A long-standing goal of materials science is to understand, predict and control the evolution of microstructures in crystalline materials. Most microstructure evolution is controlled by interface motion; hence, the establishment of rigorous interface equations of motion is a universal goal of materials science. We present a new model for the motion of arbitrarily curved interfaces that respects the underlying crystallography of the two phases/domains meeting at the interface and is consistent with microscopic mechanisms of interface motion; i.e., disconnection migration (line defects in the interface with step and dislocation character). We derive the equation of motion for interface migration under the influence of a wide range of driving forces. In Part II of this paper [Salvalaglio, Han and Srolovitz, 2021], we implement the interface model and the equation of motion proposed in this paper in a diffuse interface simulation approach for complex morphology and microstructure evolution.
The motion of interfaces is an essential feature of microstructure evolution in crystalline materials. While atomic-scale descriptions provide mechanistic clarity, continuum descriptions are important for understanding microstructural evolution and upon which microscopic features it depends. We develop a microstructure evolution simulation approach that is linked to the underlying microscopic mechanisms of interface migration. We extend the continuum approach describing the disconnection-mediated motion of interfaces introduced in Part I [Han, Srolovitz and Salvalaglio, 2021] to a diffuse inte…
Knowledge about grain boundary migration is a prerequisite for understanding and ultimately modulating the properties of polycrystalline materials. Evidence from experiments and molecular dynamics (MD) simulations suggests that the formation and motion of disconnections is a mechanism for grain boundary migration. Here, grain boundary migration is modeled using a multiphase field model based on the principle of minimum dissipation potential with nonconvex boundary energy, along with a stochastic model for thermal nucleation of disconnection pairs. In this model, disconnections arise spontaneou…
We present the results of novel, time-resolved, in situ HRTEM observations, molecular dynamics (MD) simulations, and disconnection theory that elucidate the mechanism by which the motion of grain boundaries (GBs) in polycrystalline materials are coupled through disconnection motion/reactions at/adjacent to GB triple junctions (TJs). We focus on TJs composed of a pair of coherent twin boundaries (CTBs) and a Σ9 GB. As for all GBs, disconnection theory implies that multiple modes/local mechanisms for CTB migration are possible and that the mode selection is affected by the nature of the driving …
We study the Grain Boundary (GB) migration based on the underlying disconnection structure and mechanism. Disconnections are line defects that lie solely within a GB and are characterized by both a Burgers vector and a step height, as set by the GB bicrystallography. Multiple disconnection modes can nucleate, as determined by their formation energy barriers and temperature, and move along the GB under different kinds of competing driving forces including shear stress and chemical potential jumps across the GBs. We present a continuum model in two dimensions for GB migration where the GB migrat…
The formation of basal/prismatic (BP) interfaces accompanying with the nucleation and growth of a reoriented crystal in Mg single-crystals under c-axis tension is investigated by molecular dynamics simulations. The BP interfaces nucleate by shuffling mechanism via local rearrangements of atoms. Both two-layer disconnections and one-layer disconnections contribute to the migration of BP interfaces. In a three-dimensional view, the BP interfaces relatively tend to migrate towards the [1-210] direction rather than the [-1010]/[0001] direction since the misfit disconnection or misfit dislocation c…
The microstructure of polycrystalline materials consists of networks of grain boundaries (GBs) and triple junctions (TJs), along which three GBs meet. The evolution of such microstructures may be driven by surface tension (capillarity), applied stresses, or other means that lead to a jump in chemical potential across the GBs. Here, we develop a model for the concurrent evolution of the GB/TJ network based upon the microscopic mechanism of motion; the motion of line defects (disconnections) in the GB that have both dislocation and step character. The evolution involves thermally-activated disco…
Ductility and Brittle Fracture of Tungsten by Disconnection Pile-up on Twin Boundaries
Lawrence Livermore National Laboratory（劳伦斯利弗莫尔国家实验室）；Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）；University of California Irvine（加州大学尔湾分校）；University of California Los Angeles（加州大学洛杉矶分校）；Lehigh University（理海大学）；Northwestern University（西北大学）
While deformation twinning in hexagonal close-packed metals has been widely studied due to its substantial impact on mechanical properties, an understanding of the detailed atomic processes associated with twin embryo growth is still lacking. Conducting molecular dynamics simulations on Mg, we show that the propagation of twinning disconnections emitted by basal-prismatic interfaces controls the twin boundary motion and is the rate-limiting mechanism during the initial growth of the twin embryo. The time needed for disconnection propagation is related to the distance between the twin tips, wit…
The grain boundary (GB) mobility relates GB velocity to the thermodynamic driving forces and is central to our understanding of microstructure evolution in polycrystals. Recent molecular dynamics (MD) and experimental studies have shown that the temperature-dependence of the GB mobility is much more varied than is commonly thought. GB mobility may increase, decrease, remain constant or show multiple peaks with increasing temperature. We propose a mechanistic model for GB migration, based on the formation and migration of line defects (disconnection) within the GB. We implement this model in a …
The formation and migration of disconnections (line defects constrained to the grain boundary (GB) plane with both dislocation and step character) control many of the kinetic and dynamical properties of GBs and the polycrystalline materials of which they are central constituents. We demonstrate that GBs undergo a finite-temperature topological phase transition of the Kosterlitz-Thouless (KT) type. This phase transition corresponds to the screening of long-range interactions between (and unbinding of) disconnections. This phase transition leads to abrupt change in the behavior of GB migration, …
Experiments, theory and atomistic simulations show that finite triple junction mobility results in non-equilibrium triple junction angles in evolving polycrystalline systems. These angles have been predicted and verified for cases where grain boundary migration is steady-state. Yet, steady-state never occurs during the evolution of polycrystalline microstructures as a result of changing grain size and topological events (e.g., grain face/edge switching - "$T_1$" process, or grain disappearance "$T_2$" or "$T_3$" processes). We examine the non-steady evolution of the triple junction angle in th…
The microstructure evolution due to thermomechanical treatment of metals can largely be described by viscoplastic deformation, nucleation and grain growth. These processes take place over different length and time scales which present significant challenges when formulating simulation models. In particular, no overall unified field framework exists to model concurrent viscoplastic deformation and recrystallization and grain growth in metal polycrystals. In this work a thermodynamically consistent diffuse interface framework incorporating crystal viscoplasticity and grain boundary migration is …
Predicting the microstructure during selective laser sintering (SLS) is of great interests, which can compliment the current time and cost expensive trial-and-error principle with an efficient computational design tool. However, it still remains a great challenge to simulate the microstructure evolution during SLS due to the complex underlying physical phenomena. In this work, we present a three-dimensional finite element phase-field simulation of the SLS single scan, and revealed the process-microstructure relation. We use a thermodynamically consistent non-isothermal phase-field model includ…
Kinetic equations and level-set approach for simulating solid-state microstructure evolutions at the mesoscopic scale: state of the art, limitations, and prospects
Coarsening kinetics is usually described using a linear gradient approximation for the underlying interface migration (IM) rates, wherein the migration fluxes at the interfaces vary linearly with the driving force. Recent experimental studies have shown that coarsening of nanocrystalline interface microstructures is unexpectedly stable compared to conventional parabolic coarsening kinetics. Here, we show that during early stage coarsening of these microstructures, IM rates can develop a non-linear dependence on the driving force, the mean interface curvature. We derive the modified mean field …
The Ga vacancy mediated microstructure evolution of (Ga,Mn)As during growth and post-growth annealing is studied using a multi-scale approach. The migration barriers for the Ga vacancies and substitutional Mn together with their interactions are calculated from first principles, and temporal evolution at temperatures ranging from 200 to 350$^\circ$C is studied using Lattice Kinetic Monte Carlo simulations. We show that at the typical growth and annealing temperatures (i) gallium vacancies provide the diffusion mechanism for substitutional Mn and (ii) in 10--20 h the vacancy mediated diffusion …
