One dimension domains (pscf_1d) (Prev) Command Files (Next)
The Domain block of the parameter file for pscf_pc or pscf_pg contains information about the periodic unit cell and discretization mesh for a D-dimensional periodic structure. Here D is the dimension of space specified by the argument of the "-d" command line option used to invoked pscf_pc or pscf_pg.
Example
An example of a Domain block used for an SCFT calculation for a three dimensional (D=3) gyroid structure is shown below:
The groupName parameter is an optional, as discussed below.
Parameter file format
The format for the Domain block used by these programs is
Values for all of the parameters in the Domain block are immutable after the parameter file block has been read.
mesh
The value of the variable "mesh" is a vector of integers on a single line that specify the number of grid points along each direction of the uniform spatial mesh used to discretize fields within each unit cell of the crystal. The number of integers is equal to the dimensionality D of the periodic unit cell. The format is
where N[i] is the number of grid points along axis number i, for i = 0 ,..., D-1.
The dimensions N[0], ... , N[D-1] of the spatial mesh are initialized to in the parameter file and are immutable thereafter. The only way to run simulations with different mesh sizes is to run pscf_pc and pscf_pg multiple times using different parameters files with different values for the mesh parameter.
lattice
The value of the parameter "lattice" is given by string that specifies the desired crystal system type. The set of allowed values for this string depends on the dimensionality of space. There are 7 allowed values of the lattice string for a 3D structure, corresponding to the 7 types of 3D crystal system, with names given by the strings "cubic", "tetragonal", "orthorhombic", "hexagonal", "rhombohedral", "monoclinic", and "triclinic". The allowed values for a 2D system include "square", "rectangular", "hexagonal" "rhombic" and "oblique". There is only one allowed lattice system for a 1D crystal, which is referred to as "lamellar". A more detailed discussion of each of the possible lattice systems is given in a separate page that documents conventions for unit cells.
The required lattice system parameter is initialized by the parameter file and is immutable thereafter.
groupName
The "spaceGroup" is an optional string parameter that, if present, identifies the crystallographic space group for the structure of interest. Each allowed value of the groupName string corresponds to a modified version of the name of a space group, as listed in the international tables of crystallography. In the above example, the groupName string I_m_-3_m is a modified form of the name \(Im\overline{3}m\) for the space group for a BCC lattice. PSCF uses a set of conventions for converting an international table symbol for a space group into a text string that involve insertion of underbars between logical elements and the use of - sign to represent an overbar, among other conventions.
Allowed identifiers for crystallographic space groups are listed and discussed in more detail here.
The space group identifier may not be initialized or modified after the PSCF parameter file is read. SCFT calculations for structures with different space groups must thus be performed by invoking pscf_pc or pscf_pg with different parameter files.
Space groups and symmetry-adapted bases
If the optional groupName identifer is present, it is used construct a space group (i.e., a set of symmetry operations) and a symmetry-adapted Fourier basis. A symmetry-adapted Fourier basis is a set of functions of position that are all eigenfunctions of the Laplacian and are all invariant under all symmetry operations in the specified space group. This basis can be used to expand functions that are required to exhibit a specified space group symmetry.
The groupName parameter should only be used for SCFT calculations, to search for a solution of specified space group symmetry. This parameter must be present to enable reading or writing of fields in a symmetry adapted basis format, and to enable use of any SCFT iteration algorithm that imposes a space group symmetry, such as the AmIteratorBasis that is used by default by both pscf_pc and pscf_pg.
The groupName parameter should be omitted from parameter files that are used to initialize stochastic field theoretic simulations. The fields generated during the course of such a simulation generally do not exactly preserve any nontrivial symmetry.
Unit cell parameters
To completely describe the Bravais lattice for a crystal with a known crystal system, one must assign values to a list of unit cell parameters that give the lengths of the edges of the unit cell and (for some lattice systems) sometimes angles between some of these edges. The number of unit cell parameters required to describe a unit cell is different for different lattice system. For example, a 3D cubic crystal can be described using a single parameter that gives the length of any edge of a simple cubic unit cell. Three parameters are required to describe an orthorhombic unit cell, to specify lengths of three orthogonal Bravais basis vectors, while 6 parameters are required for a triclinic unit cell, to specify 3 independent unit cell lengths and 3 angles. The unit cell parameters for each unit cell type are stored internally in an array that lists the required parameters in some pre-specified order. Conventions for the meaning of the required parameters and the order in which they are listed are described for each crystal system in a separate page of documentation about unit cells.
Values for unit cell parameters are specified within the header section of files that describe periodic chemical potential fields (w-fields) or monomer concentration fields (c-cields). Values for these parameters are not, however, provided in the parameter file. Unit cell parameters are thus normally first assigned values during execution of the first command in the command file that causes the program to set the chemical potential fields for the program, by reading these fields from a file. Unit cell parameters can also be set explicitly using a command named SET_UNIT_CELL users may invoke to manually set or reset the unit cell parameter values at any point during processing of a command file.
Unit cell parameters for a crystal are changed many times during SCFT calculations for systems with flexible unit cells, in which the unit cell parameters are adjusted so as to minimize the free energy density. At the end of such a calculation, converged values for the optimal unit cell parameters are normally output within the header of a file that contains the converged w-fields.
The algorithm used by PSCF to construct a symmetry-adapted Four basis requires knowledge of a set of initial values for the unit cell parameters. If the Domain block of the parameter file contains a space group name, a symmetry-adapted Fourier basis for that space group will be constructed immediately after the first time that unit cell parameters are assigned values. This may occur either the first time that the w-fields are set by reading these fields from a field file or the first time the SET_UNIT_CELL command is invoked, whichever occurs first.
See also:
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