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The r-grid file format is used by the pscf_pc and pscf_pg programs to describe fields in a spatially periodic microstructure. This format outputs the values of set of fields on the nodes of a regular mesh that covers one unit cell of a periodic structure. This mesh is the same one as that used by the pseudo-spectral algorithm for solving the modified diffusion equation.

Example: 2D Hex Phase

Here is example of a converged omega field for a hex phase of a diblock copolymer melt:

 format  1  0
dim                 
                   2
crystal_system      
           hexagonal
N_cell_param        
                   1
cell_param          
    1.7703537313E+00
group_name          
             P_6_m_m
N_monomer           
                   2
mesh              
                  24                  24
       0.340581085      19.518839883
       0.570887775      19.658020087
       1.199229419      19.984609517
       2.070864605      20.233012735
       2.929754416      19.853514300
            .                 .
            .                 .
            .                 .
       0.999219800      19.890258066
       0.570887775      19.658020087

File Format

Like other field formats, this file format contains a header section with crystallographic information followed by a data section. The header section is similar that for the symmetry adapted format, except that the last variable is an array "mesh" of integers giving the number of grid points in each direction. In this example, because it is a two-dimensional crystal (dim = 2), this array contains two numbers, both equal to 24, indicating a grid in which there are 24 grid points along each coordinate axis. To describe a hexagonal phase, we use a non-orthogonal coordinate system in which each axis is parallel to one of the Bravais lattice vectors, which in a hexagonal phase have an angle of 60 degrees between them.

The data section contains the values of fields associated with N_monomer monomer types at grid points given by

\[ \textbf{r}(n_1, \ldots, n_{D}) = \sum_{i=0}^{\textrm{D}-1} \frac{n_{i}}{N_{i}}\textbf{a}_{i} \]

where \(D\) is the dimensionality of the crystal (denoted by "dim" in the header file), \(\textbf{a}_{i}\)is a Bravais lattice vector, \(N_{i}\) is the number of grid points along direction \(i\), and \(n_{i}\) is an integer index in the range \(0 \leq n_{i} < N_{i}\).
The number of rows in the data section is equal to the total number of grid points. Each row in this section contains values of all field components at a single grid point. The number of columns is equal to the number of monomer types, so that data in column \(\alpha\), with columns numbered as \( \alpha = 0, 1, \ldots \), contains the values of the field associated with monomer type index \(\alpha\).

Grid points are listed in order using the first index \(n_{0}\) as the most rapidly varying (innermost) loop index. This order, which is the opposite of the order in which elements of an array are stored in in C/C++, is used to maintain backwards compatbility with order used in the file format defined in the older fortran version of PSCF. This is implemented for a three-dimensional crystal as a loop that can be given as pseudo-code of the form:

for (n2 = 0; n2 < N2; ++n2) {
   for (n1 = 0; n1 < N1; ++n1) {
      for (n0 = 0; n0 < N0; ++n0) {
         [Read or write data at grid point r(n0, n1, n2)]
      }
   }
}

in which capitalized symbols (N0, N1, N2) denote the number of grid points in each direction and lower case-variables (n0, n1, n2) denote indices for a particular grid point.

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