| Phase-field modeling has emerged as a powerful method to model interface evolution in various contexts. In this thesis, we use this general formulation to model materials interfaces in three distinct, yet related, problems. In the first problem, we characterize both analytically and numerically short-range forces between spatially diffuse interfaces in multi-phase-field models of polycrystalline materials. The results show that forces are always attractive for traditional models where each phase-field represents the phase fraction of a given grain. The implication of these results for understanding grain-boundary premelting are discussed. In the second problem, we present a phase-field model of nanowire growth with vapor-liquid-solid (VLS) growth mechanism. By carrying out an asymptotic analysis, we show that this model can recover the sharp-interface growth theory proposed by Schwarz and Tersoff [49]. In addition, we develop a method to incorporate surface energy and kinetic anisotropy within the multi-phase field context and use it in the modeling of nanowire growth. It is demonstrated that rich behaviors can rise from VLS growth system by considering energy or kinetic anisotropy. As a natural extension of our study of nanowire growth, we also tackle the related issue of understanding the morphological instability of a nanowire, which impacts its lifetime of service. The results reveal that nanowire fragmentation is controlled by a finite-amplitude Rayleigh-Plateau instability. We also develop an analytical theory to explain universal scaling properties that relate the amplitude and wavelength of instability. The third problem has practical relevance for understanding the mechanical behavior of metals in the presence of small inclusions. We work out analytical solutions for elliptically shaped inclusions using classic Eshelby theory and use those solutions to benchmark our phase-field solutions. Finally, this phase-field approach is used to investigate the response to stress of intergranular inclusions for which no analytical treatment is available. |
