Liquid Si - Freezing

From VASP Wiki

Task

In this example the goal is to simulate the freezing of liquid Si.

Input

POSCAR

Si
15.12409564534287297131
     0.5000000000000000    0.5000000000000000    0.0000000000000000
     0.0000000000000000    0.5000000000000000    0.5000000000000000
     0.5000000000000000    0.0000000000000000    0.5000000000000000
  48
Direct
  0.8550657259653851  0.3204575801875221  0.6180363868822553
  0.6045454476433229  0.0546379652195404  0.1629680405553871
  0.4803889256776521  0.2999635319377835  0.0131251454718051
  0.8413504226620471  0.7598095803296524  0.1917781560970181
  0.9754163118144437  0.6134171268457649  0.7421364242876367
  0.2668229391055025  0.0066502741664650  0.0031140604380929
  0.8935777664000575  0.3324172908647429  0.9535738516718881
  0.0527608886321274  0.5249316429131962  0.5293744880144071
  0.4396089233132741  0.7564833235979471  0.5665855438788387
  0.5907859878830199  0.5198033580597228  0.3581725847640679
  0.2120832721474721  0.4042899613004446  0.7921535013319151
  0.0225803885096466  0.8414911198321031  0.1209255489569852
  0.0992500701525566  0.3917384466892963  0.3612433325214984
  0.9673794138223195  0.5206425706394114  0.1719623236201897
  0.2774602656926126  0.8480860088162007  0.2673309412777037
  0.0196991774214161  0.8282178425383616  0.6986213756952502
  0.3570927152895376  0.2951488295546784  0.2651851032568589
  0.1663829731894614  0.9766237917413699  0.6051764245375237
  0.4931841331696695  0.8689890620771937  0.2612357008392290
  0.8006473407426477  0.1033419073227807  0.4706563716777467
  0.0161340851939779  0.9953827418297991  0.8853439845676159
  0.7827740166661069  0.1821830067208054  0.9399555168314748
  0.0720651739141343  0.2539424963694544  0.6857919074323433
  0.4443385370769313  0.0486404637002326  0.4180706114402839
  0.7055263679666055  0.6802623819082319  0.7983614866719116
  0.2237125282521105  0.4055474352416297  0.0077044950891134
  0.2963682069847125  0.5771265542042112  0.2019757061665083
  0.2782449529809642  0.0451513130915826  0.7644934848784113
  0.9312079203181675  0.9090938018377080  0.3429249881187518
  0.6341882597200124  0.2969253226419481  0.3227590981305088
  0.3587691103780569  0.1061057273904179  0.0931868777500710
  0.8710437838676732  0.6541301230631744  0.4261617089364881
  0.6784300588817769  0.3263889355408940  0.5560491395978739
  0.5597052314845080  0.0174390112509929  0.6129003207931863
  0.0595962318875451  0.1019295953521402  0.3340999072062676
  0.7689671766774326  0.1768870209149794  0.1604177484299765
  0.9603661624482890  0.3311649224573259  0.1439224909303592
  0.3792868784787023  0.2806150985211180  0.4921541531665999
  0.8079860889823454  0.9194188799048340  0.9131036494263627
  0.3002081239026374  0.7834053620019006  0.8650323716139056
  0.4704528574512951  0.7221628305989689  0.9746107190983403
  0.2886552568292480  0.5927625600330780  0.4239421203107919
  0.4116743942942291  0.2198943758058664  0.7072597030225044
  0.2104494234814825  0.6457654201409418  0.8275863924787099
  0.6784628197745537  0.7205455185203838  0.1093053357228383
  0.6344130299021448  0.1650970001101275  0.8037018707797643
  0.3965793440603315  0.5364088146415013  0.6064549771969059
  0.6686412136025504  0.7848666926903073  0.5681234351534038

INCAR

SYSTEM =  Si
# electronic degrees                                                            
LREAL = A                      # real space projection
PREC  = Normal                 # chose Low only after tests
EDIFF = 1E-5                   # do not use default (too large drift)
ISMEAR = -1 ; SIGMA = 0.130    # Fermi smearing: 1500 K 0.086 10-3
ALGO = Very Fast               # recommended for MD (fall back ALGO = Fast)
MAXMIX = 40                    # reuse mixer from one MD step to next
ISYM = 0                       # no symmetry                                    
NELMIN = 4                     # minimum 4 steps per time step, avoid breaking after 2 steps
# MD (do little writing to save disc space)
IBRION = 0                     # main molecular dynamics tag
NSW = 400                      # number of MD steps
POTIM = 3                      # time step of MD
NWRITE = 0                     
NBLOCK = 10                    #
LCHARG = .FALSE.  
LWAVE = .FALSE.
TEBEG = $i                     # starting temperature for MD
TEEND = $i                     # end temperature for MD
# canonic (Nose) MD with XDATCAR updated every 10 steps
MDALGO = 2                     ä switch to select thermostat
SMASS =  3                     # Nose mass



Since several calculations at different temperatures are required in this calculation, the INCAR is created with a script for each temperature:

for i in 2000 1900 1800 1700 1600 1500 1400 1300 1200 1100 1000 900 800
do
cat >INCAR <<!
SYSTEM =  Si
# electronic degrees                                                            
LREAL = A                      # real space projection
PREC  = Normal                 # chose Low only after tests
EDIFF = 1E-5                   # do not use default (too large drift)
ISMEAR = -1 ; SIGMA = 0.130    # Fermi smearing: 1500 K 0.086 10-3
ALGO = Very Fast               # recommended for MD (fall back ALGO = Fast)
MAXMIX = 40                    # reuse mixer from one MD step to next
ISYM = 0                       # no symmetry                                    
NELMIN = 4                     # minimum 4 steps per time step, avoid breaking after 2 steps
    
# MD (do little writing to save disc space)
IBRION = 0 ; NSW = 400 ; NWRITE = 0 ; LCHARG = .FALSE. ; LWAVE = .FALSE.
TEBEG = $i ; TEEND = $i
# canonic (Nose) MD with XDATCAR updated every 10 steps
SMASS = 3 ;  NBLOCK = 10 ; POTIM = 3
!
mpirun -np 2 /path/to/your/vasp/executable
cp XDATCAR XDATCAR.$i
cp OUTCAR OUTCAR.$i
cp PCDAT PCDAT.$i
cp CONTCAR CONTCAR.$i
cp POSCAR POSCAR.$i
cp OSZICAR OSZICAR.$i
cp CONTCAR POSCAR
done

The script performs molecular dynamics runs on liquid Si at decreasing temperatures, starting at 2000 K and ending at 800 K. This should contain the transition from liquid Si to crystalline Si (amorphous).

KPOINTS

test
0 0 0
monk
 1 1 1
 0 0 0


Calculation

Diffusion

To analyse the diffusion behaviour at a certain temperature T, the data read from XDATCAR.T can be processed using the script diffusion (caution - this script is written for VASP version 4.x output):

 awk <XDATCAR  >diffusion.xy '
 #
 # simple module function
 #
 function mod(x,y) { return x-int(x/y)*y }
 function minim(x) { return mod(x+2.5,1.0)-0.5 }
 #
 # calculate mean square displacement
 #
 function diff() {
       d=0
       for (ion=1; ion<=ions; ion++) {
         dx=minim(xn[ion]-x[ion])
         dy=minim(yn[ion]-y[ion])
         dz=minim(zn[ion]-z[ion])

         xn[ion]=x[ion]+dx
         yn[ion]=y[ion]+dy
         zn[ion]=z[ion]+dz


         d=d+(xn[ion]-x0[ion])*(xn[ion]-x0[ion])*a1*a1
         d=d+(yn[ion]-y0[ion])*(yn[ion]-y0[ion])*a2*a2
         d=d+(zn[ion]-z0[ion])*(zn[ion]-z0[ion])*a3*a3
       }
 #       d=d/(set*t)/6
        d=d/6
        print set*t,d
 }
 #
 # set the number of ions
 #
 NR==1 { ions = $1 }
 NR==2 { a1=$2*10^10 ;  a2=$3*10^10 ;  a3=$4*10^10 ; t=$5*10^12 }
 # 
 # at this point a complete set of ionic positions has been found
 #
 mod(NR-6,ions+1)==0 {
    if (set>=2) diff()
    if (set==1) {
       for (ion=1; ion<=ions; ion++) {
         x0[ion]=xn[ion]
         y0[ion]=yn[ion]
         z0[ion]=zn[ion]
       }
    }
    for (ion=1; ion<=ions; ion++) {
         x[ion]=xn[ion]
         y[ion]=yn[ion]
         z[ion]=zn[ion]
    }
    head=headn
    headn=$0
    set=set+1
 }
 # store coordinates
 mod(NR-6,ions+1)>0  {
    ion=mod(NR-6,ions+1)
    xn[ion]=$1
    yn[ion]=$2
    zn[ion]=$3
 }
 '

Pair correlation function

The pair-correlation function provides information about the probability of finding two atoms at a given distance . The pair-correlation function written on PCDAT.T should be processed using the script PCDATtoPCDATxy:

 awk <PCDAT >PCDAT.xy '
 NR==8 { pcskal=$1}
 NR==9 { pcfein=$1}
 NR>=13 {
  line=line+1
  if (line==257)  {
     print " "
     line=0
  }
  else
     print (line-0.5)*pcfein/pcskal,$1
 }
 '

Mind: You will have to set the correct path to your VASP executable and invoke VASP with the correct command (e.g., in the above: mpirun -np 2).

Download

Si_liquid.tgz