Simple models for resolving environments in disordered alloys by x-ray photoelectron spectroscopy

Abstract

In disordered alloys, atoms belonging to the same chemical element will exhibit different environments. This leads to variations in the atoms’ local electronic structures, which in turn leads to variations in the binding energies of their core levels. These binding energies can be measured experimentally using core level X-ray photoelectron spectroscopy (XPS). Therefore, in theory at least, core level XPS can be used to resolve different environments in alloys. However, to make this a reality one must understand how an atom’s local electronic structure, and hence the binding energies of its core levels, are affected by local environment. In this thesis, two simple phenomenological models are explored which purport to correctly describe the local electronic structure of disordered alloys. The first model which we consider has its roots in chemical intuition; specifically, the notion that pairs of unlike atoms, i.e. atoms belonging to different chemical elements, transfer a certain quantity of charge, while like atoms do not. Using this model - known as the optimised linear charge model (OLCM) - the relationship between an atom’s local electronic structure, core level binding energies, and its environment is explored in detail, both in the bulk of disordered alloys and near their surfaces. As well as ‘homogeneous’ disordered alloys, in which the concentrations of the alloy’s constituent elements are the same throughout the entire alloy, various ‘inhomogeneous’ disordered alloy systems are considered. These include alloys exhibiting surface segregation - in which the concentrations at the surface differ from those in the bulk - as well as interfaces between two metals with various levels of intermixing. The results of our investigation of bulk inhomogeneous alloys are compared to analogous ab initio results, which confirms the model’s viability as a tool for rationalising the relationship between local electronic structure, core level binding energies, and environment. More generally, our results also reveal a number of interesting new phenomena. Firstly, the widths of spectra in inhomogeneous disordered alloys are significantly larger in some cases than is possible in any analogous homogeneous disordered alloy. Secondly, differences between the concentrations of each element at the surface and deep within the bulk cause a shift in the work function of the alloy under consideration. The latter results in qualitatively different trends than one would expect if this phenomenon was ignored, and prompts an alternative interpretation of the results of a recent experimental study. The second model which we consider is a particular case of the charge-excess functional model, in which the realised charges on all atoms are those which minimise a particular expression for the total energy of the system, and whose accuracy has been well established. The underlying assumptions and properties of this model are explored in detail, adding insight into the nature of the screening and inter-atomic interactions in disordered alloys. The model is shown to be equivalent to the OLCM for the case of binary alloys, and can therefore be considered to be the generalisation of the OLCM for alloys containing more than two chemical elements. The model is also used to derive analytical expressions for various physical quantities for any alloy, including the width of core level XPS spectra and the Madelung energy. These expressions are then used to investigate how the physical quantities to which they pertain vary with the concentrations of each element in a homogeneous disordered alloy consisting of three elements. Among other things, it was observed that the width of the core level XPS spectra is maximised when the concentrations of the two elements in the alloy with the largest electronegativity difference have equal concentrations, while the remaining element has a vanishing concentration.