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Diffusion in the ordered phases
� Atomic diffusion mechanism in random solid solution is better
understood, however, it is least understood in the ordered phases.
�We shall discuss the complexity of the process considering B2 (NiAl)
and γ (Ni3Al) phases, in which most of the studies till date are
conducted.
Crystal structure of the B2 phase (stoichiometric composition)
α-sublattice (lets say belongs to Al)
β-sub attice (lets say belongs to Ni)
B2
� B2 or the β phase in the Ni-Al system has L1o structure. If Ni occupies the body
center position of the cubic cell then Al occupies the body corner positions.
� Similarly as explained, it can also be seen as Al occupying the body center position
and Ni occupying the body corner positions.
� Actually two simple cubic cells of Al and Ni penetrate each other.
Phase diagram from P. Nash, Phase Diagrams of Binary Nickel Alloys, Materials Park (Ohio): ASM International (1991) 3-11
Bradley and Taylor, Proc. Royal Soc. A 159 (1937)
Al
Ni
� It can be seen that the phase has a wide homogeneity range. It deviates both on
Ni and Al rich sides.
� Deviation from the stoichiometry is achieved because of the presence of
constitutional defects
� In the Al rich side, there are triple defects (2VNi+NiAl ) . That means two missing Ni
and one additional Ni on Al sublattice. Ni on Al sublattice is called Ni antisite
� In the Ni rich side, there are Ni antisites.
� NN (Nearest Neighbor) jump is not possible: because Al will go to Ni sublattice,
which is not allowed unless it is an antisite defect. Vacancy concentration on the
sublattices will change, which is not again allowed, since in equilibrium condition
different sublattices will have particular concentration of vacancies.
� Only possibility is NNN (Next Nearest Neighbour) jump to maintain the order,
since direct NNN jump is not possible because of 4 Al atoms which are present in
the middle
� Different diffusion mechanisms are proposed following which diffusion is
possible
Al
Ni
VNi
NN
NNN
Migration of atoms/vacancy in B2 structure
6 jump cycle (6JC) mechanism
Comments from Divinski and Herzig, Intermetallics, 8 (2000) 1357
� Ni, Al and VNi exchange positions 6 times after which NNN jump is
possible
� The occurrence of 6JC is limited to the stoichiomtric composition
and below 1100 K (following the model of embedded atom
potentials)
� Contribution is only 30% of the total diffusivity
Proposed by:
Huntington, private communication
Elcock and McCombie Phys. Rev. B 109 (1958) 605
Al
NiVNi
Triple defect mechanism
Proposed by Stolwijk, van
Gand, Bakker, Phil Mag. A 42
(1980) 783
VNi
NiAl
Continue……
� Possible diffusion mechanism in the Al-rich side
� After 2 jumps Ni and VNi exchange their position
without destroying triple defect structure
�Only Ni atoms migrate in this particular case
Al
NiVNi
VNi
NiAl
Triple defect mechanism
Proposed by Stolwijk, van Gand, Bakker, Phil Mag. A 42 (1980) 783
� Possible diffusion mechanism in the Al-rich side
� After 4 jumps Ni, Al and VNi exchange their position without destroying triple defect
structure
� Ni and Al atoms migrate together.
Al
NiVNi
Anti structure bridge (ASB) mechanism
Antisite atoms make a bridge to facilitate diffusion
Proposed by: Kao and Chang, Intermetallics,1 (1993) 237
Al
Ni
VNi
� Possible diffusion mechanism in the Ni-rich side
� Antisite Ni atoms make a bridge to facilitate diffusion
Crystal structure and constitutional defects in the Ni3Al phase
Al
Ni
Al-rich(by Al
antisites)
Ni-rich(by Ni
antisites)
Aoki and Izumi, Phys. Stat. Sol. 32 (1975) 657
NiAl
AlNi
Stoichiometric
composition
� Ni3Al phase has L12 structure, in which Al occupies body corner positions and
Ni occupies the face center positions.
� This phase deviates from the stoichiometric composition because of the
presence of antisite defects.
�When there are no defects present in the crystal, each Ni atom is surrounded
by 8 Ni and 4 Al atoms, whereas, each Al atom is surrounded by 12 Ni atoms.
� So Ni can diffuse through its own sublattice, if vacancies are present.
� On the other hand Al cannot diffuse if it does not have any antisite defect.
Because otherwise it cannot exchange position with vacancies on the Ni
sublattice.
� However, experimental results indicate significant diffusion of Al.
Defect concentrations calculated in Ni3Al
VNi
VAl
VNi
VNi
VAl
VAl
AlNi NiAl
AlNi
AlNi
NiAl
NiAl
1200 K 1400 K 1600 K
Numakura et al. Phil. Mag. 77 (1998) 887
� Following theoretical analysis of Numakura et al., antisite defects are always
present.
� Concentration of vacancy on the Ni sublattice is much higher than vacancy on the
Al sublattice.
� This indicates that diffusion mainly happens because of vacancies on the Ni
sublattice only.