In a crystal lattice, the ionic radius is a measure of the size of the atom's ion.6 When formed, ionic atoms change in size with respect to their orginal atom. Cation radii will decrease and the anion radii will increase in size compared to their neutral atoms. Questions such as: "What methodology is used by chemists to measure ionic radii?" and "Are there any non-experimental ways to estimate the size of ionic radii?" will be answered in this module. Accordingly, there are many ways to determine ionic radii.

## Introduction

In the past, after an atom is ionized, X-ray diffraction is used to measure how much the radius of the atom increased or decreased. However, scientists wanted to use another technique, due to the fact, that X-ray diffraction is difficult to distinguish a boundary between two ions. As a result, the hard sphere model can be used.

## Hard-Sphere model

The Hard-Sphere model are impenetrable spheres that do not overlap in space.5 The Hard-Sphere model has been tested by well-known scientists; Lande', Pauling and Goldsmidt. The ion radii measured under crystal state of ionic compound which cations and anions are stacking in pattern as shown below.

The Hard-Sphere model can be applied to metallic and ionic compounds such as NaCl, which is shown below. Figure 2: 3-D hard sphere model of Sodium Chloride, taken with permission from http://en.wikipedia.org/wiki/File:So...e-3D-ionic.png

In general, scientists uses formula of Internuclear distance to test out the radii of ion then compared with the ion radii had done on X-ray diffraction:

Internuclear distance (d) = rcation + ranion 2

*To calculate ion radii, Lande used ionic compound under solid state (ex: NaCl). This will minize the distribution of electrons.

1. Find the radii of anion (r-) atom.
2. Find internuclear distance (d) between anion and cation.
3. Use Internuclear distance formula to find the r+.