forked from lijiext/lammps
git-svn-id: svn://svn.icms.temple.edu/lammps-ro/trunk@4509 f3b2605a-c512-4ea7-a41b-209d697bcdaa
This commit is contained in:
sjplimp
parent
0f6a4b8ed3
commit
f9cffa4e0c
|
|
@ -80,48 +80,18 @@ first term in the equation for J above.
|
|||
</P>
|
||||
<HR>
|
||||
|
||||
<P>IMPORTANT NOTE: This section needs to be re-written to reflect the new
|
||||
<A HREF = "fix_ave_correlate.html">fix ave/correlate</A> command, and
|
||||
time-integration function trap() available in
|
||||
<A HREF = "variable.html">variables</A>. This simplifies the procedure for
|
||||
extracting a thermal conductivity via the Green-Kubo formula.
|
||||
</P>
|
||||
<P>The heat flux can be output every so many timesteps (e.g. via the
|
||||
<A HREF = "thermo_style.html">thermo_style custom</A> command). Then as a
|
||||
post-processing operation, an autocorrelation can be performed, its
|
||||
integral estimated, and the Green-Kubo formula above evaluated.
|
||||
</P>
|
||||
<P>Here is an example of this procedure. First a LAMMPS input script for
|
||||
solid Ar is appended below. A Python script
|
||||
<A HREF = "Scripts/correlate.py">correlate.py</A> is also given, which calculates
|
||||
the autocorrelation of the flux output in the logfile flux.log,
|
||||
produced by the LAMMPS run. It is invoked as
|
||||
<P>The <A HREF = "fix_ave_correlate.html">fix ave/correlate</A> command can calclate
|
||||
the autocorrelation. The trap() function in the
|
||||
<A HREF = "variable.html">variable</A> command can calculate the integral.
|
||||
</P>
|
||||
<PRE>correlate.py flux.log -c 3 -s 200
|
||||
</PRE>
|
||||
<P>The resulting data lists the autocorrelation in column 1 and the
|
||||
integral of the autocorrelation in column 2. After running the
|
||||
correlate.py script, the value of the integral is ~9e-11. This has to
|
||||
be multiplied by V/(kB T^2) times the sample interval and the
|
||||
appropriate unit conversion factors. For real <A HREF = "units.html">units</A> in
|
||||
LAMMPS,
|
||||
<P>An an example LAMMPS input script for solid Ar is appended below.
|
||||
The result should be: average conductivity ~0.29 in W/mK.
|
||||
</P>
|
||||
<PRE>kappa (KCal/(mol fmsec Ang K)) = V/(k_B*(T^2)) x "thermo" output frequency x timestep x Integral value
|
||||
</PRE>
|
||||
<P>where
|
||||
</P>
|
||||
<PRE>V = 10213.257 Angs^3
|
||||
k_B = 1.98721e-3 KCal/(mol K)
|
||||
T = ~70K
|
||||
</PRE>
|
||||
<P>Therefore, lamda = 3.7736e-6 (KCal/(mol fs A K)).
|
||||
</P>
|
||||
<P>Converting to W/mK gives:
|
||||
</P>
|
||||
<PRE>3.7736e-6 * (4182 / (1e-15 * 1e-10 * N_Avogradro)) =
|
||||
3.7736e-6 * 69443.837 =
|
||||
~0.26 W/mK
|
||||
</PRE>
|
||||
<HR>
|
||||
|
||||
<P><B>Output info:</B>
|
||||
|
|
@ -150,7 +120,9 @@ energy/area/time <A HREF = "units.html">units</A>
|
|||
</P>
|
||||
<P><B>Related commands:</B>
|
||||
</P>
|
||||
<P><A HREF = "fix_thermal_conductivity.html">fix thermal/conductivity</A>
|
||||
<P><A HREF = "fix_thermal_conductivity.html">fix thermal/conductivity</A>,
|
||||
<A HREF = "fix_ave_correlate.html">fix ave/correlate</A>,
|
||||
<A HREF = "variable.html">variable</A>
|
||||
</P>
|
||||
<P><B>Default:</B> none
|
||||
</P>
|
||||
|
|
@ -158,43 +130,56 @@ energy/area/time <A HREF = "units.html">units</A>
|
|||
|
||||
<H4>Sample LAMMPS input script
|
||||
</H4>
|
||||
<PRE>atom_style atomic
|
||||
units real
|
||||
dimension 3
|
||||
boundary p p p
|
||||
lattice fcc 5.376 orient x 1 0 0 orient y 0 1 0 orient z 0 0 1
|
||||
region box block 0 4 0 4 0 4
|
||||
create_box 1 box
|
||||
create_atoms 1 box
|
||||
mass 1 39.948
|
||||
pair_style lj/cut 13.0
|
||||
pair_coeff * * 0.2381 3.405
|
||||
group every region box
|
||||
velocity all create 70 102486 mom yes rot yes dist gaussian
|
||||
timestep 4.0
|
||||
thermo 10
|
||||
<PRE>atom_style atomic
|
||||
units real
|
||||
variable kB equal 1.3806504e-23 # <B>J/K</B> Boltzmann
|
||||
variable kCal2J equal 4186.0/6.02214e23
|
||||
variable T equal 70
|
||||
variable V equal vol
|
||||
variable dt equal 4.0
|
||||
variable p equal 200 # correlation length
|
||||
variable s equal 10 # sample interval
|
||||
variable d equal $p*$s # dump interval
|
||||
</PRE>
|
||||
<PRE># ------------- Equilibration and thermalisation ----------------
|
||||
<P># ---------------------------------------------------------
|
||||
</P>
|
||||
<PRE>dimension 3
|
||||
boundary p p p
|
||||
lattice fcc 5.376 orient x 1 0 0 orient y 0 1 0 orient z 0 0 1
|
||||
region box block 0 4 0 4 0 4
|
||||
create_box 1 box
|
||||
create_atoms 1 box
|
||||
mass 1 39.948
|
||||
pair_style lj/cut 13.0
|
||||
pair_coeff * * 0.2381 3.405
|
||||
timestep $<I>dt</I>
|
||||
thermo $d
|
||||
</PRE>
|
||||
<PRE>fix NPT all npt temp 70 70 10 iso 0.0 0.0 100.0 drag 0.2
|
||||
run 8000
|
||||
unfix NPT
|
||||
</PRE>
|
||||
<PRE># --------------- Equilibration in nve -----------------
|
||||
</PRE>
|
||||
<PRE>fix NVE all nve
|
||||
run 8000
|
||||
</PRE>
|
||||
<PRE># -------------- Flux calculation in nve ---------------
|
||||
<P># ------------- equilibration and thermalization ----------------
|
||||
</P>
|
||||
<PRE>velocity all create $T 102486 mom yes rot yes dist gaussian
|
||||
fix NVT all nvt temp $T $T 10 drag 0.2
|
||||
run 8000
|
||||
</PRE>
|
||||
<P># -------------- flux calculation ---------------
|
||||
</P>
|
||||
<PRE>reset_timestep 0
|
||||
compute myKE all ke/atom
|
||||
compute myPE all pe/atom
|
||||
compute myStress all stress/atom virial
|
||||
compute flux all heat/flux myKE myPE myStress
|
||||
log flux.log
|
||||
variable J equal c_flux[1]/vol
|
||||
thermo_style custom step temp v_J
|
||||
run 100000
|
||||
compute myKE all ke/atom
|
||||
compute myPE all pe/atom
|
||||
compute myStress all stress/atom virial
|
||||
compute flux all heat/flux myKE myPE myStress
|
||||
variable Jx equal c_flux<B>1</B>/vol
|
||||
variable Jy equal c_flux<B>2</B>/vol
|
||||
variable Jz equal c_flux<B>3</B>/vol
|
||||
fix JJ all ave/correlate $s $p $d &
|
||||
c_flux<B>1</B> c_flux<B>2</B> c_flux<B>3</B> type auto file J0Jt.dat ave running
|
||||
variable scale equal $<I>kCal2J</I>*$<I>kCal2J</I>/$<I>kB</I>/$T/$T/$V*$s*$<I>dt</I>*1.0e25
|
||||
variable k11 equal trap(f_JJ<B>3</B>)*$<I>scale</I>
|
||||
variable k22 equal trap(f_JJ<B>4</B>)*$<I>scale</I>
|
||||
variable k33 equal trap(f_JJ<B>5</B>)*$<I>scale</I>
|
||||
thermo_style custom step temp v_Jx v_Jy v_Jz v_k11 v_k22 v_k33
|
||||
run 100000
|
||||
variable k equal (v_k11+v_k22+v_k33)/3.0
|
||||
print "average conductivity: $k <B>W/mK</B>"
|
||||
</PRE>
|
||||
</HTML>
|
||||
|
|
|
|||
|
|
@ -77,47 +77,17 @@ first term in the equation for J above.
|
|||
|
||||
:line
|
||||
|
||||
IMPORTANT NOTE: This section needs to be re-written to reflect the new
|
||||
"fix ave/correlate"_fix_ave_correlate.html command, and
|
||||
time-integration function trap() available in
|
||||
"variables"_variable.html. This simplifies the procedure for
|
||||
extracting a thermal conductivity via the Green-Kubo formula.
|
||||
|
||||
The heat flux can be output every so many timesteps (e.g. via the
|
||||
"thermo_style custom"_thermo_style.html command). Then as a
|
||||
post-processing operation, an autocorrelation can be performed, its
|
||||
integral estimated, and the Green-Kubo formula above evaluated.
|
||||
|
||||
Here is an example of this procedure. First a LAMMPS input script for
|
||||
solid Ar is appended below. A Python script
|
||||
"correlate.py"_Scripts/correlate.py is also given, which calculates
|
||||
the autocorrelation of the flux output in the logfile flux.log,
|
||||
produced by the LAMMPS run. It is invoked as
|
||||
The "fix ave/correlate"_fix_ave_correlate.html command can calclate
|
||||
the autocorrelation. The trap() function in the
|
||||
"variable"_variable.html command can calculate the integral.
|
||||
|
||||
correlate.py flux.log -c 3 -s 200 :pre
|
||||
|
||||
The resulting data lists the autocorrelation in column 1 and the
|
||||
integral of the autocorrelation in column 2. After running the
|
||||
correlate.py script, the value of the integral is ~9e-11. This has to
|
||||
be multiplied by V/(kB T^2) times the sample interval and the
|
||||
appropriate unit conversion factors. For real "units"_units.html in
|
||||
LAMMPS,
|
||||
|
||||
kappa (KCal/(mol fmsec Ang K)) = V/(k_B*(T^2)) x "thermo" output frequency x timestep x Integral value :pre
|
||||
|
||||
where
|
||||
|
||||
V = 10213.257 Angs^3
|
||||
k_B = 1.98721e-3 KCal/(mol K)
|
||||
T = ~70K :pre
|
||||
|
||||
Therefore, lamda = 3.7736e-6 (KCal/(mol fs A K)).
|
||||
|
||||
Converting to W/mK gives:
|
||||
|
||||
3.7736e-6 * (4182 / (1e-15 * 1e-10 * N_Avogradro)) =
|
||||
3.7736e-6 * 69443.837 =
|
||||
~0.26 W/mK :pre
|
||||
An an example LAMMPS input script for solid Ar is appended below.
|
||||
The result should be: average conductivity ~0.29 in W/mK.
|
||||
|
||||
:line
|
||||
|
||||
|
|
@ -147,7 +117,9 @@ energy/area/time "units"_units.html
|
|||
|
||||
[Related commands:]
|
||||
|
||||
"fix thermal/conductivity"_fix_thermal_conductivity.html
|
||||
"fix thermal/conductivity"_fix_thermal_conductivity.html,
|
||||
"fix ave/correlate"_fix_ave_correlate.html,
|
||||
"variable"_variable.html
|
||||
|
||||
[Default:] none
|
||||
|
||||
|
|
@ -155,41 +127,54 @@ energy/area/time "units"_units.html
|
|||
|
||||
Sample LAMMPS input script :h4
|
||||
|
||||
atom_style atomic
|
||||
units real
|
||||
dimension 3
|
||||
boundary p p p
|
||||
lattice fcc 5.376 orient x 1 0 0 orient y 0 1 0 orient z 0 0 1
|
||||
region box block 0 4 0 4 0 4
|
||||
create_box 1 box
|
||||
create_atoms 1 box
|
||||
mass 1 39.948
|
||||
pair_style lj/cut 13.0
|
||||
pair_coeff * * 0.2381 3.405
|
||||
group every region box
|
||||
velocity all create 70 102486 mom yes rot yes dist gaussian
|
||||
timestep 4.0
|
||||
thermo 10 :pre
|
||||
atom_style atomic
|
||||
units real
|
||||
variable kB equal 1.3806504e-23 # [J/K] Boltzmann
|
||||
variable kCal2J equal 4186.0/6.02214e23
|
||||
variable T equal 70
|
||||
variable V equal vol
|
||||
variable dt equal 4.0
|
||||
variable p equal 200 # correlation length
|
||||
variable s equal 10 # sample interval
|
||||
variable d equal $p*$s # dump interval :pre
|
||||
|
||||
# ------------- Equilibration and thermalisation ---------------- :pre
|
||||
# ---------------------------------------------------------
|
||||
|
||||
fix NPT all npt temp 70 70 10 iso 0.0 0.0 100.0 drag 0.2
|
||||
run 8000
|
||||
unfix NPT :pre
|
||||
dimension 3
|
||||
boundary p p p
|
||||
lattice fcc 5.376 orient x 1 0 0 orient y 0 1 0 orient z 0 0 1
|
||||
region box block 0 4 0 4 0 4
|
||||
create_box 1 box
|
||||
create_atoms 1 box
|
||||
mass 1 39.948
|
||||
pair_style lj/cut 13.0
|
||||
pair_coeff * * 0.2381 3.405
|
||||
timestep ${dt}
|
||||
thermo $d :pre
|
||||
|
||||
# --------------- Equilibration in nve ----------------- :pre
|
||||
# ------------- equilibration and thermalization ----------------
|
||||
|
||||
fix NVE all nve
|
||||
run 8000 :pre
|
||||
velocity all create $T 102486 mom yes rot yes dist gaussian
|
||||
fix NVT all nvt temp $T $T 10 drag 0.2
|
||||
run 8000 :pre
|
||||
|
||||
# -------------- Flux calculation in nve --------------- :pre
|
||||
# -------------- flux calculation ---------------
|
||||
|
||||
reset_timestep 0
|
||||
compute myKE all ke/atom
|
||||
compute myPE all pe/atom
|
||||
compute myStress all stress/atom virial
|
||||
compute flux all heat/flux myKE myPE myStress
|
||||
log flux.log
|
||||
variable J equal c_flux\[1\]/vol
|
||||
thermo_style custom step temp v_J
|
||||
run 100000 :pre
|
||||
compute myKE all ke/atom
|
||||
compute myPE all pe/atom
|
||||
compute myStress all stress/atom virial
|
||||
compute flux all heat/flux myKE myPE myStress
|
||||
variable Jx equal c_flux[1]/vol
|
||||
variable Jy equal c_flux[2]/vol
|
||||
variable Jz equal c_flux[3]/vol
|
||||
fix JJ all ave/correlate $s $p $d &
|
||||
c_flux[1] c_flux[2] c_flux[3] type auto file J0Jt.dat ave running
|
||||
variable scale equal ${kCal2J}*${kCal2J}/${kB}/$T/$T/$V*$s*${dt}*1.0e25
|
||||
variable k11 equal trap(f_JJ[3])*${scale}
|
||||
variable k22 equal trap(f_JJ[4])*${scale}
|
||||
variable k33 equal trap(f_JJ[5])*${scale}
|
||||
thermo_style custom step temp v_Jx v_Jy v_Jz v_k11 v_k22 v_k33
|
||||
run 100000
|
||||
variable k equal (v_k11+v_k22+v_k33)/3.0
|
||||
print "average conductivity: $k [W/mK]" :pre
|
||||
|
|
|
|||
Loading…
Reference in New Issue