http://nanomechsim.technion.ac.il Technion - Israel Institute of Technology Faculty of Mechanical Engineering The Nanomechanics Simulations Laboratory Modeling the Strength of Ni3Al Nanocubes Using Molecular Dynamics Simulations By: Koren Shreiber, Msc Guidance: Dr. Dan Mordehai

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)

Molecular Dynamics simulation Research steps Contents Background Ni3Al 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?

Ni3Al Lattice Ni3Al alloys are important for technological applications mainly due to their high strength at elevated temperatures (200-900 [MPa] tensile yield stress). FCC – Face Centered Cubic (aluminum, copper, gold, lead, nickel, platinum, silver etc.) L12 ordered structure Aluminum atoms in corners Nickel atoms face centered Lattice parameter a = 3.57 (Å) a Al Ni

Dislocation theory (perfect dislocations) 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. Screw dislocation Edge dislocation

Partial dislocations Edislocation ̴ Gb2 (dislocation Energy) Partial dislocations – a dislocation with Burgers vector b has higher energy than a few dislocations with smaller Burgers vectors bi which satisfy b= 𝑏𝑖 . Since bi are not lattice vectors they create a planar fault between the partial dislocations. The dissociation width (the size of the “Imperfect” zone) depends on the energy of the planar faults and the elastic constants. Stacking fault

Partial dislocations in Ni3Al (FCC) Dislocation dissociates in FCC into 2 partial dislocations with a Stacking Fault (SF) L12 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). CSF LI2

Experiments Ultrahigh strength of Dislocation-free Ni3Al nanocubes, Robert Maass et al. Goal: study compressive strengths of dislocation-free Ni3Al nanocubes Size-dependent ultrahigh strength (2-10 GPa) Dislocation nucleation at free surfaces as a governing plasticity mechanism in nanosized crystals Strain “burst” (dislocation nucleation) Slip traces of dislocations on the surface

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 Ni3Al nanocubes.

Molecular Dynamics simulation 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) We do not solve quantum equation every time step and .

Step 1 – construct a Ni3Al lattice In order to examine the ability of the potential to describe dislocation properties we constructed an “infinite” (fully periodic) Ni3Al lattice with 360K atoms. 1311 Å 309 Å 10 Å Screw dislocation dipoles – two dislocations in opposite directions. Finally, we relaxed the system A screw dislocation dipole was introduce into the computational cell on (111) slip planes, according to isotropic elastic displacements. Burgers vector

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

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

Analytical results (maple) Step 2 – Calculate the dissociation widths Width of planar faults follows from the energy balance between the faults energy and the elastic interaction forces between partial dislocations Analytical results (maple) The results are in good agreement with our MD simulation

Step 3 - compression of nanoparticles We constructed a Ni3Al 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

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

Step 3 - compression of nanoparticles

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. np

Questions?

Ni3Al - 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/cm3) resulting lightweight. High resistance to creep deformation. High oxidation & corrosion resistance. precipitate bulk

Undeformed particles after extraction Experiments Deformation behavior of free standing single-crystalline Ni3Al-based nanoparticles , J. Schloesser et al. Undeformed particles after extraction Compression testing on free standing and single crystalline Ni3Al nanocube (̴ 300 nm) Dislocation nucleation of Undeformed (defect free) particles Strength of 2-3 GPa strain “burst” Tungsten needle Picking up particle compression

Partial dislocations in Ni3Al (FCC) Dislocation dissociation/separation in FCC – 2 partial dislocations with Stacking Fault (SF) L12 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 Ni3Al - With the help of thermal activation, dislocation configuration is not planar and cannot glide (Kear-Wilsdorf lock) FCC CSF LI2 Lock

Molecular Dynamics simulation 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) We do not solve quantum equation every time step and .

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.