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Input

To run a CAC simulation, one may create/modify cac.in, in which the commands provide all input parameters for a CAC simulation.

The cac.in file, along with the potential files (embed.tab, pair.tab, and edens.tab for the EAM potential; lj.para for the LJ potential), are read by the Fortran CAC code to run the CAC simulation.

The potential files for some FCC metals are provided in the potentials directory.

EAM potential

The EAM formulations for potential energy $E$ and the force on atom $k$, $\mathbf{f}_k$, are

$$E = \frac{1}{2}\sum_i\sum_{j \atop j\neq i} V_{ij}(r_{ij}) + \sum_i F(\bar{\rho}_i)$$

$$\mathbf{f}_k = \sum_{j \atop j \neq k}\left[\frac{\partial V_{kj}(r_{kj})}{\partial r_{kj}}+\left(\frac{\partial F(\bar{\rho}_k)}{\partial \bar{\rho}_k}+\frac{\partial F(\bar{\rho}_j)}{\partial \bar{\rho}_j}\right)\frac{\partial \rho_{kj}(r_{kj})}{\partial r_{kj}}\right]\frac{\mathbf{r}_{kj}}{r_{kj}}$$

where

$$\bar{\rho}_i = \sum_{j \atop j \neq i} \rho_{ij}(r_{ij})$$

Note that the force formulation above only holds for monatomic pure materials.

The first line of each *.tab file is

N first_val last_val

where N is a positive integer that equals the number of data pair (each line starting from the second line), first_val and last_val are non-negative real numbers suggesting the first and the last datum in the first column (starting from the second line), respectively.

• In embed.tab, the first column is the unitless host electron energy $\bar{\rho}$; the second column is the embedded energy $F$, in eV.
• In pair.tab, the first column is the interatomic distance $r$, in Angstrom; the second column is the pair potential $V$, in eV.
• In edens.tab, the first column is the interatomic distance $r$, in Angstrom; the second column is the unitless local electron density $\rho$.

For example, the first few lines of potentials/eam/Ag/williams/edens.tab are

3000 0.5018316703334310 5.995011000293092
0.5018316703334310       8.9800288540000004E-002
0.5036633406668621       9.0604138970000001E-002
0.5054950110002930       9.1404200869999990E-002
0.5073266813337241       9.2200486049999988E-002

In CAC simulations, an approximation is introduced to calculate the host electron density $\bar{\rho}$ of the integration points in the coarse-grained domain. For more information, read chapter 3 of Shuozhi Xu's Ph.D. dissertation.

The readers may find EAM potential files in these database:

• NIST
• University of Edinburgh
• Other resources

Note that most of these files do not have the format that suits the CAC simulation.

LJ potential

The LJ formulation for potential energy is

$$E = \frac{1}{2}\sum_i\sum_{j\neq i} 4\epsilon \left[ \left( \frac{\sigma}{r^{ij}} \right)^{12} - \left( \frac{\sigma}{r^{ij}} \right)^6 \right]$$

where $\epsilon$ and $\sigma$ are two parameters. In the PyCAC code, the interatomic force, not the energy, is shifted such that the force goes continuously to zero at the cut-off distance $r_\mathrm{c}$, i.e., if $r < r_\mathrm{c}$, $f = f(r) - f(r_\mathrm{c})$; otherwise, $f = 0$.

In lj.para, a blank line or a line with the "#" character in column one (a comment line) is ignored; three positive real numbers ($\epsilon$, $\sigma$, and $r_\mathrm{c}$) and one non-negative real number ($r_0$) are given in any sequence, where $r_0$ is a place holder that should always be 0.0 for the LJ potential. Note that for the EAM potential, $r_0$ equals the minimum interatomic distance, i.e., the smaller first_val given in pair.tab and edens.tab.

For example, potentials/lj/Cu/kluge/lj.para reads

# parameters for the LJ potential

epsilon   0.167
sigma     2.315
rcmin     0.
rcoff     5.38784

where epsilon = $\epsilon$, sigma = $\sigma$, rcmin = $r_0$, and rcoff = $r_\mathrm{c}$.

Other files

When boolean_restart = t, a cac_in.restart file needs to be provided. This file is renamed from one of the cac_out_#.restart files, where # is a positive integer.

When restart_group_number > 0, or boolean_restart_refine = t and refine_style = group, one or more group_in_*.id files need to be provided, where * is a positive integer. These files are renamed from group_out_*_#.id files, which are created automatically when the total number of groups > 0. Note that if the # here does not match that in the cac_out_#.restart file, the information of the restart group may be incorrect.

When modify_number > 0 and at least one of the modify_style = add_atom, one or more LAMMPS data files lmp_*.dat need to be provided, where * is the id of the current modify command in cac.in.