  The interplay between magnetism and crystal structures in three
CaFe$_{2}$As$_{2}$ samples is studied. For the nonmagnetic quenched crystals,
different crystalline domains with varying lattice parameters are found, and
three phases (orthorhombic, tetragonal, and collapsed tetragonal) coexist
between T$_{S}$ = 95 K and 45 K. Annealing of the quenched crystals at
350{\deg}C leads to a strain relief through a large (~1.3 %) expansion of the
c-parameter and a small (~0.2 %) contraction of the a-parameter, and to local
~0.2 {\AA} displacements at the atomic-level. This annealing procedure results
in the most homogeneous crystals for which the antiferromagnetic and
orthorhombic phase transitions occur at T$_{N}$/T$_{S}$ = 168(1) K. In the
700{\deg}C-annealed crystal, an intermediate strain regime takes place, with
tetragonal and orthorhombic structural phases coexisting between 80 to 120 K.
The origin of such strong shifts in the transition temperatures are tied to
structural parameters. Importantly, with annealing, an increase in the Fe-As
length leads to more localized Fe electrons and higher local magnetic moments
on Fe ions. Synergistic contribution of other structural parameters, including
a decrease in the Fe-Fe distance, and a dramatic increase of the c-parameter,
which enhances the Fermi surface nesting in CaFe$_{2}$As$_{2}$, are also
discussed.
