Hard sphere modeling of the effect of slip on interstitial sites in the B2 structure
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Geometrical modeling of the B2 structure indicates that the tetrahedral interstitial site is always the largest both before and after an a/2(lll) translation on {110}, such as occurs during the slip of a partial dislocation in some B2 compounds. The tetrahedral site within the APB which trails a gliding a/2(lll) dislocation is larger than in the unslipped lattice, suggesting that interstitial atoms will segregate there. Also, some interstitial sites in a B2 lattice are larger than those in a bcc lattice of the same lattice parameter, suggesting that interstitials may have greater solubility in B2 compounds.
In the present communication, hard-sphere modeling of the B2 or ordered bcc structure is used to examine the effect of the radius (R) ratio of the constituent A and B atoms, in the range 1 =£ RB/RA =£ 1.366, both before and after slip by a/2(lll) on {110}, on the sizes of interstitial sites. The purpose is to show that a tetrahedral interstice is always the largest, and that after slip the largest tetrahedral sites reside within the antiphase boundary (APB) formed by an a/2(lll) dislocation. Expressions derived here for the radii of the interstices are for comparison purposes only, since attempts to calculate their absolute size inevitably run into the difficulty of choosing the appropriate radii; i.e., it is not clear whether the metallic or the covalent radius should be used. The lattice parameter, a, of the B2 structure, shown with a smaller A atom in the middle and a larger B atom at the corners of the unit cell (Fig. 1), is related to the radii through a = 2(RA + RB)/^3. For the B2 structure there are both octahedral and tetrahedral holes, as in the bcc structure. The octahedral holes, as in the bcc structure, are at 1/2,1/2,0 and positions related by a/2(lll) translations. In the B2 structure, in contrast to the bcc structure, all octahedral sites are not equivalent; since the Bravais lattice is simple cubic only sites related by a(100) translations are equivalent (in size and orientation). Figure 1 shows the two types of octahedral holes, one at 1/2,1/2,0 (face position) and the other at 1/2,0,0 (edge position). The face (1/2,1/2,0) interstitial site has four B atoms and two A atoms for nearest neighbors. The radius of the hole defined by the A atom is a/2 — RA or 0.5%RB 0.42RA, whereas the B atoms define a hole with a radius of a/y/2 - RB or O.S2RA - 0A8RB. The latter hole is always the larger of the two, e.g., for RB/RA = 1, the Bdefined hole is 0.64RA, and the A-defined hole is 0.15RA; for RB/RA = 1.366, the B-defined hole is 0.42/?A, and J. Mater. Res., Vol. 8, No. 6, Jun 1993 http://journals.cambridge.org
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the A-defined hole is Q.21RA. Thus, the A atoms always define the 1/2,1/2,0 hole radius. The edge (1/2,0,0) interstitial site has four A atom and two B atom nearest neighbors. The radius of the hole defined by the B atoms is a/2 - RB or 0.58/?4 QA2RB. The A-atom-defined hole has a radius a/-j2 — RA. Since RB > RA, by inspection, the latter hole is always larger. Thus, the
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