Abstract Large, single-quasicrystalline grains, both cooled from the melt and annealed on cooling at ≈825°, were ground approximately into spheres with a resultant diameter of ≈0.2 mm. These crystal were then studied at the NSLS where, using λ = 1 A ̊ , integrated intensities on more than 1300 (inequivalent) reflections were collected out to Q ⊥ greater than 1.7 Å −1 ( Q || units). A crucial aspect of this work has been the careful characterization of crystal quality. For example, Bragg radial ( φ−2 λ) scans reveal a nearly perfect Gaussian profile while omega (ω) scans show essentially a pure Lorentzian shape. The Q-width (FWHM) of the radial scans increases from ≈0.006 to 0.009 A ̊ −1 as Q || increases from 1 to 11 Å −1. The FWHM in ω is characteristically about 0.065° with a mean variation of ≈0.001°, and its lineshape appears to be associated with a true mosaic spread as it does not depend in any essential way on angle or on Q ⊥ or Q λ . Through depth-dependent measurements we show that the Lorentzian profile is substantially enhanced by mechanical grinding, although an unground crystal fragment still displays Lorentzian wings. TEM on unground samples from both sources reveals sharp diffraction spots with ideal icosahedral symmetry and images thet indicate an icosahedral phase rather than an ensemble of approximant domains.