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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 (Ni 3 Al) phases, in which most of the studies till date are conducted.

Diffusion in the ordered phasesnptel.ac.in/courses/113108052/module4/lecture23.pdf · Diffusion in the ordered phases ... Bradley and Taylor, Proc. Royal Soc. ... Kao and Chang, Intermetallics,1

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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.

Numakura et al. Phil. Mag. 77 (1998) 887

� Diffusion of Ni occurs by exchanging position of atoms and vacancies on its

own sublattice .

� Presence of Ni antisites increases the diffusion rate.

� Diffusion of Al occurs because of vacancy on the Ni sublattice and Al antisite

defects.