High-purity tungsten (W) single crystals have been prepared by the electron-beam floating zone melting technique. The structural quality of these crystals was subsequently improved by the application of a strain-annealing technique. X-ray diffraction methods revealed the near-perfect crystallographic structure, and confirmed the absence of first- and second-order subgrains. The observation of the anomalous transmission of X-rays through the thick crystals, also referred to as the Borrmann effect, further substantiated the structural perfection of the crystals. Well-ordered clean W surfaces free from all contaminants, were obtained by a two-step heating procedure. First, the crystals were heated to 1500 K in an oxygen atmosphere for the removal of the carbon impurities. Subsequent flashing to high temperatures (approximately 2500 K) removed the excess oxygen remaining on the surface from the carbon-removal procedure. Low-energy ion scattering and Auger electron spectroscopy confirmed that the cleaning procedures removed all impurities and that the crystal faces expose only tungsten in the outermost atomic layers. Low-energy electron diffraction patterns showed unreconstructed(1 x 1) surfaces for the main crystallographic orientations.