Mean coordination numbers and the non-metal–metal transition in clusters
Abstract
The mean first-nearest-neighbour coordination number N1 of atoms in a cluster is an important parameter characteristic of cluster size and geometry. For metal clusters and catalysts, its value is directly measurable by EXAFS spectroscopy. Literature expressions for N1 in clusters are not accurate; ideal values have previously had to be worked out numerically by counting atomic site types. New, rigorous analytical formulae for N1 as a function of cluster edge length have now been derived for icosahedral and cuboctahedral geometries. For clusters of the same size, N1(icos) always exceeds N1(cuboct), by a factor which is greatest for small clusters. The value of N1 has recently been proposed to play an important role in the non-metal–metal transition of mercury and other metal-atom clusters; it follows that an icosahedral cluster might be ‘more metallic’ than a cuboctahedral one with the same number of atoms, a consequence which should readily be testable experimentally. The use of the N1 parameter also gives new insight into cluster growth mechanisms.