The Structure of Crystals The structure of Crystals An experiment using models N

Question

The Structure of Crystals The structure of Crystals An experiment using models Number of Cl^- ions in the unit cell (FCC) Number of Na^+ ions on edges of cell___ shared by ___ cell(s) Number of Na^+ ions in center of cell ___ shared by ___ cell(s) Total Number of Na^+ ions in unit cell Radius ratio rule necessary data is in Table 16.1, at the start of the data pages KI r, lr___ Predicted structure___ Observed structure = NaCl CuBr r, lr ___ Predicted Structure___ Observed structure = ZnS TiBr r, lr ___ Predicted structure ___ Observed structure = CsCi

Explanation / Answer

In the radius-ratio rule, the limiting ratio ie the ionic ratio of the cation and the anion (r+/r-) is used to calculate the coordination number (CN) and thus predict the structure.

For KI, the limiting ratio is 0.133/0.216 = 0.615. The K+ ions will thus prefer an octahedral arrangement (CN= 6, r+/r- = 0.414-0.732) and the possible structure will be NaCl, TiO2 and CdCl2.

For CuBr, the limiting ratio is 0.096/0.195 = 0.492. The Cu+ ions will thus prefer an octahedral arrangement (CN= 6, r+/r- = 0.414-0.732) and the possible structure will be NaCl, TiO2 and CdCl2.

For TlBr, the limiting ratio is 0.147/0.195 = 0.753. The Cu+ ions will thus prefer a cubic corner arrangement (CN= 8, r+/r- = 0.732-1) and the possible structure will be CsCl and CaF2.

NB: In the above examples only the predicted structure of CuBr varies from the actual. This is because of the large difference in the cationic and anionic radii resulting in poor fit. The Br- ions might move close to the Cu+ ion, thus resulting in the overlapping of the Br- ions. The repulsion between the Br- ions will raise the energy of the system making it less stable.

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