Interface pinning calculations: Difference between revisions

Latest revision as of 11:58, 16 October 2024

Interface pinning uses the $Np_zT$ 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^[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

↑ U. R. Pedersen, F. Hummel, G. Kresse, G. Kahl, and C. Dellago, Phys. Rev. B 88, 094101 (2013).

[pedersen:prb:13-1] U. R. Pedersen, F. Hummel, G. Kresse, G. Kahl, and C. Dellago, Phys. Rev. B 88, 094101 (2013).

[1]

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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.
+'''Interface pinning''' uses the <math>Np_zT</math> ensemble where the barostat only acts along the <math>z</math> 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 <math>x</math>-<math>y</math> plane perpendicular to the action of the barostat.
-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
+Set the following tags for the '''interface pinning''' method:
+;{{TAG|OFIELD_Q6_NEAR}}: Defines the near-fading distance <math>n</math>.
+;{{TAG|OFIELD_Q6_FAR}}: Defines the far-fading distance <math>f</math>.
+;{{TAG|OFIELD_KAPPA}}: Defines the coupling strength <math>\kappa</math> of the bias potential.
+;{{TAG|OFIELD_A}}: Defines the desired value of the order parameter <math>A</math>.
-<math>U_\textrm{bias}(\mathbf{R}) = \frac\kappa2 \left(Q_6(\mathbf{R}) - a\right)^2 </math>
+The following example {{TAG|INCAR}} file calculates the interface pinning in sodium{{cite|pedersen:prb:13}}:
+ {{TAGBL|TEBEG}} = 400                   # temperature in K
+ {{TAGBL|POTIM}} = 4                     # timestep in fs
+ {{TAGBL|IBRION}} = 0                    # run molecular dynamics
+ {{TAGBL|ISIF}} = 3                      # use Parrinello-Rahman barostat for the lattice
+ {{TAGBL|MDALGO}} = 3                    # use Langevin thermostat
+ {{TAGBL|LANGEVIN_GAMMA_L}} = 3.0        # friction coefficient for the lattice degree of freedoms (DoF)
+ {{TAGBL|LANGEVIN_GAMMA}} = 1.0          # friction coefficient for atomic DoFs for each species
+ {{TAGBL|PMASS}} = 100                   # mass for lattice DoFs
+ {{TAGBL|LATTICE_CONSTRAINTS}} = F F T   # fix x-y plane, release z lattice dynamics
+ {{TAGBL|OFIELD_Q6_NEAR}} = 3.22         # near fading distance for function w(r) in Angstrom
+ {{TAGBL|OFIELD_Q6_FAR}} = 4.384         # far fading distance for function w(r) in Angstrom
+ {{TAGBL|OFIELD_KAPPA}} = 500            # strength of bias potential in eV/(unit of Q)^2
+ {{TAGBL|OFIELD_A}} = 0.15               # desired value of the Q6 order parameter
-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.
+== References ==
+<references/>
-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
-parameter <math>a</math> one can directly compute the difference of the chemical potential of the solid and the liquid phase:
-<math> N(\mu_\textrm{solid} - \mu_\textrm{liquid}) =\kappa (Q_{6 \textrm{solid}} - Q_{6 \textrm{liquid}}) (\langle Q_6 \rangle - a) </math>
-where <math>N</math> is the number of atoms in the simulation.
-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.
-<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:
-<math> w(r) = \left\{\begin{array}{cl}
+<noinclude>
-& \textrm{for $r\leq n$}
-                        \cfrac{
-                                (f^2 - r^2)^2
-                                (f^2 - 3n^2 + 2r^2)
-                        } {
-                                (f^2 - n^2)^3
-                        } & \textrm{for $n<r<f$}
-& \textrm{for $f\leq r$}
-                \end{array}
-        \right.</math>
-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.
-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.
-The listing shows the section of the {{TAG|INCAR}} file relevant for interface pinning that was used to determine the triple point of sodium:
- TEBEG = 400              # temperature in K
- POTIM = 4                # timestep in fs
- IBRION = 0             # do MD
- ISIF = 3                 # use Parrinello-Rahman barostat for the lattice
- MDALGO = 3               # use Langevin thermostat
- LANGEVIN_GAMMA = 1.0   # friction coef. for atomic DoFs for each species
- LANGEVIN_GAMMA_L = 3.0   # friction coef. for the lattice DoFs
- PMASS = 100               # mass for lattice DoFs
- LATTICE_CONSTRAINTS = F F T   # fix x&y, release z lattice dynamics
- OFIELD_Q6_NEAR = 3.22  # fading distances for computing a continuous Q6
- OFIELD_Q6_FAR = 4.384  # in A
- OFIELD_KAPPA = 500     # strength of bias potential in eV/(unit of Q)^2
- OFIELD_A = 0.15        # desired value of the Q6 order parameter
- %TODO: ref
-For more details on the interface pinning method see reference <ref name="pedersen2013"/>.
-== Related Tags and Sections ==
-{{TAG|BSE calculations}}
-== References ==
-<references>
-<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>
-</references>
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-[[The_VASP_Manual|Contents]]
-[[Category:INCAR]]
+[[Category:Advanced molecular-dynamics sampling]][[Category:Howto]]