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Nano-Mechanics Simulations Group Nano-Mechanics Simulations Group Modeling the Strength of Ni 3 Al Nanocubes Using Molecular Dynamics Simulations By: Koren Shreiber, Msc Guidance: Dr. Dan Mordehai http://nanomechsim.technion.ac.il Technion - Israel Institute of Technology Faculty of Mechanical Engineering The Nanomechanics Simulations Laboratory

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Nano-Mechanics Simulations Group Nano-Mechanics Simulations Group Smaller is Stronger At the sub-micro meter scale, metal specimens obey different mechanical properties than their bulk counterparts. Size dependent strength. MPa compressive stresses with bulk regime, GPa with nano - particles. Bulk regime Mordehai et al. Acta Mater. 59, 2309 (2011)

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Nano-Mechanics Simulations Group Nano-Mechanics Simulations Group Background -Ni 3 Al -Dislocations theory Experiments Molecular Dynamics simulation Research steps -Step 1 – Validate screw dislocation properties in a perfect lattice -Step 2 – Calculate the dissociation widths -Step 3 – Compression of nanoparticles What’s next? Contents

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Nano-Mechanics Simulations Group Nano-Mechanics Simulations Group Ni 3 Al Lattice FCC – Face Centered Cubic (aluminum, copper, gold, lead, nickel, platinum, silver etc.) L1 2 ordered structure Aluminum atoms in corners Nickel atoms face centered Lattice parameter a = 3.57 (Å) a Al Ni Ni 3 Al alloys are important for technological applications mainly due to their high strength at elevated temperatures (200-900 [MPa] tensile yield stress).

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Nano-Mechanics Simulations Group Nano-Mechanics Simulations Group Dislocation - crystallographic line defect within a crystal structure. Mechanisms for dislocation formation: Homogeneous nucleation in the bulk. Heterogeneous nucleation on the surface or at grain boundary. Dislocation glide - Dislocations can glide on slip planes, usually with highest density of atoms. Burgers vector (b): magnitude and direction of the lattice distortion caused by dislocation. Dislocation theory (perfect dislocations) Edge dislocation Screw dislocation

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Nano-Mechanics Simulations Group Nano-Mechanics Simulations Group Partial dislocations Stacking fault

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Nano-Mechanics Simulations Group Nano-Mechanics Simulations Group Dislocation dissociates in FCC into 2 partial dislocations with a Stacking Fault (SF) L1 2 structures have super-dislocations which dissociates into two super-partials dislocations with Anti-Phase Boundary (APB). The super partials dissociates into two partials dislocations with Complex SF (CSF) or Super intrinsic SF (SISF). Partial dislocations in Ni 3 Al (FCC) FCC CSF LI 2

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Nano-Mechanics Simulations Group Nano-Mechanics Simulations Group Ultrahigh strength of Dislocation-free Ni 3 Al nanocubes, Robert Maass et al. Experiments Goal: study compressive strengths of dislocation-free Ni 3 Al nanocubes Size-dependent ultrahigh strength (2-10 GPa) Dislocation nucleation at free surfaces as a governing plasticity mechanism in nanosized crystals Slip traces of dislocations on the surface Strain “burst” (dislocation nucleation)

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Nano-Mechanics Simulations Group Nano-Mechanics Simulations Group Research goal Experiments and finite elements analysis do not give us information on the underlying dislocation mechanisms. In this research, we perform a molecular dynamics simulation, to obtain insights on the atomistic mechanisms which dominate the deformation of Ni 3 Al nanocubes.

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Nano-Mechanics Simulations Group Nano-Mechanics Simulations Group Molecular Dynamics (MD) is a computational method to determine the trajectories of atoms in phase space according to Newton’s equations of motion (F=ma). The forces acting on each atoms are derived from an interaction energy, which is calculated according to atom positions, using effective interatomic potentials. We employ an Embedded Atoms Method potential (EAM), which is reliable for FCC metals, with a set of parameters calibrated by Purja Pun, G.P. & Mishin, Y. (REF: Purja Pun, G.P. and Mishin, Y.(2009) 'Development of an interatomic potential for the Ni-Al system', Philosophical Magazine, 89: 34, 3245 — 3267) Molecular Dynamics simulation

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Nano-Mechanics Simulations Group Nano-Mechanics Simulations Group Step 1 – construct a Ni 3 Al lattice In order to examine the ability of the potential to describe dislocation properties we constructed an “infinite” (fully periodic) Ni 3 Al lattice with 360K atoms. 1311 Å 309 Å 10 Å A screw dislocation dipole was introduce into the computational cell on (111) slip planes, according to isotropic elastic displacements. Burgers vector

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Nano-Mechanics Simulations Group Nano-Mechanics Simulations Group Step 1 – Visualizing dislocations Atoms in dislocations are identified according to BOP (bond order parameters) BOP – A set of symmetry parameters that defines the local symmetry in the lattice. For instance, the BOP of an atom in the perfect bulk is different from the one in the CSF. We used Atomeye for visualization. b CSF APB dipole

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Nano-Mechanics Simulations Group Nano-Mechanics Simulations Group Step 2 - Calculate the dissociation widths Dissociation width calculation for one typical dipole APB converge to 7b (35 Å) CSF converge to 2b (10 Å) Simulation results (MD and excel)

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Nano-Mechanics Simulations Group Nano-Mechanics Simulations Group Width of planar faults follows from the energy balance between the faults energy and the elastic interaction forces between partial dislocations Analytical results (maple) Step 2 – Calculate the dissociation widths

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Nano-Mechanics Simulations Group Nano-Mechanics Simulations Group Step 3 - compression of nanoparticles We constructed a Ni 3 Al nanocube (size 17.9x17.9 nm, 250k atoms) and compressed it with a virtual planar indenter (a repulsion force field which propagates at a constant rate towards the nanocube). 178.5 Å

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Nano-Mechanics Simulations Group Nano-Mechanics Simulations Group Step 3 - compression of nanoparticles The forces on the indenter are extracted from the simulation. Stress & strain are calculated: Traces of deformation twinning made by a glide of twinning dislocations can be observed on the surface. Nucleation at 5 GPa Elastic zone

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Nano-Mechanics Simulations Group Nano-Mechanics Simulations Group Step 3 - compression of nanoparticles

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Nano-Mechanics Simulations Group Nano-Mechanics Simulations Group What‘s next? -What’s next? -Improving techniques of visualize faults in alloys (intermetallics). -Analyzing the dislocations mechanisms of the deformed nanocube. -Using other interatomic potentials.

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Nano-Mechanics Simulations Group Nano-Mechanics Simulations Group Questions?

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Nano-Mechanics Simulations Group Nano-Mechanics Simulations Group Ni 3 Al - Motivation Ni-base super alloys are important for technological applications due to their: High strength following precipitation hardening at elevated temperature (200-900 [MPa] tensile yield stress). Low density (~7 g/cm 3 ) resulting lightweight. High resistance to creep deformation. High oxidation & corrosion resistance. precipitate bulk

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Nano-Mechanics Simulations Group Nano-Mechanics Simulations Group Deformation behavior of free standing single-crystalline Ni 3 Al-based nanoparticles, J. Schloesser et al. Compression testing on free standing and single crystalline Ni 3 Al nanocube ( ̴ 300 nm) Dislocation nucleation of Undeformed (defect free) particles Strength of 2-3 GPa Experiments Undeformed particles after extraction strain “burst” Tungsten needle Picking up particle compression

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Nano-Mechanics Simulations Group Nano-Mechanics Simulations Group Dislocation dissociation/separation in FCC – 2 partial dislocations with Stacking Fault (SF) L1 2 structures have super-dislocations which dissociates into two super-partials dislocations with Anti-Phase Boundary. The super partials dissociates into two partials dislocations with Complex SF or Super intrinsic SF Anomaly of Ni 3 Al - With the help of thermal activation, dislocation configuration is not planar and cannot glide (Kear-Wilsdorf lock) Partial dislocations in Ni 3 Al (FCC) FCC CSF LI 2 Lock

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Nano-Mechanics Simulations Group Nano-Mechanics Simulations Group Molecular Dynamics (MD) is a computational method to determine the trajectories of atoms in phase space according to Newton’s equations of motion (F=ma). The forces acting on each atoms are derived from an interaction energy, which is calculated according to atom positions, using effective interatomic potentials. We employ an Embedded Atoms Method potential (EAM), which is reliable for FCC metals, with a set of parameters calibrated by Purja Pun, G.P. & Mishin, Y. (REF: Purja Pun, G.P. and Mishin, Y.(2009) 'Development of an interatomic potential for the Ni-Al system', Philosophical Magazine, 89: 34, 3245 — 3267) Molecular Dynamics simulation

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Nano-Mechanics Simulations Group Nano-Mechanics Simulations Group About Us The aim of the Nano Mechanics Simulations Laboratory is to develop and employ atomic and nanoscale simulation techniques to study the mechanical properties of nanometer- size specimens and surfaces. Understanding mechanical properties on very small scales: Fundamental understanding of plasticity Provide design guidelines for reliable nano and micro devices. Traditional approaches developed for bulk materials can no longer be used.

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