We present x-ray photoelectron diffraction (XPD) measurements at an angular resolution of \ensuremath{\sim}\ifmmode\pm\else\textpm\fi{}1.0\ifmmode^\circ\else\textdegree\fi{} which is much higher than in any prior study. Emission from the Ni 2${p}_{3/2}$ core level of Ni(001) under Al K\ensuremath{\alpha} excitation is considered. The azimuthal XPD patterns are found to exhibit considerable fine structure not observed previously, including peaks whose full widths at half-maximum intensity are only a few degrees. The experimental data are found to be well described by single-scattering-cluster calculations with spherical-wave scattering. Fine structure due to Bragg-like scattering (Kikuchi bands) is also observed in both experiment and theory.