An effective computational scheme to calculate the complete set of independent elastic constants as well as other structural parameters including bulk modulus, shear modulus, Young's modulus, and Poisson's ratio for crystals is reported. The scheme is based on the stress–strain analysis approach with the appropriate selection of strain governed by symmetry consideration. The first principles Vienna ab initio simulation package (VASP) is used in stress calculations. Comprehensive tests were performed for α‐SiO2 and spinel MgAl2O4 with different exchange‐correlation potentials, and different sets of computational parameters to investigate the relative accuracies of the calculations. A wide range of oxides, nitrides, and carbonate crystals with different crystal symmetries were chosen to test the scheme under both LDA and GGA approximations at zero temperature and pressure. Some of these calculations for large complex crystals are believed to be attempted for the first time. The calculated elastic constants show quite good agreement with the existing experimental data for almost all the examined systems with the exception of the relatively soft material such as α‐SiO2 and the C14 parameter of some trigonal crystals expressed in the hexagonal form such as in α‐Al2O3. Other structural properties derived from the elastic constants also show good agreements with the measured values.

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Magnetization studies on well characterized epitaxial magnetite ͑Fe 3 O 4 ͒ thin films grown on MgO͑100͒ show that the ultrathin films ͑Ͻ5 nm thickness͒ are ferromagnetic and their magnetic moments are much greater than those of bulk magnetite, particularly at a thickness of 20 nm or below. The observation of a ferromagnetic nature in ultrathin magnetite films ͑Ͻ5 nm͒ is in contrast to the previously accepted dead layer interface model or a superparamagnetic behavior for ultrathin films of magnetite. From detailed spin-polarized density functional theory based calculations of Fe 3 O 4 -MgO interface, we calculate a deviation in spin moment of the Fe atoms in the vicinity of the interface from their bulk values, which is insufficient to explain the observed results. Orbital moment contribution for the surface Fe atoms was found to be quite small. The noncompensation of spin moments between the tetrahedral ͑A͒ and octahedral ͑B͒ sublattices at the surface and antiphase-domain boundaries are inferred to be the main factor contributing to the observed enhanced magnetic moment.

The Y-Si-O-N quaternary crystals are an important part of structural ceramics. Their crystal structures are complex and not precisely determined. Little is known about their electronic structure and bonding which are indispensable for a fundamental understanding of structural ceramics. Within the equilibrium phase diagram of the SiO 2 -Y 2 O 3 -Si 3 N 4 system, there are only four known crystalline phases: Y 2 Si 3 N 4 O 3 (M-melilite), Y 4 Si 2 O 7 N 2 (J phase or N-YAM), YSiO 2 N (wallastonite), and Y 10 ͓SiO 4 ͔ 6 N 2 (N-apatite). With the possible exception of YSiO 2 N, these crystals have O / N disorder in that the exact positions of the anions cannot be uniquely determined. Using accurate ab initio total energy relaxation, the atomic positions of the lowest energy configurations in these crystals are determined. Based on the theoretically modeled structures, the electronic structure and bonding are investigated using the ab initio orthogonalized linear combination of atomic orbitals method, and are related to a variety of local cation-anion bonding configurations. These results are presented in the form of atom-resolved partial density of states, Mulliken effective charges and bond order values. Although the strong Si-N and Si-O bonding dominates in these crystals, it is also shown that Y-O and Y-N bonding are not negligible and should be a part of discussion of the overall bonding scheme in these crystals. It is concluded that Y 2 Si 3 N 4 O 3 has the strongest crystal bonding among the four crystals. In addition, the optical properties of these crystals are calculated using the ab initio wave functions. All four crystals are insulators with optical band gaps of 3.40, 3.19, 4.40, and 3.70 eV, respectively. These results are further discussed in the context of specific bonding configurations of the cations (Si and Y) with the anions (O and N) and their implications on the metal-containing intergranular glassy films in polycrystalline Si 3 N 4 .

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