A Simple Spreadsheet Program for the Calculation of Lattice-Site Distributions

A simple spreadsheet program is presented that can be used by undergraduate students to calculate the lattice-site distributions in solids. A major strength of the method is the natural way in which the correct number of ions or atoms are present, or absent, at specific lattice distances. The expanding-cube method utilized is straightforward to set up in a spreadsheet and is easily adapted for the prediction of highly accurate Madelung constants. Calculations performed out to the 10th cube return a value for the Madelung constant exact to 5 decimal places. From an educational point of view, the method presents students the possibility of directly observing the difference between doing a "crude" lattice-sum calculation compared to what results under the "zero-net charge" condition. Caveats, such as truncation errors that must be considered by students when comparing the results of their limited cube calculations with literature pair-distribution functions, are also encountered. The pair distribution function of the van der Waals solid formed by condensed krypton atoms is selected for comparison with that of NaCl since the unit cells of these two solids have the same lattice parameters.