Based on first-principles method, structural stability of M-Al-N (M=Ti, Zr, Hf) was investigated and mechanical properties were calculated. Firstly, enthalpies of M-Al-N compounds were calculated, and M₂AlN and M₄AlN₃ were found to be thermodynamically stable. Except for experimental structures Ti₂AlN, Ti₄AlN₃, Zr₂AlN and Hf₂AlN, two stable structures Zr₄AlN₃ and Hf₄AlN₃ were found. Mechanically and dynamically stable were verified by calculation of elastic constants and phonon spectrum. Mechanical properties of M₂AlN and M₄AlN₃ were calculated. It was found that they had high bulk modulus, shear modulus, elastic modulus, Vickers hardness and brittleness. Variation of mechanical properties of M-Al-N compounds with composition was analyzed, which provided theoretical basis for selection and application of this kind of materials. At last, electron density of states and partial DOS, electron density, Mulliken population analysis of M-Al-N (M=Ti, Zr, Hf) compounds were calculated.

At high pressures, a new graphite intercalation compound (GIC) HfC₂ was predicted. We calculate structure and properties of HfC₂ at 0 GPa using first-principles method. Lattice parameters of HfC₂ with geometrical optimization based on GGA-PBESOL, GGA-PW91 and LDA are almost the same. With phonon dispersion curve and elastic constant, dynamical and mechanical stability of structure were verified, respectively, which meant that HfC₂ could exist stability at 0 GPa. Calculated bulk modulus and shear modulus of HfC₂ are 265 GPa and 118 GPa, respectively, and Pugh ratio k<0.57. With analysis of electron density and density of states, Hf-C and C-C bond showed covalent, metallically. That is reason why it has high bulk modulus and ductility. At last, we calculated bond length, bulk modulus, shear modulus and Pugh ratios of HfC₂ in pressures ranging from 0 GPa to 500 GPa.

Crystal structure, mechanical and electronic properties of Ti-Al intermetallic compounds were studied using first-principles implemented in CASTEP. At 0 K, 0 GPa, thermodynamically stable structures are TiAl₃, TiAl₂, TiAl, Ti₃Al. Unit cells of TiAl₃, TiAl₂, TiAl are evolutions of face-centered cubic Al. Structure of Ti₃Al is similar to Ti, which is hexagonal close packing structure. Mechanical properties were calculated. It was found that with increasing of Ti molar fraction, their bulk modulus are approximate equivalent. But shear modulus and Vickers hardness decrease, and so did Pugh ratios. It shows that toughness became better. At last, density of state and Mulliken population analysis were simulated. Bonding nature of Ti-Al is a combination of metallic, covalent and weak ionic.