Atomic Size and Structural Constraint

The previous sections suggest that a thorough understanding of atomic size and the roles that it plays in relation to structural stability is most important. It is not so much the numerical value of the atomic diameter that is generally of importance, but the state of the atom that gives rise to its apparent size. This is because the state of the atom prescribes how the atom will react in any particular structural constraint and whether or not its apparent size will exert any influence. 

Atoms which have incompletely filled valence subshells normally achieve chemical bonding by the overlap of their atomic wave functions, as in covalent compounds and metals. Atoms in this state approach each other much more closely than they could if they had filled valence subshells, so that covalent or metallic radii are smaller than van der Waals or negative-ion radii. In substances where valence 

Arguments involving exact details of what should be a metallic atom s size appear to be unimportant in questions of structural stability. Any reasonable self-consistent set of radii is sufficient for discussion, and Pauling s R(i) — R( ) = 0.3 log n rule can be used to convert radii appropriate for one coordination number to another. Regardless of the failings of any particular set of metallic radii, Pauling s rule appears to be very reliable. 

The critical diameter for change from localized to collective behavior of the d electrons in transition metal compounds is also an important parameter that affects properties and structure, as discussed by Goodenough (Ref. 22, pp. 26-28, 265-266,295-297). 

The effect of relative atomic size on alloy structures was discussed on p. 134. It also influences the extent of terminal solid solubility in metallic alloys as expressed in the Hume-Rothery 15% rule and its extension by Darken and Gurry to also take account of the effect of electronegativity difference in limiting solid solubility. The Hume-Rothery rule has now come to be stated that if the sizes of the solute and solvent atoms differ by less than 15%, extended terminal solid solutions may form, whereas if they differ by more, it is very unlikely that extended solid solutions will form. The rule is only permissive for the formation of extended solid solutions at radii differing by less than 15%, since other factors such as, for example, large electronegativity difference may still prevent their forming. 

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