Diffusion Solids Fundamentals Diffusion Controlled Solid State Episode 2 Part 5 ppt

348 20 Diffusion in Binary Intermetallics Fig. 20.5. Schematic illustration of six-jump vacancy cycles in the B2 structure. The arrows show vacancy jumps; the numbers indicate the jump sequence both components, D A /D B , lies within the following fairly narrow lim- its: 1 q < D A D B <q. (20.3) q was first estimated to be 2 [29, 5] and by including correlation effects was later slightly corrected to q =2.034 [30]. The upper (lower) limit is attained when vacancies are preferentially formed on the B (A) sublat- tice As the chemical composition deviates from the stoichiometric one and as disorder increases at high temperatures, antisite atoms appear. As shown by Belova and Murch [32], interaction of the six-jump-cycles with an- tisite atoms remarkable widens the limits of Eq. (20.3). Thus, in a B2 alloy with some disorder values of D A /D B beyond the limits of Eq. (20.3) cannot be considered as an indication that the 6JC mechanism does not operate. – Triple-defect mechanism: In a B2 compound triple-defect disorder can occur according to the reaction V A + V B  2V A + A B . (20.4) V A (V B ) denotes a vacancy on the A (B) sublattice and A B an A atom on the B sublattice (see also Chap. 5). Triple-defect disorder does not change the composition. Instead of forming equal numbers of vacancies 20.3 B2 Intermetallics 349 Fig. 20.6. Illustration of the triple-defect diffusion mechanism in the B2 structure. The arrows show vacancy jumps; the numbers indicate the jump sequence on both sublattices, two vacancies on one sublattice and an antisite atom on the other sublattice can appear. Triple-defect formation according to Eq. (20.4) is favoured in intermetallics with high formation enthalpies of V B vacancies. Vacancies and antisite defects can associate to form bound triple defects (see also Chap. 5). A triple-defect mechanism involving bound triple de- fects was proposed by Stolwijk et al. [33] for the B2 compound CoGa. The triple-defect mechanism in CoGa was attributed to two nearest- neighbour jumps of Co atoms and to a next-nearest neighbour jumps of Ga atoms. Detailed calculations for NiAl predict that an Al atom per- forms two nearest-neighbour jumps instead of one second-nearest neigh- bour jump [34]. Figure 20.6 shows the triple-defect mechanism with this Fig. 20.7. Illustration of the antistructural-bridge (ASB) mechanism. The arrows show vacancy jumps; the numbers indicate the jump sequence 350 20 Diffusion in Binary Intermetallics modification. The ratio of the diffusivities for this mechanism lies within the following limits [35]: 1/13.3 <D A /D B < 13.3 . (20.5) The triple-defect mechanism is closely related to the vacancy-pair mech- anism (see below). The configurations which appear after jumps 1 and 3 of Fig. 20.6 are nearest-neighbour vacancy pairs. – Antistructural-bridge (ASB) mechanism: This mechanism was pro- posed by Kao and Chang [38] and is illustrated in Fig. 20.7. As a result of the two jumps indicated, the vacancy and the antisite atom exchange their position. For a B2 phase with some substitutional disorder, antisite defects can act as ‘bridges’ to establish low energy sequences for vacancy jumps. It is important to note that the ASB mechanism has a percolation thresh- old. Long-range diffusion via the ASB mechanism requires a sufficient concentration of antistructure atoms to reach the percolation threshold. A relatively high threshold was estimated from purely geometrical argu- ments [38]. Monte Carlo simulations yielded lower values for the percola- tion threshold of about 6 % [36, 37]. Such antistructure atom concentra- tions can indeed occur in B2 intermetallics with a wide phase field like NiAl (see below). – Vacancy-pair mechanism: A bound pair of vacancies, i.e. a vacancy in one sublattice and a scond vacancy on a neighbour site of the other sublat- tice, can mediate diffusion of both components by successive correlated next-nearest-neighbour jumps. Whereas this mechanism has some rele- Fig. 20.8. Defect site fractions in B2 NiAl as a function of composition at 0.75 T m from [39] 20.3 B2 Intermetallics 351 vance for ionic crystals such as alkali halides (see Chap.26), it is unlikely for B2 intermetallics. It seems that in those B2 compounds, which are composed of a group VIIIB metal (Co, Fe, Ni, Pd, etc.) and a group IIIA metal (Al, Ga, In, etc.), the triple-defect mechanism is important. By contrast, B2 phases composed of a noble metal (Cu, Ag, Au) and a divalent metal (Mg, Zn, Cd) and FeCo are considered as candidates for the six-jump-cycle mechanism. Clearly, the antistructural-bridge (or antisite bridge) mechanism becomes more important at larger deviations from stoichiometry, because of its percolation threshold. 20.3.2 Example B2 NiAl The phasefield of B2 NiAl is fairly wide. It extends from about 45 % Ni on the Al-rich side to about 65 % Ni on the Ni-rich side [3]. Theoretical calcula- tions of defect concentrations performed for various intermetallics have been summarised by Herzig and Divinski [39]. The concentrations of defects Fig. 20.9. Ni tracer diffusion in B2 NiAl at various compositions X according to Frank et al. [48] and Divinski and Herzig [49] 352 20 Diffusion in Binary Intermetallics in NiAl are shown in Fig. 20.8. NiAl reveals a triple-defect type of disor- der: structural Ni vacancies (V Ni ) are the dominating defects on the Ni-lean side, whereas Ni antisite atoms (Ni Al ) dominate on the Ni-rich side of the stoichiometric composition. Moreover, vacancies form mainly on the Ni sub- lattice whereas the concentration of vacancies on the Al sublattice (V Al )is remarkably smaller even on the Al-lean side. Ni diffusion in B2 NiAl alloys has been measured at various compositions on both Al- and Ni-rich sides and over wide temperature intervals by Frank et al. [48] and reviewed in a paper on NiAl interdiffusion by Divinski and Herzig [49] 1 . These data are displayed in Fig. 20.9 for various compositions. The diffusivity increases notably on the Ni-rich side of the stoichiometric composition. It is practically independent of composition on the Al-rich side in spite of the considerable amount of structural Ni vacancies (see Fig. 20.8). Theoretical studies of the atomic mechanism using embedded atom po- tentials showed that the triple-defect mechanism dominates self-diffusion Fig. 20.10. Self-diffusion of Fe and Al in Fe 3 Al 1 Older measurements of Ni diffusion in NiAl [40] are very likely influenced by grain-boundary contributions [39] and are not considered here. 20.3 B2 Intermetallics 353 Fig. 20.11. Self-diffusion of Fe and Al and interdiffusion in Fe 2 Al on the Al-rich side and for stoichiometric NiAl. The widely abundant iso- lated Ni vacancies do not contribute significantly to Ni diffusion, because their motion via the six-jump-cycle mechanism is energetically unfavourable. With increasing Ni content, after reaching the percolation threshold, the antistructural-bridge mechanism on the Ni-rich side leads to an increase in the Ni diffusivity [48]. 20.3.3 Example B2 Fe-Al The phasefield of B2 order in the Fe-Al system is fairly extended [3]. B2 order exists between about 22 and 50 at.% Al. In contrast to NiAl, B2 order does hardly extend to compositions on the Al-rich side of stoichiometry. At higher temperatures an order-disorder transition to the disordered A2 structure oc- curs. The corresponding transition temperature increases with increasing Al content. Some tracer data for 26 Al in aluminides are available from the work of Larikov et al. [22]. Tracer measurements of Fe self-diffusion were carried out by T ¨ okei et al.[24] and by Eggersmann and Mehrer [23]. Interdiffu- 354 20 Diffusion in Binary Intermetallics Fig. 20.12. Solute diffusion of Zn, In, Ni, Co, Mn, and Cr in Fe 3 Al according to [23, 51]. Fe self-diffusion in Fe 3 Al is also shown for comparison sion in the whole B2 phasefield of Fe-Al alloys has been studied by Salamon and Mehrer [50]. These authors used the Darken-Manning equation (see Chap. 10), the Kirkendall shift, calculated thermodynamic factors, and Fe tracer data of the Fe-Al system and deduced Al tracer diffusivities for al- loys with the approximate compositions Fe 3 Al, Fe 2 Al, and FeAl. Some of the results for diffusion in iron-alumindes are shown in Figs. 20.10 and 20.11. Fe 3 Al reveals A2 disordered, B2 ordered, and D0 3 ordered structures with decreasing temperature. As already indicated in Eq. (20.2), the increase in the degree of order results in an increase of the activation enthalpy, which can be seen in Fig. 20.10. Self-diffusion in Fe 2 Al and FeAl has been investigated almost exclusively in the B2 phase region. For all three compositions the diffusivities of Fe and Al are not much different indicating a coupled diffusion of both components. Solute diffusion in Fe-Al alloys has also been investigated. Typical results for ternary alloying elements in Fe 3 Al are compiled in Fig. 20.12 and com- pared with Fe self-diffusion. Zn and In are incorporated on Al sites and diffuse slightly faster than self-diffusion of both components Fe and Al [23]. Ni and 20.4 L1 2 Intermetallics 355 Co substitute Fe atoms. They are slower diffusers and have higher activation enthalpies than self-diffusion. The diffusivities of Mn and Cr are both fairly similar to Fe self-diffusion [51]. 20.4 L1 2 Intermetallics In completely ordered L1 2 compounds, each A atom is surrounded by 8 A atoms and 4 B atoms on nearest-neighbour sites (see Fig. 20.1). In con- trast to this situation, a B atom faces only A atoms on nearest-neighbour sites. This implies that the sublattice of the majority component A is inter- connected by nearest-neighbour bonds, whereas this is not the case for the sublattice of the minority component B. Vacancy motion restricted to the ma- jority sublattice can promote diffusion of A atoms as illustrated in Fig. 20.13. Diffusion of B atoms on its own sublattice requires jump lengths larger than the nearest-neighbour distance, which are energetically unfavourable. An- other possibility is the formation of antisite defects and diffusion via vacancies of the majority sublattice. Perhaps the best known L1 2 intermetallic is Ni 3 Al. It has been used as a strengthening phase in Ni-base superalloys for a long time. The Ni 3 Al phasefield in the Ni-Al system exists on both sides of the stoichiometric com- positions, but in a faily narrow composition interval. The concentrations of defects in Ni 3 Al taken from the review [39] are shown in Fig. 20.14. Ni 3 Al belongs to the antistructural-defect type of inter- metallics, in which antisite atoms (Ni Al and Al Ni ) are preferentially formed to accommodate deviations from stoichiometry. Vacancies are mainly formed on the Ni sublattice. Their concentrations are similar to thermal vacancy concentrations in pure Ni at the same homologous temperature. Vacancy formation on the Al sublattice is energetically less favourable. Ni diffusion has been studied using tracer techniques by Bronfin et al. [41], Hoshino et al. [42], Shi et al. [43], and Frank et al. [44]. Fig. 20.13. Schematic illustration of the sublattice vacancy mechanism in the majority sublattice of an L1 2 structured intermetallic. Ful l circles : majority atoms; open circles: minority atoms 356 20 Diffusion in Binary Intermetallics Fig. 20.14. Defect site fractions in L1 2 structured Ni 3 Al as a function of compo- sition at 0.75 T m from [39] Unfortunately, diffusion studies on Ni 3 Al, as for other aluminides, suffer from the lack of a suitable radiotracer for Al. On the other hand, interdiffusion co- efficients across the phase field of Ni 3 Al were measured by Ikeda et al.[45] and Watanabe et al. [46]. Using the Darken-Manning equation and the Kirkendall shift, Fujiwara and Horita [47] deduced Al tracer diffusivities. It was found that the Ni and Al diffusivities are not much different. Suit- able substitutes for Al (e.g., Ge and Ga) have been studied (see Table 20.1 and [39]) and support this finding. Diffusion in the L1 2 compounds Ni 3 Ge and Ni 3 Ga has also been studied. Fortunately, in these cases suitable radiotracers for both constituents are available. As can be seen from Fig. 20.16, diffusion of the majority component Ni in Ni 3 Ge is indeed significantly faster than that of the minority component Ge. Experiments on Ni 3 Ga revealed a trend similar to the case of Ni 3 Ge, but the difference of the diffusivities is not so large [52]. For Ni 3 Al only Ni self- diffusion is indicated. According to the above reasoning the ratio of the two tracer diffusivities, D Ni /D Al ,inNi 3 Al is not much different from unity. It is quite natural that diffusion of the majority component in L1 2 com- pounds occurs by a sublattice vacancy mechanism. The diffusion coefficient is expressed as D A = 2 3 a 2 fC eq V ω, (20.6) where a is the lattice parameter, C eq V the concentration of vacancies in the majority sublattice, and ω the vacancy jump rate. The random walk proper- ties and the tracer correlation factor for sublattice diffusion of the majority component in L1 2 compounds via the vacancy mechanism have been dis- cussed by Koiwa et al. [53]. A value of f =0.6889 has been reported for the tracer correlation factor. 20.5 D0 3 Intermetallics 357 Fig. 20.15. Self-diffusion in L1 2 structured Ni 3 Al according to [39] The diffusion mechanism of the minority elements in L1 2 compounds is less obvious. As can be seen from Fig. 20.16 and from the discussion of diffusion in Ni 3 Al, the tracer diffusivities of the minority elements in these compounds can vary from very different to similar of those of the majority elements. The diffusivity of Ge in Ni 3 Ge is rather low, whereas the diffusivity of Ga in Ni 3 Ga and very likely the diffusivity of Al in Ni 3 Al are not much different from the respective majority components. Possible mechanisms are discussed in [8]. Minority elements most likely diffuse as antisite atoms in the majority sublattice. 20.5 D0 3 Intermetallics A prominent example of a D0 3 intermetallic is Fe 3 Si. Its phase field is lo- cated between the stoichiometric composition and Fe-rich compositions up to about 82 at.% Fe. Information about the diffusion of both constituents and of Ge diffusion is available. Fe 3 Al also shows D0 3 order but only at fairly low [...]... Fujiwara, Z Horita, Acta Mater 50 , 157 1 (20 02) 48 S Frank, S.V Divinski, U S¨dervall, Chr Herzig, Acta Mater 49, 1399 (20 01) o 49 S.V Divinski, Chr Herzig, Defect and Diffusion Forum 20 3 20 5, 177 (20 02) 50 M Salamon, H Mehrer, Z Metallkd 96, 1 (20 05) 51 S Peteline, E.M Tanguep Njiokep, S Divinski, H Mehrer, Defect and Diffusion Forum 21 6 21 7, 1 75 (20 03) References 369 52 K Nonaka, T Arayashiki, H Nakajima,... (20 05) 70 S Divinski, M Salamon, H Mehrer, Philos Mag 84, 757 (20 05) 71 W Sprengel, X.Y Zhang, H Inui, H.-E Schaefer, Verhandl DPG 5, 339 (20 03) 72 D.J Thoma, J.H Perepezko, J Alloys and Compounds 22 4, 330 (19 95) 73 M Denkinger, H Mehrer, Philos Mag A 80, 124 5 (20 00) 74 F.M d’Heurle, P Gas, J Philibert, Solid State Phenomena 41, 93 (19 95) 75 F.M d’Heurle, P Gas, C Lavoie, J Philibert, Z Metallkd 95, ... 80, 121 9 (20 00) 24 Zs T¨kei, J Bernardini, P Gas, D.L Beke, Acta Mater 45, 54 1 (1997) o 25 E.W Elcock, C.W McCombie, Phys Rev 109, 6 05 (1 958 ) 26 E.W Elcock, Proc Phys Soc 73, 25 0 (1 959 ) 27 H.B Huntington, N.C Miller, V Nerses, Acta Metall 9, 749 (1961) 28 P Wynblatt, Acta Metall 47, 24 37 (1967) 29 H.A Domian, H.I Aaronson, in: Diffusion in Body-Centered Cubic Metals, American Society for Metals, 19 65, ... Ru, Os) Ni17 Ti41 .5 Zr41 .5 Ga20 Mg43 Zn37 Al37 Cu10.8 Li 32. 2 Al43 Mg43 Pd14 Zn64 .2 Mg26.4 Ho9.4 Zn60.7 Mg30.6 Y8.7 Al64 Co16 Cu20 Al71 .5 Co14 Ni14 .5 Al69.8 Pd18.1 Mn 12. 3 Al71 Fe5 Ni24 Al40 Fe 15 Ge20 Mn 25 Ta1.6 Te Fig 21 .1 Icosahedral single-quasicrystal (Zn-Mg-Ho) with the habit of a dodecahedron A dodecahedron has 12 pentagon-shaped faces and 20 vertices Nowadays, quasicrystals are no longer laboratory... Rev B 2, 1 451 (1970) 19 S.G Fishman, R.N Jeffrey, Phys Rev B 120 , 4 424 (1971) 20 Y Iijima, Ch.-G Lee, Acta Metall Mater 43, 1183 (19 95) 21 H Nitta, Y Iijima, K Tanaka, Y Yamazaki, Ch.-G Lee, T Matsuzaki, T Watanabe, Mater Sci Eng A 3 82, 24 3, 25 0 (20 04) 22 L.N Larikov, V.V Geichenko, V.M Gal’chenko, Diffusion Processes in Ordered Alloys, translated from Russion, Amerind Publ Co Ltd, New Dehli, 1981 23 M... Nakajima, Acta Mater 54 , 25 11 (20 06) 65 L Ding, P.F Ladwig, X Yan, Y.A Chang, Appl Phys Letters 80, 1186 (20 02) 66 S Peteline, H Mehrer, M.-L Huang, Y.A Chang, Defect and Diffusion Forum 23 7 24 0, 3 52 (20 05) 67 M Yamaguchi, H Inui, K Ito, Acta Mater 48, 307 (20 00) 68 M Salamon, A Strohm, T Voss, P Laitinen, I Rihim¨ki, S Divinski, W a Frank, J R¨is¨nen, H Mehrer, Philos Mag 84, 737 (20 04) a a 69 M Salamon,... Metals, 19 65, p 20 9 30 M Arita, M Koiwa, S Ishioka, Acta Metall 37, 1363 (1989) 31 R Drautz, M F¨hnle, Acta Mater 47, 24 37 (1999) a 32 I.V Belova, G.E Murch, Philos Mag A 82, 26 9 (20 02) 33 N.A Stolwijk, M van Gend, H Bakker, Philos Mag, A 42, 28 3 (1980) 34 S Frank, S.V Divinski, U S¨dervall, Chr Herzig, Acta Mater 49, 1399 (20 01) o 35 H Bakker, N.A Stolwijk, M.A Hoetjes-Eijkel, Philos Mag A 43, 25 1 (1981)... Crystal and Solid State Physics, Vol 26 , Springer-Verlag, 1990 p 21 3 5 H Bakker, Tracer Diffusion in Concentrated Alloys, in: Diffusion in Crystalline Solids, G.E Murch, A.S Nowick (Eds.), Academic Press, Orlando, 1984, p 189 6 H Wever, Defect and Diffusion Forum 83, 55 (19 92) 7 H Mehrer, Materials Transactions, JIM, 37, 1 25 9 (1996) 8 M Koiwa, H Numakura, S Ishioka, Defect and Diffusion Forum 143–147, 20 9 (1997)... 12] Quasicrystals are a prominent example for systems whose properties are mainly determined by their structure 3 72 21 Diffusion in Quasicrystalline Alloys Table 21 .1 Examples of some stable quasicrystalline phases Icosahedral quasicrystals Decagonal quasicrystals Dodecagonal quasicrystals Al70 Pd21 Re9 Al70 Pd21 Mn9 Al 62 Cu 25 TM13 (TM = Fe, Ru, Os) Ni17 Ti41 .5 Zr41 .5 Ga20 Mg43 Zn37 Al37 Cu10.8 Li 32. 2... 143–147, 20 9 (1997) 53 M Koiwa, S Ishioka, Philos Mag A 48, 1 (1983) 54 A Gude, H Mehrer, Philos Mag A 76, 1 (1997) 55 M Wellen, B Fielitz, G Borchardt, S Weber, S Scherrer, H Mehrer, H Baumann, B Sepiol, Defect and Diffusion Forum 194–199, 499 (20 01) 56 E.A K¨mmerle, K Badura, B Sepiol, H Mehrer, H.-E Schaefer, Phys Rev u B 52 , R6947 (19 95) 57 B Sepiol, G Vogl, Phys Rev Lett 71, 731 (19 95) 58 S Kroll, . diffusivity [48]. 20 .3.3 Example B2 Fe-Al The phasefield of B2 order in the Fe-Al system is fairly extended [3]. B2 order exists between about 22 and 50 at.% Al. In contrast to NiAl, B2 order does hardly. et al. [24 ] and by Eggersmann and Mehrer [23 ]. Interdiffu- 354 20 Diffusion in Binary Intermetallics Fig. 20 . 12. Solute diffusion of Zn, In, Ni, Co, Mn, and Cr in Fe 3 Al according to [23 , 51 ]. Fe. constituents concerns the cubic C 15- type phase with the approximate composition Co 2 Nb. The C 15 structure of the cubic Laves phase Co 2 Nb is shown in Fig. 20 .22 . In the completely ordered state, the unit cell