  Olivine is involved in many natural reactions and industrial reactions as a
catalyst. The catalytic ability is highly possible rely on the Fe$^{2+}$ in
olivine. We use density functional theory calculation and thermodynamics to
investigate the site preference of Fe atom in olivine which composition from
iron-rich to iron-poor and its surfaces. The Fe$^{2+}$ always shows its high
spin (quintet) state which has larger ion radius than Mg$^{2+}$ in olivine
crystal and surfaces. The Fe$^{2+}$ inside the surface slab prefers the smaller
M1 site than M2 site by enlarging the metal-oxygen octahedra when occupied the
metal site as in the bulk system. Energy contribution of entropies accumulation
caused temperature raise stops this preference at the temperature where a
cation order-disorder distribution energy crossover happen in olivine. Surface
exposed site provide Fe$^{2+}$ large space due its unsaturated nature. This
lead a higher level of preference of Fe$^{2+}$ to the surface site than any
metal site inside the crystal no matter M1 or M2 site is exposed. This indicate
the Fe$^{2+}$ in the bulk system can diffuse to a metal site exposed on the
surface driven by the energy difference. Many reactions can use the on surface
Fe$^{2+}$ as a catalyst because of the active chemical behavior of Fe.
Meanwhile this energetics preference should be considered in the future model
to explain the natural observed zoning olivine have a high Fe edge and low Fe
center. These microscopic understanding can be essential to many olivine
related geochemical and astrochemical reactions.
