Lattice vacancy migration barriers in Fe-Ni alloys, and an indication as to why Ni atoms diffuse slowly: A first-principles study

Lattice vacancy migration barriers in ferromagnetic <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mrow> <a:msub> <a:mi>Fe</a:mi> <a:mi>x</a:mi> </a:msub> <a:msub> <a:mi>Ni</a:mi> <a:mrow> <a:mn>1</a:mn> <a:mo>−</a:mo> <a:mi>x</a:mi> </a:mrow> </a:msub> </a:mrow> </a:math> alloys ( <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:mrow> <b:mn>0.4</b:mn> <b:mo>≤</b:mo> <b:mi>x</b:mi> <b:mo>≤</b:mo> <b:mn>0.6</b:mn> </b:mrow> </b:math> ) are accurately quantified within the framework of electronic structure calculations using the nudged elastic band (NEB) method. Both the atomically disordered (A1) fcc phase, as well as the atomically ordered, tetragonal <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:mrow> <c:mi mathvariant="normal">L</c:mi> <c:msub> <c:mn>1</c:mn> <c:mn>0</c:mn> </c:msub> </c:mrow> </c:math> phase—which is under consideration as a material for a rare-earth-free gap magnet for advanced engineering applications—are investigated. Across an ensemble of NEB calculations performed on supercell configurations spanning a range of compositions and containing disordered, partially ordered, and fully ordered structures, we find that Ni-vacancy interchanges encounter significantly higher energetic barriers than do Fe-vacancy interchanges. We contend that this aspect is a key factor in determining the differences in mobility between Fe and Ni atoms in this ferromagnetic alloy. Moreover, we are able to interpret these findings in terms of the ferromagnetic alloy's underlying spin-polarized electronic structure. Specifically, we report a coupling between the size of local lattice distortions and the magnitude of the local electronic spin polarization around vacancies. This causes Fe atoms to relax into lattice vacancies, while Ni atoms remain rigidly fixed to their original lattice positions. These results give atomic-scale insight into the longstanding experimental observation that Ni exhibits remarkably slow atomic diffusion in Fe-Ni alloys.