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

10-6 - 10-10 m > 10-6 m

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)

• Newton’s equations of motion
• Interatomic potential
• N-body problem

long-range electrostatic interaction—O(N2)

• 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)

Molecular Dynamics Simulation

mi d2r r

i

dt2 = − ∂V r r N

( )

∂r r

i

(i = 1,...,N) V = uij r

ij

( )

i< j

∑

+ v jik r r

ij,r

r

ik

( )

i, j<k

∑

Evaluate at x = xj (j = 1,...,N) Ves(x) = qi | x − xi |

i=1 N

∑

Density functional theory (DFT) O(CN ) O(N3 ) Constrained minimization problem:

• Minimize E[{ψn}] with orthonormal constraints,

Efficient parallelization: real-space approaches

• Finite difference (Chelikowsky, Troullier, Saad, 94) & multigrid acceleration (Bernholc, 96)

O(N) algorithm (Kim, Mauri & Galli, 95)

• Asymptotic decay of density matrix:
• Localized functions:
• Unconstrained minimization—Lagrange multiplier

Quantum Mechanical Calculation

ψ(r1,r2,K,rNel ) ψn (r) | n = 1,K,Nel

{ }

dr

∫

ψm

* (r)ψ n (r) =δmn

ρ(r, ′ r ) ≡ ψn

* (r)ψ n ( ′

r )

n=1 Nel

∑

∝ exp −C | r − ′ r |

( )

φm (r) = ψ n (r)Unm

n

∑

ψn(r) φm(r) Rcut

On 1,024 IBM SP3 processors:

• 6.44-billion-atom MD of SiO2
• 444,000-electron DFT of GaAs

Scalable Scientific Algorithm Suite

1,024 IBM SP3 & Cray T3E processors at NAVO IEEE/ACM Supercomputing 2001 Best Paper Award

Hybrid MD/QM Algorithm

QM MD Handshake atoms

Additive hybridization Reuse of existing MD & QM codes

(Morokuma et al., ‘96)

Scaled-position link atoms Seamless coupling of MD & QM systems MD simulation embeds a QM cluster described by a real-space multigrid-based density functional theory E ≅ EMD

system + EQM cluster − EMD cluster

QM MD

≅ +

−

MD QM MD

Hybrid FE/MD Algorithm

• FE nodes & MD atoms coincide in the handshake region
• Additive hybridization

MD FE

[0 1 1] [1 1 1]

_

HS

_

[1 1 1] [2 1 1]

Si/Si3N4 nanopixel

FE/MD/QM Simulation: Oxidation on Si Surface

Dissociation energy of O2 on a Si (111) surface dissipated seamlessly from the QM cluster through the MD region to the FE region MD FE

Stress Corrosion in Si

Yellow: QM-H Red: QM-O Green: QM-Si Blue: HS-Si Gray: MD-Si Reaction of H2O molecules at a Si(110) crack tip 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

• Globus/MPICH-G2 — Ian Foster (ANL)
• S. Ogata (Yamaguchi), F. Shimojo (Hiroshima),
• K. Tsuruta (Okayama), H. Iyetomi (Niigata)

MD QM1 QM3 QM2

Additive hybridization; multiple QM clustering

Multiscale Simulation on a Grid

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

Immersive & Interactive Visualization

• Octree-based fast view-frustum culling
• Parallel/distributed processing

Billion-atom walkthrough PC cluster

W A N D User

position Graphics server ImmersaDesk through DURIP Reduced data

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 Si3N 4, SiC, Al2O3 – SiO2 glass – Nanocom posite - SiC fibers in a Si3N 4 m atrix

I ssues

– Atom istics of crack propagation – Mechanism s of energy dissipation – Scaling properties of fracture surfaces

Nanophase ceram ics

Si3N4

Am orphous SiO2

0.5 1 1.5 2 5 10 15 20 Expt. MD SN(q) q (Å -1)

Validation of I nteratom ic Potential

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 KI C = 1 MPa.m 1 / 2 ( MD) 0 .8 MPa.m 1 / 2 < KI 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

( 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- SiO2

Fracture Sim ulation & Experim ent

Dynam ic Fracture in Nanophase Si3N 4

Pore Coalescence Crack Deflection Toughening Mechanism : Crack deflection, branching & coalescence w ith nanopores Nanophase Si3N 4 is m uch tougher than Si3N 4 crystal

Morphology & Scaling Behavior

• f Fracture Surfaces

Fracture surfaces are anisotropic & statistically invariant under an affine transform ation

) , , ( ) , , ( bz by x b z y x

ζ

→

z z+r ∆h(r) x

ζ is called the

roughness exponent

( )

2 / 1 2

) ( ) ( ) (

z

z x r z x r h − + = ∆

ζ

r r h ∝ ∆ ) (

• P. Daguier, B. Nghiem , E. Bouchaud & F. Creuzet ( 1 9 9 7 )

Scaling Behavior of Cracks

Tw o regim es w ith roughness exponents 0.5 & 0.8

0.5 1.0 1.5 2.0 2.5 2 3 4 5 6 ln( z) ln∆h( x) ζ = 0.58 ± 0.14 ζ = 0.84 ± 0.12

MD results for roughness exponents agree w ith experim ents

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 Nanophase Si3N 4

Color code: Si3N 4; SiC; SiO2

Fracture in a Nanocom posite

Silicon nitride m atrix-silicon carbide fiber nanocom posite 1.5 -billion-atom MD on 1,024 I BM SP3 processors

0 .3 m m

Nanoindentation in Si3N 4

Multi-m illion atom MD sim ulations

Nanohardness yields im portant inform ation about elastic and plastic deform ation

I ndentation Fracture & Am orphization

<1210>

I ndentation fracture at indenter diagonals Am orphous pile-up at indenter edges Anisotropic fracture toughness

<1010>

<0001>

Hardness of Silicon Nitride

Load-displacem ent curve

α-crystal (0001) 50GPa Amorphous 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 Si3N 4

Graduate Education

Ph.D. in the physical sciences & M.S. in com puter science

Dual-Degree Program I nternational course on com putational physics

• Synthesis
• Characterization
• Property m easurem ents

Experim ental training

• LSU/ USC
• TU Delft, The Netherlands
• 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.