FRG: Multiscale Simulation of Atomistic Processes in Nanostructured - PowerPoint PPT Presentation

FRG: Multiscale Simulation of Atomistic Processes in Nanostructured Materials Rajiv K. Kalia, Aiichiro Nakano & Priya Vashishta Concurrent Computing Laboratory for Materials Simulations Dept. of Physics, Dept. of Computer Science, Louisiana State Univ. Dept. of Materials Science, Dept. of Physics, Dept. of Computer Science, Dept. of Biomedical Engineering Univ. of Southern California (after September 2002) Email: {kalia, nakano, priyav}@bit.csc.lsu.edu URL: www.cclms.lsu.edu NSF Division of Materials Research Computational Materials Theory Program Review Program Managers: Dr. Bruce Taggart & Dr. Daryl Hess Organizers: Dr. Duane Johnson & Dr. Jeongnim Kim June 20, 2002, Urbana, IL CCLMS CCLMS CCLMS

Outline 1. Multiscale finite-element/molecular-dynamics /quantum-mechanical simulation on a computational Grid 2. Immersive & interactive visualization of billion- atom systems 3. Multimillion atom MD simulations of fracture & nanoindentation in crystalline, amorphous & nanophase materials & ceramic nanocomposites 4. New educational and outreach programs

Multiscale FE/MD/QM Simulation Multiscale simulation to seamlessly couple: • Finite-element (FE) calculation • Atomistic molecular- dynamics (MD) simulation • Quantum-mechanical (QM) calculation based on the density functional theory (DFT) > 10 -6 m 10 -6 - 10 -10 m

Molecular Dynamics Simulation • Newton’s equations of motion ( ) ∂ V r d 2 r r N r dt 2 = − ( i = 1,..., N ) i m i ∂ r r i • Interatomic potential ( ) ( ) r ij , r ∑ ∑ V = + u ij r v jik r r ij ik i < j i , j < k • N -body problem long-range electrostatic interaction— O ( N 2 ) N q i ∑ V es ( x ) = at x = x j ( j = 1,..., N ) Evaluate | x − x i | i = 1 • Efficient O ( N ) solution—space-time multiresolution algorithm 1. Fast Multipole Method (FMM) (Greengard & Rokhlin, 87) 2. Symplectic Multiple Time-Scale (MTS) method (Tuckerman et al ., 92)

Quantum Mechanical Calculation Density functional theory (DFT) { } ψ ( r 1 , r 2 , K , r N el ) ψ n ( r ) | n = 1, K , N el O ( C N ) O ( N 3 ) Constrained minimization problem: • Minimize E [{ ψ n }] with orthonormal constraints, * ( r ) ψ n ( r ) =δ mn ∫ ψ m d r Efficient parallelization: real-space approaches • Finite difference (Chelikowsky, Troullier, Saad, 94) & multigrid acceleration (Bernholc, 96) O ( N ) algorithm (Kim, Mauri & Galli, 95) N el * ( r ) ψ n ( ′ ( ) ∑ ρ ( r , ′ r ) ≡ ∝ exp − C | r − ′ • Asymptotic decay of density matrix: ψ n r ) r | • Localized functions: n = 1 ψ n ( r ) φ m ( r ) ∑ φ m ( r ) = ψ n ( r ) U nm n R cut • Unconstrained minimization—Lagrange multiplier

Scalable Scientific Algorithm Suite 1,024 IBM SP3 & Cray T3E processors at NAVO On 1,024 IBM SP3 processors: IEEE/ACM Supercomputing 2001 • 6.44-billion-atom MD of SiO 2 Best Paper Award • 444,000-electron DFT of GaAs

Hybrid MD/QM Algorithm MD simulation embeds a QM cluster described by a real-space multigrid-based density functional theory Additive hybridization Handshake QM Reuse of existing atoms MD & QM codes MD (Morokuma et al ., ‘96) system + E QM cluster − E MD E ≅ E MD cluster MD − + ≅ MD QM QM MD Scaled-position link atoms Seamless coupling of MD & QM systems

Hybrid FE/MD Algorithm • FE nodes & MD atoms coincide in the handshake region • Additive hybridization MD HS Si/Si 3 N 4 nanopixel FE [1 1 1] [1 1 1] _ _ [2 1 1] [0 1 1]

FE/MD/QM Simulation: Oxidation on Si Surface MD FE Dissociation energy of O 2 on a Si (111) surface dissipated seamlessly from the QM cluster through the MD region to the FE region

Stress Corrosion in Si Reaction of H 2 O molecules at a Si(110) crack tip Yellow: QM-H Red: QM-O Green: QM-Si Blue: HS-Si Gray: MD-Si 237 QM atoms

Stress Corrosion in Si Significant effects of stress intensity factor on the reaction Yellow: H Red: O Green: Si

Distributed Cluster Computing Additive hybridization; multiple QM clustering QM1 QM2 MD QM3 • Globus/MPICH-G2 — Ian Foster (ANL) • S. Ogata (Yamaguchi), F. Shimojo (Hiroshima), K. Tsuruta (Okayama), H. Iyetomi (Niigata)

Multiscale Simulation on a Grid • Scaled speedup, P = 1 + 8 n ( n = number of clusters) • Efficiency = 94.0% on 25 processors in the US & Japan

Immersive & Interactive Visualization Billion-atom walkthrough • Octree-based fast view-frustum culling • Parallel/distributed processing Reduced data W A N D User position PC Graphics cluster server ImmersaDesk through DURIP

Parallel & Distributed Visualization Nearly real-time walkthrough for 1 billion atoms on an SGI Onyx2 (2 MIPS R10K, 4GB RAM) connected to a PC cluster (4 800MHz P3)

Outline 1 . Multiscale finite-elem ent/ m olecular-dynam ics / quantum -m echanical sim ulation on a com putational Grid 2 . I m m ersive & interactive visualization of billion-atom system s 3 . Multim illion atom MD sim ulations of fracture and nanoindentation in crystalline, am orphous & nanophase m aterials and ceram ic nanocom posites 4 . New educational and outreach program s

Fracture in Glasses, Nanophase Ceram ics & Nanocom posites System s – Nanophase Si 3 N 4 , SiC, Al 2 O 3 – SiO 2 glass – Nanocom posite - SiC fibers in a Si 3 N 4 m atrix Nanophase ceram ics I ssues – Atom istics of crack propagation – Mechanism s of energy dissipation – Scaling properties of fracture surfaces

Validation of I nteratom ic Potential Am orphous SiO 2 2 MD 1.5 Expt. Si 3 N 4 S N (q) 1 0.5 0 0 5 10 15 20 q (Å -1 ) MD results for elastic m oduli also agree w ell w ith experim ents

Fracture in Am orphous Silica: 1 5 Million Atom MD Sim ulations Fracture Toughness K I C = 1 MPa.m 1 / 2 ( MD) 0 .8 MPa.m 1 / 2 < K I C < 1 .2 MPa.m 1 / 2 ( Experim ent)

Experim ent by Bouchaud et al. Cavity form ation & coalescence w ith crack in a glass

Fracture Sim ulation & Experim ent ( Top) AFM study in a glass: ( a) nanom etric cavities before the crack advances; ( b) grow th of cavities; ( c) crack propagation via the coalescence of cavities. ( Bottom ) MD results show ing the sam e phenom enon in a- SiO 2

Dynam ic Fracture in Nanophase Si 3 N 4 Nanophase Si 3 N 4 is m uch tougher than Si 3 N 4 crystal Crack Deflection Pore Coalescence Toughening Mechanism : Crack deflection, branching & coalescence w ith nanopores

Morphology & Scaling Behavior of Fracture Surfaces Fracture surfaces are anisotropic & statistically invariant under an affine transform ation x ζ → ( , , ) ( , , ) x y z b x by bz ( ) 1 / 2 ∆ = + − 2 ( ) ( ) ( ) h r x z r x z z ∆ h (r) ∆ ∝ ζ ( ) h r r ζ is called the roughness exponent z z+r

Scaling Behavior of Cracks Tw o regim es w ith roughness exponents 0.5 & 0.8 P. Daguier, B. Nghiem , E. Bouchaud & F. Creuzet ( 1 9 9 7 )

MD results for roughness exponents agree w ith experim ents 2.5 ζ = 0.84 ± 0.12 2.0 ln ∆ h( x) 1.5 Nanophase 1.0 Si 3 N 4 ζ = 0.58 ± 0.14 0.5 0 2 3 4 5 6 ln( z) MD results reveal that the sm aller roughness exponent is due to intrapore correlations and the larger one due to coalescence of pores and crack

Fracture in a Nanocom posite 1.5 -billion-atom MD on 1,024 I BM SP3 processors Color code: Si 3 N 4 ; SiC; SiO 2 0 .3 m m Silicon nitride m atrix-silicon carbide fiber nanocom posite

Nanoindentation in Si 3 N 4 Nanohardness yields im portant inform ation about elastic and plastic deform ation Multi-m illion atom MD sim ulations

I ndentation Fracture & Am orphization I ndentation fracture <1210> at indenter diagonals Anisotropic fracture toughness <1010> Am orphous pile-up at indenter edges <0001>

Hardness of Silicon Nitride Load-displacem ent curve α -crystal (0001) Amorphous 50GPa 32GPa Microindentation experim ents on α - crystal ( 0 0 0 1 ) : 3 1- 4 8 GPa

Sum m ary • Parallel m ultiscale MD/ QM sim ulation m ethodology • I nteractive visualization of billion atom s • Multim illion atom MD sim ulations > fracture in silica glass, nanophase ceram ics & nanocom posite > nanoindentation in crystalline & am orphous Si 3 N 4

Graduate Education Dual-Degree Program Ph.D. in the physical sciences & M.S. in com puter science I nternational course on Experim ental training com putational physics • Synthesis • LSU/ USC • Characterization • TU Delft, The Netherlands • Property m easurem ents • Niigata Univ., Japan

Undergraduate Outreach Activities Com putational Science W orkshop for Underrepresented Groups • 19 participants from 11 institutions — Hampton, Clark-Atlanta, Morehouse, Jackson State, Mississippi State, Texas Southern, Univ. of Texas –– Pan American, Xavier, Grambling, Southern & Univ. of Louisiana in Monroe • Activities: Construction of a PC cluster from off-the- shelf components & using this parallel machine for algorithmic and simulation exercises.