pasi2012 bringa md

56
COLLABORATORS: J. Rodriguez-Nieva , M. Ruda, G. Bertolino (Instituto Balseiro), S. Ramos, E. Crespo(U. Comahue), D. Farkas, J. Monk (VaTech), A. Caro, A. Misra, M. Nastasi(LANL), R.E. Johnson, T. Cassidy (University of Virginia), C. Anders, H. Urbassek (TU Kaiserslautern), D. Schwen(UIUC), J. Wark, A. Higginbotham (Oxford), N. Park (AWE), B. Remington, J. Hawreliak (LLNL), M. Meyers, Y. Tang (UCSD), D. Bertoldi, C. Ruestes, E. Millan(UN Cuyo) PASI 2012 - CMS4E Pan-American Advanced Studies Institute Computational Material Science for Energy Generation and Conversion Pontificia Universidad Católica de Chile Santiago, Chile 2012 Eduardo M. Bringa [email protected] CONICET Instituto de Ciencias Básicas, Universidad Nacional de Cuyo Mendoza, Argentina https://sites.google.com/site/simafweb Advanced Molecular Dynamics

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Page 1: Pasi2012 Bringa MD

COLLABORATORS: J. Rodriguez-Nieva , M. Ruda, G. Bertolino (InstitutoBalseiro), S. Ramos, E. Crespo (U. Comahue), D. Farkas, J. Monk (VaTech), A. Caro, A. Misra, M. Nastasi (LANL), R.E. Johnson, T. Cassidy (University of Virginia), C. Anders, H. Urbassek (TU Kaiserslautern), D. Schwen (UIUC), J. Wark, A. Higginbotham (Oxford), N. Park (AWE), B. Remington, J. Hawreliak(LLNL), M. Meyers, Y. Tang (UCSD), D. Bertoldi, C. Ruestes, E. Millan (UN Cuyo)

PASI 2012 - CMS4EPan-American Advanced Studies InstituteComputational Material Science for Energy Generation and Conversion

Pontificia Universidad Católica de ChileSantiago, Chile 2012

Eduardo M. Bringa

[email protected]

CONICET

Instituto de Ciencias Básicas, Universidad Nacional de CuyoMendoza, Argentina

https://sites.google.com/site/simafweb

Advanced Molecular Dynamics

Page 2: Pasi2012 Bringa MD

Outline• Introduction

• Main caveats of MD simulations: potentials, time step, boundary conditions.

• Nano-thermodynamics and non-LTE conditions: temperature, pressure, melting, thermalization.

•Data analysis

• Simulation of “realistic” samples (not perfect crystals): dislocations, grains, impurities, porosity.

• Mechanical properties at high strain rate.

• Electronic excitations, taking ion tracks as case study.

•Summary, conclusions and future perspective

Page 3: Pasi2012 Bringa MD

Given all the approximations and limitations involved …

Can we hope for quantitative agreement between MD and experiments?

OR …

Is MD just pretty movies and pictures?

Two questions …

Page 4: Pasi2012 Bringa MD

Need to be extremely careful about applicability of classical MD

• Generally assumes Born-Oppenheimer approximation works.

•The corresponding de Broglie wavelength, proportional to (Mass Temperature)-1 has to be much smaller than the mean atomic separation, i.e. try to avoid light elements and low temperatures ☺

•One should avoid phase transitions driven by electronic effects, like metal-insulator transitions, magnetic transitions, etc.

•One should avoid regions where electronic excitations could arise and play an important role in the evolution of the system.

Pushing the limits of validity one can sometimes obtain results resembling experiments, but possibly for the wrong reasons ☺

Page 5: Pasi2012 Bringa MD

With MD you can obtain….

“Real” time evolution of your system.

Thermodynamic properties, including T(r,t) temperature profiles that can be used in rate equations.

Mechanical properties, including elastic and plastic behavior.

Surface/bulk/cluster growth and modification.

X-ray and “IR” spectra

Etcetera …

•Can simulate only small samples (L<1 µm, up to ~109 atoms).•Can simulate only short times (t<1 µs, because ∆t~1 fs).•Computationally expensive (weeks).• Potential’s golden rule: trash in ���� trash out.• Interaction potentials for alloys, molecular solids, and excited species not well know. • Despite its limitationsMD is a very powerful tool to study nanosystems.

Limitations of MD

Atomistic simulations are extremely helpful but … still have multiple limitations

Page 6: Pasi2012 Bringa MD

“Potential” problems: EAM potentials, phonons and elastic constants or when, even if the PV EOS is OK, other things can go wrong (Paul Erhart, LLNL)

0

100

200

300

400

500

0 20 40 60 80 100

Ela

stic

con

stan

ts (

GP

a)

Pressure (GPa)

B

c11

c12

c’

0

1

2

3

4

5

6

7

ΓPHΓN 0

5

10

15

20

25

Fre

quen

cy (

TH

z)

Fre

quen

cy (

meV

)

Guellil−Adams potential, this workexperimental, Woods (1964)DFT, Bercegeay and Bernard (2005)

−100

−50

0

50

100

150

200

250

300

350

400

−30 −20 −10 0 10 20 30

Ela

stic

con

stan

ts (

GP

a)

Pressure (GPa)

c11

c12

B

c’

0

1

2

3

4

5

6

7

ΓPHΓN 0

5

10

15

20

25

Fre

quen

cy (

TH

z)

Fre

quen

cy (

meV

)

Li−Adams potential, this workexperimental, Woods (1964)DFT, Bercegeay and Bernard (2005)

Good agreement with phonons at P=0 GPa, but discontinuities in elastic constants, due to splines in the potential, lead to multiple elastic fronts

Page 7: Pasi2012 Bringa MD

Another example: EFS Ta Potential

• Excellent agreement with PV, equilibrium Hugoniot, melt line , etc.• Elastic constants OK up to ~1 Mbar.• BUT… BCC�HCP at ~65 GPa (Ravelo et al., SCCM-2011).

Tang, Bringa, Meyers, Acta Mat. 59 (2011) 1354

Z-L Liu, L-C Cai, Phys. Rev. B 77 (2008) 024103

X.D. Dai, Y. Kong , J. Phys. Cond. Mat. 18 (2006) 4527

Potential validity depends strongly on type of fit, which can emphasize a certain property, temperature & pressure range, structure, etc.

Potentials are often non-transferable �

Page 8: Pasi2012 Bringa MD

COLLISION DYNAMICS OF CARBON CLUSTERS, NVE (D. Bertoldi)

AIREBO potential

“dt reset”tmin = 1.E(-6) pstmax = 0,001 psXmax = 0,0001 Å

Time Evolution: be aware of possible energy drift

-1 0 1 2 3 4 5 6 7-0,016

-0,014

-0,012

-0,010

-0,008

-0,006

-0,004

-0,002

0,000

0,002

Tot

al e

nery

cha

nge

(%)

Time (ps)

•Energy drift caused by integrator and computational errors.

•Simulations far from equilibrium have to use variable time step schemes,

> 1% ���� problematic!

Page 9: Pasi2012 Bringa MD

• PBC in (x,y), free BC with expansion (z). Langevin bath with critical damping at the sides.

• Need to re-calculate damping for each interatomic potential and bath condition.

• There are complex schemes to have impedance matching at boundaries, but none standard.

• Size has to be large enough to capture desired phenomena. Need to verify this by running simulations of different sizes: results should not change beyond certain size L, or they could be extrapolated versus 1/L.

FixLangevin, T=0.1

Mobile, NVE

Simulation details need to include info on BC

Track T=10

Simulation of hot spot

Page 10: Pasi2012 Bringa MD

Large-scale MD links nano and microscalesin damage induced by nanoprojectiles [C. Anders et al., PRL 108, 027601 (2012)]

Rcluster =20 nm, 20 ps after impact, ~300 10 6 atoms, 15 hours using 3,840 CPU’s in Thunder (LLNL)

Only dislocations + liquid atoms are shown

Page 11: Pasi2012 Bringa MD

Tight Binding

MD

Continuum mechanics

1 meter= 1,000,000,000 nanometers

1 meter= 1,000,000 microns

Human hair’s width ~ 200 µmEstaphilococus ~ 1 µmRhinovirus ~ 200 nm

Kaxiras’ web

Nanoscale does affect macro scale and properties of

materials.

Page 12: Pasi2012 Bringa MD

Coupling TIME and length scales ….

• Concurrent coupling methods have many caveats ….

• Choose set of parameters from MD, save those parameters and “pass” them to a “higher” level code. Example: calculate defect concentrations as the initial configuration for a kinetic Monte Carlo code.

• Use some accelerated technique, which boost the time step, for instance “TAD” by A. Voter (LANL). Very expensive computationally, practical only for “2D” simulations or small 3D simulations.

Several people are currently working on improving this situation … Keep tuned!

Page 13: Pasi2012 Bringa MD

• Introduction

• Main caveats of MD simulations: potentials, time step, boundary conditions.

• Nano-thermodynamics and non-LTE conditions: temperature, pressure, melting, thermalization.

•Data analysis

• Simulation of “realistic” samples (not perfect crystals): dislocations, grains, impurities, porosity.

• Mechanical properties at high strain rate.

• Electronic excitations, taking ion tracks as case study.

•Summary, conclusions and future perspective

Page 14: Pasi2012 Bringa MD

(a) Definition of temperature in nano systems

Jellinek & Goldberg, Chem Phys. (2000)Pearson et al, PRB (1985)

Usual: (3/2) N kB T = Ekin

Nano Systems:

Correction due to non-zero flow velocity <v>:

Ekin� (m/2) (v - <v>)2

Ekin>0, but T=0

v

“Partial” T’s: T rot, Tvib, Tij

Page 15: Pasi2012 Bringa MD

R

(b) Nanoclusters de aluminio

R =

0,3nm � 13 átomos0,5nm � 43 átomos1nm � 249 átomos2nm � 1985 átomos

Potencial interatómico: átomo embebido (EAM) de Mishin[2]

Dinámica Molecular -LAMMPS[1] -

[1] www.lammps.sandia.gov[2] Y. Mishin et al., “Embedded-atom potential for B2-NiAl” PRB 65 (2002)

Ensamble Microcanónio (N,V,E)Temperatura ~ 300K

D. Bertoldi (ICB)

Page 16: Pasi2012 Bringa MD

10 100 1000240

260

280

300

320

340

360

380 simulation value theoretical value

Tim

e av

erag

e te

mpe

ratu

re (

K)

N° atoms

bulk

Cluster Temperature

---Calculated with

Td (Jellinek et al.)

---MD

Averaged during the last 0,1 ps of simulation

Page 17: Pasi2012 Bringa MD

Velocity Distribution in clustersAproximate with a Maxwell-Boltzmann distribution

When there are not enough atoms, distribution have to be averaged over time, but M-B still works reasonably well.

0 300 600 900 1200 1500 1800

f

bulk 1985 atoms249 atoms

Velocity (m/s)

25

20

15

10

5

0

0 200 400 600 800 1000

43 atoms25

0

5

10

15

f

20

Velocity (m/s)

Page 18: Pasi2012 Bringa MD

(c) Can we define an atomic stress tensor? Only with caveats

PdH nanoclusters . Using Voronoi or mean volume gives roughly the same results. Work with

G. Bertolino, M. Ruda (Centro Atomico Bariloche), S. Ramos, E. Crespo (UN Comahue, Neuquen)

Int. J. Hydrogen Energy (2012), in press .

a, b= x,y,z . Includes thermal, pair, bond, angle, dihedral, improper, and “fix” Be careful with NkBT term …it should discount flow velocity in calculation of TS = σσσσ V � how do we define “atomic” volume to calculate momentum flux?

Possible solution: use Voronoi polyhedra

Virial stress for atom I(lammps)

Page 19: Pasi2012 Bringa MD

(1700 MPa, 0 K) (12000 MPa, 5000 K)

P = 1700 + 2.06T

P= 4 γ /dEc. Laplace-Young :d = 4 γ /(1700 + 2.06T )

in equilibrium

γ= (γD + γG )/2

0 500 1000 1500 2000 2500

2

4

6

8

diam

etro

(nm

)

Temperatura (K)

Diamante

Grafito

Transitions diamond �graphite and graphite � diamond , have different cinetics

Zhao, D. et al, “Size and temperature dependence of nanodiamond-nanographite transition related with surface stress”, Diamond and Related Materials 11 (2002) 234.

(d) Phase Diagram for carbon clusters

Diagram for bulk sample Diagram for a spherical cluster

Pext =0 GPa

Temperatura (K)

Pre

sión

(G

Pa)

Page 20: Pasi2012 Bringa MD

COLLISION OF CARBON NANOGRAINS

Dalia Bertoldi (ICB)

Page 21: Pasi2012 Bringa MD

(f) Melting of Au nanoclusters

Lin, Leveugle, Bringa, Zhigilei, J. Phys. Chem. (2010)Melting temperature changes only ~15%

����difficult to detect experimentally

R=2.4 nm

Page 22: Pasi2012 Bringa MD

(g) Heating a solid without a surface (no transport)

∆ΚΕ∆ΚΕ∆ΚΕ∆ΚΕ

Equilibration

•Is thermodynamics still valid at small times and length scales?•How long does it take for a “perturbed” system to equilibrate?

LJ solidBinding energy U

Eexc/atom

Page 23: Pasi2012 Bringa MD

Thermodynamic Equilibrium?

EQUILIBRATION ISFASTER THAN

EXPECTED (compared with hard

spheres).Each atom interacts with ~80 neighbors

Equilibration time in homogeneous system

Bringa & Johnson, Nuclear Instruments and

Methods in Physics Research B 143(1998)

513-535

H(t)=

Page 24: Pasi2012 Bringa MD

Rough way to obtain equilibration time

•Large gradients (103 K/nm) ….•How long does it take for LTE?

Local equilibration time is longer than equilibration time for homogeneous heating

(h) Heating a solid without a surface (only radial transport)heating of cylinder with radius rcyl

“Local” Boltzmann H-Function constant �thermal equilibrium

“Local” M-B distribution

Page 25: Pasi2012 Bringa MD

Temperature profiles show axial energy transportLarge difference between radial and axial temperatu re

Temperature profiles (with a surface): lack of LTE and deviations from Fourier equation

Problems:•Lack of LTE more serious for molecular solids. Bringa and Johnson, Surf. Sci. (1997)

•Parabolic ���� HyperbolicD.D. Joshep, L. Preziosi, Rev. Mod. Phys. 61 (1988) 41.S. Volz, J. Saulnier, M. Lallemand, B. Perrin, P. Depondt, M. Mareschal, Phys. Rev. B 54 (1996) 340.•Stefan problem (moving boundary). Caro, Tarzia, etc.

Page 26: Pasi2012 Bringa MD

Outline• Introduction

• Main caveats of MD simulations: potentials, time step, boundary conditions.

• Nano-thermodynamics and non-LTE conditions: temperature, pressure, melting, thermalization.

•Data analysis

• Simulation of “realistic” samples (not perfect crystals): dislocations, grains, impurities, porosity.

• Mechanical properties at high strain rate.

• Electronic excitations, taking ion tracks as case study.

•Summary, conclusions and future perspective

Page 27: Pasi2012 Bringa MD

•On the fly and post-processing of data takes considerable time …•Need to choose appropriate analysis tools to avoid artificial results.• Whenever possible, carry out the analysis in parallel with domain decomposition and neighbor lists.• Care must be taken with time averaging.

Data analysis

Page 28: Pasi2012 Bringa MD

Centro-Symmetry Parameter (CSP)*� Centro-symmetry parameter (CSP): a parameter to measure the

local disorder, particularly useful to study cubic structures.

* Kelchner, Plimpton, Hamilton, Phys Rev B, 58, 11085 (1998)

f.c.c structure

CSP expression for a f.c.c. unit cell

Kelchner et al, FIG. 2, partial view. Defect structure at the first plastic yield point during indentation on Au (111), (a) view along [112], (b) rotated 45° about [111]. The colors indicate defect types as determined by the centrosymmetry parameter: partial dislocation (red), stacking fault (yellow), and surface atoms (white). Only atoms with P>0.5 are shown.

This is done for every atom in the

sample ���� high computational cost

Page 29: Pasi2012 Bringa MD

Common Neighbor Analysis• CNA: a parameter to measure the local disorder

• Sensitive to cutoff radius

• 12 nearest neighbor for perfect FCC and HCP crystals, 14 nearest neighbors for perfect BCC crystals

• Faken, Jonsson, Comput Mater Sci, 2, 279 (1994).• Tsuzuki, Branicio, Rino, Comput Phys Comm, 177, 518 (2007).

This is done for every atom in the

sample ���� high computational cost

Page 30: Pasi2012 Bringa MD

DXA (Dislocation eXtraction Algorithm)

Stepwise conversion of atomistic dislocation cores into a geometric linerepresentation.

(a) Atomistic input data.

(b) Bonds between disordered atoms.

(c) Interface mesh.

(d) Smoothed output.

A. Stukowski and K. Albe, Modelling Simul. Mater. Sci. Eng. 18 (2010) 085001.

Changes in DXA parameters can have large effect on results

Page 31: Pasi2012 Bringa MD

Outline• Introduction

• Main caveats of MD simulations: potentials, time step, boundary conditions.

• Nano-thermodynamics and non-LTE conditions: temperature, pressure, melting, thermalization.

•Data analysis

• Simulation of “realistic” samples (not perfect crystals): dislocations, grains, impurities, porosity.

• Mechanical properties at high strain rate.

• Electronic excitations, taking ion tracks as case study.

•Summary, conclusions and future perspective

Page 32: Pasi2012 Bringa MD

Perfect crystals are the `spherical horse’ of atomistic simulations

0.5 µµµµm

Cu single crystal, M. Meyers et al, TEM

150 nm

How to make more realistic simulations? Add defects: vacancies � voids � bubbles, interstitials, dislocation loops/lines,

grain boundaries (bi-cristals � polycrystals)

Polycrystal (50 nm grain size)(400 million atoms)

Few GB are ΣΣΣΣ boundaries …

Dislocation loop

He bubble + dislocation loops

M. Meyers

Page 33: Pasi2012 Bringa MD

Dislocation motion changes the stress state from 1D to ~3D

Bringa et al., Nature Materials 5, 805 (2006)Shehadeh, Bringa, et al., APL 89, 171918 (2006)

P~35 GPatR=50 ps

0 .6 0 .5 0 .4 0 .3 0 .2 0 .1 0 .00

2

4

6

8

1 00 p s

Z ; X - Y5 0 p s

Z ; X - Y

latti

ce c

om

pres

sio

n (%

)

z (µ m )

1 D

3 D

120 90 60 30 0

0.0

0.4

0.8

1.2

1.6

2.0 0 ps 50 ps

time after shock (ps)

σ SH

EA

R (

GP

a)

(a)

Difraccion simulada de rayos X

Nature Materials cover figureNature Materials cover figure

256-352 million atoms (~0.07 ××××0.07××××0.8 µm), Cu

Pre-existing dislocation loops needed to simulate realistic response to loading

1980 CPU’s in MCR (LLNL), ~15 días, 30 TB of data

Page 34: Pasi2012 Bringa MD

GBs give unique properties under pressureSimulations and experiments show ultra-hard materials

E. Bringa et al., Science (2005), APL (2005 & 2006), etc.

4 108 átomos, en 4000 CPUs

d=50 nm, 47 GPa

Friction ~ normal stress (σσσσ) � σgrows and sliding decreases

σσσσ

σσσσ

σσσσcorte

σσσσcorte

GB

d=30-50 nm, 40 GPa

DISLOCATIONS

• High pressure decreases sliding and leads to dislocations. • High dislocation density leads to enhanced hardness after unloading (MD + exp.).

Lasers Omega & Janus

Page 35: Pasi2012 Bringa MD

Role of impurities in void nucleation

(a)

(b)

(c)3% Fe

Combine MD with “parallel grand-canonical Monte Carlo” to place impurities in nano crystalline sample

“Effects of Microalloying on the Mobility and Mechanical Response of Interfaces in Nanocrystalline Cu”, Caro et al. , Materials Science Forum Vols. 633-634 (2010) 21.

G. Gilmer

This might lead to suppression of GB sliding � stronger materials

Page 36: Pasi2012 Bringa MD

Foams are another example of challenging samples

•Porosity important for mass and thermal transport, and porous materials might be

radiation resistant (Bringa et al., Nanoletters, July 2012)

•Irradiation might affect mechanical properties

important for structural integrity, and for durability of reactor walls and fuel pellets.

Plasma exposed W-C surface Takamura et al., Plasma and Fusion

Research 1, 51 (2006)

I) Novel nanofoams offer promising mechanical properties. High surface/ volume ratio, and

therefore cannot use full density properties for predictions. Often modeled as 2-phase material.

II) Understanding of early stages of spall.

III) Materials for new fission and fusion reactors

Page 37: Pasi2012 Bringa MD

Possible morphological changes under irradiation

Displacement of atoms for 5 cumulative PKAs. Color scale indicates displacement, with atoms displaced less than half a lattice parameter not shown, and atoms displaced more than 4 lattice parameters in red.

Page 38: Pasi2012 Bringa MD

Mechanical properties of irradiated foams: need “long” simulations for defect evolution

0 1 2 3 4 50,0

0,2

0,4

0,6

0,8

1,0

σ (G

Pa)

ε (%)

5.5 107/s

5.5 108/s 5.5 108/s, irradiated Eε

tension, ρ/ρo=0.64

• Irradiated foam/filaments includes defects that lead to hardenning. Kucheyev et al., J. Phys D (2009), found stiffening of irradiated silica foams.•There is slight foam compaction that increases with dose

D=50 nm, 40 keV PKA

Page 39: Pasi2012 Bringa MD

If filaments too small � melting & destruction, compaction.If filaments too large � defects take “too long” to migrate to the surface.Simple model: includes molten volume, cascade size, dose rate effects. No compaction.

Sweet spot: filaments between ~5-500 nm are radiation resistant (moderate dose)

Page 40: Pasi2012 Bringa MD

Experiments: no radiation damage for moderate dose irradiation

A. Misra, M. Nastasi and co-workers (LANL)

20 nm

(a) (b)

1 nm

77 K Ne+ irradiation to 4.5 x 1014 /cm2 (1 dpa) (a) Bright field TEM image of np-Au after irradiation. (b) high-resolution TEM image of np-Au after irradiation. (c) under focused bright field TEM images of single crystal

Au film after irradiation, showing Ne bubbles.

Bringa et al., Nanoletters, in press (2012)

(c)

Page 41: Pasi2012 Bringa MD

• Introduction

• Main caveats of MD simulations: potentials, time step, boundary conditions.

• Nano-thermodynamics and non-LTE conditions: temperature, pressure, melting, thermalization.

•Data analysis

• Simulation of “realistic” samples (not perfect crystals): dislocations, grains, impurities, porosity.

• Mechanical properties at high strain rate.

• Electronic excitations, taking ion tracks as case study.

•Summary, conclusions and future perspective

Page 42: Pasi2012 Bringa MD

Mechanical deformation: can we compare MD with experiments? Problem: strain rates, dεεεε/dt, are huge!

“Today” MD can do strain rates~106/s only at a supercomputer

Simulation time=t ∆∆∆∆L/L~1% ���� dεεεε/dt=0.01/t

MD uses ∆∆∆∆t~ 1 fs

t=10 ns (107 steps)���� dεεεε/dt=106/s

t=1 s (1015 steps)���� dεεεε/dt=101/s

In a supercomputer:106 steps���� 1-5 days

1015 steps���� millions of years …

Solutions:

a) Suplement MD with models to compare to experiments at low strain rates.

b) Compare with experiments at high strain rates (lasers, shocks, impacts, etc.).

∆∆∆∆L

L

Road-Runner (2010)A. Voter, LANL ����

nanowire at 10-3/s

Page 43: Pasi2012 Bringa MD

� Nano-scale failure under extreme conditions is not well understood.

� Continuum predictions do not typically include atomistic mechanisms.

� Atomistic Molecular Dynamics (MD) simulations can reproduce ductile failure behavior, and lead to new models at the macroscale.

� There are several postulated nano-scale mechanisms, but still relatively few simulations to test them.

� Have to compare to experiments at appropriate strain rate …

Page 44: Pasi2012 Bringa MD

Nanoporous Au Stress – Strain curves

ε = 2.5 %

ε = 2.8 %

ε = 3.0 %

ε = 3.3 %

ε = 3.8 %

J. Rodriguez-Nieva

Page 45: Pasi2012 Bringa MD

Comparison between MD & models/experiments

is promising for FCC materials

Davila et al., APL (2005) 86,161902. Traiviratana, Bringa & Meyers, several papers

-------- Reissman et al (prismatic loops)------- Lubarda (shear loops)………. Lubarda (shear loops)_____ MD Davila et al

Cu: Loading on [111] � Triplanar Loops

Void Faceting (Rudd et al., Traiviratana et al., etc.) recently observed in experiments

with sub-micron voids

Page 46: Pasi2012 Bringa MD

Modified DXA + ParaViewAtomistic simulation of the mechanical properties of a

nanoporous b.c.c. metal *

* Ruestes et al. , submitted to Acta Materialia (2012)

VMD

ParaView visualization of the results provided

by DXA for a nanoporous Ta sample subjected

to a 109/s uniaxial compressive strain rate at

an 8% strain. Preprocessed sample has 1.9

million atoms.

Run: 3 days in 32 cores

Analysis of each snapshot: 10 min run on

AMD M520 + 4Gb RAM (dual core)

10 min run

CNA analysis takes about 1/3 of the total analysis time

DXA+ParaView

Page 47: Pasi2012 Bringa MD

Can we obtain dislocation densities?

•Rough estimate of total dislocation density calculated from the number of atoms with CNA not BCC, and dividing by 10 to account for cross-section of dislocation cores.

• Mobile dislocation densities calculated from plastic heating* [A. Higginbotham et al., JAP (2011)].

Can we compare our results with

experiments?

After relaxation to P=0.Possibly, because long-

term recovery of the microstructure in bcc

samples should have minor effects on total density.

Note the absence of twins in the recovered sample,

which can be checked with X-ray diffraction.

Page 48: Pasi2012 Bringa MD

Outline• Introduction

• Main caveats of MD simulations: potentials, time step, boundary conditions.

• Nano-thermodynamics and non-LTE conditions: temperature, pressure, melting, thermalization.

•Data analysis

• Simulations of “realistic” samples (not perfect crystals): dislocations, grains, impurities, porosity.

• Mechanical properties at high strain rate.

• Electronic excitations, taking ion tracks as case study.

•Summary, conclusions and future perspective

Page 49: Pasi2012 Bringa MD

FAST ION

H2O

Track evolution and modeling

Many “analytic” models

Coulomb Explosion

Thermal Spikes (many flavors)

Fleisher, Price and Walker, J. App. Phys. 36, 3645 (1965)

Trautmann, Klaumunzer and Trinkaus,

Phys. Rev. Lett. 85, 3648 (2000)

MORE ….

MD simulations can

predict experimental track sizes

[Devanatham et al., NIMB (2008)]

and sputtering[Bringa and Johnson, PRL 88, 165501, (2002)]

G. Schiwietz

simplify greatly

but MD is better

Page 50: Pasi2012 Bringa MD

PE~(Nch

e)2/d ∆KE

Y (dJ/dx)2

dJ/dx= A (Zeff

/v)2 ln(B v2)

+

+

+

+

+ +

+

+

+

O2N2COH2O

MeV H+, He+

rtrack

∝Nch (dJ/dx)

µ (dE/dx)e

h

"Reflecting" Boundary

Free BCor PBC

Free Surface

rtrack ++

++

+

+

Neutralization Time τ

V(rij)=VL-J(rij)+ (ZiZj/rij) Exp(-rij/a). rcut-Coul= 7 a

depth of layer h > 2 rcut-Coul. rtrack / Nch-MAX= 2 charges/layer

MD Simulations of Coulomb Explosion

∝∝∝∝Nch (dJ/dx)

MD N(0) Exp(-t/τ)

Num

ber o

f Cha

rges

time

Similar to H-P. Cheng work for HCI

•Extremely difficult to determine neutralization times, both theoretically and experimentally

• If net repulsion is due to excited states, they may decay too fast, or they may diffuse far away before decaying.

Example: Coulomb explosion (CE) simulations

Page 51: Pasi2012 Bringa MD

Coulomb explosion simulations

Nch=2, a~l, rtrack~l, t=1 ps~2 tDcharged atoms have twice the radius of neutral atoms

If neutralization is too fast there is

no heating of the lattice!

Page 52: Pasi2012 Bringa MD

0.1 1 100.01

0.1

1

10

E

-2

2nd layer 1st layer

(a) Coulomb, τ ≈ τD

(b) Coulomb, τ ≈ 20 τD

(c) Thermal Spike

(dY

/dE

)/Y

E/U

Coulomb explosion leads to heating of the lattice as in TS

Y~(dJ/dx)2 ln(a)

Is there a thermal spike (TS)? YES!

Analyzing MD data, there is a clearly defined energetic track with:

1) (dE/dx)eff =A (dJ/dx)2

2) rcyl= Constant YMD-CE=YMD-TS

Coulomb

Spike

Prompt

CoulombBringa and Johnson, PRL 88, 165501 (2002)

Page 53: Pasi2012 Bringa MD

Example: Tracks in ta-C create conducting nano-wire s

Schwen & Bringa, NIMB 2007

Simulations

and

experiments

display creation

of sp2 rich

region

Cosmic ray destroying a carbon grain

Page 54: Pasi2012 Bringa MD

Hillock formation: excellent agreement with experiments

Schwen & Bringa (submitted)

Page 55: Pasi2012 Bringa MD

Example: MD simulations of silica amorphization

0

500

1000

1500

2000

2500

3000

3500

4000

0 25 50 75 100 125 150Radial Distance (A)

Tem

pera

ture

(K)

.20 ps

1.08 ps

3.88 ps

13.88 ps

28.88 ps

73.88 ps

P. Durham (LLNL/Cincinnati), R. Devanatham, R. Corrales (PNNL)

• DL_POLY with parallel domain decomposition, 32-128 CPUs, 104-1.25 106 atoms.

•Buckingham potential + SPME

•Thermal spike model

0.2 ps 13.9 ps

Devanatham et al., NIMB (2007), Bringa et al., Ap.J. (2008)

Page 56: Pasi2012 Bringa MD

Personal view of the future of MD• Sample size: in 10 years, ~tens of µµµµm, but most simulations still sub-µµµµm. •More/better hybrid codes to extend time and length scales: MD+MC, MD+kMC, MD+DD, MD+continuum, MD+BCA, MD+TB, MD+CPMD, …•Time scale problem: new algorithms to extend time scale and simulate thermal evolution.• Better description of electronic effects by: I) Physics + Chemistry + Biology ���� “reactive” potentials that are accurate and

efficient for full periodic table.II) coupling to CPMD, tight-binding, etc. (TDDFT?)III) TTM, Ehrenfest dynamics, inclusion of magnetic effects, etc.

Major roadblocks:• Computers (CPU/GPU) are becoming faster and larger, but algorithms for long range potentials(biology & oxides), ab-initio and continuum simulations typically do not scale well beyond couple thousand CPUs ���� expect better results within the next 10 years.• No set recipes to build better potentials, specially if chemistry (reactive potentials) or electronic effects (potentials for excited states, etc.) are involved.• Nobody knows yet what to do to solve the time scale problem beyond some simple model problems.