Total Energy Calculations for Predictive Modeling of Crystalline Materials Strength
Doctoral thesis, 1998
Materials properties depend on phenomena in a hierarchical order from atomic to macroscopic scales. This thesis studies possibilities for electron-structure and total-energy calculations to provide results that are valuable for the modeling of crystalline materials strength. Rather than a comprehensive approach, the thesis addresses issues at various levels, such as methodological aspects, key concepts like dislocations, micro-meso connections and interfaces.
Density-functional theory (DFT) is the formal basis for the thesis work. A study of bonding properties of atoms within the atom-in-jellium model compares local-density (LDA) and generalized-gradient approximations (GGA-PW91) for the electron exchange and correlation interactions, giving an additional positive test of the usefulness of GGA.
Computational speed is as important as accuracy for many applications, setting limits to accessible system size for first-principles electron-structure calculations. For a foreseeable future one has for extended defects, large enough for mechanical behaviour, to resort to interatomic model potentials for atomistic simulations. The effective-medium theory (EMT) model potential is derivable from DFT and parametrizable from atom-in-jellium calculations. The basis of the EMT is studied with a superposition of spherically symmetric adaptive densities. For Al and Ni the Harris density-functional test is successful, but further progress for the EMT potential is not made.
Dislocations are recognized as key concepts for understanding mechanical properties of crystalline solids. Bridges to larger scales are provided by the Peierls-Nabarro (PN) model, a conceptual framework for dislocation structure and energetics. Results of full-scale atomistic simulations for the edge dislocation in Pd are compared with those from the PN model. Furthermore, PN model results for the fcc metals Al, Ni, Cu, and Pd, using input from DFT calculations for generalized stacking-fault (GSF) surfaces, are presented. The classic PN model is found to have some quantitative capabilities, however, with room for improvements even for the supposedly favorable fcc-metal case. To improve the model a modification is presented.
At the mesoscale, interfaces are key features for mechanical properties, e.g, the strength of metals being determined by extrinsic obstacles, such as precipitates, which block the motion of dislocations. Control of appearance and particle shape should be aided by knowledge of interface structure and energetics, used in modeling of complex alloys on a thermodynamical level. The electronic and atomic structures of a model system for the semi-coherent interface between Fe and VN are calculated from first principles and interpreted in terms of the theory for bond ing in transition-metal nitrides and carbides outlined by the Grimvall group. The smallness of the calculated interface energies can in this band-filling picture be related to features of the electron structure. Nitrogen vacancies are shown to increase the interface energy, as deduced from this picture.