Abstract

The inter-atomic bonds in metals are basically (I) strong covalent bonds, but (II) metals are malleable and ductile, with the bonding structure re-arranging relatively easily. Also (III) metals tend to be good catalysts, and (IV) the formation energy of an atomic vacancy or a surface is only about half of what one might expect from counting the net number of bonds broken.

All four properties are explained by a simple model, but treated rigorously quantum mechanically, for a band of one type of electron (e.g. atomic s-electrons or five d-electrons). Then the bonding per electron is approximately proportional to the r.m.s. (root mean square) energy band width W of the electron distribution.

A simple quantum mechanical calculation shows that W is proportional to the square root of the number z of nearest neighbours, which then gives properties II to IV.

Parallels can be seen in traditional chemistry, including graphite being more stable than diamond (re I above). Unsaturated ring structures such as benzene are stabilised by ‘resonance’ combination of many different bonding patterns (re II) and the ubiquity of such ring structures throughout biochemistry parallels points II, III and IV.

Application to computer modelling of defects in metals will be mentioned: also some ab initio calculations on 18 real and artificial structures of aluminium ranging from the free atom (z=0) and di-atomic molecule (z=1) to z=12 (face centred cubic). These (surprisingly) also follow quite well the square root form, although aluminium is a Nearly Free Electron gas of predominantly hybridised 3s and 3p bonding. The crux seems to be that the square root function curves towards the axis, whereas z-squared and even the linear function z veer away from it.

• https://bham-ac-uk.zoom.us/j/85702415099?pwd=VTh5aFZ4Sm9Nc1dxZXYwelJpc1JtZz09
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