Liquid Si - Freezing - Revision history

Singraber at 21:18, 17 October 2025

2025-10-17T21:18:04Z

Karsai: /* Diffusion */

2022-04-15T15:00:25Z

Diffusion

← Older revision		Revision as of 15:00, 15 April 2022
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	<div class="toccolours mw-customtoggle-script">'''Click to show/''diffusion_coefficient.py''</div>		<div class="toccolours mw-customtoggle-script">'''Click to show/''diffusion_coefficient.py''</div>
	<div class="mw-collapsible mw-collapsed" id="mw-customcollapsible-script">{{:~~diffusion_coefficient_liquid_Si_freezing}}~~</div>		<div class="mw-collapsible mw-collapsed" id="mw-customcollapsible-script">
			<pre>
			#!/usr/bin/python

			import sys
			import re
			import math

			#setting grid for histogram

			potim = 3 #timestep from INCAR file
			readfile = open(sys.argv[1],"r") #input XDATCAR file in format XDATCAR.TEMP
			temp=re.sub("XDATCAR.",,sys.argv[1]) #extracts temperature from input file name
			z=0 #counter
			natoms=0 #number of atoms in XDATCAR file
			posion = [] #atom positions in Cartesian coordinates
			confcount = 0 #number of structures in XDATCAR file
			direct=[] #number of time steps for each structure in XDATCAR file
			a=[] #lattice parameter in 1st dimension
			b=[] #lattice parameter in 2nd dimension
			c=[] #lattice parameter in 3rd dimension
			#read in XDATCAR file
			line=readfile.readline()
			while (line):
			z=z+1
			line.strip()
			line=re.sub('^',' ',line)
			y=line.split()
			if (z==2):
			scale=float(y[0])
			if (z==3):
			a.append(float(y[0]))
			a.append(float(y[1]))
			a.append(float(y[2]))
			a_len=(a[0]a[0]+a[1]a[1]+a[2]a[2])*0.5
			if (z==4):
			b.append(float(y[0]))
			b.append(float(y[1]))
			b.append(float(y[2]))
			b_len=(b[0]b[0]+b[1]b[1]+b[2]b[2])*0.5
			if (z==5):
			c.append(float(y[0]))
			c.append(float(y[1]))
			c.append(float(y[2]))
			c_len=(c[0]c[0]+c[1]c[1]+c[2]c[2])*0.5
			if (z==7):
			natoms=int(y[0])
			if (y[0]=="Direct"):
			direct.append(int(y[2]))
			posion.append([])
			for i in range(0,natoms):
			line=readfile.readline()
			line.strip()
			line=re.sub('^',' ',line)
			f=line.split()
			cartpos_x=a[0]float(f[0])+a[1]float(f[1])+a[2]*float(f[2])
			cartpos_y=b[0]float(f[0])+b[1]float(f[1])+b[2]*float(f[2])
			cartpos_z=c[0]float(f[0])+c[1]float(f[1])+c[2]*float(f[2])
			#positions of ions for each structure are obtained here
			posion[confcount].append([cartpos_x,cartpos_y,cartpos_z])
			confcount=confcount+1
			line=readfile.readline()
			readfile.close

			#calculate diffusion coefficient
			#skip first 10 configurations corresponding to 300 fs
			d=0.0
			for i in range(10,confcount):
			for j in range(0,natoms):
			x_diff=posion[i][j][0]-posion[0][j][0]
			#if length is larger than 0.5 (in crystallographic coordinates) then we have to shift atom
			#due to periodic image to obtain the shortest distance.
			if (abs(x_diff)>(0.5*a_len)):
			if (x_diff<0):
			x_diff=x_diff+a_len
			elif (x_diff>0):
			x_diff=x_diff-a_len
			y_diff=posion[i][j][1]-posion[0][j][1]
			if (abs(y_diff)>(0.5*b_len)):
			if (y_diff<0):
			y_diff=y_diff+b_len
			elif (y_diff>0):
			y_diff=y_diff-b_len
			z_diff=posion[i][j][2]-posion[0][j][2]
			if (abs(z_diff)>(0.5*c_len)):
			if (z_diff<0):
			z_diff=z_diff+c_len
			elif (x_diff>0):
			z_diff=z_diff-c_len
			d=d+x_diff2.0+y_diff2.0+z_diff**2.0

			#print diffusion coefficient (in Ang^2/ps) vs temperature (in K)
			d=d/(confcount-1-10)/natoms/6.0
			time=(direct[confcount-1]-direct[10])potim/10*3.0 #conversion to ps
			print temp,d/time
			</pre>
			</div>

Huebsch at 08:54, 1 June 2021

2021-06-01T08:54:14Z

← Older revision		Revision as of 08:54, 1 June 2021
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	== Task ==		== Task ==

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

	== Input ==		== Input ==
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	<math> D=\frac{\langle x^{2} \rangle} {6 t}</math>		<math> D=\frac{\langle x^{2} \rangle} {6 t}</math>

	where t defines time and <math>\langle x^{2} \rangle</math>. The 6 in the denominator contains a factor of 3 accounting for the 3 spatial dimensions (usually the diffusion coefficient is written with a 2 in the denominator in literature corresponding to only one dimension). In our case we calculate the above equation as follows		where t defines time and <math>\langle x^{2} \rangle</math>. The 6 in the denominator contains a factor of 3 accounting for the 3 spatial dimensions (usually the diffusion coefficient is written with a 2 in the denominator in literature corresponding to only one dimension). In our case, we calculate the above equation as follows

	<math> D=\frac{\langle \sum_{i}^{N} [x_{i}(t)-x_{i}(0)]^{2} \rangle}{6 \Delta t} </math>.		<math> D=\frac{\langle \sum_{i}^{N} [x_{i}(t)-x_{i}(0)]^{2} \rangle}{6 \Delta t} </math>.
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	Since the atoms can move such that the distance between old and new ~~position~~ becomes larger than 0.5 (in crystallographic or fractional coordinates). Let us take for example the movement of atom 0 in the <math>x</math> direction from 0 to -0.25, which would be output in the {{TAG\|CONTCAR}} as 0.75. The distance corresponding to that would be ~~than~~ calculated as 0.75 which is wrong since we have periodic images and the real shortest distance would be 0.25. Hence all ~~distance~~ larger than 0.5 have to be shifted by -1.0. This is taken care in the script.		Since the atoms can move such that the distance between old and new positions becomes larger than 0.5 (in crystallographic or fractional coordinates). Let us take for example the movement of atom 0 in the <math>x</math> direction from 0 to -0.25, which would be output in the {{TAG\|CONTCAR}} as 0.75. The distance corresponding to that would be then calculated as 0.75 which is wrong since we have periodic images and the real shortest distance would be 0.25. Hence all distances larger than 0.5 have to be shifted by -1.0. This is taken care of in the script.

	We will use a short bash script (''dscript.sh'') to calculate the diffusion coefficient at different temperatures and plot them in a file (diff_coeff.jpg):		We will use a short bash script (''dscript.sh'') to calculate the diffusion coefficient at different temperatures and plot them in a file (diff_coeff.jpg):
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	<math> D=\mu k_{B} T</math>		<math> D=\mu k_{B} T</math>

	where <math>k_{B}</math> is the Boltzmann constant and <math>\mu</math> is the mobility of the particle. Evidently this relation is approximately fulfilled in Fig. 1. At approximately 1400 K we see a peak. This temperature should correspond to the phase transition temperature.		where <math>k_{B}</math> is the Boltzmann constant and <math>\mu</math> is the mobility of the particle. Evidently, this relation is approximately fulfilled in Fig. 1. At approximately 1400 K we see a peak. This temperature should correspond to the phase transition temperature.
	Close to the phase transition point the scaling with respect to the reduced temperature <math>T_{\mathrm{red}}</math> becomes		Close to the phase transition point the scaling with respect to the reduced temperature <math>T_{\mathrm{red}}</math> becomes

	<math> \langle x^{2} \rangle \propto T_{\mathrm{red}}^{1-\alpha},\qquad \qquad \qquad T_{\mathrm{red}}=\frac{T-T_{c}}{T_{c}}</math>		<math> \langle x^{2} \rangle \propto T_{\mathrm{red}}^{1-\alpha},\qquad \qquad \qquad T_{\mathrm{red}}=\frac{T-T_{c}}{T_{c}}</math>

	where <math> \alpha </math> is an anomalous dimension (it may be positive or negative) and <math>T_{c}</math> is the critical temperature. For infinite large systems and infinite time this would lead to a singularity in the plot, but since we are dealing with a finite sized system it results in a finite peak at the phase transition point.		where <math> \alpha </math> is an anomalous dimension (it may be positive or negative) and <math>T_{c}</math> is the critical temperature. For infinite large systems and infinite time, this would lead to a singularity in the plot, but since we are dealing with a finite-sized system it results in a finite peak at the phase transition point.
	</div>		</div>

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	<div class="toccolours mw-customtoggle-script3">'''Click to show/Solution'''</div>		<div class="toccolours mw-customtoggle-script3">'''Click to show/Solution'''</div>
	<div class="mw-collapsible mw-collapsed" id="mw-customcollapsible-script3">'''Solution''':		<div class="mw-collapsible mw-collapsed" id="mw-customcollapsible-script3">'''Solution''':
	Crystalline structures usually have less diffuse pair correlation functions since the atoms are usually vibrating around high symmetry points. In liquids the average positions are smeared out over a wider range of distances. With decreasing temperature the pair correlation function in the plot gets more structured. This indicates that crystallization is happening.		Crystalline structures usually have less diffuse pair correlation functions since the atoms are usually vibrating around high symmetry points. In liquids, the average positions are smeared out over a wider range of distances. With decreasing temperature, the pair correlation function in the plot gets more structured. This indicates that crystallization is happening.
	</div>		</div>

Karsai: /* Download */

2019-11-14T09:44:16Z

Download

← Older revision		Revision as of 09:44, 14 November 2019
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	== Download ==		== Download ==
	[~~http~~:~~//www.vasp.at/vasp-workshop/examples/~~Si_Liquid_Freezing.tgz Si_Liquid_Freezing.tgz]		[[Media:Si_Liquid_Freezing.tgz\| Si_Liquid_Freezing.tgz]]

	{{Template:Molecular dynamics - Tutorial}}		{{Template:Molecular dynamics - Tutorial}}

	[[Category:Examples]]		[[Category:Examples]]

Karsai at 11:06, 4 October 2019

2019-10-04T11:06:01Z

← Older revision		Revision as of 11:06, 4 October 2019
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	[http://www.vasp.at/vasp-workshop/examples/Si_Liquid_Freezing.tgz Si_Liquid_Freezing.tgz]		[http://www.vasp.at/vasp-workshop/examples/Si_Liquid_Freezing.tgz Si_Liquid_Freezing.tgz]

	{{Template:~~Bulk_systems~~}}		{{Template:Molecular dynamics - Tutorial}}

	[[Category:Examples]]		[[Category:Examples]]

Karsai at 11:05, 4 October 2019

2019-10-04T11:05:31Z

← Older revision		Revision as of 11:05, 4 October 2019
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	</div>		</div>



	'''Solution:''' Crystalline structures usually have less diffuse pair correlation functions since the atoms are usually vibrating around high symmetry points. In liquids the average positions are smeared out over a wider range of distances. With decreasing temperature the pair correlation function in the plot gets more structured. This indicates that crystallization is happening.

	== Download ==		== Download ==

Karsai at 11:05, 4 October 2019

2019-10-04T11:05:05Z

← Older revision		Revision as of 11:05, 4 October 2019
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	[[File:Pair liquid Si freezing.jpg\|300px]]		[[File:Pair liquid Si freezing.jpg\|300px]]

	'''~~User task~~:''' Interpret the figure yourself!		'''Exercise:''' Interpret the figure yourself!

			<div class="toccolours mw-customtoggle-script3">'''Click to show/Solution'''</div>
			<div class="mw-collapsible mw-collapsed" id="mw-customcollapsible-script3">'''Solution''':
			Crystalline structures usually have less diffuse pair correlation functions since the atoms are usually vibrating around high symmetry points. In liquids the average positions are smeared out over a wider range of distances. With decreasing temperature the pair correlation function in the plot gets more structured. This indicates that crystallization is happening.
			</div>

Karsai: /* Diffusion */

2019-10-01T12:04:24Z

Diffusion

@@ Line 197: / Line 197: @@
 where <math> \alpha </math> is an anomalous dimension (it may be positive or negative) and <math>T_{c}</math> is the critical temperature. For infinite large systems and infinite time this would lead to a singularity in the plot, but since we are dealing with a finite sized system it results in a finite peak at the phase transition point.
 </div>
 === Pair correlation function ===

Karsai at 12:03, 1 October 2019

2019-10-01T12:03:51Z

← Older revision		Revision as of 12:03, 1 October 2019
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	'''Exercise''': Interpret Fig. 1 yourself!		'''Exercise''': Interpret Fig. 1 yourself!

	<div class="toccolours mw-customtoggle-~~script~~">'''Click to show/Solution'''</div>		<div class="toccolours mw-customtoggle-script2">'''Click to show/Solution'''</div>
	<div class="mw-collapsible mw-collapsed" id="mw-customcollapsible-~~script~~">'''Solution''':		<div class="mw-collapsible mw-collapsed" id="mw-customcollapsible-script2">'''Solution''':
	For a given phase the diffusion coefficient depends directly on the temperature by		For a given phase the diffusion coefficient depends directly on the temperature by

Karsai: /* Diffusion */

2019-10-01T12:03:08Z

Diffusion

← Older revision		Revision as of 12:03, 1 October 2019
Line 184:		Line 184:
	'''Exercise''': Interpret Fig. 1 yourself!		'''Exercise''': Interpret Fig. 1 yourself!

			<div class="toccolours mw-customtoggle-script">'''Click to show/Solution'''</div>
			<div class="mw-collapsible mw-collapsed" id="mw-customcollapsible-script">'''Solution''':
			For a given phase the diffusion coefficient depends directly on the temperature by

			<math> D=\mu k_{B} T</math>

			where <math>k_{B}</math> is the Boltzmann constant and <math>\mu</math> is the mobility of the particle. Evidently this relation is approximately fulfilled in Fig. 1. At approximately 1400 K we see a peak. This temperature should correspond to the phase transition temperature.
			Close to the phase transition point the scaling with respect to the reduced temperature <math>T_{\mathrm{red}}</math> becomes

			<math> \langle x^{2} \rangle \propto T_{\mathrm{red}}^{1-\alpha},\qquad \qquad \qquad T_{\mathrm{red}}=\frac{T-T_{c}}{T_{c}}</math>

			where <math> \alpha </math> is an anomalous dimension (it may be positive or negative) and <math>T_{c}</math> is the critical temperature. For infinite large systems and infinite time this would lead to a singularity in the plot, but since we are dealing with a finite sized system it results in a finite peak at the phase transition point.
			</div>

← Older revision		Revision as of 21:18, 17 October 2025
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	{{TAGBL\|TEBEG}} = $i # starting temperature for MD		{{TAGBL\|TEBEG}} = $i # starting temperature for MD
	{{TAGBL\|TEEND}} = $i # end temperature for MD		{{TAGBL\|TEEND}} = $i # end temperature for MD
	# canonic (~~Nose~~) MD with {{TAGBL\|XDATCAR}} updated every 10 steps		# canonic (Nosé) MD with {{TAGBL\|XDATCAR}} updated every 10 steps
	{{TAGBL\|MDALGO}} = 2 ä switch to select thermostat		{{TAGBL\|MDALGO}} = 2 ä switch to select thermostat
	{{TAGBL\|SMASS}} = 3 # ~~Nose~~ mass		{{TAGBL\|SMASS}} = 3 # Nosé mass
	{{TAGBL\|ISIF}} = 2 # this tag selects the ensemble in combination with the thermostat		{{TAGBL\|ISIF}} = 2 # this tag selects the ensemble in combination with the thermostat
	*Most of the tags here are very similar to the tags used in the previous example ({{TAG\|Liquid Si - Standard MD}}).		*Most of the tags here are very similar to the tags used in the previous example ({{TAG\|Liquid Si - Standard MD}}).
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	{{TAGBL\|TEBEG}} = $i # starting temperature for MD		{{TAGBL\|TEBEG}} = $i # starting temperature for MD
	{{TAGBL\|TEEND}} = $i # end temperature for MD		{{TAGBL\|TEEND}} = $i # end temperature for MD
	# canonic (~~Nose~~) MD with {{TAGBL\|XDATCAR}} updated every 10 steps		# canonic (Nosé) MD with {{TAGBL\|XDATCAR}} updated every 10 steps
	{{TAGBL\|MDALGO}} = 2 ä switch to select thermostat		{{TAGBL\|MDALGO}} = 2 # switch to select thermostat
	{{TAGBL\|SMASS}} = 3 # ~~Nose~~ mass		{{TAGBL\|SMASS}} = 3 # Nosé mass
	{{TAGBL\|ISIF}} = 2 # this tag selects the ensemble in combination with the thermostat		{{TAGBL\|ISIF}} = 2 # this tag selects the ensemble in combination with the thermostat
	!		!