Category:Interface pinning: Difference between revisions
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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. | |||
== Theory == | == Theory == | ||
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. | |||
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 | 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 |
Revision as of 15:51, 6 April 2022
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.
Theory
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.
The Steinhardt-Nelson order parameter Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): Q_{6} is used for discriminating the solid from the liquid phase and the bias potential is given by
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): U_{{\textrm {bias}}}({\mathbf {R}})={\frac \kappa 2}\left(Q_{6}({\mathbf {R}})-a\right)^{2}
where Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): Q_{6}({{\mathbf {R}}}) is the Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): Q_{6} order parameter for the current configuration Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): {\mathbf {R}} and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): a 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 of the average order parameter Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): \langle Q_{6}\rangle in equilibrium and the desired order parameter Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): a one can directly compute the difference of the chemical potential of the solid and the liquid phase:
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): N(\mu _{{\textrm {solid}}}-\mu _{{\textrm {liquid}}})=\kappa (Q_{{6{\textrm {solid}}}}-Q_{{6{\textrm {liquid}}}})(\langle Q_{6}\rangle -a)
where Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): N 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.
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): Q_{6}({\mathbf {R}}) needs to be continuous for computing the forces on the atoms originating from the bias potential. We use a smooth fading function Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): w(r) to weight each pair of atoms at distance Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): r for the calculation of the Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): Q_{6} order parameter
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): 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.
Here Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): n and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): f are the near- and far-fading distances given in the INCAR file respectively. A good choice for the fading range can be made from the radial distribution function Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): g(r) of the crystal phase. We recommend to use the distance where Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): g(r) goes below 1 after the first peak as the near fading distance Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): n and the distance where Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): g(r) goes above 1 again before the second peak as the far fading distance Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): f . Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): g(r) should be low where the fading function has a high derivative to prevent spurious stress.
How to
The interface pinning method uses the Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): Np_{z}T 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:
- OFIELD_Q6_NEAR: This tag defines the near-fading distance Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): n .
- OFIELD_Q6_FAR: This tag defines the far-fading distance Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): f .
- OFIELD_KAPPA: This tag defines the coupling strength Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): \kappa of the bias potential.
- OFIELD_A: This tag defines the desired value of the order parameter Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): a .
The following is a sample INCAR file for interface pinning of sodium[1]:
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 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
Pages in category "Interface pinning"
The following 4 pages are in this category, out of 4 total.