  The thermal desorption of ammonia (NH$_3$) from single crystal forsterite
(010) has been investigated using temperature-programmed desorption. The effect
of defects on the desorption process has been probed by the use of a rough cut
forsterite surface prepared from the cleaved forsterite sample. Several
approaches have been used to extract the desorption energy and pre-exponential
factor describing the desorption kinetics. In the sub-monolayer coverage
regime, the NH$_3$ desorption shows a broad distribution of desorption
energies, indicating the presence of different adsorption sites, which results
in an apparent coverage-dependent desorption energy. This distribution is
sensitive to the surface roughness with the cut forsterite surface displaying a
significantly broader distribution of desorption energies compared to the
cleaved forsterite surface. The cut forsterite surface exhibits sites with
desorption energies up to 62.5 kJ mol$^{-1} $ in comparison to a desorption
energy of up to 58.0 kJ mol$^{-1} $ for the cleaved surface. Multilayer
desorption is independent of the nature of the forsterite surface used, with a
desorption energy of ($25.8\pm0.9$) kJ mol$^{-1} $. On astrophysically relevant
heating time-scales, the presence of a coverage dependent desorption energy
distribution results in a lengthening of the NH$_3$ desorption time-scale by
$5.9\times 10^4$ yr compared to that expected for a single desorption energy.
In addition, the presence of a larger number of high-energy adsorption sites on
the rougher cut forsterite surface leads to a further lengthening of ca. 7000
yr.
