Generalized Stacking Fault Energy Calculated From First Principles And Analysis Of Local Approximation

It has been full 40 years since the concept of generalized stacking fault energy that was put forward in studying face-centered cubic crystal in 1968 by Vitek. Generalized stacking fault energy plays a crucial role in studying the brittle-to-ductile transition (BDT) and dislocation theory. However, because generalized stacking fault energy can only be calculated by computer simulation, its calculations gradually increase in the last decades.The paper has computed the generalized stacking fault energy of aluminum, zigzag single-walled carbon nanotubes and graphene by the fist principles. We discusses the local approximation of the generalized stacking fault energy and get the conclusion that the generalized stacking fault energy is from the nearest neighbor atomic layers in two half-crystals. Graphene will be seen as the limit case of infinite radius, we have compared the generalized stacking fault energies of zigzag single-walled carbon nanotubes with different radius and graphene. By comparison, we know that the energy value is become bigger with the increasing radius, but the rage of the change is not large.The paper can be divided into three parts, the fist part mainly introduce the generalized stacking fault energy and the background of calculation method from first section and second section. In the first section, we mainly introduce the concept of generalized stacking fault energy and recent research achievements. The study of generalized stacking fault energy is relatively less. The density functional theory and the ABINIT package have been introduced in the second section. The second part is the third section, we compute the generalized stacking fault energy of aluminum that can be computed well in the section. By the compute, we have verified the dependability of ABINIT firstly, and discuss carefully the local approximation of generalized stacking fault energy. The local approximation is the key word that dislocation equation uses of the generalized stacking fault energy. Through this section we know ABINIT in the calculation of the generalized stacking fault energy is reliable. Analysis shows that it has local approximation. That is, the generalized stacking fault energy is from the nearest neighbor atomic layers in two half-crystals. The restoring force Fb ( u ) = ??(γ( u)) that be obtained by generalized stacking fault energy is the force between upper and lower crystals. The use of the restoring force in the dislocation theory is totally feasible. Finally, we fitted the aluminum (111) surface of the analytical expression of the generalized stacking fault energy. The third part is the forth section. In this section, we have firstly computed the generalized stacking fault energy of zigzag single-walled carbon nanotubes (5, 8) through the surface of revolution of the horizontal and sloppy c-c bond. The results show that the value of generalized stacking fault energy through the surface of revolution of horizontal c-c bond is less than the other. Then, we computed the generalized stacking fault energy of zigzag single-walled carbon nanotubes (10, 8) and graphene through the sloppy c-c bond. Graphene will be seen as the limit case of infinite radius, we have compared the generalized stacking fault energies of zigzag single-walled carbon nanotubes (5, 8), (10, 8) and graphene. By comparison, we know that the energy value is become bigger with the increasing radius, but the rage of the change is not large. The energy curves of zigzag single-walled carbon nanotubes (10, 8) and graphene have been basically coincidence on the graph. Final of the section, we fit the three energy curves in small displacement and get the shear modulus values consistent with other literature through the fitted parameters.In the last chapter, the main contents and conclusions of my dissertation have been summarized, and sequential research work is specified.