Bond-order potential for magnetic body-centered-cubic iron and its transferability
We derived and thoroughly tested a bond-order potential (BOP) for body-centered-cubic (bcc) magnetic iron that can be employed in atomistic calculations of a broad variety of crystal defects that control structural, mechanical, and thermodynamic properties of this technologically important metal. The constructed BOP reflects correctly the mixed nearly free electron and covalent bonding arising from the partially filled d band as well as the ferromagnetism that is actually responsible for the stability of the bcc structure of iron at low temperatures. The covalent part of the cohesive energy is determined within the tight-binding bond model with the Green's function of the Schrödinger equation determined using the method of continued fractions terminated at a sufficient level of the moments of the density of states. This makes the BOP an O(N) method usable for very large numbers of particles. Only dd bonds are included explicitly, but the effect of s electrons on the covalent energy is included via their screening of the corresponding dd bonds. The magnetic part of the cohesive energy is included using the Stoner model of itinerant magnetism. The repulsive part of the cohesive energy is represented, as in any tight-binding scheme, by an empirical formula. Its functional form is physically justified by studies of the repulsion in face-centered-cubic (fcc) solid argon under very high pressure where the repulsion originates from overlapping s and p closed-shell electrons just as it does from closed-shell s electrons in transition metals squeezed into the ion core under the influence of the large covalent d bonding. Testing of the transferability of the developed BOP to environments significantly different from those of the ideal bcc lattice was carried out by studying crystal structures and magnetic states alternative to the ferromagnetic bcc lattice, vacancies, divacancies, self-interstitial atoms (SIAs), paths continuously transforming the bcc structure to different less symmetric structures and phonons. The results of these calculations are compared with either experiments or calculations based on the density functional theory (DFT), and they all show very good agreement. Importantly, the lowest energy configuration of SIAs agrees with DFT calculations that show that it is an exception within bcc transition metals controlled by magnetism. Moreover, the migration energy of interstitials is significantly lower than that of vacancies, which is essential for correct analysis of the effects of irradiation. Finally, the core structure and glide of ½⟨111⟩ screw dislocations that control the plastic flow in single crystals of bcc metals was explored. The results fully agree with available DFT based studies and with experimental observations of the slip geometry of bcc iron at low temperatures.