Elucidating the kinetics of twin boundaries from thermal fluctuations

There is compelling evidence for the critical role of twin boundaries (TBs) in imparting the extraordinary combination of strength and ductility to nanotwinned metals. Here, we investigate the thermal fluctuations of TBs in face-centered-cubic metals to elucidate the deformation mechanisms governing their kinetic properties using molecular dynamics simulations. Our results show that the TB motion is strongly coupled to shear deformation up to 0.95 homologous temperature. A rather unexpected observation is that coherent TBs do not exhibit any capillarityinduced fluctuations even at high temperatures, in sharp contrast to other high-angle grain boundaries. Nanotwinned metals are known to demonstrate a remarkable combination of mechanical properties, namely, ultra-high strength, enhanced ductility, and high strain rate sensitivity. This is in contrast to nanocrystalline materials, which exhibit a loss of ductility, and grain stability with decreasing grain size, thereby offsetting the initial excitement generated by their very high yield strength (see for review). It is well documented, through many experimental and theoretical studies, that this loss of stability of nanograined metals, which has severely limited their practical application, is associated with thermally-activated or stress-assisted grain growth caused by grain boundary (GB)-mediated processes such as migration and sliding. It is natural then, that the grain growth and twin lamella stability in nanotwinned metals would also be intimately connected to the thermodynamic and kinetic properties of twin boundaries (TBs) and GBs. Although the prospect of the stability of nanotwinned structures is of vital concern, one which defines their ultimate utility and raises fundamental questions regarding the underlying physics, the issue has remained relatively unaddressed until recently. In this Research Letter, we report our investigation of the motion of TBs by atomistic modeling of their thermal fluctuations over a range of temperatures. In the theory of statistical mechanics of interfaces, thermal fluctuations have been effectively used to elucidate the thermodynamic and kinetic properties of fluid and solid membranes and interfaces. In the case of high-angle GBs, the capillary wave theory has been successfully applied to relate their long wavelength thermal fluctuations to important quantities such as the GB stiffness and mobility. According to the capillarity theory, the energetic cost for these out-of-plane fluctuations is attributed to the surface tension, or in other words, the increase in the area of the interface to accommodate the bending due to fluctuations. The Fourier spectrum of these capillarity-induced fluctuations is given by k|A(k)|2l = kBT SGk2 , (1) where k is the wave vector, A(k) is the amplitude of the mode k fluctuation, S is the area of the interface or gain boundary, and Γ is the interfacial stiffness. The initial aim of our work was to furnish a constitutive description for TBs based on this relation. However, as described in what follows, our molecular dynamics simulations revealed that a fluctuating TB, unlike other high-angle GBs, does not follow the relation in Eq. (1), even at very high temperatures. In fact, our observation that the TBs show 1/k dependence of the fluctuation average and consequently, do not show capillarity-induced fluctuations, was not obvious to us when we started the study and has not been reported in the literature before. While this study was ongoing, a paper by Karma et al. appeared, which investigated the fluctuations of low-angle GBs and proposed the relation between the 1/k dependence of equilibrium fluctuations of low-angle GBs and their kinetics via shear-coupled motion. In this paper, we present our thermal fluctuation simulations for TBs, interpret them within the context of this recent work by Karma et al. as well as discuss the relevance of this study within the current literature on TBs and nanotwinned metals. The TB fluctuations were modeled by molecular dynamics simulations using Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS). All of the simulations were performed on Cu using the embedded-atom method developed by Mishin et al. At each temperature, the simulation cell was first equilibrated for 100 ps at zero pressure using the NPT ensemble. The molecular dynamics run was then conducted for 1 ns under the NVT ensemble using the Nose–Hoover thermostat. The system configuration was MRS Communications (2013), 3, 241–244 © Materials Research Society, 2013 doi:10.1557/mrc.2013.37 MRS COMMUNICATIONS • VOLUME 3 • ISSUE 4 • www.mrs.org/mrc ▪ 241 observed at every 1000 time steps. To investigate the effect of temperature on the fluctuations, the simulations were conducted over temperatures ranging from 100 to 1300 K. The simulation box dimensions were Lx≈ 300 Å, Ly≈ 100 Å, and Lz≈ 20 Å with periodic boundary conditions in the xand z (lateral)directions as shown in Fig. 1. The specimen was oriented along the [ 112], [ 11 1], and [ 1 10] crystallographic directions. Since the cell dimension was much smaller in the z-direction, the fluctuations along this direction were neglected. The y-direction was aligned normal to the TB, and the fluctuations were observed along the x-direction. To assess the effect of cell size on the fluctuation measurements, we also performed the simulation at 1000 K on a larger specimen with dimensions 600 Å × 200 Å × 40 Å. The results changed only negligibly confirming that our initial choice of dimensions was appropriate for extracting the thermal fluctuations of a single interface. At 0 K, the TB is a flat interface located at the center of the simulation box as shown by the dotted lines in Fig. 1. At finite temperature, the interface fluctuates and we denote the instantaneous out-of-plane displacement by h(x). Figure 2 shows the atomistic structure of a fluctuating TB at an instant with red atoms being the farthest distance above the initial flat configuration and blue atoms being the lowest. Many approaches have been proposed to locate the instantaneous position of a fluctuating interface in molecular dynamics simulations. In this work, we used the centrosymmetry parameter to distinguish between atoms belonging to the interface and the bulk and thus, identify the instantaneous TB position. The centrosymmetry parameter of an atom is defined as