Lattice defects are unavoidable structural units in materials and play an important role in determining material properties.Compared with the periodic structure of crystals,the atomic configurations of the lattice defects are determined by the coordinates of a large number of atoms,making it difficult to experimentally investigate them.In computational materials science,multiparameter optimization is also a difficult problem and experimental verification is usually required to determine the possibility of obtaining the structure and properties predicted by calculations.Using our recent studies on oxide surfaces as examples,we introduce the method of integrated aberration-corrected electron microscopy and the first-principles calculations to analyze the atomic structure of lattice defects.The atomic configurations of defects were measured using quantitative high-resolution electron microscopy at subangstrom resolution and picometer precision,and then the electronic structure and dynamic behavior of materials can be studied at the atomic scale using the firstprinciples calculations.The two methods complement each other and can be combined to increase the understanding of the atomic structure of materials in both the time and space dimensions,which will benefit materials design at the atomic scale.
Single-crystal elastic constants and mechanical hardness of covalent and ionic crystals have been studied using first-principles calculations.The results show that the hardness is dominated by the softest elastic mode,not by the averaged elastic moduli as generally assumed.It reveals that the mechanical stability and anisotropy play an important role in determining the hardness of materials.The concept is then employed in designing hard alloys.By strengthening the softest elastic mode of tungsten carbide,which is the primary component in industrial hard alloys,we show that the carbide can be made even harder by alloying with nitrogen or rhenium via Fermi-level tuning.
