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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 for two differences:

The last variable in the header is an array "mesh" of integers giving the number of grid points in each direction.
The space_group parameter is optional element of the header for an r-grid field file.

In this example, because it is a two-dimensional crystal (dim = 2), the mesh parameter 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 group_name parameter, which is present in the above example, is an optional element of r-grid file. This parameter may be included to document that the field is invariant under a known space group, though the r-grid file format does not impose any space group symmetry. When a w-field in is read from an r-grid file by the READ_W_GRID command, however, the presence of any group_name parameter is actually ignored, and the field is treated as if it has no nontrivial space group symmetry.

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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