nterdffuson coeffcents at 755 K can be evaluated from the concentraton profles (Fg. 1 n Ref. 13)) by usng Dayananda method n eq. (3). Zn,L eff = m 2 /s,,l eff = m 2 /s, Zn,R eff = m 2 /s,,r eff = m 2 /s, Zn,C eff = m 2 /s, Mg,L = m 2 /s, Mg,R = m 2 /s, Mg,C = m 2 /s,,c = m 2 /s, (8)

5 236 T. Takahash, Y. Mnamno and T. Yamane Table 2 Effectve nterdffuson coeffcents (10 14 m 2 /s) n 7000 alumnaum alloys at 755 K. Zn Mg Couple name Zn,L Zn,R Mg,L Mg,R,L,R P P P M M M Zn Mg Couple name Zn,C Mg,C,C P P P M M M3 3.7 The effectve nterdffuson coeffcents are lsted n Table 2 n 7000 commercal and laboratory alloys at 755 K. These effectve nterdffuson coeffcents for each component on,r left- and rght-hand sdes of the Matano plane [,L eff, ( = Zn, Mg, )] have smlar values n eq. (8), although ther values of Zn have a slght dfference among them. Smlar tendency s also observed n Table 2. Also, the effectve nterdffuson coeffcents,c eff ( = Zn, Mg, ) for each component are good agreement wth the nterdffuson coeffcents evaluated by Matano-Krkaldy method (eq. (7)) over the entre concentraton range of the dffuson couple. The concentraton gradents n the Darken couple of the present alloys are approxmately equal to zero, except for the gradents of elements for evaluatng the nterdffuson coeffcents. For nstance, n eq. (5); and ( C 2 / x) 0, ( C 3 / x) 0 (9) 1 eff = That s to say, the effectve nterdffuson coeffcents are equal to the nterdffuson coeffcents n the quaternary alloys. In addton, the effectve nterdffuson coeffcents n 7000 alumnum alloys are n the order Zn,C eff > Mg,C eff >,C eff. As shown n Table 1(a), the small amounts of alloyng elements of Mn, Cr, T etc. are added to 7000 alumnum alloys. Snce the solublty of these elements n alumnum s very low, fne dsperse phases precptate n the matrx and gran boundary durng the homogenzng treatment and the dffuson annealng. It was consdered that the vacancy concentraton was reduced by the precptated dspersed phases ) Therefore, t was predcted that the dffuson coeffcents of Zn, Mg and n 7000 alumnum alloys decreased by the addton of Mn, Cr, T etc. However, when comparng the values of,c ( = Zn, Mg, ) n Table 2 wth those values n eq. (8), t s apparent that the average effectve nterdffuson coeffcents have not a pronounced tendency of the decrease n ther values. In addton, snce the Zn and Mg elements n M1 couple have the qute smlar profles to each other as shown n Fg. 2(b), t follows that ( C Zn / x) ( C Mg / x) at the composton of Matano nterface; eq. (5) becomes eff = ( C 3/ x)/( C 1 / x). (10) When substtutng the expermental nterdffuson coeffcents and concentraton gradents at 755 K by Thompson-Morral method n the rght-hand sde of eq. (10), we obtan the followng effectve nterdffuson coeffcents. 1 eff = m 2 /s [ m 2 /s] 2 eff = m 2 /s [ m 2 /s] 3 eff = m 2 /s [ m 2 /s] (1 = Zn, 2 = Mg, 3 = ) (11) The above values are n agreement wth the effectve nterdffuson coeffcents by Dayananda method (the data n brackets, see the data n the couple M1 n Table 2). It s confrmed that eq. (10) holds Interdffuson coeffcents and mpurty dffuson coeffcents n quaternary alloys Ssson and Dayananda 28) have correlated the drect and ndrect nterdffuson coeffcents wth the ntrnsc and selfdffuson coeffcents n ternary alloys as follows: 3 j = D 3 j N 3 Dkj 3 (, j = 1, 2) (12) k=1 D 3 j = D C ( ln a / C j ) (, j = 1, 2) (13) where Dj 3 are the ntrnsc dffuson coeffcents n ternary alloys; D, the tracer-dffuson coeffcent of element ; a, the thermodynamc actvty of and N, the atom fracton of. When these relatonshps of eqs. (12) and (13) are extended to the quaternary dffuson, 33 4 and 33 4 are as follows: 33 4 = D4 33 N 3(D D D D4 43 ) (14) D33 4 = D 3 C 3( ln a 3 / C 3 ) (15) The value of (C 3 ln a 3 / C 3 ) goes to 1 when N 3 approaches zero. Therefore, the followng relatons can be obtaned from eqs. (14) and (15) when N 3 approaches zero: 29) lm N = D 3(1 2 4) (16) where D3(1 2 4) s the tracer dffuson coeffcent of element 3 n a ternary alloy. In the present work, the D3(1 2 4) corresponds to the mpurty dffuson coeffcent of n the Al Zn Mg alloy. The temperature dependence of the mpurty dffuson coeffcents of n the Al Zn Mg alloy s gven by the expresson: 13) D (Al 3.37Zn 2.75Mg) = exp( 132 kj mol 1 /RT 1 ) m 2 /s. (17)

6 Quaternary Dffuson n 7000 Alumnum Alloys 237 The M3 couple has the smlar concentratons of Zn and Mg n the termnal alloys as already lsted n Tables 1(a) and (b). In addton, the concentraton dstrbuton of Zn and Mg are almost constant over the entre dffuson zone, although the fgure of concentraton profles s omtted. Therefore, as smlarly descrbed n Secton 3.2.2, the concentraton gradents ( C / x) (, j = 1, 2) are nearly equal to zero. In the M3 couple, by regardng the component 1 n eq. (5) as the component 3 (3 = ) and usng eqs. (14) to (16), we can obtan,c eff = 4 = (Al Zn Mg). (18) The value of (Al Zn Mg) at 755 K n eq. (17) s m 2 /s. Ths value s smlar to that of,c eff (M3 couple, m 2 /s) n Table 2. Thus, t s thought that eq. (18) holds n the M3 couple. 3.3 Thermodynamc nteractons among the solute components The relaton between j 3 / 3 and Wagner s nteracton parameter, ε ( j) has been presented n very dlute solutons of the ternary alloy by Krkaldy et al., 30) as follows. j 3 / 3 ={1 + ε ( j) }N. (19) Also, Tanaka et al. 31, 32) have derved a method for evaluaton of nteracton parameter n dlute lqud alloy n a ternary A- -C alloy on the bases of the free volume theory by Shmoj and Nwa. 33) ε (C) ={( GEx / N C N ) N 0,N C 0}/kT (20) = (η (C) T σ (C) )/kt where G Ex s the excess Gbbs free energy, k the oltzmann constant, η (C) and σ (C) are the enthalpy and entropy nteracton parameters, 31) respectvely. The value of η (C) can be calculated by usng Medema s enthalpy 34) of soluton at nfnte dluton relatng the consttuent elements. In addton, the value of σ (C) can be evaluated on the bass of molar volume 32, 35) of the consttuent elements, the meltng pont, and the coeffcent (β) 36) to transfer the sold state frequency to that n the lqud at the meltng pont. Accordng to eq. (19), the relaton of the MgZn Al / MgMg Al to Mg concentraton the Al Zn Mg system at 725 K (86.84 ks) s plotted by the closed crcles n Fg. 5. Fgure 5 also ncludes the MgZn 4 / MgMg 4 and Mg 4 / MgMg 4 n the quaternary Al Zn Mg alloy at 725 K, 755 K and 803 K. The broken lne s drawn by eq. (19) wth the value of ε (Zn) Mg = 8 n Al Zn Mg alloy. Whle eq. (20) s appled for the calculaton of nteracton parameters, one has ε (Mg) Zn = 1.1, ε (Mg) =+2.5 and ε (Zn) =+1.6 n the α sold solutons of Al Zn Mg, Al Mg and Al Zn alloys, respectvely. The expermental values of MgZn Al / MgMg Al decrease wth ncreasng the Mg concentraton n the Al Zn Mg alloys, although they scatter around the lne of ε (Zn) Mg = 8. The (rato) values of MgZn 4 / MgMg 4 n the quaternary Al Zn Mg alloy exhbt the negatve values. These negatve ratos and ε (Mg) Zn ndcate that attractve nteractons between Zn and Mg atoms exst n the Al Zn Mg and Al Zn Mg systems. Smlarly, the postve sgn of ε (Mg) by eq. (19) s agreement wth Fg. 5 Relaton between MgZn Al / MgMg Al and Mg concentraton n Al Zn Mg and Al Zn Mg systems. that of value obtaned by eq. (20) (ε (Mg) =+2.5). It s evdent that the repulsve nteractons of Mg and atoms exst n the ternary system. 6, 13) In the quaternary system, however, the value of Mg 4 / MgMg 4 has comparatvely large negatve value. From the results, t s expected that the nteractons between Mg and atoms n the ternary system change from repulsve nteracton to attractve ones. In the ternary Al Zn alloys at 796 K, 8) t s thought that the value of ε (Zn) s negatve, because the consderable strong nteractons exst n the alloys. ut, the postve value obtaned by eq. (20) does not agree wth the sgn of the above value. The causes of the dfferent sgns are not clear. The authors have reported the results that the dffuson of Zn s affected by the copper atoms ( Zn Al / ZnZn Al < 0) n the ternary Al Zn alloys, but, that of s not strongly affected by the znc atoms ( Zn Al / Al 0).8) It appears that the facts are partly attrbuted to the causes of the dfferent sgns. On the other hand, the value of Zn 4 / ZnZn 4 s 0.069, and that of Zn Al / Al s n the quaternary alloy. It s thought that the nteractons between the copper and znc atoms s not so strong. 4. Summary Quaternary and ternary nterdffuson experments of 7000 alumnum alloys have been performed at 725 K and 755 K. The results are summarzed as follows. (1) The concentraton profles ndcate that the dffuson dstance of s shorter than those of Zn and Mg n the sold solutons. (2) The drect nterdffuson coeffcents Al ZnZn, Al MgMg are postve, and ndrect coeffcents ZnMg Al, MgZn Al are negatve n the ternary Al Zn Mg alloys. The effectve nterdffuson coeffcents n 7000 alumnum alloys are n the order Zn,C eff > Mg,C eff >,C eff. (3) When the concentraton dstrbuton of Zn and Mg are almost constant and the concentraton of approaches zero n the Al Zn Mg/Al Zn Mg couple, t s obvous that,c = 4 = (Al Zn Mg). (4) The rato values of ndrect to drect dffuson coeff-

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