Interface pinning calculations - Revision history

Karsai: /* References */

2024-10-16T11:58:31Z

References

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	[[Category:~~VASP\|Interface pinning~~]][[Category:~~Advanced molecular-dynamics sampling~~]]		[[Category:Advanced molecular-dynamics sampling]][[Category:Howto]]

Karsai at 11:50, 16 October 2024

2024-10-16T11:50:38Z

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	[[Category:VASP\|Interface pinning]][[Category:~~Molecular~~ dynamics]]		[[Category:VASP\|Interface pinning]][[Category:Advanced molecular-dynamics sampling]]

Karsai at 11:48, 16 October 2024

2024-10-16T11:48:13Z

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	'''Interface pinning'''~~{{cite\|pedersen:prb:13}} is used to determine~~ the ~~melting point from a [[:Category: Molecular dynamics\|molecular-dynamics]] simulation of~~ the ~~interface between~~ a ~~liquid~~ and a ~~solid phase~~.		'''Interface pinning''' uses the <math>Np_zT</math> ensemble where the barostat only acts along the <math>z</math> direction.
	<~~!-- == Theory == -~~->		This ensemble uses a Langevin thermostat and a Parrinello-Rahman barostat with lattice constraints in the remaining two dimensions.
	~~The typical behavior of such a simulation is~~ to ~~freeze or melt, while~~ the ~~interface is ''pinned'' with a bias potential.~~		The solid-liquid interface must be in the <math>x</math>-<math>y</math> plane perpendicular to the action of the barostat.
	~~This potential applies an energy penalty for deviations from the desired two-phase system.~~
	~~It is preferred simulating above the melting point because~~ the ~~bias potential prevents melting better than freezing~~.

	~~The Steinhardt~~-~~Nelson~~{{~~cite~~\|~~steinhardt~~:~~prb~~:83}} order parameter <math>~~Q_6~~</math> ~~discriminates between the solid and the liquid phase~~.		Set the following tags for the '''interface pinning''' method:
	~~With the bias potential~~		;{{TAG\|OFIELD_Q6_NEAR}}: Defines the near-fading distance <math>n</math>.
			;{{TAG\|OFIELD_Q6_FAR}}: Defines the far-fading distance <math>f</math>.
			;{{TAG\|OFIELD_KAPPA}}: Defines the coupling strength <math>\kappa</math> of the bias potential.
			;{{TAG\|OFIELD_A}}: Defines the desired value of the order parameter <math>A</math>.

	~~:<math>U_\text~~{~~bias~~}~~(\mathbf~~{R}~~) = \frac\kappa2 \left(Q_6(\mathbf{R~~}~~) - A\right)^2 </math>~~		The following example {{TAG\|INCAR}} file calculates the interface pinning in sodium{{cite\|pedersen:prb:13}}:
			{{TAGBL\|TEBEG}} = 400 # temperature in K
	~~penalizes differences between the order parameter for the current configuration <math>Q_6(~~{~~\mathbf~~{R}}~~)</math> and the one for the desired interface <math>A</math>.~~		{{TAGBL\|POTIM}} = 4 # timestep in fs
	~~<math>\kappa</math> is an adjustable parameter determining the strength of the pinning.~~		{{TAGBL\|IBRION}} = 0 # run molecular dynamics
			{{TAGBL\|ISIF}} = 3 # use Parrinello-Rahman barostat for the lattice
	~~Under the action of the bias potential, the system equilibrates to the desired two-phase configuration.~~		{{TAGBL\|MDALGO}} = 3 # use Langevin thermostat
	~~An important observable is the difference between the average order parameter <math>\langle Q_6\rangle</math>~~ in ~~equilibrium and the desired order parameter <math>A</math>.~~		{{TAGBL\|LANGEVIN_GAMMA_L}} = 3.0 # friction coefficient for the lattice degree of freedoms (DoF)
	~~This difference relates to the the chemical potentials of the solid <math>\mu_\text~~{~~solid~~}~~</math> and the liquid <math>\mu_\text{liquid~~}~~</math> phase~~		{{TAGBL\|LANGEVIN_GAMMA}} = 1.0 # friction coefficient for atomic DoFs for each species
			{{TAGBL\|PMASS}} = 100 # mass for lattice DoFs
	~~:<math>~~		{{TAGBL\|LATTICE_CONSTRAINTS}} = F F T # fix x-y plane, release z lattice dynamics
	~~N(\mu_\text~~{~~solid~~} ~~- \mu_\text{liquid~~}) =		{{TAGBL\|OFIELD_Q6_NEAR}} = 3.22 # near fading distance for function w(r) in Angstrom
	~~\kappa (Q_~~{~~6,\text~~{~~solid~~}} - Q_{~~6,\text~~{~~liquid~~}}~~)(\langle Q_6 \rangle - A)~~		{{TAGBL\|OFIELD_Q6_FAR}} = 4.384 # far fading distance for function w(r) in Angstrom
	~~</math>~~		{{TAGBL\|OFIELD_KAPPA}} = 500 # strength of bias potential in eV/(unit of Q)^2
			{{TAGBL\|OFIELD_A}} = 0.15 # desired value of the Q6 order parameter
	~~where <math>N</math> is the number of atoms in the simulation.~~

	~~Computing the forces requires a differentiable <math>Q_6(\mathbf~~{R}~~)</math>~~.
	~~<!-- PLEASE REPHRASE - I did not understand this part and how it relates to Q_6(R) -->~~
	~~In the VASP implementation a smooth fading function <math>w(r)</math> is used to weight each pair of atoms at distance <math>r</math>~~ for the ~~calculation~~ of ~~the <math>Q_6~~(~~\mathbf{R},w~~)~~</math> order parameter. This fading function is given as~~

	~~:<math> w(r) = \left\~~{ ~~\begin~~{~~array~~}~~{cl~~} 1 ~~&\textrm~~{for~~} \,\, r\leq n \\~~
	~~\frac~~{~~(f^2 - r^2)^2 (f^2 - 3n^2 + 2r^2)}~~{~~(f^2 - n^2)^3~~} ~~&\textrm{for~~} ~~\,\~~, ~~n<r<f \\~~
	0 ~~&\textrm~~{~~for~~} ~~\,\,f\leq r \end{array~~}~~\right~~. ~~</math>~~

	~~<!-- is~~ w(r) ~~equivalent to (1 - t)^2(1 + 2t) with t~~ = ~~(r - n) / (f - n)? -->~~

	~~Here <math>n</math> and <math>f</math> are the near- and~~ far-fading ~~distances, respectively.~~
	~~<!-- END REPHRASE -->~~
	~~The radial distribution~~ function ~~<math>g~~(r)</~~math> of the crystal phase yields a good choice for the fading range.~~
	~~To prevent spurious stress, <math>g~~(~~r)</math> should be small where the derivative~~ of ~~<math>w(r~~)~~</math> is large.~~
	~~Set the near fading distance <math>n</math> to the distance where <math>g(r)</math> goes below 1 after the first peak~~.
	~~Set~~ the ~~far fading distance <math>f</math> to the distance where <math>g(r)</math> goes above 1 again before the second peak.~~

	== References ==		== References ==

Karsai: Removed redirect to Category:Interface pinning

2024-10-16T11:46:39Z

Removed redirect to Category:Interface pinning

← Older revision		Revision as of 11:46, 16 October 2024
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	~~#REDIRECT~~ [[Category:Interface pinning]]		'''Interface pinning'''{{cite\|pedersen:prb:13}} is used to determine the melting point from a [[:Category: Molecular dynamics\|molecular-dynamics]] simulation of the interface between a liquid and a solid phase.
			<!-- == Theory == -->
			The typical behavior of such a simulation is to freeze or melt, while the interface is ''pinned'' with a bias potential.
			This potential applies an energy penalty for deviations from the desired two-phase system.
			It is preferred simulating above the melting point because the bias potential prevents melting better than freezing.

			The Steinhardt-Nelson{{cite\|steinhardt:prb:83}} order parameter <math>Q_6</math> discriminates between the solid and the liquid phase.
			With the bias potential

			:<math>U_\text{bias}(\mathbf{R}) = \frac\kappa2 \left(Q_6(\mathbf{R}) - A\right)^2 </math>

			penalizes differences between the order parameter for the current configuration <math>Q_6({\mathbf{R}})</math> and the one for the desired interface <math>A</math>.
			<math>\kappa</math> is an adjustable parameter determining the strength of the pinning.

			Under the action of the bias potential, the system equilibrates to the desired two-phase configuration.
			An important observable is the difference between the average order parameter <math>\langle Q_6\rangle</math> in equilibrium and the desired order parameter <math>A</math>.
			This difference relates to the the chemical potentials of the solid <math>\mu_\text{solid}</math> and the liquid <math>\mu_\text{liquid}</math> phase

			:<math>
			N(\mu_\text{solid} - \mu_\text{liquid}) =
			\kappa (Q_{6,\text{solid}} - Q_{6,\text{liquid}})(\langle Q_6 \rangle - A)
			</math>

			where <math>N</math> is the number of atoms in the simulation.

			Computing the forces requires a differentiable <math>Q_6(\mathbf{R})</math>.
			<!-- PLEASE REPHRASE - I did not understand this part and how it relates to Q_6(R) -->
			In the VASP implementation a smooth fading function <math>w(r)</math> is used to weight each pair of atoms at distance <math>r</math> for the calculation of the <math>Q_6(\mathbf{R},w)</math> order parameter. This fading function is given as

			:<math> w(r) = \left\{ \begin{array}{cl} 1 &\textrm{for} \,\, r\leq n \\
			\frac{(f^2 - r^2)^2 (f^2 - 3n^2 + 2r^2)}{(f^2 - n^2)^3} &\textrm{for} \,\, n<r<f \\
			0 &\textrm{for} \,\,f\leq r \end{array}\right. </math>

			<!-- is w(r) equivalent to (1 - t)^2(1 + 2t) with t = (r - n) / (f - n)? -->

			Here <math>n</math> and <math>f</math> are the near- and far-fading distances, respectively.
			<!-- END REPHRASE -->
			The radial distribution function <math>g(r)</math> of the crystal phase yields a good choice for the fading range.
			To prevent spurious stress, <math>g(r)</math> should be small where the derivative of <math>w(r)</math> is large.
			Set the near fading distance <math>n</math> to the distance where <math>g(r)</math> goes below 1 after the first peak.
			Set the far fading distance <math>f</math> to the distance where <math>g(r)</math> goes above 1 again before the second peak.

			== References ==
			<references/>

			<noinclude>

			----

			[[Category:VASP\|Interface pinning]][[Category:Molecular dynamics]]

Karsai: Redirected page to Category:Interface pinning

2022-04-06T14:55:15Z

Redirected page to Category:Interface pinning

← Older revision		Revision as of 14:55, 6 April 2022
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	Interface Pinning is a method for finding melting points from an MD simulation of a system where the liquid and the solid phase are in contact. To prevent melting or freezing at constant pressure and constant temperature, a bias potential applies a penalty energy for deviations from the desired two phase system.		#REDIRECT [[Category:Interface pinning]]

	~~The Steinhardt-Nelson <math>Q_6</math> order parameter is used for discriminating the solid from the liquid phase and the bias potential is given by~~

	~~<math>U_\textrm{bias}(\mathbf{R}) = \frac\kappa2 \left(Q_6(\mathbf{R}) - a\right)^2 </math>~~

	where <math>Q_6({\mathbf{R}})</math> is the Steinhardt-Nelson <math>Q_6</math> orientational order parameter for the current configuration <math>\mathbf{R}</math> and <math>a</math> is the desired value of the order parameter close to the order parameter of the initial two phase configuration.

	With the bias potential enabled, the system can equilibrate while staying in the two phase configuration. From the difference of the average order parameter <math>\langle Q_6 \rangle</math> in equilibrium and the desired order
	~~parameter <math>a</math> one can directly compute the difference of the chemical potential of the solid and the liquid phase:~~

	~~<math> N(\mu_\textrm{solid} - \mu_\textrm{liquid}) =\kappa (Q_{6 \textrm{solid}} - Q_{6 \textrm{liquid}}) (\langle Q_6 \rangle - a) </math>~~

	~~where <math>N</math> is the number of atoms in the simulation.~~

	~~It is preferable to simulate in the super heated regime, as it is easier for the bias potential to prevent a system from melting than to prevent a system from freezing.~~

	<math>Q_6(\mathbf{R})</math> needs to be continuous for computing the forces on the atoms originating from the bias potential. We use a smooth fading function <math>w(r)</math> to weight each pair of atoms at distance <math>r</math> for the calculation of the <math>Q_6</math> order parameter:

	~~<math> w(r) = \left\{ \begin{array}{cl} 1 &\textrm{for} \,\, r\leq n \\~~
	~~\frac{(f^2 - r^2)^2 (f^2 - 3n^2 + 2r^2)}{(f^2 - n^2)^3} &\textrm{for} \,\, n<r<f \\~~
	~~0 &\textrm{for} \,\,f\leq r \end{array}\right. </math>~~

	where <math>n</math> and <math>f</math> are the near and far fading distances given in the {{TAG\|INCAR}} file respectively. A good choice for the fading range can be made from the radial distribution function <math>g(r)</math> of the crystal phase. We recommend to use the distance where <math>g(r)</math> goes below 1 after the first peak as the near fading distance <math>n</math> and the distance where <math>g(r)</math> goes above 1 again before the second peak as the far fading distance <math>f</math>. <math>g(r)</math> should be low where the fading function has a high derivative to prevent spurious stress.

	The interface pinning method uses the <math>Np_zT</math> ensemble where the barostat only acts on the direction of the lattice that is perpendicular to the solid liquid interface. We recommend to use a Langevin thermostat and a Parrinello-Rahman barostat with lattice constraints as demonstrated in the listing below assuming a solid liquid interface perpendicular to the <math>z</math> direction.
	~~The listing shows the section of the {{TAG\|INCAR}} file relevant for interface pinning that was used to determine the triple point of sodium:~~
	~~{{TAGBL\|TEBEG}} = 400~~ # ~~temperature in K~~
	~~{{TAGBL\|POTIM}} = 4 # timestep in fs~~
	~~{{TAGBL\|IBRION}} = 0 # do MD~~
	~~{{TAGBL\|ISIF}} = 3 # use Parrinello-Rahman barostat for the lattice~~
	~~{{TAGBL\|MDALGO}} = 3 # use Langevin thermostat~~
	~~{{TAGBL\|LANGEVIN_GAMMA}} = 1.0 # friction coef. for atomic DoFs for each species~~
	~~{{TAGBL\|LANGEVIN_GAMMA_L}} = 3.0 # friction coef. for the lattice DoFs~~
	~~{{TAGBL\|PMASS}} = 100 # mass for lattice DoFs~~
	~~{{TAGBL\|LATTICE_CONSTRAINTS}} = F F T # fix x&y, release z lattice dynamics~~
	~~{{TAGBL\|OFIELD_Q6_NEAR}} = 3.22 # fading distances for computing a continuous Q6~~
	~~{{TAGBL\|OFIELD_Q6_FAR}} = 4.384 # in Angstrom~~
	~~{{TAGBL\|OFIELD_KAPPA}} = 500 # strength of bias potential in eV/(unit of Q)^2~~
	~~{{TAGBL\|OFIELD_A}} = 0.15 # desired value of the Q6 order parameter~~
	~~For more details on the interface pinning method see reference <ref name="pedersen2013"/>.~~

	~~== Related Tags and Sections ==~~
	~~{{TAG\|OFIELD_A}},{{TAG\|OFIELD_KAPPA}},{{TAG\|OFIELD_Q6_FAR}},{{TAG\|OFIELD_Q6_NEAR}},{{TAG\|LATTICE_CONSTRAINTS}}~~

	~~{{sc\|Interface pinning\|Examples\|Examples that use this tag}}~~

	~~== References ==~~
	~~<references>~~
	~~<ref name="pedersen2013">[http://journals.aps.org/prb/abstract/10.1103/PhysRevB.88.094101 U. R. Pedersen, F. Hummel, G. Kresse, G. Kahl, and C. Dellago, Phys. Rev. B 88, 094101 (2013).]</ref>~~
	~~</references>~~
	~~----~~

	[[Category:~~Molecular Dynamics]][[Category:Interface_pinning]][[Category:Theory]][[Category:Howto~~]]

Karsai at 11:56, 12 August 2019

2019-08-12T11:56:43Z

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	{{TAGBL\|OFIELD_KAPPA}} = 500 # strength of bias potential in eV/(unit of Q)^2		{{TAGBL\|OFIELD_KAPPA}} = 500 # strength of bias potential in eV/(unit of Q)^2
	{{TAGBL\|OFIELD_A}} = 0.15 # desired value of the Q6 order parameter		{{TAGBL\|OFIELD_A}} = 0.15 # desired value of the Q6 order parameter
	~~%TODO: ref~~
	For more details on the interface pinning method see reference <ref name="pedersen2013"/>.		For more details on the interface pinning method see reference <ref name="pedersen2013"/>.

Karsai at 11:31, 12 August 2019

2019-08-12T11:31:43Z

← Older revision		Revision as of 11:31, 12 August 2019
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	{{TAGBL\|LATTICE_CONSTRAINTS}} = F F T # fix x&y, release z lattice dynamics		{{TAGBL\|LATTICE_CONSTRAINTS}} = F F T # fix x&y, release z lattice dynamics
	{{TAGBL\|OFIELD_Q6_NEAR}} = 3.22 # fading distances for computing a continuous Q6		{{TAGBL\|OFIELD_Q6_NEAR}} = 3.22 # fading distances for computing a continuous Q6
	{{TAGBL\|OFIELD_Q6_FAR}} = 4.384 # in A		{{TAGBL\|OFIELD_Q6_FAR}} = 4.384 # in Angstrom
	{{TAGBL\|OFIELD_KAPPA}} = 500 # strength of bias potential in eV/(unit of Q)^2		{{TAGBL\|OFIELD_KAPPA}} = 500 # strength of bias potential in eV/(unit of Q)^2
	{{TAGBL\|OFIELD_A}} = 0.15 # desired value of the Q6 order parameter		{{TAGBL\|OFIELD_A}} = 0.15 # desired value of the Q6 order parameter

Karsai: /* References */

2019-03-14T15:55:45Z

References

← Older revision		Revision as of 15:55, 14 March 2019
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	</references>		</references>
	----		----
	~~[[The_VASP_Manual\|Contents]]~~

	[[Category:Molecular Dynamics]][[Category:Interface_pinning]][[Category:Theory]][[Category:Howto]]		[[Category:Molecular Dynamics]][[Category:Interface_pinning]][[Category:Theory]][[Category:Howto]]

Karsai: Undo revision 7008 by Karsai (talk)

2019-03-13T15:24:45Z

Undo revision 7008 by Karsai (talk)

← Older revision		Revision as of 15:24, 13 March 2019
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	== References ==		== References ==
	<references>		<references>
	<ref name="pedersen2013">[~~https~~://~~pubs~~.~~acs~~.org/~~doi~~/~~abs~~/10.~~1021~~/~~jp9717296~~ U. R. Pedersen, F. Hummel, G. Kresse, G. Kahl, and C. Dellago, Phys. Rev. B 88, 094101 (2013).]</ref>		<ref name="pedersen2013">[http://journals.aps.org/prb/abstract/10.1103/PhysRevB.88.094101 U. R. Pedersen, F. Hummel, G. Kresse, G. Kahl, and C. Dellago, Phys. Rev. B 88, 094101 (2013).]</ref>
	</references>		</references>
	----		----

Karsai: /* References */

2019-03-13T15:24:24Z

References

← Older revision		Revision as of 15:24, 13 March 2019
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	== References ==		== References ==
	<references>		<references>
	<ref name="pedersen2013">[~~http~~://~~journals~~.~~aps~~.org/~~prb~~/~~abstract~~/10.~~1103~~/~~PhysRevB.88.094101~~ U. R. Pedersen, F. Hummel, G. Kresse, G. Kahl, and C. Dellago, Phys. Rev. B 88, 094101 (2013).]</ref>		<ref name="pedersen2013">[https://pubs.acs.org/doi/abs/10.1021/jp9717296 U. R. Pedersen, F. Hummel, G. Kresse, G. Kahl, and C. Dellago, Phys. Rev. B 88, 094101 (2013).]</ref>
	</references>		</references>
	----		----

← Older revision		Revision as of 11:31, 12 August 2019
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	{{TAGBL\|LATTICE_CONSTRAINTS}} = F F T # fix x&y, release z lattice dynamics		{{TAGBL\|LATTICE_CONSTRAINTS}} = F F T # fix x&y, release z lattice dynamics
	{{TAGBL\|OFIELD_Q6_NEAR}} = 3.22 # fading distances for computing a continuous Q6		{{TAGBL\|OFIELD_Q6_NEAR}} = 3.22 # fading distances for computing a continuous Q6
	{{TAGBL\|OFIELD_Q6_FAR}} = 4.384 # in A		{{TAGBL\|OFIELD_Q6_FAR}} = 4.384 # in Angstrom
	{{TAGBL\|OFIELD_KAPPA}} = 500 # strength of bias potential in eV/(unit of Q)^2		{{TAGBL\|OFIELD_KAPPA}} = 500 # strength of bias potential in eV/(unit of Q)^2
	{{TAGBL\|OFIELD_A}} = 0.15 # desired value of the Q6 order parameter		{{TAGBL\|OFIELD_A}} = 0.15 # desired value of the Q6 order parameter