Category:Interface pinning: Difference between revisions

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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


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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</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 \\

Revision as of 12:22, 7 April 2022

Interface pinning[1] is used to determine the melting point from a molecular-dynamics simulation of the interface between a liquid and a solid phase. 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[2] order parameter discriminates between the solid and the liquid phase. With the bias potential

penalizes differences between the order parameter for the current configuration and the one for the desired interface . 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 in equilibrium and the desired order parameter . This difference relates to the the chemical potentials of the solid and the liquid phase

where is the number of atoms in the simulation.

Computing the forces requires a differentiable . We use a smooth fading function to weight each pair of atoms at distance for the calculation of the order parameter


Here and are the near- and far-fading distances given in the INCAR file respectively. The radial distribution function of the crystal phase yields a good choice for the fading range. To prevent spurious stress, should be small where the derivative of is large. Set the near fading distance to the distance where goes below 1 after the first peak. Set the far fading distance to the distance where goes above 1 again before the second peak.

How to

Interface pinning uses the ensemble where the barostat only acts along the direction. This 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 - plane perpendicular to the action of the barostat.

Set the following tags for the interface pinning method:

OFIELD_Q6_NEAR
Defines the near-fading distance .
OFIELD_Q6_FAR
Defines the far-fading distance .
OFIELD_KAPPA
Defines the coupling strength of the bias potential.
OFIELD_A
Defines the desired value of the order parameter .

The following example INCAR file calculates the interface pinning in sodium[1]:

TEBEG = 400                   # temperature in K
POTIM = 4                     # timestep in fs
IBRION = 0                    # run molecular dynamics
ISIF = 3                      # use Parrinello-Rahman barostat for the lattice
MDALGO = 3                    # use Langevin thermostat
LANGEVIN_GAMMA_L = 3.0        # friction coefficient for the lattice degree of freedoms (DoF)
LANGEVIN_GAMMA = 1.0          # friction coefficient for atomic DoFs for each species
PMASS = 100                   # mass for lattice DoFs
LATTICE_CONSTRAINTS = F F T   # fix x-y plane, release z lattice dynamics
OFIELD_Q6_NEAR = 3.22         # near fading distance for function w(r) in Angstrom
OFIELD_Q6_FAR = 4.384         # far fading distance for function w(r) in Angstrom
OFIELD_KAPPA = 500            # strength of bias potential in eV/(unit of Q)^2
OFIELD_A = 0.15               # desired value of the Q6 order parameter

References



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