In the continuing effort to learn more about the nature of metals, the rare earth elements in particular, the crystal structures and precision lattice parameters of these metals were investigated. High purity metals were examined by powder, single crystal and back reflection x-ray diffraction techniques. All but four of the back reflection samples were prepared by distillation in high vacuum (approximately 2 x 10-7 mm. mercury). The back reflection examinations, by which very accurate lattice parameters can be determined, were considered necessary if quantitative comparisons of the properties of the rare earths are to be made. Although scandium and yttrium are not classified as rare earths, they were considered similar enough in their behavior to include them in this study