Chapter 5

As can be seen in Fig. \(5.33\), not all unit cells are cubic. Other types of unit cells have different restrictions placed on the lattice parameters (edge lengths and angles). Unit cell properties such as cell volume, density, and distances between atoms are calculated just as the calculations are done for cubic unit cells, except the geometry is more complex. (a) With this in mind, calculate the distance between a corner atom and the atom at the body center of a tetragonal unit cell that has \(a=b=549 \mathrm{pm}\) and \(c=769 \mathrm{pm}\). (b) What is the volume of this unit cell?

Salts can be prepared from organic molecules such as acetic acid and methanol. For example, it is possible to prepare sodium acetate, \(\mathrm{NaCH}_{3} \mathrm{CO}_{2}\), and sodium methoxide, \(\mathrm{NaOCH}_{3}\). How do you expect the forces that hold these compounds together in the solid state to differ from those that hold together salts like sodium chloride or sodium bromide?

A commonly occurring mineral has a cubic unit cell in which the metal cations \(\mathrm{M}\) occupy the comers and face centers. Inside the unit cell, there are anions \(\mathrm{A}\) that occupy all the tetrahedral holes created by the cations. What is the chemical formula of the \(M_{x} A_{y}\) compound?

Tetrahedral and octahedral interstitial holes are formed by the spaces left when anions pack in a cubic close-packed array. (a) Which hole can accommodate the larger ions? (b) What is the size ratio of the largest metal cation that can occupy an octahedral hole to the largest that can occupy the tetrahedral hole while maintaining the close-packed nature of the anion lattice? (c) If half the tetrahedral holes are occupied, what will the chemical formula of the compound \(\mathrm{M}_{2} \mathrm{~A}_{2}\) be, where \(\mathrm{M}\) represents the cations and \(\mathrm{A}\) the anions?