  The GECAM series of satellites utilize LaBr3(Ce), LaBr3(Ce,Sr), and NaI(Tl)
crystals as sensitive materials for gamma-ray detectors (GRDs). To investigate
the non-linearity in the detection of low-energy gamma rays and address errors
in the E-C relationship calibration, comprehensive tests and comparative
studies of the non-linearity of these three crystals were conducted using
Compton electrons, radioactive sources, and mono-energetic X-rays. The
non-linearity test results for Compton electrons and X-rays displayed
substantial differences, with all three crystals showing higher non-linearity
for X-rays and gamma-rays than for Compton electrons. Despite LaBr3(Ce) and
LaBr3(Ce,Sr) crystals having higher absolute light yields, they exhibited a
noticeable non-linear decrease in light yield, especially at energies below 400
keV. The NaI(Tl) crystal demonstrated excess light output in the 6~200 keV
range, reaching a maximum excess of 9.2% at 30 keV in X-ray testing and up to
15.5% at 14 keV during Compton electron testing, indicating a significant
advantage in the detection of low-energy gamma rays. Furthermore, this paper
explores the underlying causes of the observed non-linearity in these crystals.
This study not only elucidates the detector responses of GECAM, but also marks
the inaugural comprehensive investigation into the non-linearity of
domestically produced lanthanum bromide and sodium iodide crystals.
