Atomic radii of metals

Key point: The Goldschmidt correction converts atomic radii of metals to the value they would have in a close-packed structure with 12-fold coordination. An informal definition of the atomic radius of a metallic element was given in Section 1.9 as half the distance between the centres of adjacent atoms in the solid. However, it is found that this distance generally increases with the coordination number of the lattice. The same atom in structures with different coordination numbers may therefore appear to have different radii, and an atom of an element with coordination number 12 appears bigger than one with coordination number 8. In an extensive study of internuclear separations in a wide variety of polymorphic elements and alloys, V. Goldschmidt found that the average relative radii are related as shown in Table 3.3. It is desirable to put all elements on the same footing when comparing trends in their characteristics; that is when comparing the intrinsic properties of their atoms rather than the properties that stem from their environment. Therefore, it is common to adjust the empirical internuclear separation to the value that would be expected if the element were in fact close-packed (with coordination number 12).

 ■ A brief illustration. The empirical atomic radius of Na is 185 pm, but that is for the bcc structure in which the coordination number is 8. To adjust to 12-coordination we multiply this radius by 1/0.97 1.03 and obtain 191 pm as the radius that a Na atom would have if it were in a close-packed structure.

 ■ Goldschmidt radii of the elements were in fact the ones listed in Table 1.4 as ‘metallic radii’ and used in the discussion of the periodicity of atomic radius (Section 1.9). The essential fea tures of that discussion to bear in mind now, with ‘atomic radius’ interpreted as Goldschmidt- corrected metallic radius in the case of metallic elements, are that metallic radii generally increase down a group and decrease from left to right across a period. As remarked in Section 1.9, trends in atomic radii reveal the presence of the lanthanide contraction in Period 6, with atomic radii of the elements that follow the lanthanoids found to be smaller than simple extrapolation from earlier periods would suggest. As also remarked there, this contraction can be traced to the poor shielding effect of f electrons. A similar contraction occurs across each row of the d block.

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مواضيع ذات صلة

The Born–Mayer equation

Structure maps

The radius ratio

Ionic radii

Characteristic structures of ionic solids

Nonclose-packed structures

Polytypism

The close packing of spheres

Lattices and unit cells

The orbitals

Bonding and antibonding orbitals

Hybridization