Introduction to atomistic simulations
Lecture 1
1/22/18
1Harvard SEAS AP 275 Atomistic Modeling of Materials Boris Kozinsky
Computer are getting bigger
• Computation emerged as a new science/engineering paradigm
• Computer power up by x1,000 in last decade
• Robust computation and data science methods available
• e-Science: Data-Intensive Scientific Discovery
4
2012: 1TF = 22nm chip1997: 1TF= 72 cabinets
Harvard SEAS AP 275 Atomistic Modeling of Materials Boris Kozinsky
Atomic effects: core of future systems
• Future devices are systems of materials
• Atom-level design for component functionality
• Nano-scale coupling of components
• Complexity impedes rapid progress
• Fundamental interactions are unclear
• Slow progress without understanding
• Understand cause-effect relationships
6
Mobility
Lighting
Sensing
Heat recovery
Harvard SEAS AP 275 Atomistic Modeling of Materials Boris Kozinsky
Why simulate?
• New way of designing materials systems
• Deeper understanding of interacting active material components
• Property prediction without experiments
• Quantum mechanical accuracy
• Rapid rational screening of materials
• Enabled by rapid growth of HPC
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Structural changes
Phase stability
Reaction energies
System properties:
Electronic conductivity
Voltage
Ionic transport
HPC
Input Parameters:
Chemical composition Atomic arrangement
t
iH
ˆ
Harvard SEAS AP 275 Atomistic Modeling of Materials Boris Kozinsky
Novel carbon bonding at high pressure (80 GPa)
Phase transformation in ferromagnesite (Mg,Fe)CO3
Experiment can be too difficult
8
E. Boulard et al, Nature Communications 2014
Harvard SEAS AP 275 Atomistic Modeling of Materials Boris Kozinsky
Need a virtual microscope / spectroscope
Fingerprinting with computational Raman spectroscopy
9
Molecular identification using a library of signatures
R. Sánchez-Carrera and B. Kozinsky, Phys. Chem. Chem. Phys., 2014,16, 24549
Harvard SEAS AP 275 Atomistic Modeling of Materials Boris Kozinsky
Need a new theory
What enables high ionic conductivity in general?
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Tet
Undistorted Oct
Distorted Oct
Tet
Undistorted Oct
Distorted Oct
Ionic conductivity vs Li concentration
B. Kozinsky et al, PRL 116, 055901 (2016)
Optimization recipe
1. Reduce Li content
2. Avoid ordered states
Disorder is good
Harvard SEAS AP 275 Atomistic Modeling of Materials Boris Kozinsky
Theory can be too complicated
Resistivity of graphene from first principles
11
Electron-phonon self-energy
Credit: Y. Z. Zhang et al.
C.H. Park et al, Nano Lett 14, 1113 (2014)
qkqkqkq
qkqkqkqq
k qk
mnm
mnmm
mnn
TfTn
TfTngN
T
,1
,,2
,21
electron-phonon matrix element
Bose-Einstein statistics
electron energy phonon frequency
Harvard SEAS AP 275 Atomistic Modeling of Materials Boris Kozinsky
Atomistic simulations in industry
12
20
40
60
80
100
2002 2004 2006 2008 2010 2012
# atomistic groups in industry
Harvard SEAS AP 275 Atomistic Modeling of Materials Boris Kozinsky
Atomistic design in industry
Gummetal® developed at Toyota R&D
• Ab-initio models used to predict the effect of crystal structure, valence electrons density of states on material stiffness
• Super elasto-plastic Ti alloy is licensed for manufacturing and distribution
Virtual Aluminum Casting at Ford
• Predictions of microstructure and intermetallic phase morphology based on atomistic and FEM modeling
• New Al-Si-Cu alloy composition used in engine blocks
• $15M investment in methods results in $100M savings
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Evolution of ’ precipitates in Al-Si-Cu:
Simulation Experiment
Strength vs. stiffness and applications:
Harvard SEAS AP 275 Atomistic Modeling of Materials Boris Kozinsky
Atomistic design in industry
Hard disk drives at Seagate Technology
• Material development towards enhanced magnetic anisotropy and saturation needed to increased record density of hard disk drives
• Tetragonally distorted FeCo alloys were identified using ab-initio computations
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Magnetic anisotropy and saturation:
Harvard SEAS AP 275 Atomistic Modeling of Materials Boris Kozinsky
Materials Genome Initiative
• $100M US President’s initiative announced in 2011
• Goal: 50% reduction of cost and time to develop and commercialize new materials
• Focus on computational tools in materials engineering
• Computational materials screening
• Big data management
• Accelerate by closely coupling to experiments
15Harvard SEAS AP 275 Atomistic Modeling of Materials Boris Kozinsky
Need a better candidate material
Screening for better thermoelectrics with first-principles methods
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$350/kg 15 years
15 months
$40/kg
conventional
computational
timecost
ZT = 0.9
ZT = 1.1
performance
G.Joshi, et al, Energy and Env. Sci, 7, 4070 (2014)B. Kozinsky et al, Patent Application 2015148493A1 (2015)
Harvard SEAS AP 275 Atomistic Modeling of Materials Boris Kozinsky
Which properties are determined on atomic scale?
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MicroscopicAtomic Componentscale
Ab-initio Meso-scale Continuum
strength, reliability
battery energy
electronic conductivity
Ionic conductivity
magnetic energy
surface reactivity
Harvard SEAS AP 275 Atomistic Modeling of Materials Boris Kozinsky
Scales of materials simulation
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Atomistic dynamics
Batteries
Domain phase fields
Electrochemistry
Micro-mechanics
Fuel Cells
Magnets
Photovoltaics
Thermoelectrics
Piezoelectrics
Films, Coatings
Alloys
Plastics
Inter-grain transport
Nanostructures
MicroscopicAtomic Componentscale
Mo
de
ling
app
roac
he
s
Discovery, design Optimization
Harvard SEAS AP 275 Atomistic Modeling of Materials Boris Kozinsky
Atomistic materials design applications
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Photovoltaics Piezoelectrics
High-k ceramicsLi batteriesCoatings
Thermoelectrics
Atom-driven systems
Sensors
Steel
NanostructuresMotors
Harvard SEAS AP 275 Atomistic Modeling of Materials Boris Kozinsky
Atomistic modeling zoo
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Accuracy, transferability
Co
mp
uta
tio
n s
pe
ed
Classical pair potentials
Reactive force fields
GW
Correlated wavefunction
DFT
Quantum Monte Carlo
Large systems
Small systems
Hartree-FockTD-DFT
“first-principles, ab-initio”
102-103 atoms
105-108 atoms
10 atoms
“empirical, classical”
Many-body potentials
Harvard SEAS AP 275 Atomistic Modeling of Materials Boris Kozinsky
Computable properties
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Crystal structure of solids, bulk modulus
Reaction energies, electrochemical voltages
Thermodynamic phase stability
Dielectric properties, piezoelectric coefficients
Vibrational spectra
Thermo-mechanical properties, heat capacity, expansion
Ionic transport, molecular dynamics
Raman spectra, NMR spectra
Electronic conductivity, electron-phonon coupling
Thermal conductivity, phonon-phonon scattering
Optical excitations, photoelectricity
Co
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om
ple
xity
1 hour
1 day
1 week
1 month
Harvard SEAS AP 275 Atomistic Modeling of Materials Boris Kozinsky
22
Understand
Compute
Simplify
Automate
Validate
Design
Harvard SEAS AP 275 Atomistic Modeling of Materials Boris Kozinsky
Course Information
Objective: The class is aimed at beginning graduate students and will introduce a variety of atomistic simulation methods used in different fields of materials science
Instructor: Boris Kozinsky (MD 347, [email protected] )
Organization: 90 minute lectures with some lectures replaced by an in-class lab
Time/place: Mon and Wed, 10am-11.30pm, Room MD 323
Teaching Assistants: TBD
Web site: https://canvas.harvard.edu/courses/36431
Grade: ≈ 5 lab assignments + final project, NO EXAMS
Registration: All students are required to register for credit
23Harvard SEAS AP 275 Atomistic Modeling of Materials Boris Kozinsky
Course Objectives
• Teach the tools of modern computational materials science at the atomistic level
• Evaluate common methods and their applicability to diverse materials problems
• Review materials theory, physics and chemistry as is required to understand the basis for a particular method
• Provide overview of algorithms with broad applicability
• Teach hands-on practical skills for computational materials science (Linux, Python)
• Establish basis for independent research in materials computations
24Harvard SEAS AP 275 Atomistic Modeling of Materials Boris Kozinsky
Schedule
25Harvard SEAS AP 275 Atomistic Modeling of Materials Boris Kozinsky
1 M 1/22/18 Introduction to Atomistic simulation
2 W 1/24/18 Potentials, Supercells, Relaxation
M 1/29/18 No class
3 W 1/31/18 Numerical aspects. Periodicity.
4 F 2/2/18 Lab 1: Energetics and structure with empirical potentials
5 M 2/5/18 QM review
6 W 2/7/18 First principles Energy Methods: Hartree-Fock, SCF
7 M 2/12/18 Beyond HF, Intro to DFT
8 W 2/14/18 Crystals, plane wave basis
M 2/19/18 President's day
9 W 2/21/18 Lab 2: Density Functional Theory I
10 M 2/26/18 Case studies of DFT. Properties and accuracy
11 W 2/28/18 Advanced DFT. New developments and alternative algorithms
12 M 3/5/18 Lab 3: Density Functional Theory II
13 W 3/7/18 DFT continued
Schedule
26Harvard SEAS AP 275 Atomistic Modeling of Materials Boris Kozinsky
M 3/12/18 spring break
W 3/14/18 spring break
14 M 3/19/18 Finite temperature: Review of Stat Mech and Excitations
15 W 3/21/18 Molecular Dynamics formalism
16 M 3/26/18 Molecular Dynamics: technical aspects
17 W 3/28/18 MD applications, transport phenomena
18 M 4/2/18 Lab 4: Molecular Dynamics II
19 W 4/4/18 Transitions, energy landscapes, free energy
20 M 4/9/18 Monte Carlo
21 W 4/11/18 Lab 5: Monte Carlo
22 M 4/16/18 Lattice models
23 W 4/18/18 Cluster expansions and KMC
24 M 4/23/18 Case studies, materials design
25 W 4/25/17 Project presentations
Survey
https://www.surveymonkey.com/r/5NP28K8
27Harvard SEAS AP 275 Atomistic Modeling of Materials Boris Kozinsky
Lab logistics
• Install Oracle VirtualBox on your laptop• https://www.virtualbox.org/wiki/Downloads• Linux Mint 18.1 Xfce (preconfigured VM image will be provided)• https://www.linuxmint.com/edition.php?id=230
• Google Cloud computing resources will be provided
• Remember basic Linux commands• http://linuxcommand.org/
• Learn Python• https://www.programiz.com/python-programming• http://hetland.org/writing/instant-python.html
• Detailed setup instructions will be posted on website
28Harvard SEAS AP 275 Atomistic Modeling of Materials Boris Kozinsky
General Literature
• F. Jensen, " Introduction to Computational Chemistry", Wiley.
• D. Frenkel and B. Smit, "Understanding Molecular Simulation", Academic Press.
• M.P. Allen and Tildesley, "Computer Simulation of Liquids", Oxford Science Publishers
• R. Phillips, "Crystals, Defects and Microstructures", Cambridge University Press.
• J.M. Thijsen, "Computational Physics", Cambridge University Press.
• T. Schlick “Molecular Modeling and Simulation” Springer
• Leach, “Molecular Modelling: Principles and Applications”, Prentice Hall
• Haile, “Molecular Dynamics Simulation: Elementary Methods”, Wiley Professional
• Tuckerman, “Statistical Mechanics: Theory and Molecular Simulation”, Oxford University Press
• Specific references will be provided per topic
29Harvard SEAS AP 275 Atomistic Modeling of Materials Boris Kozinsky
Can we decouple ions from electrons?
Separation of time scales
Born Oppenheimer (adiabatic) approximation:For a System characterized by wavefunction and atomic configuration
every atomic configuration electrons are in their ground state
When is adiabatic approximation not valid?
Temperature (OK if excitations are fast on nuclear motion time scale)
Long lived excitations (two BO surfaces in semiconductors)
Coupling of nuclear and electron degrees of freedom
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E(R i) min E(
R i , )
iR
410/ Mme
Harvard SEAS AP 275 Atomistic Modeling of Materials Boris Kozinsky
Example of Born-Oppenheimer violation
• Strong coupling between electron and nuclear coordinates for phonons with q ~ 2kF (Kohn anomaly)
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Shift of Raman frequency with doping of a single graphene layer
Non-adiabatic modelAdiabatic (BO) DFT
Harvard SEAS AP 275 Atomistic Modeling of Materials Boris Kozinsky
What is the simplest atomistic model
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One type of atom
Hard core repulsion
Can describe nanoparticle colloids
Exhibits solid-liquid phase transitionB. J. Alder and T. E. Wainwright, J. Chem. Phys. 27, 1208 (1957)
First ever MD publication
Not so good for atoms
Harvard SEAS AP 275 Atomistic Modeling of Materials Boris Kozinsky
• Bonding and anti-bonding states form in locally overlapping electron orbitals
• Inert shells can still interact via dipole-dipole interactions
Atomic interaction is often local
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H H
H H
He He
Harvard SEAS AP 275 Atomistic Modeling of Materials Boris Kozinsky
Pair potentials forms
• Pairwise energy summation
• Attractive at long range
• Repulsive at short range (caution at high speed)
• Usually requires a cutoff• Watch out for discontinuous forces
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)(2
10 j
jii RRVEE
Harvard SEAS AP 275 Atomistic Modeling of Materials Boris Kozinsky
Lennard-Jones: a simple two-parameter form
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V(r) A
r12
B
r6
V(r)
r
12
2
r
6
When expressing Temperature, Pressure and Density in renormalized units all LJ systems are identical
is unit of energy scale is unit of length
3
3
1:Density
:Pressure
:eΤemperatur
Bk
Harvard SEAS AP 275 Atomistic Modeling of Materials Boris Kozinsky
First MD simulation with a continuous potential
500-atom simulation was performed on an IBM 704
36Harvard SEAS AP 275 Atomistic Modeling of Materials Boris Kozinsky
Other potential forms
Morse potential
Born-Mayer/Buckingham
Many other potential forms are used
37
201)( rreDrV
86)(
r
D
r
CAerV Br
C-H stretch energy in methane
Figure from Jensen
Harvard SEAS AP 275 Atomistic Modeling of Materials Boris Kozinsky
Applications
Applications of potentials to oxides, metals, organics
Applicability of pair potentials Embedded Atom Method (EAM)
Many-body potentials for Si
Electrostatic interaction, ionic crystals
Force fields for organic compounds
Recent developments
38Harvard SEAS AP 275 Atomistic Modeling of Materials Boris Kozinsky
Pair potential forms
Morse potential
Born-Mayer/Buckingham
Potentials can be wrong because of parameters or functional form (physics)
OK for noble gases (Ar, He)
39
201)( rreDrV
86)(
r
D
r
CAerV Br
Pauli repulsion
dipole-dipole interactions
Harvard SEAS AP 275 Atomistic Modeling of Materials Boris Kozinsky
Numerical aspects
Computational speed 104-106 faster than DFT
Short-range potentials can be cut off (and shifted)
Keep fixed or updated neighbor lists
Reduce computation cost scaling from N2 to N
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Total energy
Force
Harvard SEAS AP 275 Atomistic Modeling of Materials Boris Kozinsky
Potentials enable large simulations
https://www.youtube.com/watch?v=Wr7WbKODM2Q
9 Billion atoms
200,000 cpus (IBM BlueGene at LLNL)
2 ns of time (1M steps)
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https://arxiv.org/abs/0810.3037
Harvard SEAS AP 275 Atomistic Modeling of Materials Boris Kozinsky
Which of these green atoms has the highest bonding energy?
Which of these molecules has the lowest energy/atom?
Tendency to form close-packed structuresPrefer high coordination number (many bonds)
Energy depends on the number of bonds
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No angular dependenceproblem for localized covalently bonded materials
)(2
10 j
jii RRVEE
Harvard SEAS AP 275 Atomistic Modeling of Materials Boris Kozinsky
Crystal issues
Pair Potentials cannot predict crystal structures in metals or covalent solids
fcc - bcc energy difference can be shown to be “fourth moment” effect (i.e. it needs four-body interactions)
No stability against shear. Lack of Cauchy Pressure
Shear elastic constants C12 = C44 for any pair potential
43Harvard SEAS AP 275 Atomistic Modeling of Materials Boris Kozinsky