ME346C Advanced Techniques for Molecular Simulations

Transcription

ME346C Advanced Techniques for Molecular Simulations -- Syllabus
Summer quarter, 2011-2012, 3 units, Stanford
MW(F) 11:00-12:15pm, 200-305
Instructor: Wei Cai, caiwei@stanford.edu, http://www.stanford.edu/~caiwei
Office hour: see coursework homepage
TA: William (Billy) Cash, wcash@stanford.edu
Office hour: see coursework homepage
Course website:
http://coursework.stanford.edu (official)
(last modified 6/24/2012)
Course objective
The students will learn to perform free energy and free energy barrier calculations by
molecular simulations, and understand the statistical mechanics basis of the
computational methods. Methods for free energy calculation, such as thermodynamic
integration (TI) and adiabatic switching (AS), will be applied to accurately predict the
melting point of crystals. Methods for (free) energy barrier calculation, such as nudgedelastic band (NEB) and umbrella sampling (US), will be applied to predict the rate of rare
transition events.
Prerequisite: ME346A and B
Relation with other courses
The statistical mechanics basis has been introduced in ME346A Introduction to statistical
mechanics. Basic molecular dynamics and Monte Carlo simulation techniques as well as
how to use the MD++ program have been introduced in ME346B Introduction to
molecular simulations. This is the first time ME346C is offered, even though the
ME346ABC sequence have been contemplated for many years.
Grading Policies
The final grade is given based on a final score, which is computed from homework
(20%), midterm project (40%) and final project (40%). Homework will be issued
biweekly and due on Wednesdays in class unless otherwise announced. To be fair to all
students, homeworks that are late by n days will have their grades multiplied by a factor
f(n) = (0.8)n. Students are encouraged to discuss with and learn from others when solving
the homework problems, but are required to write up the solution (including computer
programs) individually. Each projects require a written report and a ppt presentation
from each team. Students with a final score higher than 90 will receive an A.
Homework problems involve programming and numerical calculations in Matlab,
simulations using MD++, and theoretical problems. Homework reports are submitted in
paper. Numerical codes are submitted electronically to coursework.stanford.edu.
Textbooks and course materials
Daan Frenkel and Berend Smit, Understanding Molecular Simulation: From Algorithms
to Applications, 2nd ed. Computational science series; v.1, Academic Press, (2002).
QD461.F86
Course lecture notes will be distributed in class and posted on coursework.
The MD++ program and tutorial materials are available through a link on coursework.
Tutorials of MD++ will be given in TA sessions (location to be announced).
Other suggested readings:
Vasily V. Bulatov and Wei Cai, Computer Simulation of Dislocations, Oxford University
Press. Companion website: http://micro.stanford.edu/
Course outline
Part I.
1.
2.
3.
4.
5.
6.
Free Energy Methods
Statistical Mechanics Basis (2 lectures)
Thermodynamic Integration (1 lectures)
Reversible Scaling (1 lecture)
Free Energy of Solids (1 lecture)
Free Energy of Fluids (1 lecture)
Predicting Melting Temperature (1 lecture)
Midterm project presentation
Part II. Free Energy Barrier Methods
7. Rate of Rare Events, Nucleation Theory (2 lectures)
8. Energy Barrier Methods, Nudged Elastic Band (2 lectures)
9. Free Energy Barrier Methods, Unbrella Sampling (2 lectures)
Final project presentation
Important dates
Mon
6/25
Wed
Fri
6/27
6/29
7/2
7/4
7/6
7/9
7/11
7/13
7/16
7/18
7/20
7/23
7/25
7/27
7/30
8/1
8/3
8/6
8/8
8/10
8/13
8/15
8/17
8/20
Tentative topics
Overview
Stat Mech of Free Energy
Thermodynamic Integration
Reversible Scaling
------------------------------------------------------------------------------------------------Free Energy of Solids
Free Energy of Fluids
Melting Temperature
------------------------Student presentation
Nucleation Theory
------------------------Energy barrier methods
Energy barrier methods
------------------------Umbrella Sampling
Umbrella Sampling
------------------------Applications
Applications
Student presentation
-------------------------
*Exact dates of lectures may subject to change.
Finding a computer to run
MD++ / Matlab
Start looking for team mates
Make-up lecture
Pick midterm project topics
Independence day, No class
Travel, No class
Travel, No class
Final day to add / drop
Travel, No class
HW 1 due
Make-up lecture
Midterm project presentation
Pick final project topics
Final project proposal due
Course withdraw deadline
HW 2 due
Final project presentation
Final report due
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ME346C
Lecture 10
8/1/2012
Cai
Adatom Diffusion on Au Surface
Wei Cai
8/1/2012
Department of Mechanical Engineering, Stanford University, Stanford 94305-4040
1. Prepare Au (111) Surface
The atomistic calculations below will be based on the EAM Foiles potential for Au. The
tcl file can be download from ME346C Coursework web site.
bin/eam_mc2 scripts/work/au/au_surface_atom.tcl 0
A perfect FCC crystal of Au is created with dimensions: 4[1 -2 1] x 4[1 0 –1] x 3[1 1 1]
(1152 atoms).
A 1.4% bi-axial compressive strain is applied in the x and y directions. (Otherwise the
surface is under a large tension stress and adatoms will tend to be incorporated into the
top surface instead of staying on top of it.)
Figure 1. Au (111) surface. The top surface layer atoms are in orange.
Click on the atoms to get the (scaled) coordinates of various sites on the (111) surface.
These coordinates will be used in step 2.
2. Add One Adatom to Au (111) Surface
bin/eam_mc2 scripts/work/au/au_surface_atom.tcl 1
One more atom is added on top of the (111) surface. The total number of atoms is 1153.
There are two different types of sites to put the adatom: type A and type B. We create
four different structures: A, Ap, B, Bp. A and Ap are of the same type. B and Bp are of
the same type. The structures are saved in folder runs/au-surf-1-0-0.
1
2
Ap
Bp
B
A
Figure 2. Orange atoms are the top layer of Au (111) surface. There are two types
of sites (type A and type B) for adatom, both avoiding the orange atoms. A, Ap
are equivalent sites. B, Bp are equivalent sites.
A
B
Ap
Bp
Figure 3. For different adatom structures created by MD++.
3. Find Minimum Energy Path
The string method is used to search for the minimum energy path between state A (or Ap)
and state B (or Bp).
bin/eam_mc2 scripts/work/au/au_surface_atom.tcl 2 A B
or
bin/eam_mc2 scripts/work/au/au_surface_atom.tcl 2 A Bp
Figure 4 shows the energy profile for minimum energy path (after 1000 step of
stringrelax) between different states.
3
Plot energy profile:
cd runs/au-surf-2-A-B
octave
data=load('stringeng.out'); plot(data(end-10:end,3:5:end)', '*-');
xlabel(‘replica ID’); ylabel(‘Energy (eV)’);
Figure 4. The energy profile for adatom migration on Au (111) surface.
From these calculations, we see that the energy difference between the two adatom sites
is:
EB - EA = 0.065 eV
The energy barriers for the jump are (approximately):
E* - EA = 0.083 eV
E* - EB = 0.018 eV
The calculation can be repeated with more relaxation steps to make sure the results have
converged. It is also of interest to find out whether there are multiple transition paths
ways between meta-stable states (e.g. between A and B).
Further Reading:
R. C. Jaklevic and L. Elie, Scanning-Tunneling-Microscope Observation of Surface
Diffusion on an Atomic Scale: Au on Au(111), Phys. Rev. Lett. 60, 120–123 (1988)
http://prl.aps.org/pdf/PRL/v60/i2/p120_1
au_surface_atom.tcl
1/5
~/Codes/MD++.svn/scripts/work/au/
08/05/2012
# −*−shell−script−*−
# compute energy barrier of surface atom diffusion in FCC Au
#
# make eam build=R SYS=mc2
source "scripts/Examples/Tcl/startup.tcl"
#*******************************************
# Definition of procedures
#*******************************************
proc initmd { status n m } {
#MD++ setnolog
MD++ setoverwrite
MD++ dirname = runs/au−surf−$status−$n−$m
MD++ NNM = 200
}
#−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−
proc readeam { material } {
#Read in MEAM potential (MD++ format)
MD++ potfile = "~/Codes/MD++/potentials/EAMDATA/eamdata.${material}Foiles"
MD++ eamgrid = 500 readeam NNM=300
MD++ element0 = $material
}
proc make_perfect_crystal { nx ny nz } {
MD++ crystalstructure = face−centered−cubic latticeconst = 4.08
MD++ latticesize = \[
1 −2 1 $nx 1 0 −1 $ny 1 1 1 $nz \]
MD++ makecrystal #finalcnfile = perf.cn writecn #eval
}
proc make_dislocation_loop { } {
# create structure B’
set bz [expr −0.5/ [MD++_Get latticesize(11)] ]
MD++ input = \[ 3 1 0 0 $bz 0.02 −0.25 0.25 0.3 −10 10 −10 10 1
MD++ makedipole
}
1 −0.25 0.25 0 \]
#−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−
proc relax_fixbox { } { MD++ {
# Conjugate−Gradient relaxation
conj_ftol = 1e−4 conj_itmax = 1000 conj_fevalmax = 1000
conj_fixbox = 1
relax
} }
#end of proc relax_fixbox
#−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−
proc relax_freebox { } { MD++ {
# Conjugate−Gradient relaxation
conj_ftol = 1e−4 conj_itmax = 1000 conj_fevalmax = 1000
conj_fixbox = 0
conj_fixboxvec = [ 0 0 1
1 0 1
0 0 0 ]
relax
} }
#end of proc relax_freebox
proc setup_window { } { MD++ {
#−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−
#colors for Central symmetry view
color00 = "red" color01 = "blue" color02 = "green"
color03 = "magenta" color04 = "cyan" color05 = "purple"
color06 = "gray80" color07 = "white" color08 = "orange"
#−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−
# Plot Configuration
#
atomradius = [0.7 0.78] bondradius = 0.3 bondlength = 0 #2.8285 #for Si
win_width=600 win_height=600
#atomradius = 0.9 bondradius = 0.3 bondlength = 0 #2.8285 #for Si
atomcolor = cyan highlightcolor = purple bondcolor = red
au_surface_atom.tcl
2/5
08/05/2012
fixatomcolor = yellow backgroundcolor = gray70
#atomcolor = lightgrey highlightcolor = purple bondcolor = darkgrey
plot_color_axis = 2 NCS = 12
plot_color_windows = [ 5
0.6 10 1
10 20
6
20 80
8
80 5000 5
0 0.6 4
]
#plot_limits = [ 1 −10 10 −10 0.35 −10 10 ]
#plot_color_windows = 0
plot_atom_info = 1 # reduced coordinates of atoms
#plot_atom_info = 2 # real coordinates of atoms
#plot_atom_info = 3 # energy of atoms
#plot_highlight = [ 0 0 1 2 3 4 5 6 7 8 9 ]
plotfreq = 10
#
#rotateangles = [ 0 0 0 1.7 ]
#rotateangles = [ 0 −90 0 1.7 ]
#openwin alloccolors rotate saverot plot
#plot_color_axis = 0 input = [ −8 −3 10] GnuPlotHistogram
#plot_color_axis = 2 input = [ 0.6 50 50 ] GnuPlotHistogram
} }
proc openwindow { } {
setup_window
MD++ openwin alloccolors rotate saverot eval plot
}
#−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−
proc exitmd { } { MD++ quit }
#end of proc exitmd
#−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−
#−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−
proc setup_md { } { MD++ {
equilsteps = 0 timestep = 0.001 # (ps)
atommass = 196.96655 # (g/mol)
DOUBLE_T = 1
totalsteps = 1000
saveprop = 1 savepropfreq = 100 openpropfile #run
savecn = 1 savecnfreq = 10000 openintercnfile
plotfreq = 100 printfreq = 100
ensemble_type = "NVT" integrator_type = "VVerlet" implementation_type = 0
vt2 = 1e28 #1e28 2e28 5e28
wallmass = 2e3
# atommass * NP = 14380
boxdamp = 1e−3
# optimal damping for 216 atoms and wallmass 1e−3
saveH # Use current H as reference (H0), needed for specifying stress
fixboxvec = [ 0 0 1
1 0 1
0 0 0 ]
output_fmt = "curstep EPOT KATOM Tinst HELM HELMP TSTRESS_xx TSTRESS_yy TSTRESS_zz H_11 H_22 H_33
"
} }
#end of proc setup_md
#*******************************************
# Main program starts here
#*******************************************
# status 0:
#
1:
#
2:
#
# read in status from command line argument
if { $argc == 0 } {
set status 0
} elseif { $argc > 0 } {
set status [lindex $argv 0]
}
puts "status = $status"
au_surface_atom.tcl
3/5
if { $argc <= 1 } {
set n 0
set n [lindex $argv 1]
}
puts "n = $n"
if { $argc <= 2 } {
set m 0
set m [lindex $argv 2]
}
puts "m = $m"
if { $status == 0 } {
# create initial structure with (111) surface
MD++ setnolog
initmd $status $n $m
readeam Au
make_perfect_crystal 4 4 3
setup_window
openwindow
relax_freebox
MD++ eval
MD++ finalcnfile = "au−perf.cn" writecn
# make surface
MD++ input = \[ 3 3 0.5
\]
changeH_keepR
# apply bi−axial compression
MD++ input = \[ 1 1 −0.014 \]
MD++ input = \[ 2 2 −0.014 \]
changeH_keepS
changeH_keepS
relax_fixbox
MD++ eval plot
#setup_md
#MD++ T_OBJ = 30 initvelocity totalsteps = 1000 run
#relax_fixbox
MD++ finalcnfile = "au−surf.cn" writecn
# click on atoms to get (sx,sy) coordinates of sites A, B, C
MD++ sleep
exitmd
} elseif { $status == 1 } {
# put adatom on surface
# prepare and relax dislocation structure
MD++ setnolog
readeam Au
# allocate more memory than needed because we will add atom later
MD++ allocmultiple = 2
MD++ incnfile = "../au−surf−0−0−0/au−surf.cn" readcn
set
set
set
set
n [MD++_Get "NP"]
indx [expr $n*3 ]
indy [expr $n*3+1]
indz [expr $n*3+2]
# add one more atom on surface (site A)
MD++ NP = [expr $n + 1]
08/05/2012
au_surface_atom.tcl
setup_md
# put new atom
MD++ SR($indx)
MD++ SR($indy)
MD++ SR($indz)
on
=
=
=
site A
0.0416
0.0
0.35
setup_window
openwindow
relax_fixbox
MD++ T_OBJ = 30 initvelocity totalsteps = 1000 run
relax_fixbox
MD++ finalcnfile = "au−surf−A.cn" writecn
MD++ finalcnfile = "au−surf−A.cfg" writeatomeyecfg
# put new atom on site B
MD++ NP = [expr $n + 1]
MD++ SR($indx) = 0.0
MD++ SR($indy) = 0.0
MD++ SR($indz) = 0.35
relax_fixbox
relax_fixbox
MD++ finalcnfile = "au−surf−B.cn" writecn
MD++ finalcnfile = "au−surf−B.cfg" writeatomeyecfg
# put new atom on site Ap
MD++ NP = [expr $n + 1]
MD++ SR($indx) = −0.0208
MD++ SR($indy) = 0.0625
MD++ SR($indz) = 0.35
relax_fixbox
relax_fixbox
MD++ finalcnfile = "au−surf−Ap.cn" writecn
MD++ finalcnfile = "au−surf−Ap.cfg" writeatomeyecfg
# put new atom on site Bp
MD++ NP = [expr $n + 1]
MD++ SR($indx) = 0.0625
MD++ SR($indy) = 0.0625
MD++ SR($indz) = 0.35
relax_fixbox
relax_fixbox
MD++ finalcnfile = "au−surf−Bp.cn" writecn
MD++ finalcnfile = "au−surf−Bp.cfg" writeatomeyecfg
MD++ sleep
exitmd
# find minimum energy path for dislocation loop nucleation
MD++ setnolog
readeam Au
MD++ incnfile = "../au−surf−1−0−0/au−surf−$n.cn" readcn saveH
MD++ incnfile = "../au−surf−1−0−0/au−surf−$m.cn" readcn restoreH SHtoR setconfig2
MD++ incnfile = "../au−surf−1−0−0/au−surf−$n.cn" readcn readcn setconfig1
setup_window
#openwindow
MD++ eval
MD++ fixallatoms constrain_fixedatoms freeallatoms
MD++ chainlength = 25 totalsteps = 1000
4/5
08/05/2012
au_surface_atom.tcl
5/5
08/05/2012
MD++ timestep = 0.01 printfreq = 2
MD++ allocchain initRchain
# nebspec = [ relax_surounding_atoms reparam_freq fix_left_end fix_right_end climb_image]
MD++ { nebspec = [ 0 1 1 1 1 ] stringrelax }
MD++ finalcnfile = stringrelax.chain.cn writeRchain
#MD++ sleep
exitmd
exitmd
exitmd
# visualization
MD++ setnolog
initmd "view" $n $m
readpot
MD++ incnfile = "../au−surf−1−0−0/au−surf−$n.cn" readcn saveH
MD++ incnfile = "../au−surf−1−0−0/au−surf−$m.cn" readcn restoreH SHtoR setconfig2
MD++ incnfile = "../au−surf−1−0−0/au−surf−$n.cn" readcn readcn setconfig1
MD++ zipfiles = 0
for { set iter 0 } { $iter <= 25 } { incr iter 1 } {
MD++ incnfile ="../w−disl−nuc−${strain_yz}/stringrelax.chain.cn" readRchain
# set chain number
set chain_no $iter
set total_no 25
MD++ input = $iter
copyRchaintoCN eval
if { $iter == 0 } {
openwindow
}
MD++ eval plot
# write cn or cfg file
MD++ finalcnfile = "chain_no_${chain_no}.cn" writecn
MD++ finalcnfile = "chain_no_${chain_no}.cfg" writeatomeyecfg
MD++ sleepseconds = 1 sleep
}
MD++ sleepseconds = 100
exitmd
sleep
} else {
puts "unknown status = $status"
exitmd
}
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ME346C Advanced Techniques for Molecular Simulations

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