First-principles investigation of perfect and diffuse antiphase boundaries in HCP-based Ti-Al alloys
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NTRODUCTION
THE presence of chemical short-range order (SRO) in ␣ -Ti-Al was proposed over thirty years ago by Blackburn and Williams[1] to explain planar slip exhibited by alloys with concentrations greater than roughly 4 wt pct Al (7 at. pct Al).[2,3] Since that time SRO has been discussed as an important factor contributing to the anomalous solid-solution strengthening of ␣ -Ti-Al,[1,4–6] as well as the low strainhardening exponents exhibited by these alloys.[3,4,7] Only very recently, however, has direct evidence for SRO been provided from diffuse neutron scattering measurements.[3,8] These measurements confirm the presence of appreciable SRO in Ti-6 wt pct Al alloys, of a type consistent with the ordered DO19 structure of ␣2-Ti3Al. As first proposed by Fisher,[9] SRO in solid solutions can provide a significant source of strengthening due to the energy cost associated with the creation of “diffuse” antiphase boundaries (DAPB) arising from shearing of the lattice by dislocation slip. The DAPB is the analogue for structures with SRO of the more familiar antiphase boundary (APB) in a long-range-ordered crystal structure. In solid solutions with chemical SRO, the energy cost of creating a DAPB (␥SRO , defined as the excess energy per unit area of a DAPB) during slip gives rise to a friction stress on moving dislocations: SROb ⫽ ␥SRO. A plot of the DAPB energy vs the number of shearing events, calculated from first-principles for ␣ -Ti-Al alloys using the approach described below, is shown in Figure 4. This plot is qualitatively similar to theoretical results obtained for fcc-based alloy systems previously.[10–13] The energy of the DAPB after the first shear A. VAN DE WALLE, Postdoctoral Fellow, and M. ASTA, Professor, are with the Department of Materials Science and Engineering, Northwestern University, Evanston, IL 60208-3108. This article is based on a presentation made in the symposium entitled “Defect Properties and Mechanical Behavior of HCP Metals and Alloys” at the TMS Annual Meeting, February 11–15, 2001, in New Orleans, Louisiana, under the auspices of the following ASM committees: Materials Science Critical Technology Sector, Structural Materials Division, Electronic, Magnetic & Photonic Materials Division, Chemistry & Physics of Materials Committee, Joint Nuclear Materials Committee, and Titanium Committee. METALLURGICAL AND MATERIALS TRANSACTIONS A
(to be referred to as ␥1) is seen to be larger than the values (␥2, ␥3, etc.) of ␥SRO after multiple shearing events. As pointed out originally by Cohen and Fine[14] the second slip event in a solid-solution with SRO can partially restore the state of order, giving rise to a decrease in ␥SRO (cf. Figure 4) and a driving force for the pairing of leading dislocations in pile ups. Such pairing has been observed recently by transmission electronic microscopy (TEM) for dislocation pile ups in ␣ -Ti-Al.[15] Figure 4 also illustrates that after a small number of slip events the state of order is largely destroyed and subsequent dislocations experience negligible f
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