Diffusion in the ordered phases

Transcription

1 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 () and γ ( 3 ) phases, in which most of the studies till date are conducted.

2 Crystal structure of the B2 phase (stoichiometric composition) B2 α-sublattice (lets say belongs to ) β-sub attice (lets say belongs to ) B2 or the β phase in the - system has L1 o structure. If occupies the body center position of the cubic cell then occupies the body corner positions. Similarly as explained, it can also be seen as occupying the body center position and occupying the body corner positions. Actually two simple cubic cells of and penetrate each other. Phase diagram from P. Nash, Phase Diagrams of Binary ckel loys, Materials Park (Ohio): ASM International (1991) 3-11

3 It can be seen that the phase has a wide homogeneity range. It deviates both on and rich sides. Deviation from the stoichiometry is achieved because of constitutional defects the presence of In the rich side, there are triple defects (2 + ). That means two missing and one additional on sublattice. on sublattice is called antisite In the rich side, there are antisites. Bradley and Taylor, Proc. Royal Soc. A 159 (1937)

4 Migration of atoms/vacancy in B2 structure NNN NN NN (Nearest Neighbor) jump is not possible: because will go to 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 atoms which are present in the middle Different diffusion mechanisms are proposed following which diffusion is possible

5 6 jump cycle (6JC) mechanism Proposed by: Huntington, private communication Elcock and McCombie Phys. Rev. B 109 (1958) 605 Comments from Divinski and Herzig, Intermetallics, 8 (2000) 1357, and 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

6 Triple defect mechanism Proposed by Stolwijk, van Gand, Bakker, Phil Mag. A 42 (1980) 783 Possible diffusion mechanism in the -rich side After 2 jumps and exchange their position without destroying triple defect structure Only atoms migrate in this particular case Continue

7 Triple defect mechanism Proposed by Stolwijk, van Gand, Bakker, Phil Mag. A 42 (1980) 783 Possible diffusion mechanism in the -rich side After 4 jumps, and exchange their position without destroying triple defect structure and atoms migrate together.

8 Anti structure bridge (ASB) mechanism Antisite atoms make a bridge to facilitate diffusion Proposed by: Kao and Chang, Intermetallics,1 (1993) 237 Possible diffusion mechanism in the -rich side Antisite atoms make a bridge to facilitate diffusion

9 Crystal structure and constitutional defects in the 3 phase Stoichiometric composition -rich(by antisites) -rich(by antisites) 3 phase has L12 structure, in which occupies body corner positions and occupies the face center positions. This phase deviates from the stoichiometric composition because of presence of antisite defects. the Aoki and Izumi, Phys. Stat. Sol. 32 (1975) 657

10 When there are no defects present in the crystal, each atom is surrounded by 8 and 4 atoms, whereas, each atom is surrounded by 12 atoms. So can diffuse through its own sublattice, if vacancies are present. On the other hand cannot diffuse if it does not have any antisite defect. Because otherwise it cannot exchange position with vacancies on the sublattice. However, experimental results indicate significant diffusion of.

11 Defect concentrations calculated in 3 A l A l A l V V V 1200 K 1400 K 1600 K Following theoretical analysis of Numakura et al., antisite defects are always present. Concentration of vacancy on the sublattice is much higher than vacancy on the sublattice. This indicates that diffusion mainly happens because of vacancies on the sublattice only. Numakura et al. Phil. Mag. 77 (1998) 887

12 Diffusion of occurs by exchanging position of atoms and vacancies on its own sublattice. Presence of antisites increases the diffusion rate. Diffusion of occurs because of vacancy on the sublattice and antisite defects. Numakura et al. Phil. Mag. 77 (1998) 887