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Olivine is involved in many natural reactions and industrial reactions as acatalyst. The catalytic ability is highly possible rely on the Fe$^{2+}$ inolivine. We use density functional theory calculation and thermodynamics toinvestigate the site preference of Fe atom in olivine which composition fromiron-rich to iron-poor and its surfaces. The Fe$^{2+}$ always shows its highspin (quintet) state which has larger ion radius than Mg$^{2+}$ in olivinecrystal and surfaces. The Fe$^{2+}$ inside the surface slab prefers the smallerM1 site than M2 site by enlarging the metal-oxygen octahedra when occupied themetal site as in the bulk system. Energy contribution of entropies accumulationcaused temperature raise stops this preference at the temperature where acation order-disorder distribution energy crossover happen in olivine. Surfaceexposed site provide Fe$^{2+}$ large space due its unsaturated nature. Thislead a higher level of preference of Fe$^{2+}$ to the surface site than anymetal site inside the crystal no matter M1 or M2 site is exposed. This indicatethe Fe$^{2+}$ in the bulk system can diffuse to a metal site exposed on thesurface driven by the energy difference. Many reactions can use the on surfaceFe$^{2+}$ as a catalyst because of the active chemical behavior of Fe.Meanwhile this energetics preference should be considered in the future modelto explain the natural observed zoning olivine have a high Fe edge and low Fecenter. These microscopic understanding can be essential to many olivinerelated geochemical and astrochemical reactions.

Site preference of Fe atoms in the olivine (Fe$_x$Mg$_{2-x}$)SiO$_4$ and its surface