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| 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.
| | #REDIRECT [[Category:Interface pinning]] |
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| The Steinhardt-Nelson <math>Q_6</math> order parameter is used for discriminating the solid from the liquid phase and the bias potential is given by
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| <math>U_\textnormal{bias}({\mathbf{R}}) = \frac\kappa2 \left(Q_6({\mathbf{R}}) - a\right)^2 </math>
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| where <math>Q_6({\mathbf{R}})</math> is the Steinhardt-Nelson <math>Q_6</math> orientational order parameter for the current configuration <math>\mathbf{R}</math> and <math>a</math> is the desired value of the order parameter close to the order parameter of the initial two phase configuration.
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| With the bias potential enabled, the system can equilibrate while staying in the two phase configuration. From the difference of the average order parameter <math>\langle Q_6 \rangle</math> in equilibrium and the desired order
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| parameter <math>a</math> one can directly compute the difference of the chemical potential of the solid and the liquid phase:
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| <math> N(\mu_\textnormal{solid} - \mu_\textnormal{liquid}) =\kappa (Q_{6_\textnormal{solid}} - Q_{6_\textnormal{liquid}}) (\langle Q_6 \rangle - a) </math>
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| where <math>N</math> is the number of atoms in the simulation.
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| It is preferable to simulate in the super heated regime, as it is easier for the bias potential to prevent a system from melting than to prevent a system from freezing.
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| <math>Q_6(\mathbf{R})</math> needs to be continuous for computing the forces on the atoms originating from the bias potential. 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:
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| <math> w(r) = \left\{\begin{array}{cl}
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| 1 & \textnormal{for $r\leq n$}\\
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| \cfrac{
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| (f^2 - r^2)^2
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| (f^2 - 3n^2 + 2r^2)
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| } {
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| (f^2 - n^2)^3
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| } & \textnormal{for $n<r<f$}\\
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| 0 & \textnormal{for $f\leq r$}\\
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| \end{array}
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| \right.</math>
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| where <math>n</math> and <math>f</math> are the near and far fading distances given in the {{TAG|INCAR}} file respectively. A good choice for the fading range can be made from the radial distribution function <math>g(r)</math> of the crystal phase. We recommend to use the distance where <math>g(r)</math> goes below 1 after the first peak as the near fading distance <math>n</math> and the distance where <math>g(r)</math> goes above 1 again before the second peak as the far fading distance <math>f</math>. <math>g(r)</math> should be low where the fading function has a high derivative to prevent spurious stress.
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| The interface pinning method uses the <math>Np_zT</math> ensemble where the barostat only acts on the direction of the lattice that is perpendicular to the solid liquid interface. We recommend to use a Langevin thermostat and a Parrinello-Rahman barostat with lattice constraints as demonstrated in the listing below assuming a solid liquid interface perpendicular to the <math>z</math> direction.
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| The listing shows the section of the {{TAG|INCAR}} file relevant for interface pinning that was used to determine the triple point of sodium:
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| TEBEG = 400 # temperature in K
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| POTIM = 4 # timestep in fs
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| IBRION = 0 # do MD
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| ISIF = 3 # use Parrinello-Rahman barostat for the lattice
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| MDALGO = 3 # use Langevin thermostat
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| LANGEVIN_GAMMA = 1.0 # friction coef. for atomic DoFs for each species
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| LANGEVIN_GAMMA_L = 3.0 # friction coef. for the lattice DoFs
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| PMASS = 100 # mass for lattice DoFs
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| LATTICE_CONSTRAINTS = F F T # fix x&y, release z lattice dynamics
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| OFIELD_Q6_NEAR = 3.22 # fading distances for computing a continuous Q6
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| OFIELD_Q6_FAR = 4.384 # in A
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| OFIELD_KAPPA = 500 # strength of bias potential in eV/(unit of Q)^2
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| OFIELD_A = 0.15 # desired value of the Q6 order parameter
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| %TODO: ref
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| For more details on the interface pinning method see reference <ref name="pedersen2013"/>.
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| == Related Tags and Sections ==
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| {{TAG|BSE calculations}}
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| == References ==
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| <references>
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| <ref name="pedersen2013">[http://journals.aps.org/prb/abstract/10.1103/PhysRevB.88.094101 U. R. Pedersen, F. Hummel, G. Kresse, G. Kahl, and C. Dellago, Phys. Rev. B 88, 094101 (2013).]</ref>
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| </references>
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| ----
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| [[The_VASP_Manual|Contents]]
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| [[Category:INCAR]] | |