Simulation-based Nanomaterials Design and …Simulation-based Nanomaterials Design and...

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Multiscale Systems Engineering Research Group

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Simulation-based Nanomaterials Design and Nanomanufacturing

Prof. Yan WangWoodruff School of Mechanical Engineering

Georgia Institute of TechnologyAtlanta, GA 30332, [email protected]

mailto:[email protected]

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Computer-Aided Nano-DesignObjective: To investigate the feasibility of modeling and simulating nano structures

based on a proposed periodic surface model from atomic to meso scales and to expand the horizon of available shapes for design engineers.

P D G I-WP Grid

Lamellar Rod Spherical Micelle Mesh Membrane

( )1 1

( ) cos 2 ( )L M

Tlm l m

l m

ψ μ πκ= =

= ⋅∑∑r p r

(1b) intersection of P surface and 2 Grid surfaces

(1a) Sodalite cages. Vertices are Si (Al). Edges represent Si-O-Si (Si-O-Al) bonds.

(1c) P surface and its modulation with a Grid surface

Reverse engineering and visualization

Model construction

(2b) Reconstructed loci surface from a synthetic Zeolite crystal (Each tetrahedron encloses a Si, each vertex of the tetrahedral is a O, and each green sphere is a Na)

(2a) Reconstructed loci surface from a Faujasitecrystal (Each tetradecahedron encloses a Fe, each hexagonal prism encloses an Al, and each vertex of the polygons represents a Si)

Cubic

Simple Body-Centered Face-Centered

Orthorhombic Simple

a b c≠ ≠

Base-Centered

a b c≠ ≠

Body-Centered

a b c≠ ≠

Face-Centered

a b c≠ ≠

Tetragonal Monoclinic Simple

a c≠

Body-Centered

a c≠

Simple

90 90,α β γ≠ ° = = °

Base-Centered

90 90,α β γ≠ ° = = °

Triclinic Rhombohedral Hexagonal

90, ,α β γ ≠ °

90, ,α β γ ≠ °

a c≠

ab

c

ab

c

ab

c

ab

c

α

β

γ

α

β

γ

aa

c

aa

c

c aα

β

γ

a a

aα

β

γ

Mathematical models of Bravais Lattice

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Computer-Aided Nano-Design Periodic Surface (PS) Model

cos(x)+cos(y)+cos(z)=0

cos(z)=0

cos(x)cos(y)cos(z)=0

2cos(x)cos(y)+2cos(y)cos(z)+2cos(x)cos(z) −cos(2x) − cos(2y) −cos(2z) =0

9+4cos(x)+4cos(y)+ 4cos(z )=0

( ) 0)(2cos)(1 1

=⋅= ∑∑= =

L

l

M

m

Tmllmrpr πκμψ

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Computer-Aided Nano-Design Complex and porous structures by PS models

Feature-based crystal construction

Mask operation

Union operation

Insertion operation

Fractal structures

Tmask[

, ,

10]=

Tun[

,

] =

Tins[

,

] =

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Phase-Change Materials Design

A phase transition is a geometric and topological transformation process of materials from one phase to another, each of which has a unique and homogeneous physical property.Important to design various phase-change materials (e.g. for information storage and energy storage)

The most critical step is to estimate the saddle points along the minimal energy path on high-dimensional potential energy surfaces

current statestate j

ΔEj

state itransition path

saddle point

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Geometry Guided Saddle Point Search

Provide initial guess of transition path: FeTi+H

Guess 1: by linear surface interpolation

Guess 2: by potential-driven surface interpolation

(a) FeTi (b) FeTiH

Fe

Ti

H

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−4715.7775

−4709.3970

Energy (eV)

(initial state)

−4715.4974

−4722.7941

−4708.5716

−4715.4812

−4717.9910(final state)

−4716.4783−4715.9963

−4717.9640 −4717.9351

Saddle-point energy level

−4715.2376

−4713.9203

−4717.1825

Coordinate linear interpolationSurface linear interpolationPotential-driven surface interpolation

Search Results by the Nudged Elastic Band Method

Activation Energy:Experimental result = 0.2912 eV per atomThe default coordinate linear interpolation failed to find saddle pointSurface linear interpolation = 0.26285 eV per atomPotential-driven surface interpolation =1.1543 eV per atom

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Concurrent Saddle Point SearchSearch both local minimums and saddle point at the same timeSearch multiple transition paths with only one initial pathway guess to provide a global view of energy landscape

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Computer-Aided Nano-Manufacturing Controlled Kinetic Monte Carlo (cKMC)

cKMC is developed as a generalization of KMC to simulate both top-down and bottom-up processes in nanomanufacturing

KMC cannot simulate top-down processescKMC defines two types of events

Self-assembly events – occur spontaneously (as in classical KMC)Controlled events – occur at certain locations or at particular times deterministically to model particle re-arrangement as the direct result of external energy (force, light, field, etc.)

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cKMC: Scanning Probe Lithography

Number of sites involved

Reaction/transition event

1 R1: controlled_species → activated_controlled_species (controlled)

2 R2: activated_controlled_species + vacancy → vacancy + activated_controlled_species (controlled)R3: vaporized_workpiece_species + vacancy → vacancy + vaporized_workpiece_speciesR4: workpiece_species + vacancy → vacancy + workpiece_speciesR5: vaporized_workpiece_species + absorbent → vacancy + absorbentR6: activated_controlled_species + absorbent → vacancy + absorbent

3 R7: workpiece_species + workpiece_species + vacancy → vacancy + workpiece_species + workpiece_speciesR8: vaporized_workpiece_species + workpiece_species + workpiece_species → workpiece_species + workpiece_species + workpiece_species

4 R9: activated_ controlled_species + workpiece_species + vacancy + vacancy → vacancy + workpiece_species + vacancy + vaporized_workpiece_speciesR10: activated_ controlled_species + workpiece_species + workpiece_species + workpiece_species → workpiece_species + workpiece_species + workpiece_species + workpiece_species

workpiece species

controlled species

controlled diffusion events

vaporized workpiecespecies

absorbent species

activated controlled

species

vacancy

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cKMC: nanomanufacturing processes

workpiecespecies

Ga_src

Ga+

absorbent

substrate

absorbent

target

deposited metal

absorbent

resist

mold2path2mold1

path1_activepath1

mobilized_resist

Physical vapor deposition (PVD)

Ionized PVDNano-imprint lithography

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Uncertainty in Modeling & SimulationAleatory Uncertainty:

inherent random dispersionin the system. Also known as:

• variability

• random error

• irreducible uncertainty

Epistemic Uncertainty:due to lack of perfect knowledge about the system. Also known as:

• incertitude

• systematic error

• reducible uncertainty

• model-form uncertainty

Lack ofdata Epistemic

Uncertainty in Models & Inputs

Conflictingbeliefs

Conflictinginformation

Lack ofintrospection

Measurementsystematic

errors

Lack ofinformation

aboutdependency

Truncationerrors

Round-offerrors

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Generalized Hidden Markov Model for Cross-Scale Model Validation

Similar to the Bayesian approach in model validation [Babuška et al. 2008, Oden et al. 2010]

Observable

,1ix iX

jy jY

,1jy

,2jy

Hidden

kz ,1kz kZ

,4ix,3ix

,2ix

ix

yΩ

xΩ

zΩ

Scale Z

Scale Y

Scale X

( )

( )( )( )( )( )

( )( )( )( )

1 1

1 11 1 1

1 1

1 1

1 1 1

1 1

1 1

1 1

1 1

1

, , | , ,

, , | , ,, ,

, , | , ,

, , | , ,, , | , , , , ,

, , | , ,

, , | , ,

dual , , | , ,

, , | , ,

N N

M ML N M

N M

M L

L M N

N N

M M

N M

M L

Z Z z z

Y Y y yx x dz dz dy dy

z z y y

y y x xx x Y Y Z Z

Z Z z z

Y Y y y

z z y y

y y x x

x

⎡ ⎤⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎣ ⎦=

∫ ∫

p

pp

p

pp

p

p

p

p

p

… …… …

…… …… …

… … …… …… …… …… …

( )

1 1 1

, ,

N M L

L

dz dz dy dy dx dx

x

⎡ ⎤⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎣ ⎦

∫ ∫

…

( )pda m adN

αγ=

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Reliable Atomistic Simulation –Model Form Uncertainty in Molecular Dynamics

Imprecise probabilistic distributions for uncertainty: damage function (v) from irradiation - the probability that a stable Frenkel pair is generated at certain level of transfer or recoil energy (T)

MD simulation observation (with uncertainty)bounds based on std. dev. of binomial distributions

16 simulation runs for each energy-radiation angle combination

0 50 1000

0.5

1angle=57.0

Recoil energy (T)

Dam

age

func

tion

(v)

midlowerupper

0 50 1000

0.5

1angle=0.0

Recoil energy (T)

Dam

age

func

tion

(v)

midlowerupper

0 50 1000

0.5

1angle=90.0

Recoil energy (T)

Dam

age

func

tion

(v)

midlowerupper

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Reliable Atomistic Simulation Reliable kinetic Monte Carlo

Simulate kMC with imprecise ratesAn efficient alternative to sensitivity analysis

Event type Species and reactions Rate constant

R1: water dissociation H2O ↔ OH− + H+ 101

R2: carbonic acid dissociation CO2 + H2O ↔ HCO3− + H+ 101

R3: acetic acid dissociation AcH ↔ Ac− + H+ 101

R4: reduced thionine first dissociation

MH3+ ↔ MH2 + H+ 101

R5: reduced thionine second dissociation

MH42+ ↔ MH3

+ + H+ 101

R6: acetate with oxidized mediator

Ac− + MH+ + NH4+ + H2O →

XAc + MH3+ + HCO3

− + H+101

R7: oxidation double protonated mediator

MH42+ → MH+ + 3H+ + 2e− 101

R8: oxidation single protonatedmediator

MH3+ → MH+ + 2H+ + 2e− 101

R9: oxidation neutral mediator MH2 → MH+ + H+ + 2e− 101

R10: proton diffusion through PEM

H+ → H_+ 10−2

R11: electron transport from anode to cathode

e− → e_− 10−2

R12: reduction of oxygen with current generated

2H_+ + 1/2O2_ + 2e_− →H2O_

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R13: reduction of oxygen with current generated

O2_ + 4e_− + 2H2O_ →4OH_−

103

anode chamber

cathode chamber

(a) H2O in anode chamber

(b) H+ in cathode chamber

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NSF Grant No.1001040NSF Grant No.1306996

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Date post:	15-Feb-2020
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Simulation-based Nanomaterials Design and …Simulation-based Nanomaterials Design and...

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