  The one-loop quantum corrections to the internal energy of some lattices due
to the quantum fluctuations of the scalar field of phonons are studied. The
band spectrum of the lattice is characterised in terms of the scattering data,
allowing to compute the quantum vacuum interaction energy between nodes at zero
temperature, as well as the total Helmholtz free energy, the entropy, and the
Casimir pressure between nodes at finite non-zero temperature. Some examples of
periodic potentials built from the repetition in one of the three spatial
dimensions of the same punctual or compact supported potential are addressed: a
stack of parallel plates constructed by positioning $\delta\delta'$-functions
at the lattice nodes, and an 'upside-down tiled roof' of parallel
two-dimensional P\"oschl-Teller wells centred at the nodes. They will be called
generalised Dirac comb and P\"oschl-Teller comb, respectively. Positive
one-loop quantum corrections to the entropy appear for both combs at non-zero
temperatures. Moreover, the Casimir force between the lattice nodes is always
repulsive for both chains when non-trivial temperatures are considered,
implying that the primitive cell increases its size due to the quantum
interaction of the phonon field.
