Ionic Radius - The Soft-sphere Model

The Soft-sphere Model

Soft-sphere ionic radii (in pm) of some ions
Cation, M RM Anion, X RX
Li+ 109.4 Cl- 218.1
Na+ 149.7 Br- 237.2

For many compounds, the model of ions as hard spheres does not reproduce the distance between ions, to the accuracy with which it can be measured in crystals. One approach to improving the calculated accuracy is to model ions as "soft spheres" that overlap in the crystal. Because the ions overlap, their separation in the crystal will be less than the sum of their soft-sphere radii.

The relation between soft-sphere ionic radii, and, and, is given by

,

where is an exponent that varies with the type of crystal structure. In the hard-sphere model, would be 1, giving . In the soft-sphere model, has a value between 1 and 2. For example, for crystals of group 1 halides with the sodium chloride structure, a value of 1.6667 gives good agreement with experiment. Some soft-sphere ionic radii are in the table. These radii are larger than the crystal radii given above (Li+, 90 pm; Cl-, 167 pm).

Comparison between observed and calculated ion separations (in pm)
MX Observed Soft-sphere model
LiCl 257.0 257.2
LiBr 275.1 274.4
NaCl 282.0 281.9
NaBr 298.7 298.2

Inter-ionic separations calculated with these radii give remarkably good agreement with experimental values. Some data are given in the table. Curiously, no theoretical justification for the equation containing has been given.

Read more about this topic:  Ionic Radius

Famous quotes containing the word model:

    The best way to teach a child restraint and generosity is to be a model of those qualities yourself. If your child sees that you want a particular item but refrain from buying it, either because it isn’t practical or because you can’t afford it, he will begin to understand restraint. Likewise, if you donate books or clothing to charity, take him with you to distribute the items to teach him about generosity.
    Lawrence Balter (20th century)