diff --git a/examples/USER/pinning/readme.md b/examples/USER/pinning/readme.md index ee758b6f0..2071b63b4 100644 --- a/examples/USER/pinning/readme.md +++ b/examples/USER/pinning/readme.md @@ -1,49 +1,68 @@ -This example demonstrate using a bias potential that can be used to study solid-liquid transitions with the interface pinning method. This is done by adding a harmonic potential to the Hamiltonian that bias the system towards two-phase configurations. +This example demonstrate using a bias potential that can be used to study solid-liquid transitions +with the interface pinning method. This is done by adding a harmonic potential to the Hamiltonian +that bias the system towards two-phase configurations. - U_bias = 0.5*k*(Q-a)^2 + U_bias = 0.5*K*(Q-a)^2 -The bias field couple to an order-parameter of crystallinity Q -This implimentation use long-range order: Q=|rho_k|, where rho_k is the collective density field of the wave-vector k. +The bias field couple to an order-parameter of crystallinity Q. The implementation use long-range order: + + Q=|rho_k|, + +where rho_k is the collective density field of the wave-vector k. +For future reference we note that the structure factor S(k) is given by the variance of the collective density field: + + S(k)=|rho_k|^2. # Reference -[Ulf R. Pedersen, J. Chem. Phys. 139, 104102 (2013)] -Please visit +It is recommended to get familiar with the interface pinning method by reading: + + [Ulf R. Pedersen, J. Chem. Phys. 139, 104102 (2013)] + +A detailed bibliography is provided at + urp.dk/interface_pinning.htm -for a detailed bibliography. -# Use +# Use of rhok fix - fix [name] [groupID] rhok [nx] [ny] [nz] [spring-constant] [anchor-point] +For this example we will be using the rhok fix. -include a harmonic bias potential U_bias=0.5*k*(|rho_k|-a)^2 to the force calculation. -The elements of the wave-vector rho_k is k_x = (2 pi / L_x) * n_x, k_y = (2 pi / L_y) * n_y and k_z = (2 pi / L_z) * n_z. + fix [name] [groupID] rhok [nx] [ny] [nz] [K] [a] -# The Interface Pinning method for studying melting transitions -We will use the interface pinning method to study melting of the Lennard-Jones system +This fix include a harmonic bias potential U_bias=0.5*K*(|rho_k|-a)^2 to the force calculation. +The elements of the wave-vector k is given by the nx, ny and nz input: + + k_x = (2 pi / L_x) * n_x, k_y = (2 pi / L_y) * n_y and k_z = (2 pi / L_z) * n_z. + +We will use a k vector that correspond to a Bragg peak. + +# The Interface Pinning method for studying melting transitions of the Lennard-Jones (LJ) system + +We will use the interface pinning method to study melting of the LJ system at temperature 0.8 and pressure 2.185. This is a coexistence state-point, and the method -can be used to show this. The present directory contains the input files: +can be used to show this. The present directory contains the input files that we will use: - crystal.lmp - setup.lmp - pinning.lmp + in.crystal + in.setup + in.pinning -1. First we will determine the density of the crystal with the LAMMPS input file crystal.lmp. - From the output we get that the average density after equbriliation is 0.9731. - We need this density to ensure hydrostatic pressure when in a two-phase simulation. +1. First we will determine the density of the crystal with the LAMMPS input file in.crystal. + From the output we get that the average density after equilibration is 0.9731. + We need this density to ensure hydrostatic pressure when in a two-phase simulation. -2. Next, we setup a two-phase configuration using setup.lmp. +2. Next, we setup a two-phase configuration using in.setup. -3. Finally, we run a two-phase simulation with the bias-field applied using pinning.lmp. - The last coulmn in the output show |rho_k|. We note that after a equbriliation period - the value fluctuates aroung the anchor point (a) -- showing that this is indeed a coexistence - state point. +3. Finally, we run a two-phase simulation with the bias-field applied using in.pinning. + The last column in the output show |rho_k|. We note that after a equilibration period + the value fluctuates around the anchor point (a) -- showing that this is indeed a coexistence + state point. -The reference [J. Chem. Phys. 139, 104102 (2013)] gives details on using the method to find coexitence state points, -and the referecee [J. Chem. Phys. 142, 044104 (2015)] show how the crystal growth rate can be computed. +The reference [J. Chem. Phys. 139, 104102 (2013)] gives details on using the method to find coexistence state points, +and the reference [J. Chem. Phys. 142, 044104 (2015)] show how the crystal growth rate can be computed from fluctuations. That method have been experienced to be most effective in the slightly super-heated regime above the melting temperature. # Contact + Ulf R. Pedersen http://www.urp.dk ulf AT urp.dk