Antiphase-boundary energies

For the phase stability analysis we follow the method given by Kanamori and Kakehashi of geometrical inequalities and compute the antiphase boundary energy defined by... 

Figure 1 (a) The nearest neighbor pair interactions and (b) antiphase boundary energies as functions of energy for Pdj,Vi j, alloys x=0.25, x = 0.5 and x = 0.75 ( from top to bottom). Vertical lines mark the Fermi energy for the three different concentrations. 

M. Asta and A. Quong, The concentration and temperature dependences of antiphase-boundary energies in 7-TiAl a first-principle study, Phil. Mag. Lett. 76(5), 331-339 (1997). 

In this Section we use Eqs. (2)-(10) to derive several relations for the free energy F ci of a stationary noiiuniform alloy. These relations can be used to study properties of interphase and antiphase boundaries, nucleation problems, etc. 

The interatomic interaction is described by an EAM potential specifically developed for NiAl in the B2 structure [12]. Compared to the older potential [16], which was used in most of the previous atomistic studies, our new potential gives considerably higher antiphase boundary (APB) energies = 0.82 J/m, yj pg = 1.06 J/m in good agreement with the APB... 

Using the constructed potentials the y-surface for the (111) plane was calculated. (For more details see Girshick and Vitek 1995). T e lowest energy minimum on this surface corresponds to the ideal Llo structure. However, there are three different metastable stacking fault type defects on (111) the antiphase boundary (APB), the complex stacking fault (CSF) and the superlattice intrinsic stacking fault (SISF). The displacements... 

Fine-scale, spatially periodic microstructures are characteristic of spinodal decomposition. In elastically anisotropic crystalline solutions, spinodal microstructures are aligned along elastically soft directions to minimize elastic energy. Microstructures resulting from continuous ordering contain interfaces called antiphase boundaries which coarsen slowly in comparison to the rate of the ordering transformation. 

A second type of boundary, in which there is no misorientation between grains, is the antiphase boundary. This occurs when wrong atoms are next to each other on the boundary plane. For example, with hexagonal close-packed (HCP) crystals, the sequence. .. ABABAB... can be reversed at the boundary to ABABA ABABA, where represents the boundary plane. Antiphase boundaries and stacking faults are typically of very low energy, comparable to that of a coherent twin boundary. 

In layered misfit structures of the type we are discussing, bonds at the layer surfaces (within and between the layers) will be strained periodically along a non-commensurate lattice direction parallel to the layers after a certain number of subcells there is a near match of the layers. Clapp has pointed out that, for a simple case, layer mismatch will cause tension in one layer type and compression in the other. The resulting strain energy may be relieved by the introduction of periodic antiphase boundary (apb) planes so that alternate contraction and extension occurs in all layers (Fig. 22) and hence cancels out (at the price of a small deformation of coordination polyhedra). 

---