Large size detectors based on Cs2LiYCl6:Ce (CLYC) are capable of performing a combined $gamma$-ray and neutron spectrometry and constitute a promising technology for a wide range of applications in nuclear and high energy physics. Due to their novelty, the comprehensive characterization of the performance of individual CLYC detectors is of great importance for determining their range of applicability. In this work we report on a wide series measurements performed with a commercial 2x2 CLYC crystal. Good energy and timing resolution values of 4.7% (@ 662 keV) and 1340 ps (FWHM), respectively, were achieved, and a neutron/$gamma$ separation figure of merit value of 4.2 was obtained. A dedicated measurement for investigating the intrinsic background of the detector was performed at the Laboratorio Subterraneo de Canfranc (Spain). It evidenced a sizeable contamination in the detector materials which poses limits in the use of CLYC in low background experiments. In addition, detailed Monte Carlo simulations with the GEANT4 toolkit were performed for modeling the response function of the CLYC detector to gamma-rays. An excellent agreement with the experimental data has been achieved.
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