Martensitic phase transformation in NiTi shape memory alloys (SMA) occurs over a hierarchy of spatial scales, as evidenced from observed multiscale patterns of the martensitic phase fraction, which depend on the material microstructure and on the size of the SMA specimen. This paper presents a methodology for the multiscale tracking of the thermally induced martensitic phase transformation process in NiTi SMA. Fine scale stochastic phase field simulations are coupled to macroscale experimental measurements through the compound wavelet matrix method (CWM). A novel process for obtaining CWM fine scale wavelet coefficients is used that enhances the effectiveness of the method in transferring uncertainties from fine to coarse scales, and also ensures the preservation of spatial correlations in the phase fraction pattern. Size effects, well-documented in the literature, play an important role in designing the multiscale tracking methodology. Molecular dynamics (MD) simulations are employed to verify the phase field simulations in terms of different statistical measures and to demonstrate size effects at the nanometer scale. The effects of thermally induced martensite phase fraction uncertainties on the constitutive response of NiTi SMA is demonstrated.

<div> <div> <div> <p>The material responses and the deformation pattern of crystals are strongly influ- enced by their microstructure, crystallographic texture and the presence of defects of various types. </p> <p>In electronics, Sn coatings are widely used in circuits to protect conductors, reduce oxidation and improve solderability. However, the spontaneous growth of whiskers in Sn films causes severe system failures. Based on extensive experimental results, whiskers are observed to grow from surface grains with shallow grain boundaries. The underlying mechanism for these surface grains formation is crucial to predict potential whisker sites. A phase field model is coupled with a single crystal plasticity model and applied to simulate the grain boundary migration as well as the grain rotation process in Sn thin film, which are two possible mechanisms for surface grain formation. The grain boundary migration of three columnar grains is modeled and no surface grain is formed due to large plastic dissipation. In polycrystal Sn thin film, the nucleation of subgrains with shallow grain boundaries is observed for certain grain orientations on the film surface and the location of which corresponds to the regions with high strain energy density. From these simulations, it can be concluded that the grain rotation is the mechanism for whisker grain formation and the nucleated subgrains may be the potential whisker sites. </p> <p>Sn-based solders are also widely used in electronics packaging. The reliability and the performance of SAC (Sn-Ag-Cu) solders are of key importance for the miniaturiza- tion of electronics. The interfacial reaction between Cu substrates and Sn-based sol- ders forms two types of brittle intermetallic compounds (IMCs), Cu6Sn5 and Cu3Sn. </p> </div> </div> <div> <div> <p>During the operation, the interconnecting solders usually experience thermal loading and electric currents. These environmental conditions result in the nucleation of voids in Cu3Sn layer and the growth of the IMCs. A phase field damage model is applied to model the fracture behavior in Cu/Sn system with different initial void densities and different Cu3Sn thickness. The simulation results show the fracture location is dependent on the Cu3Sn thickness and the critical stress for fracture can be increased by lowering the void density and Cu3Sn thickness.<br></p></div></div></div><div><div><div> <p>In alloys, the stacking fault energy varies with the local chemical composition. The effects of the stacking fault energy fluctuation on the strengthening of alloys are studied using phase field dislocation method (PFDM) simulations that model the evolution of partial dislocations in materials at zero temperature. Some examples are shown to study the dependency of the yield stress on the stacking fault energy, the decorrelation of partial dislocations in the presence of impenetrable and penetrable particles. Simulations of the evolution of partial dislocations in a stacking fault energy landscape with local fluctuations are presented to model the responses of high entropy alloys. A strong size dependency is observed with a maximum strength when the mean region size approaches the average equilibrium stacking fault width. The strength of high entropy alloys could be improved by controlling the disorder in the chemical misfit. </p> </div> </div> </div>

<p>A thermodynamically consistent coarsed-grained phase field model was developed to find the conditions under which a heterogeneous porous electrode can be treated as homogeneous in the description of Lithium-ions in rechargeable batteries. Four regimes of behavior under which the transport phenomena can be homogenized to describe porous LIBs were identied: regime (a), where the model is inaccurate, for physically accessible particle packings of aspect ratios smaller than c/a = 0.5 and electrode porosities between 0.34 to 0.45; regime (b), where the model is valid, for particles of aspect ratios greater than c/a = 0.7 and electrode porosities greater than 0.35; regime (c), where the model is valid, but the microstructures are physically inaccessible, and correspond to particles with aspect ratios greater than c/a = 0.7 and electrode porosities smaller than 0.34; and regime (d), where the model is invalid and the porous microstructures are physically inaccessible, and correspond to particles with aspect ratios smaller than c/a = 1 and electrode porosities smaller than 0.34.</p> <p>The developed formulation was applied to the graphite | LixNi1/3Mn1/3Co1/3O2 system to analyze the effect of microstructure and coarsed-grained long-range chemomechanical effects on the electrochemical behavior. Specically, quantiable lithium distribution populations in the cathode, as a result of long range interactions of the diffuse interface, charge effects and mechanical stresses were identified: i) diffusion limited population due to negligible composition gradients, ii) stress-induced population as a result of chemically induced stresses, and iii) lithiation-induced population, as a consequence of the electrochemical potential gradients.</p>

Title: Studies of Relaxor Ferroelectrics with Spontaneous Polar Nanoregions Author: Petr Ondrejkovič Institute: Institute of Physics of the Czech Academy of Sciences Supervisor: Ing. Jiří Hlinka, Ph.D., Institute of Physics of the Czech Academy of Sciences Abstract: The thesis is devoted to relaxor ferroelectrics with spontaneous polar nanoregions. We have investigated one of the canonical representatives, uniaxial strontium barium niobate, by means of neutron scattering, and also performed computer simulations with a model of a uniaxial ferroelectric with point defects. Neutron scattering studies of strontium barium niobate single crystals under a defined sequence of thermal and electric field treatments elucidate nature of distinct components of its transverse diffuse scattering. These components are associated mainly with the static ferroelectric nanodomain structure and the dynamic order-parameter (polarization) fluctuations. Moreover, high-resolution neutron backscattering experiments allowed us to resolve characteristic frequencies of the order-parameter fluctuations and prove that this component is caused by the same polar fluctuations that are responsible for the Vogel-Fulcher dielectric relaxation, the hallmark of relaxor ferroelectrics. The model system of a uniaxial ferroelectric with point...