A systematic study of symmetric tilt-boundaries in hard-sphere f.c.c. crystals

A new method is developed for the search of mechanically stable configurations of symmetric tilt boundaries in hard sphere f.c.c. crystals. The problem of finding out relative displacements which minimize the total volume of two crystal blocks forming a boundary, is simplified to a problem of positioning a single atom sphere relative to a block which consists of real and “image” atoms; the lattter are placed in such a way to reflect the arrangement in the other crystal block. The method (the image atom method) has been applied to the analysis of symmetric coincidence boundaries with [100], [110] and [111] tilt axes with ∑-values 3–103. For the [100] (013)∑5 boundary, the procedure of the analysis is described in detail; the derived structures are compared with those by computer simulation. Numerical data are given in tabulated forms for some boundaries.