Karsai: /* References */

2024-10-16T11:52:15Z

References

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

Karsai: /* References */

2024-10-16T11:51:53Z

References

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

Karsai: /* References */

2024-10-16T11:51:00Z

References

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	----		----

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

Karsai: Removed redirect to Category:Interface pinning

2024-10-16T11:47:58Z

Removed redirect to Category:Interface pinning

← Older revision		Revision as of 11:47, 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: Changed redirect target from Interface pinning calculations to Category:Interface pinning

2022-04-07T15:29:57Z

Changed redirect target from Interface pinning calculations to Category:Interface pinning

← Older revision		Revision as of 15:29, 7 April 2022
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	#REDIRECT [[Interface pinning ~~calculations~~]]		#REDIRECT [[Category:Interface pinning]]

Karsai: Karsai moved page Interface pinning to Interface pinning calculations

2019-02-15T13:36:47Z

Karsai moved page Interface pinning to Interface pinning calculations

New page

#REDIRECT [[Interface pinning calculations]]

Interface pinning - Revision history

Karsai: /* References */

Karsai: /* References */

Karsai: /* References */

Karsai: Removed redirect to Category:Interface pinning

Karsai: Changed redirect target from Interface pinning calculations to Category:Interface pinning

Karsai: Karsai moved page Interface pinning to Interface pinning calculations