# Category:Interface pinning

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 $Q_{6}$ discriminates between the solid and the liquid phase. With the bias potential

$U_{\text{bias}}(\mathbf {R} )={\frac {\kappa }{2}}\left(Q_{6}(\mathbf {R} )-A\right)^{2}$ penalizes differences between the order parameter for the current configuration $Q_{6}({\mathbf {R} })$ and the one for the desired interface $A$ . $\kappa$ 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 $\langle Q_{6}\rangle$ in equilibrium and the desired order parameter $A$ . This difference relates to the the chemical potentials of the solid $\mu _{\text{solid}}$ and the liquid $\mu _{\text{liquid}}$ phase

$N(\mu _{\text{solid}}-\mu _{\text{liquid}})=\kappa (Q_{6,{\text{solid}}}-Q_{6,{\text{liquid}}})(\langle Q_{6}\rangle -A)$ where $N$ is the number of atoms in the simulation.

Computing the forces requires a differentiable $Q_{6}(\mathbf {R} )$ . In the VASP implementation a smooth fading function $w(r)$ is used to weight each pair of atoms at distance $r$ for the calculation of the $Q_{6}(\mathbf {R} ,w)$ order parameter. This fading function is given as

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

## How to

Interface pinning uses the $Np_{z}T$ ensemble where the barostat only acts along the $z$ 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 $x$ -$y$ 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 $n$ .
OFIELD_Q6_FAR
Defines the far-fading distance $f$ .
OFIELD_KAPPA
Defines the coupling strength $\kappa$ of the bias potential.
OFIELD_A
Defines the desired value of the order parameter $A$ .

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

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


## Pages in category "Interface pinning"

The following 4 pages are in this category, out of 4 total.