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Abstract This work introduces a theoretical formulation and develops numerical methods for finite element implementation of the formulation so as to extend the concurrent atomistic-continuum (CAC) method for modeling and simulation of finite-temperature materials processes. With significantly reduced degrees of freedom, the CAC simulations are shown to reproduce the results of atomically resolved molecular dynamics simulations for phonon density of states, velocity distributions, equilibrium temperature field of the underlying atomistic model, and also the density, type, and structure of dislocations formed during the kinetic processes of heteroepitaxy. This work also demonstrates the need of a mesoscale tool for simulations of heteroepitaxy, as well as the unique advantage of the CAC method in simulation of the defect formation processes during heteroepitaxy. 

This work presents a multiscale study of the uniaxial compression of Si pillars, with diameters ranging from 50 nm to 360 nm, using the Concurrent Atomistic-Continuum (CAC) method. The simulations reproduce the brittle and ductile deformation behaviors of Si pillars observed in experiments. For defect-free Si pillars compressed by a perfectly smooth flat punch with a repulsive force field to reflect an assumed rigid indenter, dislocations are nucleated from the corner of the bottom surface for pillars with diameters of 100 nm and below, while for pillars with diameters of 220 nm and above, dislocations nucleate from the top surface; multiple slip systems are activated in all pillars except for the pillar with a diameter of 50 nm. A strong size effect is thus demonstrated with regard to the nucleation of dislocations. Another key finding is the critical role of defects on the indenter surface. For a perfectly flat indenter, all the defect-free Si pillars with diameters ranging from 50 nm to 360 nm exhibit ductile deformation. By contrast, for an indenter with surface steps, all pillars with diameters of 100 nm and above deform in a brittle manner. These surface steps cause sequential nucleation of dislocations and activation of two slip systems, leading to dislocation intersection and formation of a sessile Lomer lock. Continued pileups of dislocations against the Lomer lock lead to the initiation of a crack at the intersection. The deformation mechanism underlying the crack formation is thus demonstrated. 

In this work, a field representation of the conservation law of linear momentum is derived from the atomistic, using the theory of distributions as the mathematical tool, and expressed in terms of temperature field by defining temperature as a derived quantity as that in molecular kinetic theory and atomistic simulations. The formulation leads to a unified atomistic and continuum description of temperature and a new linear momentum equation that, supplemented by an interatomic potential, completely governs thermal and mechanical processes across scales from the atomic to the continuum. The conservation equation can be used to solve atomistic trajectories for systems at finite temperatures, as well as the evolution of field quantities in space and time, with atomic or multiscale resolution. Four sets of numerical examples are presented to demonstrate the efficacy of the formulation in capturing the effect of temperature and thermal fluctuations, including phonon density of states, thermally activated dislocation motion, dislocation formation during epitaxial processes, and attenuation of longitudinal acoustic waves as a result of their interaction with thermal phonons. 

We present a molecular dynamics study of the thermal transport properties of PbTe/PbSe (111) and PbTe/PbSe (100) interfaces at room temperature. The PbTe/PbSe heterostructures are obtained through simulations of the kinetic processes of direct bonding of PbTe and PbSe crystals. The atomic-scale dislocation core structures and the misfit dislocation networks in the heterostructures obtained in the simulations are found to closely match experimental data. Two types of heat transfer experiments are then simulated: a heat-sink heat-source experiment and an ultrashort heat pulse experiment. Thermal boundary resistance is calculated for three distinct interface types: coherent, semi-coherent, and semi-coherent with pinned dislocations. Both types of simulations consistently capture the significant role of the misfit dislocations on thermal resistance. The effect of the mobility of dislocations on thermal resistance is demonstrated for the first time through comparing the thermal boundary resistance of interfaces containing pinned dislocations and with those containing unpinned dislocations. In addition, the thermal boundary resistance is found to strongly depend on the length of the specimen and the area of the interface. 

The dynamic interaction between phonons and dislocations in LiF has been studied using molecular dynamics simulations. The simulations have captured the strong dynamic interactions between low-frequency slow transverse acoustic phonons and dislocations that were observed in experiments. Simulation results reveal that the strong dynamic interaction is attributed to resonant interactions between dislocations and slow transverse acoustic phonons. Each dislocation segment is found to possess a set of resonant modes characterized by large-amplitude out-of-phase vibrations of atoms on both sides of the dislocation slip plane. The resonant frequencies associated with these modes exhibit a nearly linear distribution with respect to the mode order. Contrary to previous beliefs, the resonant frequencies of dislocations exhibit only a weak correlation with the dislocation length. Additionally, each dislocation exhibits a dominant resonant mode that corresponds to the strongest vibration mode in response to phonons. This dominant resonant mode is not always the first resonant mode with the lowest frequency. Its specific order depends on the dislocation length. Simulation results have also demonstrated that the resonant modes of dislocations can be influenced by the interactions from neighboring dislocations. 

The paper presents a multiscale study of the kinetic processes of the heteroepitaxial growth of the PbSe/PbTe (111) and PbTe/PbSe(001) systems, using the Concurrent Atomistic-Continuum (CAC) method as the simulation tool. The CAC simulations have reproduced the Stranski–Krastanov growth mode and the layer-by-layer growth mode of the two systems, respectively; the pyramid-shaped island morphology of the PbSe epilayer on PbTe (111), the square-like misfit dislocation networks within the PbTe/PbSe(001) interface, and the critical thickness for the PbTe/PbSe(001) system at which coherent interfaces transit to semi-coherent interfaces with the formation of misfit dislocations, all in good agreement with experimental observations. Four types of misfit dislocations are found to form during the growth of the two PbTe/PbSe heterosystems, and hexagonal-like misfit dislocation networks are observed within the PbSe/PbTe(111) interfaces. The growth processes, including the formation of misfit dislocations, have been visualized. Dislocation half-loops have been observed to nucleate from the epilayer surfaces. These half-loops extend towards the interface by climb or glide motions, interact with other half-loops, and form misfit dislocation networks at the interfaces and threading dislocations extending from interfaces to epilayer surfaces. The dominant types of misfit dislocations in both systems are found to be those with Burgers vectors parallel to the interfaces, whereas the misfit dislocations with Burgers vectors inclined to the interface have a low likelihood of generation and tend to annihilate. The size of the substrate is demonstrated to have a significant effect on the formation, evolution, and distribution of dislocations on the growth of PbSe on PbTe(111).