  In this work we investigate the properties of macroscopic bulk acoustic wave
(BAW) devices, manufactured from crystalline piezoelectric lithium niobate at
both room temperature and 4 K. We identify the fundamental acoustic modes in
the crystal samples structures as well as characterise their loss properties
and non-linear effects at both room and cryogenic temperatures. We compare
these results to similar resonators made from quartz and conclude that lithium
niobate may be suitable for certain experiments due to its low-loss and strong
piezoelectric coupling. Additionally, we provide evidence for the reduction of
crystal lattice defect sites by thermal annealing. We report exceptional
quality factors for bulk acoustic modes in lithium niobate, with a maximum
recorded quality factor of 8.9 million with a corresponding quality factor
$\times$ frequency product of 3.8 $\times 10^{14}$ Hz.
