Ab initio prediction of the mechanical properties of alloys

Sammanfattning: At the time of the 50th anniversary of the Kohn-Sham method, ab initio calculations based on density functional theory have formed an accurate, efficient, and reliable method to work on the properties of engineering materials. In this thesis, we use the exact muffin-tin orbitals method combined with the coherent-potential approximation to study the mechanical properties of high-technology materials. The thesis includes two parts: a study of long-range chemical order effects and a study of alloying effects on the mechanical properties of alloys. In the first part, we concentrate on the impact of chemical ordering on the mechanical properties. The long range order effect on the elastic constants behaves in a very different way for non-magnetic materials and ferromagnetic materials. For a non-magnetic Cu3Au, the long-range order effect on the elastic constants is very small. The Debye temperature does not show a strong chemical order dependence either. For a ferromagnetic material, on the other hand, the long-range chemical order produces considerable influence on C' in the ferromagnetic state, but negligible effect on C' in the paramagnetic state. The lattice parameter, bulk modulus $B$, and shear elastic constant C44 change slightly with the degree of long-rang order for both magnetic states. The Young's modulus E and the shear modulus G increase significantly with the degree of order in the ferromagnetic state, but the effect becomes weak as the system approaches the random regime.In the second part, the alloying effect of Mn/Ni on the lattice parameter, elastic constants, surface energy, and unstable stacking fault energy of bcc Fe is examined. The calculated results show that the lattice parameter of ferrite Fe is slightly altered upon Ni/Mn alloying the trend of which can be explained by the magnetism-induced pressure. Nickel addition decreases C' but has a negligible effect on C44, whereas manganese addition increases C44 and has a weak influence on C'. In both systems, the bulk modulus B shows a smooth second order variation. On the other hand, the surface energy and the unstable stacking fault (USF) energy decrease by adding Mn or Ni to Fe. For both planar fault energies, Ni shows a stronger effect than Mn. Segregation seems to have a minor effect on the surface and USF energies for dilute Fe-Ni and Fe-Mn alloys. The ductility can be estimated using available physical parameters via traditional phenomenological criteria like the Pugh ratio B/G, the Poisson ratio ?, the Cauchy pressure C12-C44, and the Rice ratio ?s/?u .According to dislocation theory, a dislocation can not cross a grain boundary. Therefore, the study of dislocations is assumed to be limited to single-crystals. Several theoretical studies indicate that the cleavage plane is {001} in bcc crystals. Based on these information, we suggest that the resolved single-crystal tensile strength E[001] and the resolved single crystal shear strength G{110}<111> should be used to describe brittle cleavage and dislocation movement rather than polycrystalline parameters such as B and G. We demonstrate that all shear moduli G{lmn}<111> associated with the <111> Burgers vector take the same value 3C44C'/(C'+2C44), which could in fact explain the observed multiple slip in bcc systems. Due to the discrepancy between the resolved single-crystal elastic constants and the averaged polycrystalline elastic constants, the Pugh ratio B/G and the traditional criteria based on polycrystalline elastic constants lead to large differences for magnetic systems. Finally, we propose a new measure of the ductile-bittle behavior based on the ratio ?clevage/Gresolved which gives the right experimental trend for Fe-Mn and Fe-Ni system.