M09 Computing Ideal Strength - Revision history

Kwkang: /* Matlab Program cal_idealstr.m */

2014-11-21T11:49:46Z

Matlab Program cal_idealstr.m

← Older revision		Revision as of 11:49, 21 November 2014
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	for i = 1:MM(1),		for i = 1:MM(1),
	a = E(i,:);		a = E(i,:);
			if length(a)> 1
	a_interp = interp1(normalgrid,a,normalfinegrid,~~’spline’~~);		a_interp = interp1(normalgrid,a,normalfinegrid,'spline');
			else
			a_interp = a;
			end
	[Erlx(i), ind] = min(a_interp);		[Erlx(i), ind] = min(a_interp);
	Zrlx(i) = normalfinegrid(ind);		Zrlx(i) = normalfinegrid(ind);
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	end		end
	</pre>		</pre>


	=== Shell script for Computing Ideal Tensile strength by VASP ===		=== Shell script for Computing Ideal Tensile strength by VASP ===

Kwkang: /* MD++ Input Script idealstr.tcl */

2014-11-21T11:46:51Z

MD++ Input Script idealstr.tcl

@@ Line 334: / Line 334: @@
   openwindow
   MD++ sleep quit
   MD++ quit

Kwkang: /* Computing Ideal Shear Strength without Tilting Simulation Cell */

2014-11-21T11:42:35Z

Computing Ideal Shear Strength without Tilting Simulation Cell

← Older revision		Revision as of 11:42, 21 November 2014
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	The first ten parameters have the same meaning as those for '''calmisfit'''. The last 6 parameters specify the parallelepiped volume (enclosed by the solid lines in Fig. 4(a)) which will be shifted w.r.t. the remaining part of the crystal. The command '''calmisfit2''' also produces a text file, “Emisfit.out”, which has the same format as that produced by '''calmisfit'''. The same Matlab program (cal_idealstr.m) is able to compute the ideal strength using it as the input.		The first ten parameters have the same meaning as those for '''calmisfit'''. The last 6 parameters specify the parallelepiped volume (enclosed by the solid lines in Fig. 4(a)) which will be shifted w.r.t. the remaining part of the crystal. The command '''calmisfit2''' also produces a text file, “Emisfit.out”, which has the same format as that produced by '''calmisfit'''. The same Matlab program (cal_idealstr.m) is able to compute the ideal strength using it as the input.

			You may try '''calmisfit2_rigidrlx'''. Its syntax is given below.

			<pre>
			input = [ surfacenormal
			x0 dx x1
			y0 dy y1
			z0 dz z1
			xmin xmax ymin ymax zmin zmax
			nogrp grpid]
			calmisfit2_rigidrlx
			</pre>

			Here, two more input parameters are added. The atoms in xmin<math>\le</math>sx<xmax, ymin<math>\le</math>sy<ymax, and zmin<math>\le</math>sz<zmax are grouped and their group ID is given as '''grpid'''. And the number of groups '''nogrp''' = 1 in most cases, here. The command '''calmisfit2_rigidrlx''' rigidly relaxes the group of atoms labeled as '''grpid''' along the surface normal direction. So, the "Emisfit.out" already contains relaxed surface energy.

	<gallery caption="Fig.4" widths="300px" heights="300px" perrow="2">		<gallery caption="Fig.4" widths="300px" heights="300px" perrow="2">

Yanmingw: /* Gamma Surface */

2011-07-10T03:58:31Z

Gamma Surface

← Older revision		Revision as of 03:58, 10 July 2011
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	== Gamma Surface ==		== Gamma Surface ==
	The above procedure allows us to compute the ideal shear strength on a specified plane along a specific slip direction. However, there are two ~~orthgonal~~ directions within every plane along which slip can occur. The excess energy per unit area as a function of the two-dimensional slip vector can be visualized as a surface, and is usually called the <math>\gamma</math>-surface, or the generalized stacking fault energy.		The above procedure allows us to compute the ideal shear strength on a specified plane along a specific slip direction. However, there are two orthogonal directions within every plane along which slip can occur. The excess energy per unit area as a function of the two-dimensional slip vector can be visualized as a surface, and is usually called the <math>\gamma</math>-surface, or the generalized stacking fault energy.

	We have implemented a command '''calmisfit''' in MD++ that, together with an external Matlab program, computes the <math>\gamma</math>-surface. The command '''calmisfit''' itself computes the misfit energy <math>\gamma</math> as a function of three parameters: two for the 2-dimensional slip vector within the plane and one for the opening displacement <math>\delta</math> perpendicular to the plane. The minimization w.r.t. <math>\delta</math> is performed in the Matlab program. The syntax for this command is		We have implemented a command '''calmisfit''' in MD++ that, together with an external Matlab program, computes the <math>\gamma</math>-surface. The command '''calmisfit''' itself computes the misfit energy <math>\gamma</math> as a function of three parameters: two for the 2-dimensional slip vector within the plane and one for the opening displacement <math>\delta</math> perpendicular to the plane. The minimization w.r.t. <math>\delta</math> is performed in the Matlab program. The syntax for this command is

Caiwei: /* Script */

2008-02-26T01:05:01Z

Script

@@ Line 455: / Line 455: @@
 let x+=100
 done
 </pre>

Caiwei: /* Shell script for Computing Ideal Tensile strength by VASP */

2008-02-26T00:02:33Z

Shell script for Computing Ideal Tensile strength by VASP

← Older revision		Revision as of 00:02, 26 February 2008
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	=== Shell script for Computing Ideal Tensile strength by VASP ===		=== Shell script for Computing Ideal Tensile strength by VASP ===
	The following shell script will create the '''POSCAR''' file which specifies the atomic positions for VASP. You will also need to prepare '''INCAR''', '''KPOINTS''', '''POTCAR''' files in the same directory for VASP to run. This script will run VASP in serial mode. You can modify it to submit VASP jobs in parallel.		The following shell script will create the '''POSCAR''' file which specifies the atomic positions for VASP. You will also need to prepare '''INCAR''', '''KPOINTS''', '''POTCAR''' files in the same directory for VASP to run. This script will run VASP in serial mode. You can modify it to submit VASP jobs in parallel.

			In this script, the length of the first lattice vector is changed from 0.9 to 1.6 of its equilibrium length in steps of 0.01. A VASP calculation is performed for each length of the lattice vector to obtain the potential energy, which is then saved into file ''summary''.

	<pre>		<pre>
	#!/bin/bash		#!/bin/bash
		⚫	declare -i x=9000
	#rm WAVECAR summary
		⚫	while (($x <= 16000))
⚫	#declare -i x=9000
	declare -i x=15000
⚫	while (($x < ~~16100~~))
	do		do
	a=$(echo "scale=3; $x/10000" \| bc -l)		a=$(echo "scale=3; $x/10000" \| bc -l)
Line 450:		Line 450:
	FIN		FIN

	#echo "a=$a"
	#./vasp
	vasp		vasp
	#~/Codes/VASP/Si_Bulk/vasp
	E=`tail -1 OSZICAR`		E=`tail -1 OSZICAR`
	echo $a $E >> summary		echo $a $E >> summary
	#cp CONTCAR POSCAR
	let x+=100		let x+=100
	done		done

Caiwei: /* Shell script for Computing Ideal Tensile strength by VASP */

2008-02-25T23:58:39Z

Shell script for Computing Ideal Tensile strength by VASP

← Older revision		Revision as of 23:58, 25 February 2008
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	=== Shell script for Computing Ideal Tensile strength by VASP ===		=== Shell script for Computing Ideal Tensile strength by VASP ===
			The following shell script will create the '''POSCAR''' file which specifies the atomic positions for VASP. You will also need to prepare '''INCAR''', '''KPOINTS''', '''POTCAR''' files in the same directory for VASP to run. This script will run VASP in serial mode. You can modify it to submit VASP jobs in parallel.

	<pre>		<pre>

Caiwei: /* Ideal Tensile Strength */

2008-02-25T23:56:08Z

Ideal Tensile Strength

← Older revision		Revision as of 23:56, 25 February 2008
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	Fig. 2(a) plots the excess energy per unit area of the simulation cell, <math>\gamma</math>, as a function of separation distance <math>d</math> for the Stillinger-Weber (SW) model of Si. For large enough <math>d</math>, <math>\gamma(d)</math> reaches a plateau, whose value is <math>2\gamma_s</math>, where <math>\gamma_s</math> is the (unrelaxed) surface energy of (1 1 0) plane of Si. The plateau is reached when <math>d</math> becomes greater than the cut-off distance of the interatomic potential. The slope of the <math>\gamma(d)</math> has the unit of stress. The maximum slope of this curve can be interpreted as the maximum stress required to separate two rigid blocks of Si along the [1 1 0] direction, i.e. the ideal tensile strength. For the SW model of Si, <math>\sigma_{[110]}^{\mathrm{th}}</math> = 41.7 GPa.		Fig. 2(a) plots the excess energy per unit area of the simulation cell, <math>\gamma</math>, as a function of separation distance <math>d</math> for the Stillinger-Weber (SW) model of Si. For large enough <math>d</math>, <math>\gamma(d)</math> reaches a plateau, whose value is <math>2\gamma_s</math>, where <math>\gamma_s</math> is the (unrelaxed) surface energy of (1 1 0) plane of Si. The plateau is reached when <math>d</math> becomes greater than the cut-off distance of the interatomic potential. The slope of the <math>\gamma(d)</math> has the unit of stress. The maximum slope of this curve can be interpreted as the maximum stress required to separate two rigid blocks of Si along the [1 1 0] direction, i.e. the ideal tensile strength. For the SW model of Si, <math>\sigma_{[110]}^{\mathrm{th}}</math> = 41.7 GPa. The same procedure described here can also be applied to compute ideal tensile strength by first-principles methods such as VASP. The shell script for this calculation is attached at the end of this manual.

	<gallery caption="Fig.2" widths="300px" heights="300px" perrow="2">		<gallery caption="Fig.2" widths="300px" heights="300px" perrow="2">

Caiwei: /* VASP script */

2008-02-25T23:53:17Z

VASP script

← Older revision		Revision as of 23:53, 25 February 2008
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	=== ~~VASP~~ script ===		=== Shell script for Computing Ideal Tensile strength by VASP ===

	<pre>		<pre>
	#!/bin/bash		#!/bin/bash
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	a=$(echo "scale=3; $x/10000" \| bc -l)		a=$(echo "scale=3; $x/10000" \| bc -l)
	cat > POSCAR << FIN		cat > POSCAR << FIN
	Ge comment line		Si comment line
	5.78 universal scaling factor		5.389 universal scaling factor
	$a $a 0.0 first lattice vector		$a $a 0.0 first lattice vector
	-1.0 1.0 0.0 second lattice vector		-1.0 1.0 0.0 second lattice vector

Caiwei: /* Script */ added VASP script

2008-02-25T23:51:05Z

Script: added VASP script

@@ Line 409: / Line 409: @@
     ylabel({’Lowest energy height,’; ’\delta/|c_2| where c_2 = [1 1 1]’},’fontsize’,16)
 end
 </pre>