  We investigate bulk thermodynamic and microscopic structural properties of
amorphous solids in the framework of the phase-field crystal (PFC) model. These
are metastable states with a non-uniform density distribution having no
long-range order. From extensive numerical simulations we determine the
distribution of free energy density values in varying size amorphous systems
and also the point-to-set correlation length, which is the radius of the
largest volume of amorphous one can take while still having the particle
arrangements within the volume determined by the particle ordering at the
surface of the chosen volume. We find that in the thermodynamic limit, the free
energy density of the amorphous tends to a value that has a slight dependence
on the initial state from which it was formed -- i.e.\ it has a formation
history dependence. The amorphous phase is observed to form on both sides of
the liquid linear-stability limit, showing that the liquid to amorphous
transition is first order, with an associated finite free energy barrier when
the liquid is metastable. In our simulations this is demonstrated when noise in
the initial density distribution is used to induce nucleation events from the
metastable liquid. Depending on the strength of the initial noise, we observe a
variety of nucleation pathways, in agreement with previous results for the PFC
model, and which show that amorphous precursor mediated multi-step crystal
nucleation can occur in colloidal systems.
