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.. a vac
Trang 1348 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 its:
– Triple-defect mechanism: In a B2 compound triple-defect disorder can
occur according to the reaction
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 notchange the composition Instead of forming equal numbers of vacancies
Trang 220.3 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
VB 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 forms two nearest-neighbour jumps instead of one second-nearest neigh-bour jump [34] Figure 20.6 shows the triple-defect mechanism with this
per-Fig 20.7 Illustration of the antistructural-bridge (ASB) mechanism The arrows
show vacancy jumps; the numbers indicate the jump sequence
Trang 3350 20 Diffusion in Binary Intermetallics
modification The ratio of the diffusivities for this mechanism lies withinthe 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 exchangetheir position For a B2 phase with some substitutional disorder, antisitedefects can act as ‘bridges’ to establish low energy sequences for vacancyjumps
It is important to note that the ASB mechanism has a percolation old Long-range diffusion via the ASB mechanism requires a sufficientconcentration of antistructure atoms to reach the percolation threshold
thresh-A relatively high threshold was estimated from purely geometrical 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 likeNiAl (see below)
argu-– 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 tice, can mediate diffusion of both components by successive correlatednext-nearest-neighbour jumps Whereas this mechanism has some rele-
sublat-Fig 20.8 Defect site fractions in B2 NiAl as a function of composition at 0.75 Tm
from [39]
Trang 420.3 B2 Intermetallics 351vance for ionic crystals such as alkali halides (see Chap.26), it is unlikelyfor B2 intermetallics.
It seems that in those B2 compounds, which are composed of a group VIIIBmetal (Co, Fe, Ni, Pd, etc.) and a group IIIA metal (Al, Ga, In, etc.), thetriple-defect mechanism is important By contrast, B2 phases composed of
a noble metal (Cu, Ag, Au) and a divalent metal (Mg, Zn, Cd) and FeCoare considered as candidates for the six-jump-cycle mechanism Clearly, theantistructural-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 onthe Al-rich side to about 65 % Ni on the Ni-rich side [3] Theoretical calcula-tions of defect concentrations performed for various intermetallics have beensummarised by Herzig and Divinski [39] The concentrations of defects
Fig 20.9 Ni tracer diffusion in B2 NiAl at various compositions X according to
[48] and Divinski and Herzig [49]
Trang 5352 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 N i) are the dominating defects on the Ni-lean
side, whereas Ni antisite atoms (N i Al) dominate on the Ni-rich side of thestoichiometric composition Moreover, vacancies form mainly on the Ni sub-
lattice whereas the concentration of vacancies on the Al sublattice (V Al) isremarkably 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 andHerzig[49]1 These data are displayed in Fig 20.9 for various compositions.The diffusivity increases notably on the Ni-rich side of the stoichiometriccomposition 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 Fe3Al
1 Older measurements of Ni diffusion in NiAl [40] are very likely influenced by
grain-boundary contributions [39] and are not considered here
Trang 620.3 B2 Intermetallics 353
Fig 20.11 Self-diffusion of Fe and Al and interdiffusion in Fe2Al
on the Al-rich side and for stoichiometric NiAl The widely abundant lated Ni vacancies do not contribute significantly to Ni diffusion, becausetheir motion via the six-jump-cycle mechanism is energetically unfavourable.With increasing Ni content, after reaching the percolation threshold, theantistructural-bridge mechanism on the Ni-rich side leads to an increase inthe Ni diffusivity [48]
iso-20.3.3 Example B2 Fe-Al
The phasefield of B2 order in the Fe-Al system is fairly extended [3] B2 orderexists between about 22 and 50 at.% Al In contrast to NiAl, B2 order doeshardly extend to compositions on the Al-rich side of stoichiometry At highertemperatures an order-disorder transition to the disordered A2 structure oc-curs The corresponding transition temperature increases with increasing Alcontent
Some tracer data for26Al in aluminides are available from the work ofLarikov et al.[22] Tracer measurements of Fe self-diffusion were carriedout by T¨okei et al.[24] and by Eggersmann and Mehrer [23] Interdiffu-
Trang 7354 20 Diffusion in Binary Intermetallics
Fig 20.12 Solute diffusion of Zn, In, Ni, Co, Mn, and Cr in Fe3Al according
to [23, 51] Fe self-diffusion in Fe3Al is also shown for comparison
sion in the whole B2 phasefield of Fe-Al alloys has been studied by Salamonand Mehrer [50] These authors used the Darken-Manning equation (seeChap 10), the Kirkendall shift, calculated thermodynamic factors, and Fetracer data of the Fe-Al system and deduced Al tracer diffusivities for al-loys with the approximate compositions Fe3Al, Fe2Al, and FeAl Some of theresults for diffusion in iron-alumindes are shown in Figs 20.10 and 20.11
Fe3Al reveals A2 disordered, B2 ordered, and D03ordered structures withdecreasing temperature As already indicated in Eq (20.2), the increase inthe degree of order results in an increase of the activation enthalpy, which can
be seen in Fig 20.10 Self-diffusion in Fe2Al and FeAl has been investigatedalmost exclusively in the B2 phase region For all three compositions thediffusivities 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 resultsfor ternary alloying elements in Fe3Al are compiled in Fig 20.12 and com-pared with Fe self-diffusion Zn and In are incorporated on Al sites and diffuseslightly faster than self-diffusion of both components Fe and Al [23] Ni and
Trang 820.4 L12 Intermetallics 355
Co substitute Fe atoms They are slower diffusers and have higher activationenthalpies than self-diffusion The diffusivities of Mn and Cr are both fairlysimilar to Fe self-diffusion [51]
20.4 L12 Intermetallics
In completely ordered L12 compounds, each A atom is surrounded by
8 A atoms and 4 B atoms on nearest-neighbour sites (see Fig 20.1) In trast to this situation, a B atom faces only A atoms on nearest-neighboursites This implies that the sublattice of the majority component A is inter-connected by nearest-neighbour bonds, whereas this is not the case for thesublattice 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 thanthe nearest-neighbour distance, which are energetically unfavourable An-other possibility is the formation of antisite defects and diffusion via vacancies
con-of the majority sublattice
Perhaps the best known L12 intermetallic is Ni3Al It has been used as
a strengthening phase in Ni-base superalloys for a long time The Ni3Alphasefield 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 Ni3Al taken from the review [39] areshown in Fig 20.14 Ni3Al belongs to the antistructural-defect type of inter-metallics, in which antisite atoms (NiAl and AlN i) are preferentially formed
to accommodate deviations from stoichiometry Vacancies are mainly formed
on the Ni sublattice Their concentrations are similar to thermal vacancyconcentrations in pure Ni at the same homologous temperature Vacancyformation 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 L12structured intermetallic Full circles: majority atoms; open circles: minority atoms
Trang 9356 20 Diffusion in Binary Intermetallics
Fig 20.14 Defect site fractions in L12 structured Ni3Al as a function of
compo-sition at 0.75 T m from [39]
Unfortunately, diffusion studies on Ni3Al, as for other aluminides, suffer fromthe lack of a suitable radiotracer for Al On the other hand, interdiffusion co-efficients across the phase field of Ni3Al were measured by Ikeda et al.[45]and Watanabe et al [46] Using the Darken-Manning equation and theKirkendall shift, Fujiwara and Horita [47] deduced Al tracer diffusivities
It was found that the Ni and Al diffusivities are not much different able substitutes for Al (e.g., Ge and Ga) have been studied (see Table 20.1and [39]) and support this finding
Suit-Diffusion in the L12compounds Ni3Ge and Ni3Ga has also been studied.Fortunately, in these cases suitable radiotracers for both constituents areavailable As can be seen from Fig 20.16, diffusion of the majority component
Ni in Ni3Ge is indeed significantly faster than that of the minority component
Ge Experiments on Ni3Ga revealed a trend similar to the case of Ni3Ge, butthe difference of the diffusivities is not so large [52] For Ni3Al only Ni self-diffusion is indicated According to the above reasoning the ratio of the two
tracer diffusivities, D N i/DAl, in Ni3Al is not much different from unity
It is quite natural that diffusion of the majority component in L12pounds occurs by a sublattice vacancy mechanism The diffusion coefficient
com-is expressed as
DA=2
3a
where a is the lattice parameter, C V eq 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 majoritycomponent in L12 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
Trang 1020.5 D03 Intermetallics 357
Fig 20.15 Self-diffusion in L12 structured Ni3Al according to [39]
The diffusion mechanism of the minority elements in L12 compounds isless obvious As can be seen from Fig 20.16 and from the discussion ofdiffusion in Ni3Al, the tracer diffusivities of the minority elements in thesecompounds can vary from very different to similar of those of the majorityelements The diffusivity of Ge in Ni3Ge is rather low, whereas the diffusivity
of Ga in Ni3Ga and very likely the diffusivity of Al in Ni3Al are not muchdifferent from the respective majority components Possible mechanisms arediscussed in [8] Minority elements most likely diffuse as antisite atoms in themajority sublattice
20.5 D03 Intermetallics
A prominent example of a D03 intermetallic is Fe3Si Its phase field is cated between the stoichiometric composition and Fe-rich compositions up
lo-to about 82 at.% Fe Information about the diffusion of both constituents and
of Ge diffusion is available Fe Al also shows D0 order but only at fairly low
Trang 11358 20 Diffusion in Binary Intermetallics
Fig 20.16 Self-diffusion in the L12intermetallics Ni3Ge, Ni3Ga, and Ni3Al Thetemperature scale is normalised to the corresounding melting temperatures Forcomparison self-diffusion in Ni is also shown For references see [7]
tempertaures Fe3Al is formed on cooling by ordering reactions in the solidstate that transform the bcc ordered solid solution, which is stable aboveabout 1000 K, into a B2 phase and then at about 800 K into the D03 struc-ture Diffusion studies in D03 ordered Fe3Al are difficult due to the fairlylow diffusivities (see above) Some high-temperature intermetallics (Cu3Sn,
Ni3Sn, ) crystallise in the D03structure Only for Cu3Sn diffusion of bothconstituents has been investigated (see Table 20.1)
The majority sublattice (A sublattice) in D03 compounds, similar to theL12 structure, is interconnected by nearest-neighbour bonds, whereas this isnot the case for the B sublattice (see Fig 20.1) An A atom can diffuse withinits own sublattice via nearest-neighbour jumps If B atoms migrate withintheir own sublattice, their jump vector would be a third-nearest neighbourjump with respect to the bcc unit cell An alternative for the diffusion of Batoms are nearest-neighbour jumps, which create B antisite defects Then,
B atoms can diffuse as ‘imperities’ in the majority sublattice Both optionsrequire higher activation enthalpies for diffusion of B atoms
Figure 20.17 shows an Arrhenius plot of Fe- and Ge tracer diffusion forthree compositions of Fe3Si according to Gude and Mehrer [54] The datacover rather wide temperature ranges mostly within the D03 phasefield Oneexperiment with the short-lived isotope31Si confirmed that Ge and Si diffuse
Trang 1220.5 D03 Intermetallics 359
Fig 20.17 Fe self-diffusion and Ge solute diffusion in three compositions of the
D03 phase Fe3Si according to Gude and Mehrer [54] The temperatures arenormalised to the corresponding liquidus temperatures A slight influence of theparamagnetic-ferromagnetic transition can be seen for Fe diffusion in Fe79Si21and
Fe82Si18
at very similar rates [54] Diffusion studies of Si and Ge after ion implantationusing SIMS profiling also showed that Ge is a ‘good’ substitute to mimic Sidiffusion [55] The most salient features of Fig 20.17 are: (i) The asymmetrybetween the fast Fe diffusion and the relatively slow Ge or Si diffusion islarge (ii) The Fe diffusivity increases with Si content and Fe diffuses fastest
in the nearly stoichiometric compound
Positron annihilation studies by Schaefer and coworkers [56] haveshown that the increase in Fe diffusivity is accompanied by a comparableincrease of the content in thermal vacancies In addition, M¨ossbauer experi-ments on stoichiometric Fe3Si by Sepiol and Vogl [57] have demonstratedthat the atomic jump vector of Fe atoms is in agreement with nearest-neighbour jumps in the Fe sublattice These findings clearly support a sub-