Peierls stresses estimated via the Peierls-Nabarro model using ab-initio γ-surface and their comparison with experiments

Abstract In order to rationalize the homologous nature of the Peierls stress reported in a previous paper (Y. Kamimura et al., Acta Mater. 61 (2013) 294–309), we have calculated numerically the Peierls stresses via the Peierls-Nabarro model (P-N model) of the planar core dislocation, using calculated ab-initio γ -surface for a variety of crystals: fcc metals, bcc metals, NaCl type crystals, CsCl type ionic crystals and various tetrahedrally coordinated crystals. The obtained γ- surfaces for the same group of crystals are found to have similar shape and height when normalized by materials parameters, indicating homologous nature. Except for some very soft crystals ( τ P exp / G ≪ 1 × 10 −4 ), the calculated Peierls stresses for majority of crystals ( τ P exp / G > 1 × 10 −4 ) are shown, for the first time, to have a correlation with experimental ones reflecting the homologous nature of the γ -surface, although the former are generally larger than the latter by half an order on the average, with an exception of bcc metal in which the strain field of the controlling screw dislocation is known to be non-planar. For very soft crystals, the calculated Peierls stresses are orders of magnitude larger than experimental ones; possible origins of this large discrepancy are discussed.