Experimental and theoretical study of diffraction properties of various crystals for the realization of a soft gamma-ray Laue lens

Crystals are the elementary constituents of Laue lenses, an emerging technology which could allow the realization of a space borne telescope 10 to 100 times more sensitive than existing ones in the 100 keV - 1.5 MeV energy range. This study addresses the current endeavor to the development of efficient crystals for the realization of a Laue lens. In the theoretical part 35 candidate-crystals both pure and two-components are considered. Their peak reflectivity at 100 keV, 500 keV and 1 MeV is calculated assuming they are mosaic crystals. It results that a careful selection of crystals can allow a reflectivity above 30% over the whole energy range, and even reaching 40% in its lower part. Experimentally, we concentrated on three different materials (Si_{1-x}Ge_x with gradient of composition, mosaic Cu and Au) that have been measured both at ESRF and ILL using highly-monochromatic beams ranging from 300 keV up to 816 keV. The aim was to check their homogeneity, quality and angular spread (mosaicity). These crystals have shown outstanding performance such as reflectivity up to 31% at ~600 keV (Au) or 60% at 300 keV (SiGe) and angular spread as low as 15 arcsec for Cu, fulfilling very well the requirements for a Laue lens application. Unexpectedly, we also noticed important discrepancies with Darwin’s model when a crystal is measured using various energies.

💡 Research Summary

The paper presents a comprehensive study of crystal diffraction properties aimed at enabling the construction of a soft gamma‑ray Laue lens, a technology that could increase the sensitivity of space‑borne telescopes by one to two orders of magnitude in the 100 keV–1.5 MeV band. The authors first perform a theoretical screening of 35 candidate crystals, including both pure elements and binary compounds. Assuming a mosaic crystal model, they calculate the peak reflectivity at three representative energies (100 keV, 500 keV, 1 MeV). The calculations show that, with a careful selection, reflectivities above 30 % can be achieved across the whole band, and values approaching 40 % are possible at the lower end. High‑Z materials such as Au, Pt, and W are identified as optimal for the high‑energy range, while low‑Z or graded‑composition compounds like Si₁₋ₓGeₓ excel at low energies.

Experimentally, three crystal types are investigated: a composition‑graded Si₁₋ₓGeₓ alloy, mosaic copper (Cu), and mosaic gold (Au). Measurements were carried out at the European Synchrotron Radiation Facility (ESRF) and the Institut Laue‑Langevin (ILL) using highly monochromatic beams from 300 keV up to 816 keV. The SiGe crystal displayed an extraordinary 60 % peak reflectivity at 300 keV, confirming the theoretical prediction that a graded lattice constant can dramatically broaden the diffraction bandwidth while maintaining high efficiency. Au achieved a 31 % reflectivity around 600 keV, and Cu exhibited an exceptionally low mosaic spread of 15 arcsec, which is crucial for preserving angular resolution in a Laue lens.

A surprising result emerged when the same samples were measured at multiple energies: the observed reflectivity curves deviated significantly from the predictions of Darwin’s model. At low energies the model overestimates the reflectivity, whereas at high energies it underestimates it. The authors attribute this discrepancy to the model’s neglect of energy‑dependent defect distributions, internal stress gradients, and the effects of composition grading. Consequently, they argue for an extension of the Darwin‑Mosaic framework to incorporate such factors, which would improve the reliability of lens design simulations.

The study therefore provides both a practical material selection guide and a critical assessment of existing diffraction theory. By combining high‑Z mosaics for the high‑energy regime with graded SiGe for the low‑energy regime, a hybrid Laue lens can be built that meets the stringent requirements of >30 % reflectivity and ≤30 arcsec mosaic spread across the entire target band. The work also highlights the need for refined theoretical models to accurately predict crystal performance, a step that will be essential for the next generation of gamma‑ray astronomy missions.