Ionic radii

Key point: The sizes of ions, ionic radii, generally increase down a group, decrease across a period, increase with coordination number, and decrease with increasing charge number.

A difficulty that confronts us at the outset is the meaning of the term ‘ionic radius’. As remarked in Section 1.9, it is necessary to apportion the single internuclear separation of nearest-neighbour ions between the two different species (for example, an Na ion and a Clion in contact). The most direct way to solve the problem is to make an assumption about the radius of one ion, and then to use that value to compile a set of self-consistent values for all other ions. The O^-2 ion has the advantage of being found in combination with a wide range of elements. It is also reasonably unpolarizable, so its size does not vary much as the identity of the accompanying cation is changed. In a number of compilations, therefore, the values are based on r(O^-2) 140 pm. However, this value is by no means sacrosanct: a set of values compiled by Goldschmidt was based on r(O^-2) 132 pm and other values use the F ion as the basis. For certain purposes (such as for predicting the sizes of unit cells) ionic radii can be helpful, but they are reliable only if they are all based on the same fundamental choice (such as the value 140 pm for O^-2). If values of ionic radii are used from different sources, it is essential to verify that they are based on the same convention. An additional com plication that was first noted by Goldschmidt is that, as we have already seen for metals, ionic radii increase with coordination number (Fig. 3.45). Hence, when comparing ionic radii, we should compare like with like, and use values for a single coordination number (typically 6). The problems of the early workers have been resolved only partly by developments in X-ray diffraction (Section 8.1). It is now possible to measure the electron density between two neighbouring ions and identify the minimum as the boundary between them. How ever, as can be seen from Fig. 3.46, the electron density passes through a very broad minimum, and its exact location may be very sensitive to experimental uncertainties and to the identities of the two neighbours. That being so, it is still probably more useful to express the sizes of ions in a self-consistent manner than to seek calculated values of individual radii in certain combinations. After all, we are interested in compounds where we always have interactions between pairs of ions so we are consistent in the method of determination and application of ionic radii. Very extensive lists of self-consistent values that have been compiled by analysing X-ray data on thousands of compounds, particularly oxides and fluorides, exist and some are given in Table 1.4 and Resource section 1. The general trends for ionic radii are the same as for atomic radii. Thus:

1. Ionic radii increase down a group. (The lanthanide contraction, Section 1.9, restricts the increase between the 4d- and 5d-series metal ions.)

2. The radii of ions of the same charge decrease across a period.

3. If an element can form cations with different charge numbers, then for a given coordination number its ionic radius decreases with increasing charge number.

4. Because a positive charge indicates a reduced number of electrons, and hence a more dominant nuclear attraction, cations are smaller than anions for elements with similar atomic numbers.

 5. When an ion can occur in environments with different coordination numbers, the observed radius, as measured by considering the average distances to the nearest neighbours, increases as the coordination number increases. This increase reflects the fact that the repulsions between the surrounding ions are reduced if they move apart, so leaving more room for the central ion.

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مواضيع ذات صلة

The Born–Mayer equation

Structure maps

The radius ratio

Characteristic structures of ionic solids

Atomic radii of metals

Nonclose-packed structures

Polytypism

The close packing of spheres

Lattices and unit cells

The orbitals

Bonding and antibonding orbitals

Hybridization