University of Virginia, MSE 4270/6270: Introduction to Atomistic ...

University of Virginia, MSE 4270/6270: Introduction to Atomistic Simulations, Leonid Zhigilei

Instructor: Leonid Zhigilei

Office: Wilsdorf Hall 303D

Office Hours: open

Telephone: (434) 243 3582E-mail: [email protected]

Class web page: http://www.people.virginia.edu/~lz2n/mse627/

Class e-mail list: [email protected]

Contact Information:

Spring 2018, Tuesday and Thursday, 2:00 - 3:15 pmThornton Hall D115

MSE 4270/6270: Introduction to Atomistic Simulations


Research in Computational Materials Group:

nanofibrous and nanocrystalline materials

crystal defects, phase transformations:

Group Web Site: http://faculty.virginia.edu/CompMat/

laser-materials interactions: nano-structured materials:

Development of computational methods for materials modeling at multiple length & time-scales

Investigation of non-equilibrium materials processing, properties of nanostructured materials,mechanisms of phase transformations

acoustic activation of surface processes:

acoustic pulse


Term project 50% Homework 40% Presentation/discussion of research articles 10%

Grading:

Homework - cooperation among students is permitted. Discussionsthrough the course e-mail list are especially encouraged.

Each student will lead one discussion of a research paper in the area ofatomistic simulations (10 min). You can propose a paper that looksinteresting to you or is relevant to your research work (but not to yourterm project).

Discussion of published research articles:


Term project:

Objective: To get experience in designing and performing computersimulations

Parts of the project:

Choose a problem that is of scientific or computational interest to you.

Choose an appropriate computational approach, justify your choice.

Write a computer code (or add parts to MSE627-MD or MSE627-MCcodes).

Perform simulations and analyze the results.

Prepare a report/paper. Use format typical for a research paper, withabstract, introduction, computational setup, results, discussion, conclusions,references. Figures and figure captions should be included in the text.

Make a presentation to the class at a mini-symposium that substitutesthe final exam.


Term project:

Timeline:

February 1st – decide in the topic/title of your project and inform theinstructor

March 1st – prepare the first draft of the introduction (with referencesto relevant papers) and discuss progress with instructor (optional)

May 5th and 6th (tentative dates) – turn in a report; give a presentationto the class at a mini-symposium

A problem chosen for the term project should have some science contentand be doable in the timeframe of one semester.

If the intention is to continue computational work in the future, the termproject may be a well-defined part of a larger research project.


Textbooks:

Online Version is available through UVa library: M. P. Allen and D. J. Tildesley, Computer simulation of liquids (Oxford

Scholarship Online: 2017). D. Frenkel and B. Smit, Understanding molecular simulation: from

algorithms to applications (Academic Press: San Diego, 1996).

Books placed on reserve circulate: M. P. Allen and D.J. Tildesley, Computer simulation of liquids (Clarendon

Press: Oxford, 1990, 1987). D. Frenkel and B. Smit, Understanding molecular simulation: from

algorithms to applications (Academic Press: San Diego, 1996). M. Metcalf and J. Reid, Fortran 90/95 explained (Oxford University Press:

Oxford, New York, 1999) – two copies.

Additional books that may be useful are listed athttp://www.people.virginia.edu/~lz2n/mse627/mse627-books.html

Main text: Handouts and lecture notes.


“The underlying physical laws necessary for the mathematical theory of a largepart of physics and the whole of chemistry are thus completely known, and thedifficulty is only that the exact application of these laws leads to equationsmuch too complicated to be soluble.” – Dirac, 1929.

The equations that describe quantum mechanics, classical mechanics, gas/fluidflow, electrical/magnetic fields induced by static or moving charges, are wellknown. But analytical solutions are often intractable.

The invention of computers has provided a new exciting direction – to solve thecomplex equations numerically, in a computer simulation.

Experiments - mathematical description - computer simulation

Once a certain number of experiments have been performed, it is necessary todescribe the results mathematically. If we succeed in describing thephenomenon with mathematical equations, then we can predict the behavior ofthe system of interest for a wide range of conditions, including the ones forwhich experiments are difficult, too expensive, or not possible at all.


What are the classical “atomistic simulations”?

Materials Science

Physics

ChemistryComputer ScienceMathematics

MechanicalEngineering

Atomistic Simulations

Basic units of the model – atoms/molecules But… the same methods are often applicable to systems consisting of other types of discrete particles, e.g. granules, particles in fluids, planets, etc.

Atomistic simulations are different from (a) continuum simulations operating with “fields” – quantity is defined at every point in space; (b) electronic structure calculation performed for fixed positions of nuclei.

Interdisciplinary nature of “atomistic simulations”


“Classical” Materials Science: analysis of individual defects, connectionbetween the microstructure and properties of materials, formation ofmicrostructure in processing, mechanisms of phase transformations…

Chemistry and Biochemistry: nature of interatomic bonding, reactions,vibrational relaxation and energy transfer, molecular structures, drug design,structure of membranes, protein folding, …

Mechanical Engineering: large-scale problems are typically solved at continuumlevel, where the atomic-level details are incorporated through averaging andformulation of constitutive laws. Atomistic simulations are used for conditionswhen continuum constitutive laws fail, e.g. large gradients, flows far fromequilibrium, high/intermediate Knudsen number flows, heat transfer, mechanicalproperties, and friction at nanoscale…

Statistical Mechanics, Physics: theory of liquids, correlated many-bodymotion, properties of statistical ensembles, structure of small clusters …

Computer Science and Mathematics: Numerical algorithms, analyticalmethods, development of computational tools.

Interdisciplinary nature of “atomistic simulations”


Nano-scale: Characteristic length ~10-9 - 10-7 m. Characteristic times ~10-14 -10-10 s. Atomic level, properties of individual defects (dislocations, vacancies,interstitials, dopants), defect mobility, diffusion, clusters, surface reactions.

Micro-scale: Characteristic length ~10-8 - 10-6 m. Characteristic times ~10-11 –10-8 s. Small ensembles of lattice defects at length scale below the grain size,defect interactions, precipitates, dislocation reactions, microcrack nucleation.

Meso-scale: Characteristic length ~10-7 - 10-4 m. Characteristic times ~10-9 -10-3 s. Ensembles of lattice defects at length scale of the grain size, shearbands, dislocation walls, disclinations, collective dynamics of microstructure,interface diffusion, grain coarsening, recrystallization, crack growth, fracture.

Macro-scale: Characteristic length 10-3 m. Characteristic times 10-3 s.Sample geometry, mechanics, plasticity of polycrystalline materials,temperature fields, hydrodynamic motion, microstructure homogenization etc.

Structural hierarchy, characteristic length- and time-scales

University of Virginia, MSE 4270/6270: Introduction to Atomistic Simulations, Leonid Zhigileiquantum nano micro meso macro

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structure of diamond surface Zhigilei, Srivastava & Garrison

crack propagation, F. F. Abraham, IBM

Nanocrystalline material, M. Li, JHU plastic deformation of a crystalhttp://zig.onera.fr/DisGallery/index.html

Computational methods in materials science


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quantum nano micro meso macro

Ab initio MD, Quantum MC

Classical MD, Metropolis MC

Kinetic MC (up to 108 atoms)

Dislocation Dynamics: early stages of plastic deformation

MC Potts Model: grain structures in polycrystalline materials

Phase Field Models: solidification, phase transformations…

Coarse-Grained Models: molecular systems, polymers…

Finite element or finite differences methodsare used to solve a system of PDE.

Continuum, constitutive relations

Mesoscopic models

Microscopic/atomistic models

general

System-specific

Computational methods


Length and time scales in materials modeling

by Greg Odegard, NASA


An emerging understanding of the connections between the structureand properties of materials has lead to a remarkable progress in thedesign of new advanced materials.

from M. A. White, Properties of Materials


Computational methods in materials science

by Dierk Raabe

# of atoms

109

103

1024

billions of atoms


Particle and continuum computational models

by W. Dzwinel


Multiscale modeling of dislocations in semiconductors

by V. Bulatov, LLNL

TMS report, 2015


Plan of the course

Numerical integration of differential equations (ODE for particle dynamics).– hands on

Atomistic methods - Molecular dynamics, kinetic and Metropolis MonteCarlo. Computer codes will be provided. The knowledge from this part ofthe course should be sufficient to design and perform your own simulations.– hands on

Advanced techniques in atomistic simulation that may be useful in yourresearch projects. Control of temperature and pressure. Methods for analysisof simulation results, diffusion, spatial and time correlation functionsReview of interatomic potentials.

Mesoscopic techniques (Dislocation Dynamics, Kinetic MC, Potts model,Cellular automata etc.) – overview/examples (time permitting)

Multiscale approaches (hierarchical and combined). Coupling of continuumand atomistic models. – brief overview (time permitting)


Examples: Computational molecular nanotechnology at NASA

Carbon nanotubes are considered as potentialbuilding block in future nanoscale materials,sensors, machines, and computers.

by Deepak Srivastava, NASA Ames


Examples: Large-scale simulation of crack propagation

Molecular dynamics simulation with ~1 billion atoms illustrates crackpropagation in a ductile metal. At first, the crack moves very rapidly and localbonds break in a "brittle" manner, but at some point the crack-tip begins to emitdislocations (the tangles in the picture) and stops propagating. Such a crack issaid to become blunted and begins to cause intense local deformation but notfailure.

by F. F. Abraham et al.


Examples: Deformation of nanocrystalline aluminium

Four grains 20 and 70nm in size (97,000 and1,021,000 atoms) aresimulated.

V. Yamakov, D. Wolf, S.R. Phillpot, A. K. Mukherjee, and H. Gleiter, Nature Materials 1, 45–49 (2002).

Mechanical twinning plays an important role in plastic deformation of nanocrystalline Al.

MD simulations with EAM - type potential for Alwere carried out under constant tensile loads of2.3–2.5 GPa and at a temperature of T = 300 K.

A movie from the simulation can be found athttp://www.nature.com/nmat/journal/v1/n1/extref/nmat700-s1.mov


Examples: Nanodroplet Activated Folding of Graphene

Patra, Wang, Král, Nano Lett. 9, 3766 (2009)

Molecular dynamics simulations of spontaneous folding of atomically thin layers of graphite (graphene sheets) induced by droplets of water

nano-origami


Examples: Collision of a droplet with a substrate

Target

Emitter voltage (+8 kV)

Extractor voltage (+4 kV)

Mass analyzer entrance (+10V)

Target voltage (+30V)

3). Analyte ions

release in the

gas phase

1) Analyte dissolved in the electrolyte solution for electrospray

2) Clusters are destroyed by the impact

Grid

MD simulation by Yasushi Katsumi (term project for MSE 4270)

Experiment: Sergei Aksyonov and Peter Williams (Impact Desolvation of Electrosprayed Clusters (IDEC)




Impact velocity is 2000 m/s




Impact velocity is 500 m/s


Examples: Growth of fractal structures in fullerene layers

Monte Carlo simulation by Hui Liu (term project for MSE 6270)

STM images of C60 film growing on graphite


“Big picture” of laser spallation and ablation from atomistic simulations

mechanisms of ablation & spallation

“mosaic” approach to mapping the processes occurring at the scale of the whole laser spot

surface morphology

Ionin et al., JETP Lett. 94, 753, 2011

Appl. Phys. A 114, 11, 2014

Vorobyev and GuoPRB 72, 195422, 2005

Al target 150 ps after

irradiation by a 100 fs pulse


Examples: Modeling of matrix-assisted pulsed laser evaporation (MAPLE)

MAPLE is used for “gentle” ejection & deposition of thin polymer and nanocomposite films

Polymer molecules & CNTs are deposited on

a substrate

Volatile solvent molecules are pumped away

Frozen solution of polymer molecules and other nanoscale elements, e.g. CNT


Examples: MD simulation of the ejection of carbon nanotubes in MAPLE

More animations can be found athttp://www.faculty.virginia.edu/CompMat/maple/

Large scale coarse-grained MD simulation (~20 millions of matrix molecules + more than a thousand of CNTs)

This animation shows the ejection of carbon nanotubes (CNTs) from a target where a network of interconnected CNT bundles is embedded into a solvent that strongly absorbs laser light.

Short pulse laser irradiation results in the explosive boiling of the solvent and ejection of large tangles of CNT bundles (up to 50 MDa in mass).


Examples: MD simulation of Rayleigh-Bénard phenomenon

D. C. Rapaport, J. Phys.: Condens. Matter. 26, 503104, 2014

Streamlines from MD simulation of Rayleigh–Bénard flow pattern produced by convection in a fluid layer heated from below.

color coded streamlines show temperature variation

Simulations is done for 107 particles

nascent flow state after 4 × 104 timesteps

well-ordered cell array after 107 timesteps


Examples: Dislocation Dynamics Method

A nice collection of animations from dislocation dynamics simulations can be found at http://zig.onera.fr/DisGallery/index.html

One of the main mechanisms for dislocationmultiplication under stress is the Frank-Readmill or Frank-Read source. The operation of aFrank-Read source can be observed on adislocation segment pinned at its ends.

Dislocation dynamics during deformation ofa FCC single crystal (Cu) with lineardimension of 15 micrometers.


Mesoscopic modeling of carbon nanotube materials

Structure of CNT network materials

0.005 g/cm3 0.025 g/cm3

density

homogeneous poorly connected network

heterogeneous “star” structure, large pores

spontaneous formation of bundles in a thin CNT film

500 500 20 nm3 sample, density 0.2 g/cm3, ~1500

(10,10) CNTs of 200 nm length

Periodic boundary conditions in the plane of the film

Color of nanotubes corresponds to their local inter-tube interaction energy

Heat transfer in CNT materials

Phys. Rev. B, 71, 165417, 2005Phys. Rev. Lett. 104, 215902, 2010ACS Nano 4, 6187, 2010Appl. Phys. Lett. 101, 043113, 2012


Optional Reading

R. LeSar and D. C. Chrzan, Is computational materials science overrated? Materials Today 2, 21-23, 1999.

R. Gomperts, E. Renner, and M. Mehta, Enabling technologies for innovative new materials simulations, American Laboratory 37, 12-14 2005.

U. Landman, Materials by numbers: Computations as tools of discovery, PNAS 102, 6671-6678, 2005. [read 1st and last 2 pages]

NSF White Paper on “Matter by design,“ 2011.

White House Materials Genome Initiative, 2011.

Report on Mesoscale Science from the DOE Basic Energy Sciences Advisory Committee, 2012.

Overview of modeling projects funded by EU FP7 in 2007-13.

A roadmapping study for connecting materials models and simulations across length and time scales, TMS and NIST, 2015.

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