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The discrete variational method within the framework of density functional theory is used to study the effect of zirconium on the electronic structure of the grain boundary in . The results for the interatomic energies show that the strength of the grain boundary is increased by the substitution of Zr for Al. The calculation of the charge distribution indicates that the directionality of the bonds in the grain boundary region is weakened by the addition of Zr. These results show that the alloying effect of Zr introduced into can significantly improve the ductility of , while strengthening the grain boundary.

The electronic structure of and grain boundaries in containing B are investigated by the use of the discrete variational method. The effects of B on grain boundaries are discussed. The results show that B forms stronger bonding states with its neighbouring host atoms, and it can be expected that the cohesive strength of the grain boundaries will be increased.

Based on the tight-binding bond recursion method, the energetics parameters of ∑3[111] grain boundary in nickel are investigated. The theoretical results indicate that the boron enhances interatomic energy between the host atoms, and between impurity and nickel atoms. Calculations of the energy of the grain boundary segregation show that boron, nitrogen, and phosphorus have the tendency to segregate onto the grain boundary and segregation property of boron is stronger than that of nitrogen and phosphorus.