Use MEAM in MD++ - Revision history

Caiwei: /* Technical Note */

2009-08-19T07:42:14Z

Technical Note

← Older revision		Revision as of 07:42, 19 August 2009
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	erose=-esub(1.+x+an3x*3/(r/re))exp(-x)		erose=-esub(1.+x+an3x*3/(r/re))exp(-x)

	where an3 = attrac (if x > 0) and an3 = repuls (if x < 0).		where an3 = attrac (if x > 0) and an3 = repuls (if x < 0). x = alpha*(r/re - 1.0).

	In MD++/Fortran/MEAM-Lammps/meam_setup_done.F, we can find the following line,		In MD++/Fortran/MEAM-Lammps/meam_setup_done.F, we can find the following line,

	c erose = -Ec * (1 + astar + a3(astar3)/(r/re)) exp(-astar)		c erose = -Ec * (1 + astar + a3(astar3)/(r/re)) exp(-astar)
	erose = -Ec(1+astar+(-attrac+repuls/r)(astar*3))exp(-astar)		erose = -Ec(1+astar+(-attrac+repuls/r)(astar*3))exp(-astar)

			where <tt>astar</tt> is the same as <tt>x</tt> in DYNAMO.
⚫	The first line should be the same as that in DYNAMO, but it is commented out. The second one has a different form for attrac (not divided by r). The two lines are equivalent only when attrac = 0, and when repuls is scaled by re. Of course, you can always modify the source code to make the equation of state function behave the way you want.

		⚫	The first line should be the same as that in DYNAMO, but it is commented out. The second one has a different form for attrac (not divided by r). The two lines are equivalent only when <tt>attrac = 0</tt>, and when <tt>repuls</tt> is scaled by <tt>re</tt>(nearest neighbor distance). Of course, you can always modify the source code to make the equation of state function behave the way you want.
⚫	DYNAMO also has some special treatment when <math>\rho^2</math> becomes negative. This unphysical situation occurs when two atoms become too close to each other. MD++/LAMMPS does not have this special treatment so that the numerical results can be different from DYNAMO.

		⚫	DYNAMO also has some special treatment when square of the electron density <math>\overline{\rho}^2</math> becomes negative. This unphysical situation occurs when two atoms become too close to each other. MD++/LAMMPS does not have this special treatment so that the numerical results can be different from DYNAMO.

Caiwei at 07:34, 19 August 2009

2009-08-19T07:34:55Z

← Older revision		Revision as of 07:34, 19 August 2009
Line 92:		Line 92:

	Huang, Ghoniem, Wong and Baskes, Molecular dynamics determination of defect energetics in <math>\beta</math>-SiC using three representative empirical potentials, ''Model. Sim. Mater. Sci. Eng.'' '''3''', 615 (1995).		Huang, Ghoniem, Wong and Baskes, Molecular dynamics determination of defect energetics in <math>\beta</math>-SiC using three representative empirical potentials, ''Model. Sim. Mater. Sci. Eng.'' '''3''', 615 (1995).


			==Technical Note==

			Because MEAM potential is quite complex, different implementations (e.g. MD++/LAMMPS and DYNAMO) can have small differences.

			For example, in DYNAMO, the equation of state function contains the following line,

			erose=-esub(1.+x+an3x*3/(r/re))exp(-x)

			where an3 = attrac (if x > 0) and an3 = repuls (if x < 0).

			In MD++/Fortran/MEAM-Lammps/meam_setup_done.F, we can find the following line,

			c erose = -Ec * (1 + astar + a3(astar3)/(r/re)) exp(-astar)
			erose = -Ec(1+astar+(-attrac+repuls/r)(astar*3))exp(-astar)

			The first line should be the same as that in DYNAMO, but it is commented out. The second one has a different form for attrac (not divided by r). The two lines are equivalent only when attrac = 0, and when repuls is scaled by re. Of course, you can always modify the source code to make the equation of state function behave the way you want.

			DYNAMO also has some special treatment when <math>\rho^2</math> becomes negative. This unphysical situation occurs when two atoms become too close to each other. MD++/LAMMPS does not have this special treatment so that the numerical results can be different from DYNAMO.

Caiwei: /* Download files */

2009-07-23T06:06:42Z

Download files

← Older revision		Revision as of 06:06, 23 July 2009
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	mkdir -p ${MDPP}/scripts/work/meam		mkdir -p ${MDPP}/scripts/work/meam
	cd ${MDPP}/scripts/work/meam		cd ${MDPP}/scripts/work/meam
	wget http://micro.stanford.edu/mediawiki-1.11.0/images/~~Meam_test~~.tcl.txt -O ~~meam_test~~.tcl		wget http://micro.stanford.edu/mediawiki-1.11.0/images/Meam-si-c.tcl.txt -O meam-si-c.tcl
	wget http://micro.stanford.edu/mediawiki-1.11.0/images/Meamf.txt -O meamf		wget http://micro.stanford.edu/mediawiki-1.11.0/images/Meamf.txt -O meamf
	wget http://micro.stanford.edu/mediawiki-1.11.0/images/SiC.meam.txt -O SiC.meam		wget http://micro.stanford.edu/mediawiki-1.11.0/images/SiC.meam.txt -O SiC.meam

Caiwei: /* MD of Si crystal in N $\sigma$ T ensemble */

2009-07-23T05:57:18Z

MD of Si crystal in N<math>\sigma</math>T ensemble

← Older revision		Revision as of 05:57, 23 July 2009
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	A shear stress <math>\sigma_{xy}</math> = 1000 MPa is applied to the simulation cell. All other stress components are zero. The simulation cell is allowed to adjust its shape during the simulation. Three of the nine component of the <math>H</math> matrix (whose three column vectors are the repeat vectors) are fixed (specified by <tt>fixboxvec</tt>) to remove arbitrary rotation.		A shear stress <math>\sigma_{xy}</math> = 1000 MPa is applied to the simulation cell. All other stress components are zero. The simulation cell is allowed to adjust its shape during the simulation. Three of the nine component of the <math>H</math> matrix (whose three column vectors are the repeat vectors) are fixed (specified by <tt>fixboxvec</tt>) to remove arbitrary rotation.

	The 7,8,9 columns of the output file <tt>prop.out</tt> saves the instantaneous values of <math>H_{12}</math>, <math>H_{22}</math>, <math>H_{32}</math> (in angstrom). We can see that <math>H_{12}</math> changes from 0 to -0.43 in response to the applied shear stress. (The negative sign is due to the sign convention of the stress in the Parrinello-Rahman boundary condition, J. Appl. Phys. 52, 7182, 1981.) This corresponds to a shear modulus <math>C_{44}</math> of approximately 60 GPa (at T = 1000 K). <math>H_{22}</math> changes from 27.2 to 27.5 due to thermal expansion.		The 7,8,9 columns of the output file <tt>prop.out</tt> saves the instantaneous values of <math>H_{12}</math>, <math>H_{22}</math>, <math>H_{32}</math> (in angstrom). We can see that <math>H_{12}</math> changes from 0 to -0.43 in response to the applied shear stress. (The negative sign is due to the sign convention of the stress in the Parrinello-Rahman boundary condition, J. Appl. Phys. 52, 7182, 1981.) This corresponds to a shear modulus <math>C_{44}</math> of approximately 60 GPa (at T = 1000 K). We may compare this with [http://www.ioffe.rssi.ru/SVA/NSM/Semicond/Si/mechanic.html experimental data] (80 GPa at T = 300 K). <math>H_{22}</math> changes from 27.2 to 27.5 due to thermal expansion.

	The 10,11,12 columns of the output file <tt>prop.out</tt> saves the instantaneous values of <math>\sigma_{xy}</math>, <math>\sigma_{yy}</math>, <math>\sigma_{zy}</math> (in MPa). We can see that <math>\sigma_{xy}</math> eventually fluctuates around 1000 MPa as it should. The other stress components fluctuate around zero after equilibrium is reached.		The 10,11,12 columns of the output file <tt>prop.out</tt> saves the instantaneous values of <math>\sigma_{xy}</math>, <math>\sigma_{yy}</math>, <math>\sigma_{zy}</math> (in MPa). We can see that <math>\sigma_{xy}</math> eventually fluctuates around 1000 MPa as it should. The other stress components fluctuate around zero after equilibrium is reached.

Caiwei: /* MD of SiC crystal in N $\sigma$ T ensemble */

2009-07-23T05:54:52Z

MD of SiC crystal in N<math>\sigma</math>T ensemble

← Older revision		Revision as of 05:54, 23 July 2009
Line 87:		Line 87:
	</pre>		</pre>

	This simulation requires not only the standard <tt>meamf</tt> file, but also the <tt>SiC.meam</tt> file to specify the interaction between Si (species = 0) and C (species = 1) atoms. <tt>augt1 = 1</tt> in <tt>[[media:SiC.meam.txt \| SiC.meam]]</tt> (for [http://lammps.sandia.gov LAMMPS] code) is equivalent to <tt>legend = 0</tt> in <tt>[[media:meafile_SiC.txt \| meafile]]</tt> (for Baskes's <tt>dynamo</tt> code). This corresponds to the earliest version of MEAM potential where regular polynomials (instead of Legendre polynomials) are used. Other simulation settings are the same as the previous test case. From this simulation, we can estimate the shear modulus C44 to be approximately 200 GPa (at T = ~~1000~~ K).		This simulation requires not only the standard <tt>meamf</tt> file, but also the <tt>SiC.meam</tt> file to specify the interaction between Si (species = 0) and C (species = 1) atoms. <tt>augt1 = 1</tt> in <tt>[[media:SiC.meam.txt \| SiC.meam]]</tt> (for [http://lammps.sandia.gov LAMMPS] code) is equivalent to <tt>legend = 0</tt> in <tt>[[media:meafile_SiC.txt \| meafile]]</tt> (for Baskes's <tt>dynamo</tt> code). This corresponds to the earliest version of MEAM potential where regular polynomials (instead of Legendre polynomials) are used. Other simulation settings are the same as the previous test case. From this simulation, we can estimate the shear modulus C44 (at T = 1000 K) to be approximately 200 GPa. We may compare this with [http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6TWV-4TYJTXR-1&_user=145269&_rdoc=1&_fmt=&_orig=search&_sort=d&_docanchor=&view=c&_searchStrId=964933215&_rerunOrigin=google&_acct=C000012078&_version=1&_urlVersion=0&_userid=145269&md5=9f19571815707cdaee91272c4465f2ac ab initio result] (237 GPa at T = 0 K).

	The SiC/MEAM potential used in this case study is described in		The SiC/MEAM potential used in this case study is described in

Caiwei: /* MD of SiC crystal in N $\sigma$ T ensemble */

2009-07-23T05:37:48Z

MD of SiC crystal in N<math>\sigma</math>T ensemble

← Older revision		Revision as of 05:37, 23 July 2009
Line 87:		Line 87:
	</pre>		</pre>

	This simulation requires not only the standard <tt>meamf</tt> file, but also the <tt>SiC.meam</tt> file to specify the interaction between Si (species = 0) and C (species = 1) atoms. <tt>augt1 = 1</tt> in <tt>[[media:SiC.meam.txt \| SiC.meam]]</tt> (for [http://lammps.sandia.gov LAMMPS] code) is equivalent to <tt>legend = 0</tt> in <tt>[[media:meafile_SiC.txt \| meafile]]</tt> (for Baskes's <tt>dynamo</tt> code). This corresponds to the earliest version of MEAM potential where regular polynomials (instead of Legendre polynomials) are used. Other simulation settings are the same as the previous test case.		This simulation requires not only the standard <tt>meamf</tt> file, but also the <tt>SiC.meam</tt> file to specify the interaction between Si (species = 0) and C (species = 1) atoms. <tt>augt1 = 1</tt> in <tt>[[media:SiC.meam.txt \| SiC.meam]]</tt> (for [http://lammps.sandia.gov LAMMPS] code) is equivalent to <tt>legend = 0</tt> in <tt>[[media:meafile_SiC.txt \| meafile]]</tt> (for Baskes's <tt>dynamo</tt> code). This corresponds to the earliest version of MEAM potential where regular polynomials (instead of Legendre polynomials) are used. Other simulation settings are the same as the previous test case. From this simulation, we can estimate the shear modulus C44 to be approximately 200 GPa (at T = 1000 K).

	The SiC/MEAM potential used in this case study is described in		The SiC/MEAM potential used in this case study is described in

Caiwei: /* MD of Si crystal in N $\sigma$ T ensemble */

2009-07-23T05:35:21Z

MD of Si crystal in N<math>\sigma</math>T ensemble

← Older revision		Revision as of 05:35, 23 July 2009
Line 73:		Line 73:
	A shear stress <math>\sigma_{xy}</math> = 1000 MPa is applied to the simulation cell. All other stress components are zero. The simulation cell is allowed to adjust its shape during the simulation. Three of the nine component of the <math>H</math> matrix (whose three column vectors are the repeat vectors) are fixed (specified by <tt>fixboxvec</tt>) to remove arbitrary rotation.		A shear stress <math>\sigma_{xy}</math> = 1000 MPa is applied to the simulation cell. All other stress components are zero. The simulation cell is allowed to adjust its shape during the simulation. Three of the nine component of the <math>H</math> matrix (whose three column vectors are the repeat vectors) are fixed (specified by <tt>fixboxvec</tt>) to remove arbitrary rotation.

	The 7,8,9 columns of the output file <tt>prop.out</tt> saves the instantaneous values of <math>H_{12}</math>, <math>H_{22}</math>, <math>H_{32}</math> (in angstrom). We can see that <math>H_{12}</math> changes from 0 to -0.43 in response to the applied shear stress. (The negative sign is due to the sign convention of the stress in the Parrinello-Rahman boundary condition, J. Appl. Phys. 52, 7182, 1981.) <math>H_{22}</math> changes from 27.2 to 27.5 due to thermal expansion.		The 7,8,9 columns of the output file <tt>prop.out</tt> saves the instantaneous values of <math>H_{12}</math>, <math>H_{22}</math>, <math>H_{32}</math> (in angstrom). We can see that <math>H_{12}</math> changes from 0 to -0.43 in response to the applied shear stress. (The negative sign is due to the sign convention of the stress in the Parrinello-Rahman boundary condition, J. Appl. Phys. 52, 7182, 1981.) This corresponds to a shear modulus <math>C_{44}</math> of approximately 60 GPa (at T = 1000 K). <math>H_{22}</math> changes from 27.2 to 27.5 due to thermal expansion.

	The 10,11,12 columns of the output file <tt>prop.out</tt> saves the instantaneous values of <math>\sigma_{xy}</math>, <math>\sigma_{yy}</math>, <math>\sigma_{zy}</math> (in MPa). We can see that <math>\sigma_{xy}</math> eventually fluctuates around 1000 MPa as it should. The other stress components fluctuate around zero after equilibrium is reached.		The 10,11,12 columns of the output file <tt>prop.out</tt> saves the instantaneous values of <math>\sigma_{xy}</math>, <math>\sigma_{yy}</math>, <math>\sigma_{zy}</math> (in MPa). We can see that <math>\sigma_{xy}</math> eventually fluctuates around 1000 MPa as it should. The other stress components fluctuate around zero after equilibrium is reached.

	After the MD simulation, the structure is relaxed by conjugate gradient algorithm with the box fixed.		After the MD simulation, the structure is relaxed by conjugate gradient algorithm with the box fixed.


	==MD of SiC crystal in N<math>\sigma</math>T ensemble==		==MD of SiC crystal in N<math>\sigma</math>T ensemble==

Caiwei: /* MD of SiC crystal in N $\sigma$ T ensemble */

2009-07-23T05:27:47Z

MD of SiC crystal in N<math>\sigma</math>T ensemble

← Older revision		Revision as of 05:27, 23 July 2009
Line 92:		Line 92:
	The SiC/MEAM potential used in this case study is described in		The SiC/MEAM potential used in this case study is described in

	Huang, Ghoniem, Wong and Baskes, Molecular dynamics determination of defect energetics in <math>\beta</math>-SiC using three representative empirical potentials, ''Model. Sim. Mater. Sci. Eng.'' 3, 615 (1995).		Huang, Ghoniem, Wong and Baskes, Molecular dynamics determination of defect energetics in <math>\beta</math>-SiC using three representative empirical potentials, ''Model. Sim. Mater. Sci. Eng.'' '''3''', 615 (1995).

Caiwei: /* MD of SiC crystal in N $\sigma$ T ensemble */

2009-07-23T05:26:27Z

MD of SiC crystal in N<math>\sigma</math>T ensemble

← Older revision		Revision as of 05:26, 23 July 2009
Line 92:		Line 92:
	The SiC/MEAM potential used in this case study is described in		The SiC/MEAM potential used in this case study is described in

	Huang, Ghoniem, Wong and Baskes, Molecular dynamics determination of defect energetics in <math>\beta</math>-SiC using three representative empirical potentials, Model. Sim. Mater. Sci. Eng. 3, 615 (1995).		Huang, Ghoniem, Wong and Baskes, Molecular dynamics determination of defect energetics in <math>\beta</math>-SiC using three representative empirical potentials, ''Model. Sim. Mater. Sci. Eng.'' 3, 615 (1995).

Caiwei: /* MD of SiC crystal in N $\sigma$ T ensemble */

2009-07-23T05:26:08Z

MD of SiC crystal in N<math>\sigma</math>T ensemble

← Older revision		Revision as of 05:26, 23 July 2009
Line 89:		Line 89:

	This simulation requires not only the standard <tt>meamf</tt> file, but also the <tt>SiC.meam</tt> file to specify the interaction between Si (species = 0) and C (species = 1) atoms. <tt>augt1 = 1</tt> in <tt>[[media:SiC.meam.txt \| SiC.meam]]</tt> (for [http://lammps.sandia.gov LAMMPS] code) is equivalent to <tt>legend = 0</tt> in <tt>[[media:meafile_SiC.txt \| meafile]]</tt> (for Baskes's <tt>dynamo</tt> code). This corresponds to the earliest version of MEAM potential where regular polynomials (instead of Legendre polynomials) are used. Other simulation settings are the same as the previous test case.		This simulation requires not only the standard <tt>meamf</tt> file, but also the <tt>SiC.meam</tt> file to specify the interaction between Si (species = 0) and C (species = 1) atoms. <tt>augt1 = 1</tt> in <tt>[[media:SiC.meam.txt \| SiC.meam]]</tt> (for [http://lammps.sandia.gov LAMMPS] code) is equivalent to <tt>legend = 0</tt> in <tt>[[media:meafile_SiC.txt \| meafile]]</tt> (for Baskes's <tt>dynamo</tt> code). This corresponds to the earliest version of MEAM potential where regular polynomials (instead of Legendre polynomials) are used. Other simulation settings are the same as the previous test case.

			The SiC/MEAM potential used in this case study is described in

			Huang, Ghoniem, Wong and Baskes, Molecular dynamics determination of defect energetics in <math>\beta</math>-SiC using three representative empirical potentials, Model. Sim. Mater. Sci. Eng. 3, 615 (1995).

Use MEAM in MD++ - Revision history

Caiwei: /* Technical Note */

Caiwei at 07:34, 19 August 2009

Caiwei: /* Download files */

Caiwei: /* MD of Si crystal in N\sigmaT ensemble */

Caiwei: /* MD of SiC crystal in N\sigmaT ensemble */

Caiwei: /* MD of SiC crystal in N\sigmaT ensemble */

Caiwei: /* MD of Si crystal in N\sigmaT ensemble */

Caiwei: /* MD of SiC crystal in N\sigmaT ensemble */

Caiwei: /* MD of SiC crystal in N\sigmaT ensemble */

Caiwei: /* MD of SiC crystal in N\sigmaT ensemble */

Caiwei: /* MD of Si crystal in N $\sigma$ T ensemble */

Caiwei: /* MD of SiC crystal in N $\sigma$ T ensemble */

Caiwei: /* MD of SiC crystal in N $\sigma$ T ensemble */

Caiwei: /* MD of Si crystal in N $\sigma$ T ensemble */

Caiwei: /* MD of SiC crystal in N $\sigma$ T ensemble */

Caiwei: /* MD of SiC crystal in N $\sigma$ T ensemble */

Caiwei: /* MD of SiC crystal in N $\sigma$ T ensemble */