|
|
| (17 intermediate revisions by 3 users not shown) |
| Line 1: |
Line 1: |
| '''Interface pinning''' is a method for finding melting points from a [[:Category:Molecular dynamics|molecular-dynamics]] simulation of a system where the liquid and the solid phase are in contact.
| |
|
| |
|
| == Theory ==
| |
| To prevent melting or freezing at constant pressure and constant temperature, a bias potential applies penalty energy for deviations from the desired two-phase system.
| |
|
| |
| The Steinhardt-Nelson order parameter <math>Q_6</math> is used for discriminating the solid from the liquid phase and the bias potential is given by
| |
|
| |
| :<math>U_\textrm{bias}(\mathbf{R}) = \frac\kappa2 \left(Q_6(\mathbf{R}) - a\right)^2 </math>
| |
|
| |
| where <math>Q_6({\mathbf{R}})</math> is the <math>Q_6</math> 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.
| |
|
| |
| With the bias potential enabled, the system can equilibrate while staying in the two-phase configuration. From the difference between 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} 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<r<f \\
| |
| 0 &\textrm{for} \,\,f\leq r \end{array}\right. </math>
| |
|
| |
| Here <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.
| |
|
| |
| == How to ==
| |
|
| |
| 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. This uses a Langevin thermostat and a Parrinello-Rahman barostat with lattice constraints in the remaining two dimensions.
| |
|
| |
| The following variables need to be set for the '''interface pinning''' method:
| |
| *{{TAG|OFIELD_Q6_NEAR}}: This tag defines the near-fading distance <math>n</math>.
| |
| *{{TAG|OFIELD_Q6_FAR}}: This tag defines the far-fading distance <math>f</math>.
| |
| *{{TAG|OFIELD_KAPPA}}: This tag defines the coupling strength <math>\kappa</math> of the bias potential.
| |
| *{{TAG|OFIELD_A}}: This tag defines the desired value of the order parameter <math>a</math>.
| |
|
| |
| The following is a sample {{TAG|INCAR}} file for interface pinning of sodium{{cite|pedersen:prb:13}}:
| |
| {{TAGBL|TEBEG}} = 400 # temperature in K
| |
| {{TAGBL|POTIM}} = 4 # timestep in fs
| |
| {{TAGBL|IBRION}} = 0 # do MD
| |
| {{TAGBL|ISIF}} = 3 # use Parrinello-Rahman barostat for the lattice
| |
| {{TAGBL|MDALGO}} = 3 # use Langevin thermostat
| |
| {{TAGBL|LANGEVIN_GAMMA}} = 1.0 # friction coef. for atomic DoFs for each species
| |
| {{TAGBL|LANGEVIN_GAMMA_L}} = 3.0 # friction coef. for the lattice DoFs
| |
| {{TAGBL|PMASS}} = 100 # mass for lattice DoFs
| |
| {{TAGBL|LATTICE_CONSTRAINTS}} = F F T # fix x&y, release z lattice dynamics
| |
| {{TAGBL|OFIELD_Q6_NEAR}} = 3.22 # fading distances for computing a continuous Q6
| |
| {{TAGBL|OFIELD_Q6_FAR}} = 4.384 # 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
| |
|
| |
| == References ==
| |
| <references/>
| |
|
| |
| <noinclude>
| |
|
| |
| ----
| |
| [[The_VASP_Manual|Contents]]
| |
|
| |
| [[Category:VASP|Interface Pinning]][[Category:Molecular Dynamics]]
| |
