Crystal Structure of Ni3Al

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When an alien atom is introduced into a host lattice, the added atom could occupy any of a number of lattice positions. In such a case a random distribution of the different atoms is often observed for alloys. Ordered alloys are certain specific cases where the atoms of a particular kind have a higher probability to occupy certain specific sites in the lattice. Therefore, the resultant lattice structure could be imagined as two different lattices interpenetrating into each other, this type of lattice is called a superlattice.
The ordered NhAl alloy has a so called ‘Lli Super Lattice structure’, The Llz structure is very similar to the f.c.c. structure. A f.c.c. cell with Nickel atoms in the face center positions and Aluminum atoms at the cube edge positions can be thought of as the NbAl structure , (see Figure (3).) Some researchers also describe the Llz structure as a simple cubic type where the s.c. lattice is formed by the repetition of a motif. A motif is an aggregate of four different atoms each of which belong to a certain sublattice. It is easy to realize that if three face center positions and a cube edge position is treated as a single lattice point then the f.c.c. cell could be treated as a simple cubic lattice.

Coincidence Site Lattice Boundaries

The coincidence site lattice (C.S.L.) model is a well established geometric model used to study the grain boundary structure. The main reason for its popularity in this field is the simplicity involved in comprehension and calculation of these types of boundaries. The coincidence site lattice concept can most easily be understood by imagining two crystals lattice at some relative misorientation which interpenetrate. If we let a lattice point from each crystal to be brought into coincidence by relative rotation, at certain relative orientations called the ‘Coincidence Orientations’, a three dimensional lattice of coincidence of crystal lattice points exists, which is known as the coincidence site lattice. The reciprocal density of the coincidence sites relative to the crystaf lattice site is denoted by l: and is used to characterize different coincidence boundaries. l: = 5 would imply that one in every five atoms of one lattices coincides with the atoms of the lattice on the other side of the boundary. Figure( 4) shows two interpenetrating f.c.c lattices, the coincidence sites can be clearly seen to be one fifth of the total number of lattice sites, hence this is a l: = 5 boundary. The misorientation angle for this boundary is 36 °87′, circles and squares denote atoms on two successive (0021 planes projected about [001]. from the definition on: it is obvious that the low I: boundaries have more coincident sites and :E = I would imply an absence of any boundary.
It is also interesting to note that certain repeating structural units can be identified at the grain boundary. A structural unit is defined as a small group of atoms arranged in a characteristic configuration. The size of this repeating structural unit has been found to be dependent [251 upon the l: value for the boundary with low l: boundaries having smaller structural units.

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Anti-Phase Boundary

The anti-phase boundary ( A. P. B.) has a similar defect structure as a superintrinsic stacking fault, and A.P.B is bound by a pair of a/3 < 211 >, superpartial dislocations l42J. However, the energy of an A.P.B is considerably more than that of a stacking fault. This is quite natural as the formation of an A.P.B. forces a ;-.;ickel atom to an Al atom position. The A.P.B. also creates a Al- Al bond and its bond length is about 27% more than the equilibrium Al-Al separation. Unlike the previous results, the Al atoms close to the A.P.B. also undergo a displacement in the direction parallel to the boundary. The relative displacements undergone by the :–.:ickel and Al atoms can be seen in the Figure ( 17). The movement of atoms on a { 11 0} plane on the domains on eithe side of the A.P.B. are also shown in this figure. Quite unlike the other planar defects the antiphase boundary does not require a rigid body displacement in the direction perpendicular to the anti-phase plane. Since the Aluminum atoms also move in the 1211], (Figure(l8)), an acoustic mode of oscillation is also observed in this direction as can be seen from the Figure ( 19). Figure (20). shows only the antisymmetruc optical oscillations in the 1110] direction.

1.0 Introduction
2.0 ll1eory
2.1 Analytical considerations
2.2 Numerical Technique
3.0 lnteratomic Potentials
3.1 Pair Interaction Potentials
3.2 Volume Dependent Potentials
3.3 Limitations
4.0 Structural Considerations
4.1 Crystal Structure of Ni3Al
4.2 Grain Boundary Structure
5.0 Computational procedure
5.1 Generation of Defects
5.2 Defect Interactions
5.3 Rigid Body Translation
5.4 Energy Minimization Procedure
6.0 Simulation Results
6.1 Twin
6.2 Stacking Fault
6.3 Anti-Phase Boundary
6.4 Surfaces
6.5 Structure of l: = 5 Boundary
6.6 Grain Boundary Interaction with the Vacancy
7.0 Discussion
7.1 Oscillation Modes
7.2 Grain Boundary Interaction with the Vacancy
8.0 Conclusions