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Interface pinning 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 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 . In the VASP implementation a smooth fading function is used to weight each pair of atoms at distance for the calculation of the order parameter. This fading function is given as
Here and are the near- and far-fading distances, 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.
Interface pinning uses the ensemble where the barostat only acts along the 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 - plane perpendicular to the action of the barostat.
Set the following tags for the interface pinning method:
- Defines the near-fading distance .
- Defines the far-fading distance .
- Defines the coupling strength of the bias potential.
- Defines the desired value of the order parameter .
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