The structure of metallic solid solutions - Introductory lecture

Abstract

2014 A discussion will be given of the properties of a dissolved atom, with particular reference to those properties which can be assigned to the exact many-electron wave-function of the metal and those which can be defined only in terms of an approximate model. For example, as Anderson has emphasized, one can ask whether there is an uncompensated spin moment in the neighbourhood of a dissolved atom or whether there is none. The concept of bound states is discussed in this connection ; the writer believes there to be no exact division between the situation’in which there is a bound state present and that in which there is not. In terms of models, the nature of the wave-functions round a dissolved atom is discussed, particularly with reference to size effects. LE JOURNAL DE PHYSIQUE ET LE RADIUM TOME 23, OCTOBRE 1962, In looking at the properties of a metal, it is first useful to ask which of them can be assigned to the exact many electron wave-function, and which are properties only of a one-electron model. Thus we now believe that the Fermi surface can be described in terms of excitations cf the exact many electron wave-tunction ; a solid in its lowest state may have free electrons and a Fermi surface, or it may be a non-cond uctor. It may or may not have an antiferromagnetlc superlattice. On the other hand there is in my view never any sharp distinction, in terms of the exact wave-function, between the description of electrons by localised (Wannier) wave-functions and by Bloch-type wave-functions. In the same way, when we are considering dissolved metal atoms in a normal metal, we can ask whether the atom carries a magnetic moment. The moment, usually zero but, when the sclute is a transition metal, often finite, is a property of the exact wave-function. This moment can be described in terms of localised wave functions [1] or non-localised [2] Bloch functions. This is a matter of choice. But the moment is in general non-integral. Anderson shows that, as any parameter (e.g. the sharpness of the resonance in the virtual state) is varied, the moment will vary continuously and reach zero at a’fixed value of the parameter. As far as 1 know, finite moments are only found on dissolved transition metals -though there is no reason in principale why this should be so. In another case one can trace theoretically the variation of the moment on an atom from an integral value to zero. Consider a hydrogen (or moncvalent metal) atom approaching a metal surface. At large distances the atom will carry a moment of one Bohr magneton ; when adsorbed to the surface, particularly at a kink site, it will not carry any moment at all. It would be interesting to trace theoretically the way the magnetic moment varies, with distance from the metal surface, from one Bohr magneton to zero. The screening of impurities and the long-range fluctuation of charge are too well known for it to be necessary for me to give any review of their properties, particularly here in Paris where Professor Friedel and his school have made such important contributions to our understanding of these matters. 1 would however like to make a few remarks about the bound states which appear in the one electron model at a potential well of sufficient depth, and ask whether, in terms of exact manyelectron wave functions, one can ask whether a bound state exists or not. A trivalent metal (Ga) dissolved in copper is an example ; can one ask whether the two 4s functions are in bound states ? 1 think one can in terms of excited states of tbe whole system, such as might be investigated by the X-ray emission BDectrUl11 of tlle impurity,. If the Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphysrad:019620023010059400