There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Modeling hardness of polycrystalline materials and bulk metallic glasses

The elastic constant tensor of an inorganic compound provides a complete description of the response of the material to external stresses in the elastic limit. It thus provides fundamental insight into the nature of the bonding in the material, and it is known to correlate with many mechanical properties. Despite the importance of the elastic constant tensor, it has been measured for a very small fraction of all known inorganic compounds, a situation that limits the ability of materials scientists to develop new materials with targeted mechanical responses. To address this deficiency, we present here the largest database of calculated elastic properties for inorganic compounds to date. The database currently contains full elastic information for 1,181 inorganic compounds, and this number is growing steadily. The methods used to develop the database are described, as are results of tests that establish the accuracy of the data. In addition, we document the database format and describe the different ways it can be accessed and analyzed in efforts related to materials discovery and design.

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Charting the complete elastic properties of inorganic crystalline compounds

Iron oxide surfaces

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Charting the complete elastic properties of inorganic crystalline

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.

Ab Initio Calculation of Elastic Constants of Ceramic Crystals

Based on the most recently determined noncubic structure for -Al2O3 by Menendez-Proupin and Gutierrez, a comprehensive list of physical properties is investigated theoretically. These include lattice dynamics and phonon spectra, elastic constants and bulk structural parameters, electronic structure and interatomic bonding, optical properties, and x-ray absorption near-edge structure XANES spectra. Compared to similar calculations of -Al2O3, we find a smaller lowest zone-center vibrational mode at 97.6 cm −1, a lower heat capacity, a smaller bulk modulus, and a much larger thermal-expansion coefficient. The threefold bonded O ions introduce highly localized vibrational modes near 751 cm−1. The calculated thermal Gruneisen parameter indicates a strong anharmonicity in -Al2O3. The elastic tensor and the elastic wave velocities are also evaluated showing the longitudinal wave to be nearly isotropic. For the electronic structure, we find that -Al2O3 has a smaller band gap but a refractive index similar to -Al2O3. Highly localized states at the top of the valence band originating from threefold bonded O in the more covalently bonded AlO4 tetrahedra are identified. The calculated Mulliken effective charges and bond order values indicate that the structural model for -Al2O3 has a high degree of disorder. The octahedral unit AlO6 is a stronger polyhedron than the tetrahedral unit AlO4 although the latter has stronger Al–O bonds. The calculated Al-K, Al-L3, and O-K edges for Al and O in -Al2O3 show strong dependence on their local coordination and environments. These results are in good agreement with available experimental data but the effect of the -Al2O3 samples’ porosity should be properly assessed. It is argued that the traditional view that stoichiometric -Al2O3 is a defective spinel with cation vacancies or its variations should be modified. -Al2O3 is better described as an amorphous networklike structure such that the ratio of tetrahedrally coordinated Al to octahedrally coordinated Al is close to 0.6; and the O ions are bonded to Al in either a threefold or fourfold configurations in about equal proportion.

Ab initiostudy of the physical properties ofγ-Al2O3: Lattice dynamics, bulk properties, electronic structure, bonding, optical properties, and ELNES/XANES spectra

Magnetization studies on well characterized epitaxial magnetite $({\text{Fe}}_{3}{\text{O}}_{4})$ thin films grown on MgO(100) show that the ultrathin films ($l5\text{ }\text{nm}$ thickness) 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 $(l5\text{ }\text{nm})$ 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 ${\text{Fe}}_{3}{\text{O}}_{4}\text{-MgO}$ 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 $(A)$ and octahedral $(B)$ sublattices at the surface and antiphase-domain boundaries are inferred to be the main factor contributing to the observed enhanced magnetic moment.

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Giant magnetic moment in epitaxial Fe 3 O 4 thin films on MgO(100)

Fluorapatite (FAP) and hydroxyapatite (HAP) are two very important bioceramic crystals. The (001) surfaces of FAP and HAP crystals are studied by ab initio density functional calculations using a supercell slab geometry. It is shown that in both crystals, the O-terminated (001) surface is more stable with calculated surface energies of 0.865 and $0.871\phantom{\rule{0.3em}{0ex}}\mathrm{J}∕{\mathrm{m}}^{2}$ for FAP and HAP, respectively. In FAP, the two surfaces are symmetric. In HAP, the orientation of the OH group along the $c$ axis reduces the symmetry such that the top and bottom surfaces are no longer symmetric. It is revealed that the atoms near the surface and subsurface are significantly relaxed especially in the case of HAP. The largest relaxations occurred via the lateral movements of the O ions at the subsurface level. The electronic structures of the surface models in the form of layer-by-layer resolved partial density of states for all the atoms show systematic variation from the surface region toward the bulk region. The calculated Mulliken effective charge on each type of atom and the bond order values between cations (Ca, P) and anions (O, F) show different charge transfers and bond strength variations from the bulk crystal values. Electron charge density calculations show that the surfaces of both FAP and HAP crystals are mostly positively charged due to the presence of Ca ions at the surface. The positively charged surfaces have implications for the absorption on apatite surfaces of water and other organic molecules in an aqueous environment which are an important part of its bioactivity. The x-ray absorption near-edge structure (XANES) spectra ($\mathrm{Ca}\text{\ensuremath{-}}K$, $\mathrm{O}\text{\ensuremath{-}}K$, $\mathrm{F}\text{\ensuremath{-}}K$, $\mathrm{P}\text{\ensuremath{-}}K$, and $\mathrm{P}\text{\ensuremath{-}}{L}_{3}$ edges) of both the surface models and the bulk crystals are calculated and compared. The calculations use a supercell approach which takes into account the electron--core-hole interaction. It is shown that the site-specific XANES spectra show significant differences between atoms near the surface and in the bulk and are very sensitive to the local atomic environment of each atom. This information will be very valuable for characterizing the apatite materials and in the interpretation of experimental data. Comparisons of several sets of experimental data with the weighted sums of the calculated spectra at different sites for the same element show very good agreement.

Electronic structure, bonding, charge distribution, and x-ray absorption spectra of the (001) surfaces of fluorapatite and hydroxyapatite from first principles

Hongzhi Yao

Papers

Ab Initio Calculation of Elastic Constants of Ceramic Crystals

Ab initiostudy of the physical properties ofγ-Al2O3: Lattice dynamics, bulk properties, electronic structure, bonding, optical properties, and ELNES/XANES spectra

Giant magnetic moment in epitaxial Fe 3 O 4 thin films on MgO(100)

Electronic structure, bonding, charge distribution, and x-ray absorption spectra of the (001) surfaces of fluorapatite and hydroxyapatite from first principles

Electronic structure and bonding in the Y-Si-O-N quaternary crystals