Category:Interface pinning: Difference between revisions

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Theoretical Background

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.

The Steinhardt-Nelson Q 6 {\displaystyle Q_{6}} order parameter is used for discriminating the solid from the liquid phase and the bias potential is given by

U bias ( R ) = κ 2 ( Q 6 ( R ) − a ) 2 {\displaystyle U_{{\textrm {bias}}}({\mathbf {R}})={\frac \kappa 2}\left(Q_{6}({\mathbf {R}})-a\right)^{2}}

where Q 6 ( R ) {\displaystyle Q_{6}({{\mathbf {R}}})} is the Steinhardt-Nelson Q 6 {\displaystyle Q_{6}} orientational order parameter for the current configuration R {\displaystyle {\mathbf {R}}} and a {\displaystyle a} 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 ⟨ Q 6 ⟩ {\displaystyle \langle Q_{6}\rangle } in equilibrium and the desired order parameter a {\displaystyle a} one can directly compute the difference of the chemical potential of the solid and the liquid phase:

N ( μ solid − μ liquid ) = κ ( Q 6 solid − Q 6 liquid ) ( ⟨ Q 6 ⟩ − a ) {\displaystyle N(\mu _{{\textrm {solid}}}-\mu _{{\textrm {liquid}}})=\kappa (Q_{{6{\textrm {solid}}}}-Q_{{6{\textrm {liquid}}}})(\langle Q_{6}\rangle -a)}

where N {\displaystyle N} is the number of atoms in the simulation.

How to

A comprehensive documentation on interface pinning calculations is given in Interface pinning calculations.

Contents