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Phase field crystal (PFC) model is employed to simulate the process of growth of epitaxial layer on plane-convex substrate with a lattice mismatch and a small inclination angle. The variation of the systematic free energy, the total atomic number of the epitaxial layer, and the effect of the curvature and the angle of the substrate are analyzed. The results show that when the surface of the substrate is plane, the free energy increases with the increase of the substrate inclination angle, and also the total atomic number of the epitaxial layer increases; while the surface of the substrate is convex, the free energy decreases with the increase of substrate angle and so also the total atomic number of the epitaxial layer decrease. This is the reason that the frontier of surface of epitaxial layer changes from the step bunching to the hill-and-valley facet structure with the increasing of the inclination angle of convex substrate. These results are in good agreement with the other method results.

The phase field crystal (PFC) model is used to simulate the premelting dislocation movement of the symmetric tilt grain boundary (STGB) under strain action when the system temperature is at far from the melting point and close to the melting point, respectively. The results show a local premelting occurs surrounding the dislocations as the premelting temperature is approached to from below temperature. The premelting dislocations of the STGB can glide under strain action, and the premelting region is a companion for dislocation gliding. The process of STGB decay is very similar at the two high temperature conditions. As premelting presents, it diminishes the gliding resistance for the dislocations and leads to a faster movement of dislocations, and also brings about more energy reduction of the system during the decay process of STGB. In spite of applying strain to these premelting samples in whole decay processes of STGB, the premelting dislocation region does not obviously develop and extend. This indicates that the external strain action does not promote the premelting at the high temperature, and cannot induce more premelting dislocation, which can be owed to the premelting phase around the dislocation exhibit fluid-like properties and to the premelting dislocation easily gliding and relaxing the strain energy; this is in agreement with the results of experiments and molecular dynamics.

The two-mode phase field-crystal (PFC) method is used to simulate the nanograin growth, including the grain growth in different sets of crystal planes, the grain boundary structure with mismatch, the grain orientation and also the incoherent grain boundary in two dimensional plane. It is obviously observed that there are dislocation structures in nanograin boundary due to mismatch and misorientation of grains. These simulation results can not only be used in artificial controlling the grain boundary of nanograin, but also is of significant for designing new nanograin with a good grain boundary for structure materials.

The second phase nucleation and precipitation around an edge dislocation are studied using phase field method. A new free energy function including the elastic strain energy is established to describe the dislocation interaction with the solute. The results give the distribution of strain field of dislocation and show the precipitates grow up according to the power growth law with the index 2. The simulated results are in good agreement with that of theory of non-uniform nucleation.

The phase field method was applied to study the effect of second-phase particles (SPP) with different geometric orientations and shapes on grain growth. The results show that, in the grain growth process, most of the spherical second-phase particles located at triple junctions, while the stick SPPs located at the grain boundaries along the grain boundary. The second-phase particles are of the strong pinning effect on grain boundary and the limiting grain radius can be expressed by Zener relations. In the condition of the second-phase particles area fraction and size remaining the same, the stick SPPs are of more effective pinning on grain growth than that for spherical SPPs, and the orientation of disk second-phase particles is also an influence factor for pinning effect. Stick second-phase particles with multiple orientations can make a better pining effect than those with only one orientation.

The second phase nucleation and precipitation around the edge dislocation are studied using phase-field method. A new free energy function is established. The simulation results are in good agreement with that of theory of dislocation and theory of non-uniform nucleation.

Photonic crystals (PCs) containing defects have important applications in optical filtering with super narrow transmission band and photo phase adjustment. Resonance transmission bands in one-dimensional PCs with a defect mode are calculated by the transfer matrix method. The effect of two primitive dielectric refractive index ratios and position of the defect in PCs on filter quality are analyzed. The photonic band gap of PCs, the narrow resonance transmission band made by defect, and the relationship between refractive index of defect layer and the peak value of narrow resonance transmission band are discussed. The physical mechanisms can be explained by the photonic potential well and potential barrier scattering for photons.

The atomic bonding of the segregated cell of Al-Li alloy in earlier ageing condition was calculated according to the empirical electron theory (EET) in solid. The results showed that the strongest covalent bond was the Al-Al bond in the segregated cell without vacancy, while the strongest covalent bond was the Al-Li bond in the cell containing vacancy. Since the difference of electronagativity between the Al and Li atoms was obvious, it was inclined to form the Al-Li segregated cell of short range order structure in the condition of vacancy joining. The short range order structure with vacancy was probably the embryo or precursor structure of the metastable phase ' δ (Al3Li). As the ' δ (Al3Li) was coherence with matrix, the bond net strength was enhanced by the precipitation of ' δ (Al3Li) and hence the alloy was strengthened.

Atomic bonding of the GPB zone and S′′ phase of Al-Cu-Mg alloys in early aging stage are calculated using the empirical electron theory (EET) in Solid. The results show that not only the covalence bond-net is very strong in GPB zone, but the whole covalence bond energy of S′′ phase is also very large, all the primary bond-net framework of these precipitates can consolidate the matrix of alloy. Phase transformation from GPB zone to S′′ phase is explained reasonably based on atomic bonding and total binding capacity of Al and Cu atoms in these precipitates.

Atomic bonding of ϑ (Al2Cu) in an Al-Cu thin-film alloy is calculated by using empirical electron theory (EET) in solids. Results show that the Cu-Cu bond in the ϑ phase is the strongest, while the second strongest bond is the Al-Cu bond. All of these bonds are stronger than the strongest Cu-Cu bond in pure Cu metal. This is the reason that only ϑ precipitation in the Al-Cu thin-film alloy can be found and not ϑ″ and ϑ′ phases. The electromigration lifetime of Al-Cu thin-film alloy for interconnects is influenced by the stronger atomic bonding in ϑ particles, which are dispersed in the matrix of the alloy. The ϑ precipitation in the Al-Cu thin-film alloy can enhance the strength of the alloy by the stronger bond net and increase the electromigration lifetime for interconnects.