Chapter 1 gives an introduction to X-ray and neutron powder diffraction and the use of these techniques for crystal structure determination and refinement. The Rietveld structure refinement method is described and examples of different methods of structure determination from powder diffraction data are given. The techniques of EXAFS and Mossbauer spectroscopy, which were used to provide additional structural information, are also introduced. Chapter 2 describes the different radiation sources and experimental techniques used in this work. Chapter 3 describes a structural study of magnetite, Fe$3$O$4$, below the Verwey phase transition (~120 K). The P:2/c structure of Fe$3$O$4$ at 60 K has been refined with lattice parameters of a= 5.9412(3) Å, b = 5.9290(3) Å, c = 16.789(1) Å and β = 90.196$\mathrm{<mrow\; data-mjx-texclass="ORD">\circ </mrow>}$. A variable temperature study of the Fe$3$O$4$ lattice parameters between 2-280 K shows this transition is first-order. An EXAFS study between 80-270 K shows that there is no significant change in the average Fe-0 distance in Fe$3$O$4$ around the transition. Chapter 4 describes a structural study on a material related to magnetite, Fe$2$OBO$3$. Two phase transitions have been found for this material. The first of these is due to magnetic ordering and takes place at -155 K. The second is due to charge ordering and takes place at 315 K, this is a structural (P2$1$/c $⟺$ Pnma) transition. Chapter 5 describes a resonant scattering experiment done on CsI. Resonant scattering parameters have been refined from synchrotron X-ray powder diffraction data collected at room ' temperature ,md al -+ K close to the Cs and I K-edges. The refined f parameters are -6.2(2) e/atorn (Cs. A = 0.3453 A), -9.0(1) e/atom (I. A = 0.374105 A.) and -6.2(2) e/atom (I, 4 K, A = 0.37367 Å). Chapter 6 describes the ab initio structure determination of 4-(2'3'4'-trifluorophenyl)-1235 dithiadiazolyl (C$7$S$2$N$2$F$3$H$2$ P2 /n, a = 11.543(4) Å, b = 20.666(8) Å, c = 7.045(2) Å and β = 100.35(4)) using synchrotron X-ray powder diffraction data. A global optimisation method was used to provide a starting model for Rietveld refinement.