First Principles Study Of Structure And Stacking Fault Energies In Some Metallic Systems

Abstract

Plastic deformation in crystalline materials largely depends on the properties of dislocations, in particular their mobility. While continuum description of deformation of a crystalline metal can be made reasonably well by considering the elastic properties of dislocations and neglecting the core, crystallographic aspects of dislocation motion require precise understanding of the core effects. The concept of the generalized stacking fault (GSF) energy was proposed as means to describe this. GSF energy, a fundamental property of a given material, can be determined using first principles total energy calculations. In this thesis, we use GSF to understand some of the intriguing mechanical responses recently observed in some metallic systems. First, we examine the structures and stacking fault energies in Mg-Zn-Y alloy system. This system is unique in the sense that trace additions of Zn and or Y result in long period stacking sequences such as 6l and 14l, as reported in recent literature. Further, these alloys exhibit extraordinary mechanical properties. We attempt to rationalize these experimental observations through first principles calculations of energies of periodic structures with different stacking sequences and stacking faults. For pure Mg, we find that the 6-layer structure with the ABACAB stacking is most stable after the lowest energy hcp structure with ABAB stacking. Charge density analysis shows that the 2l and 6l structures are electronically similar, which might be a cause for better stability of 6l structure over a 4l sequence or other periodic structures. Addition of 2 atomic% Y leads to stabilization of the structure to 6l sequence whereas the addition of 2 atomic% Zn makes the 6l energetically comparable to that of the hcp. Stacking fault (SF) on the basal plane of 6l structure is higher in energy than that of the hcp 2l Mg, which further increases upon Y doping and decreases significantly with Zn doping. SF energy surface for the prismatic slip indicates dissociation of dislocations in alloys with a 6l structure. Thus, in an Mg-Zn-Y alloy, Y stabilizes the long periodicity, while Zn doping provides a synergistic effect in improving the mechanical properties alongwith strengthening due to long periodic phases. Our investigation of surface properties and magnetism in Ni revealed that, the universal binding energy relation (UBER) derived earlier to describe the cohesion between two rigid atomic planes, does not accurately capture the cohesive properties when the cleavage cracked surfaces are allowed to relax through atomic displacements. We find that two characteristic length-scales are involved in the cleavage of a crystal accompanied by structural relaxation at the cleaved surface. Based on that, we suggest a modified functional form of UBER that is analytical and at the same time accurately models the properties of relaxed surfaces upon cleavage. We demonstrate the generality as well as the validity of this modified UBER through first-principles density functional theory calculations of cleavage in fcc, bcc, and hcp metals, as well as covalently bonded materials. We also found that the cohesive law (stress-displacement relation) differs significantly in the case where cracked surfaces are allowed to relax, with lower peak stresses occuring at higher displacements. We have attempted understanding these ideas through images obtained from electronic densities and eigen states. Our work should be useful in providing inputs to multi-scale simulations of fracture in materials. The third phase of the work reports the stacking fault energy and twinning in Ni with a particular emphasis on the size effect. Experimental and computational research on Nan crystalline metals (mostly on Ni) indicates unique facets of dislocation activity (extended partial dislocations) and modes of deformation (twinning). In order to capture the intrinsic scaling eject in the nano-regime, it is imperative to account for the complex electronic structure of the metal in question. The stacking fault (SF) and twinning fault (TF) energies in nano-thin elm of Ni with 7, 13, 19, and 25 layers of (111) planes were determined using rest-principles density functional theory (DFT) total energy calculations. Generalized planar fault (GPF) energy curves of the nano-thin alms show higher extreme vis-a-vis the bulk, indicating that creation of SFs in nano-Ni is relatively difficult. In contrast, the ratios of energy barriers relevant to nucleation of dislocations and twinning support the observed enhanced tendency for extended partial dislocation formation and twinning in the nano-thin films in comparison with bulk. Our results should be useful in understanding deformation behavior of nano-structured Ni-based alloys used as advanced structural materials.