The Laue lens is an emerging technology that uses crystal diffraction to concentrate gamma-rays. The Darwin model describes diffraction in mosaic crystals at high energies (>50 keV) and is the basis for assessing the throughput of a Laue lens. While the Darwin model has been used successfully to describe binary alloys, it has shown inconsistencies when applied to diffraction with pure-metal crystals. This paper presents a systematic study of diffraction in pure-metal silver mosaic crystals and the performance of the Darwin model when applied to the data. Two cut silver crystals were tested at the Institute Laue–Langevin facility at three gamma-ray energies and at three different crystallographic orientations. The rocking curves were fitted using the Darwin model. A single Gaussian for the distribution of crystallite orientations leads to poor quality fits. A crystallite distribution that is the sum of two Gaussians gives improved fits. However, for each crystal, the Darwin model gives mosaicities and crystallite sizes that are not consistent with one another as a function either of energy or of crystallographic orientation, despite these being physical properties of the materials. Without an adequate model to describe diffraction in pure-metal crystals, either a Laue lens design must severely limit its catalogue of usable materials or each crystal in the design must be tested at the exact energy at which it is to be used. A more general theory to describe hard X-ray diffraction using pure-metal mosaic crystals, possibly involving a distribution of crystallite sizes, is therefore required.