Understanding metal bonding.
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This theoretical discussion covers several effects of metallic bonding based on a simple formula. It comes from the first steps in the Moment Method for calculating the local electronic structure of a solid (such as at a surface or in a random alloy), and depends on the square root of the total coordination numberCof near neighbours. Each atom is covalently bonded to its cluster of near neighboursas a whole. The properties of metals touched on include malleability, crystal structure and phase transitions, vacancy formation energy, surface catalysis, surface reconstruction, graphite stability, and some aspects of the benzene molecule seen as an atomic metal ring. In most of these, the 'saturation' type of curvature of the square root function plays a crucial role. A short historical survey indicates the development of the ideas from Bloch (1929Z. Phys.52555) to recent times.
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Acknowledgements: The authors are hugely indebted to Dr R O (Bob) Jones for encouragement and especially his guidance to the relevant chemical literature. Also, crucial to the thinking in the present work were three visits, all around 1955–1965 by V H. One was a visit to the group of Prof. J Friedel in Paris, learning about formulating quantum calculations about materials in local terms for situations with different atoms having different local situations such as at surfaces. That was the ‘Method of Moments’ later leading to equation (2). Another was spending two summers as a visitor in the theory group at Harwell, where the problem of modelling radiation damage in metals was an important issue (section 2). Thirdly there was a visit by Prof. J Friedel to Cambridge during which V H heard about the ‘Friedel’ oscillations of electron density around an impurity in a metal, and was struck by the analogy to the variation of reactivity at the ‘ortho’, ‘meta’, and ‘para’ positions around a benzene ring from an attached side-group. Also formative for V H as an undergraduate in New Zealand in the early 1950s were three lectures by the Head of Chemistry, Prof. F G Soper, on his return after a sabbatical leave overseas. These lectures (non-examenable!) for senior students introduced quantum mechanics with its applications to chemistry. S C acknowledges financial support from the Cambridge Trust and from the Winton Programme for the Physics of Sustainability. Finally, we apologise that in trying to communicate equally with physicists, chemists and material scientists with their different backgrounds, we will have been either too elementary or assumed too much in places for some of them.
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