Phosphorus-induced relaxation in an iron grain boundary: A cluster-model study.

Abstract

The DMol molecular-cluster method, based on local density-functional theory, is employed to study the electronic structure and structural relaxation of a P impurity in the Fe \ensuremath{\Sigma}3[11\ifmmode\bar\else\textasciimacron\fi{}0](111) grain boundary (GB). Large clusters (53 and 91 atoms) are used to simulate the local environment of the Fe grain boundary; by calculating the force on the nearby Fe atoms around the impurity and minimizing the total energy of the cluster, an optimized atomic geometry with minimum energy is obtained. In the pure grain boundary, the center Fe atoms above the GB core have the tendency to move toward each other keeping a bond length very close to the Fe bulk bond length. From the 91-atom cluster, the P-induced relaxation of the Fe GB extends to at least eight Fe layers and the bond length between P and the nearest vertical Fe is 2.34 \AA{}, which is 3.5% larger than that in bulk ${\mathrm{Fe}}_{3}$P. Although the nearest Fe-P distance is the same in the vertical and horizontal directions, we found a stronger bonding between P and the in-plane Fe than in the vertical direction, which may contribute to the P embrittlement of Fe. A lesson from the present study with two cluster models is that even a cluster as large as 53 atoms does not provide the correct bonding picture around the impurity. This is due to the large relaxation induced by the P atom, which cannot be treated by a 53-atom cluster.