• PDF / 492,610 Bytes
• 6 Pages / 420.48 x 639 pts Page_size
• 91 Downloads / 261 Views

DOWNLOAD

REPORT

---

ANTIPHASE BOUNDARY CALCULATIONS FOR THE L12 STRUCTURE USING AN EMBEDDED ATOM METHOD MODEL JEANNE R. BROWN AND ROBERT A. JOHNSON Department of Materials Science, University of Virginia, Charlottesville, VA 22903 ABSTRACT A model based on the embedded atom method [1] has been used to calculate antiphase boundary (APB) energies of three low-index planes for alloys having the L12 structure. The lattice constant, cohesive energy, unrelaxed vacancy formation energy, bulk modulus, and average shear modulus for each element are used as inputs into the model. Effects of the APB orientation and of the range of interaction in the model are examined. Both unrelaxed and relaxed APB energies are compared with available experimental values and earlier theoretical results. A strong anisotropy was found in six of the seven alloys studied. The ( I 1) APB energy was consistently smaller than that for the I 110) APB, while the (100) APB energy was found to be very close to zero with very little difference between the unrelaxed and relaxed values. For both energy and relaxation amounts, the results did not vary much with the range of interaction, so that 3rd nearest-neighbor calculations were found to be satisfactory approximations. INTRODUCTION A method that is proving useful in studying intermetallic properties is the embedded-atom method (EAM), derived from density functional theory by Daw and Baskes [2,3]. The EAM calculations use a linear superposition of electron densities from individual spherical atoms to obtain an embedding energy. This embedding energy is then combined with traditional pair potentials to overcome two problems that were encountered previously, the Cauchy discrepancy and the cohesive energy-vacancy formation energy dilemma [4]. The method has had diverse applications for monotomic metals, and has been further developed for binary alloys [5]. In this report, an EAM model is applied to intermetallic alloys having the L1 2 structure. Although ordered alloys can deviate from the ideal stoichiometry, this study will involve only the perfect ordered structure of composition AB 3 . The components are limited to those which have had embedding functions previously determined for them, specifically Cu, Au, Ag, Pt, Ni and Pd. The possible intermetallics composed of these metals that exhibit an L1 2 structure are Cu 3Au, Au 3 Cu, Ni 3Pt, Pt3 Ag, Ag 3Pt, Au 3 Pt, and Cu 3Pt. APB energies for both the unrelaxed and relaxed structures are calculated for the three low-index planes (111), (110), and (100), using an !- dislocation in each. The results are compared with previous theoretical calculations and with available experimental results. Atomistic relaxations of the APB and of the bulk material are also examined. COMPUTATIONAL PROCEDURE EAM Model. The notation used by Johnson [6,7] in the development of an analytic nearest-neighbor fcc model and its extension to alloys [8] is used in this report. The basic EAM equations are

E,=

F(pa) E@(rb) + atoms bonds

,

Pi

= .f(rij)

(1-2)

joL

where Et is the total internal energy