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Structure-property relationships of two crystal structures were investigated using computational methodologies in two different length scales:electronic and atomistic length scales. Electronic structure calculations were performed using density functional theory (DFT) with generalized gradient approximation (GGA), GGA+U (U is "on-site" electronelectron repulsion) and hybrid functional forms. Atomistic calculations were performed utilizing the semi-empirical interatomic formulation, Modified Embedded Atom Method (MEAM). Classical molecular dynamics simulations were performed on the atomistic length scale in order to investigate thermal properties. In the first study, structural, elastic and thermal properties of cementite (Fe₃C) were investigated using a Modified Embedded Atom Method (MEAM) potential for iron-carbon (Fe-C) alloys. Previously developed Fe and C single element potentials were used to develop a Fe-C alloy MEAM potential, using a statistically-based optimization scheme to reproduce structural and elastic properties of cementite, the interstitial energies of C in bcc Fe as well as heat of formation of Fe-C alloys in L₁₂ and B₁ structures. The stability of cementite at high temperatures was investigated by molecular dynamics simulations. The nine single crystal elastic constants for cementite were obtained by computing total energies for strained cells. Polycrystalline elastic moduli for cementite were calculated from the single crystal elastic constants of cementite. The formation energies of (001), (010), and (100) surfaces of cementite were also calculated. The melting temperature and the variation of both the specific heat and volume with respect to temperature were investigated by performing a two-phase (solid/liquid) molecular dynamics simulation of cementite. The predictions of the potential are in good agreement with first-principles calculations and experiments. In the second study the site occupancy and magnetic properties of Zn-Sn substituted M-type Sr-hexaferrite (SrFe₁₂x̳(Zn₀.₅Sn₀.₅)x̳O₁₉ with x = 1) were investigated using firstprinciples total-energy calculations. We find that in the ground-state configuration Zn-Sn ions preferentially occupy 4f₁ and 4f₂ sites unlike the model previously suggested by Ghasemi et al. where Zn-Sn ions occupy 2b and 4f₂ sites. Our model predicts a rapid increase in saturation magnetic moment (Ms̳) as well as decrease in magnetic anisotropy compared to the pure M-type Sr-hexaferrite, which is consistent with experimental observations.