Abstract
At 0 K, phonon instability controls the ideal strength and the ultrafast dynamics of defect nucleation in perfect crystals under high stress. However, how a soft phonon evolves into a lattice defect is still unclear. Here, we develop a full-Brillouin zone soft-phonon-searching algorithm that shows outstanding accuracy and efficiency for pinpointing general phonon instability within the joint material-reciprocal (x–k) spaces. By combining finite-element modeling with embedded phonon algorithm and atomistic simulation, we show how a zone-boundary soft phonon is first triggered in a simple metal (aluminum) under nanoindentation, subsequently leading to a transient new crystal phase and ensuing nucleation of a deformation twin with only one-half of the transformation strain of the conventional twin. We propose a two-stage mechanism governing the transformation of unstable short-wave phonons into lattice defects, which is fundamentally different from that initially triggered by soft long-wavelength phonons. The uncovered material dynamics at stress extremes reveal deep connections between delocalized phonons and localized defects trapped by the full nonlinear potential energy landscape and add to the rich repertoire of nonlinear dynamics found in nature. Simulations of nanoscale indentations reveal the critical link between unstable vibrational waves and nucleation of crystal defects. Researchers looking to maximize the strength of devices such as transistors, solar cells, and superconductors through strain engineering are often frustrated by spontaneous defect nucleation. Ju Li from the Massachusetts Institute of Technology and colleagues have now developed an algorithm that can search for specific crystal vibrations, known as soft phonons, that can trigger defects to form. The team created a constrained optimization program to search for phonon instability, and then employed finite element modeling and molecular dynamic calculations to simulate nano-indentations in a model aluminum crystal. These computations showed that at extreme deformation stress points, a two-step mechanism transforms soft phonons into discrete atomic defects within tens of picoseconds. We develop a robust full-Brillouin zone soft-phonon-searching algorithm, with outstanding accuracy and efficiency in pinpointing general phonon instability within the joint material-reciprocal spaces in crystals. By combining finite-element modeling with embedded phonon algorithm and atomistic simulation, we show how a zone-boundary soft phonon is first triggered in a perfect aluminum crystal under nanoindentation, which subsequently leads to a transient new crystal phase and ensuing nucleation of a deformation twin. We propose a two-stage mechanism governing the transformation of unstable short-wave phonons into lattice defects, fundamentally different from that initially triggered by soft long-wavelength phonons.
Highlights
The strength of solids at temperature T = 0 K limits the attainable range of elastic strain engineering,[1] whereby finite elastic strain field[2,3] ε(x) is tuned to yield better transistors,[1] solar cells,[2] superconductors[4] and other devices
While for crystals with inhomogeneous strain during nanoindentation, where Brillouin zone (BZ) and periodical boundary conditions (PBCs) become ill-defined as a result of losing the lattice translational symmetry, it is reasonable to turn to examine the structural stability of each infinite lattice Θ that is homogeneously strained according to the local deformation at each material point x, if the material strain field is slowly varied
Combining finite-element modeling incorporating Phorion and atomistic simulations, we show how a zone-boundary phonon instability is first triggered in a simple metal under nanoindentation and how it metamorphoses into a deformation twin (DT)
Summary
When a phonon frequency ω becomes imaginary, the harmonic oscillation will grow in amplitude and subsequently break lattice translational symmetry leading to defect nucleation.[7,8] Such processes are believed to occur in some low-temperature nanoindentation experiments where near-ideal strengths are experimentally measured.[6] Previous simulation studies have focused on the long-wave phonon instability (elastic instability) with wave vector k≈0 (Γ point) in the Brillouin zone (BZ) where an analytical formula can be derived based on the elastic constants and stress.[7,8,9,10,11,12] the long-wave instability is just one special class of the general phonon instability in full BZ,[13,14,15,16,17,18,19,20,21,22,23] which may be diagnosed by phonon calculation for homogeneously strained crystals under periodical boundary conditions (PBCs).[5] While for crystals with inhomogeneous strain during nanoindentation, where BZ and PBC become ill-defined as a result of losing the lattice translational symmetry, it is reasonable to turn to examine the structural stability of each infinite lattice Θ that is homogeneously strained according to the local deformation at each material point x, if the material strain field is slowly varied. Development of new efficient algorithm is required, because in principle all the phonons in the full BZ (k space) of Θ for every material point within x space should be treated
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