Category:Interface pinning - Revision history

Karsai: Blanked the page

2024-10-16T11:48:23Z

Blanked the page

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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.
	~~<!-- == 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.~~

	~~== How to ==~~

	~~'''Interface pinning''' uses the <math>Np_zT</math> ensemble where the barostat only acts along the <math>z</math> direction.~~
	~~This ensemble uses a Langevin thermostat and a Parrinello-Rahman barostat with lattice constraints in the remaining two dimensions.~~
	~~The solid-liquid interface must be in the <math>x</math>-<math>y</math> plane perpendicular to the action of the barostat.~~

	~~Set the following tags for the '''interface pinning''' method:~~
	~~;{{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>.~~

	~~The following example {{TAG\|INCAR}} file calculates the interface pinning in sodium{{cite\|pedersen:prb:13}}:~~
	~~{{TAGBL\|TEBEG}} = 400 # temperature in K~~
	~~{{TAGBL\|POTIM}} = 4 # timestep in fs~~
	~~{{TAGBL\|IBRION}} = 0 # run molecular dynamics~~
	~~{{TAGBL\|ISIF}} = 3 # use Parrinello-Rahman barostat for the lattice~~
	~~{{TAGBL\|MDALGO}} = 3 # use Langevin thermostat~~
	~~{{TAGBL\|LANGEVIN_GAMMA_L}} = 3.0 # friction coefficient for the lattice degree of freedoms (DoF)~~
	~~{{TAGBL\|LANGEVIN_GAMMA}} = 1.0 # friction coefficient for atomic DoFs for each species~~
	~~{{TAGBL\|PMASS}} = 100 # mass for lattice DoFs~~
	~~{{TAGBL\|LATTICE_CONSTRAINTS}} = F F T # fix x-y plane, release z lattice dynamics~~
	~~{{TAGBL\|OFIELD_Q6_NEAR}} = 3.22 # near fading distance for function w(r) in Angstrom~~
	~~{{TAGBL\|OFIELD_Q6_FAR}} = 4.384 # far fading distance for function w(r) 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~~

	~~== References ==~~
	~~<references/>~~

	~~<noinclude>~~

	~~----~~

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

Karsai: /* References */

2023-10-18T10:25:15Z

References

← Older revision		Revision as of 10:25, 18 October 2023
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	----		----
	~~[[The_VASP_Manual\|Contents]]~~

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

Huebsch at 14:41, 7 April 2022

2022-04-07T14:41:00Z

← Older revision		Revision as of 14:41, 7 April 2022
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	[[The_VASP_Manual\|Contents]]		[[The_VASP_Manual\|Contents]]

	[[Category:VASP\|Interface ~~Pinning~~]][[Category:Molecular ~~Dynamics~~]]		[[Category:VASP\|Interface pinning]][[Category:Molecular dynamics]]

Karsai: /* How to */

2022-04-07T12:30:42Z

How to

← Older revision		Revision as of 12:30, 7 April 2022
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	'''Interface pinning''' uses the <math>Np_zT</math> ensemble where the barostat only acts along the <math>z</math> direction.		'''Interface pinning''' uses the <math>Np_zT</math> ensemble where the barostat only acts along the <math>z</math> direction.
	This uses a Langevin thermostat and a Parrinello-Rahman barostat with lattice constraints in the remaining two dimensions.		This ensemble uses a Langevin thermostat and a Parrinello-Rahman barostat with lattice constraints in the remaining two dimensions.
	The solid-liquid interface must be in the <math>x</math>-<math>y</math> plane perpendicular to the action of the barostat.		The solid-liquid interface must be in the <math>x</math>-<math>y</math> plane perpendicular to the action of the barostat.

Karsai at 12:28, 7 April 2022

2022-04-07T12:28:21Z

← Older revision		Revision as of 12:28, 7 April 2022
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	Computing the forces requires a differentiable <math>Q_6(\mathbf{R})</math>.		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) -->		<!-- PLEASE REPHRASE - I did not understand this part and how it relates to Q_6(R) -->
	In the VASP implementation 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		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 \\		:<math> w(r) = \left\{ \begin{array}{cl} 1 &\textrm{for} \,\, r\leq n \\

Karsai at 12:26, 7 April 2022

2022-04-07T12:26:44Z

← Older revision		Revision as of 12:26, 7 April 2022
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	Computing the forces requires a differentiable <math>Q_6(\mathbf{R})</math>.		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) -->		<!-- PLEASE REPHRASE - I did not understand this part and how it relates to Q_6(R) -->
	~~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(\mathbf{R},w)</math> order parameter		In the VASP implementation 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

	:<math> w(r) = \left\{ \begin{array}{cl} 1 &\textrm{for} \,\, r\leq n \\		:<math> w(r) = \left\{ \begin{array}{cl} 1 &\textrm{for} \,\, r\leq n \\

Karsai at 12:25, 7 April 2022

2022-04-07T12:25:37Z

← Older revision		Revision as of 12:25, 7 April 2022
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	<!-- is w(r) equivalent to (1 - t)^2(1 + 2t) with t = (r - n) / (f - n)? -->		<!-- 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 ~~given in the {{TAG\|INCAR}} file~~ respectively.		Here <math>n</math> and <math>f</math> are the near- and far-fading distances, respectively.
	<!-- END REPHRASE -->		<!-- END REPHRASE -->
	The radial distribution function <math>g(r)</math> of the crystal phase yields a good choice for the fading range.		The radial distribution function <math>g(r)</math> of the crystal phase yields a good choice for the fading range.

Karsai at 12:24, 7 April 2022

2022-04-07T12:24:02Z

← Older revision		Revision as of 12:24, 7 April 2022
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	Computing the forces requires a differentiable <math>Q_6(\mathbf{R})</math>.		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) -->		<!-- PLEASE REPHRASE - I did not understand this part and how it relates to Q_6(R) -->
	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[w(r)]</math> order parameter		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(\mathbf{R},w)</math> order parameter

	:<math> w(r) = \left\{ \begin{array}{cl} 1 &\textrm{for} \,\, r\leq n \\		:<math> w(r) = \left\{ \begin{array}{cl} 1 &\textrm{for} \,\, r\leq n \\

Karsai at 12:22, 7 April 2022

2022-04-07T12:22:29Z

← Older revision		Revision as of 12:22, 7 April 2022
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	Under the action of the bias potential, the system equilibrates to the desired two-phase configuration.		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>.		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		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

Line 26:		Line 26:
	Computing the forces requires a differentiable <math>Q_6(\mathbf{R})</math>.		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) -->		<!-- PLEASE REPHRASE - I did not understand this part and how it relates to Q_6(R) -->
	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		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[w(r)]</math> order parameter

	:<math> w(r) = \left\{ \begin{array}{cl} 1 &\textrm{for} \,\, r\leq n \\		:<math> w(r) = \left\{ \begin{array}{cl} 1 &\textrm{for} \,\, r\leq n \\

Karsai at 11:35, 7 April 2022

2022-04-07T11:35:48Z

← Older revision		Revision as of 11:35, 7 April 2022
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	It is preferred simulating above the melting point because the bias potential prevents melting better than freezing.		It is preferred simulating above the melting point because the bias potential prevents melting better than freezing.

	The Steinhardt-Nelson order parameter <math>Q_6</math> discriminates between the solid and the liquid phase.		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		With the bias potential