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 in the parameter file and are immutable thereafter. To perform simulations with different mesh sizes, one must thus run pscf_pc or 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. The possible lattice systems for D=1, 2, 3 are discussed on separate page that documents conventions for
A brief summary is given below.
For 3D systems, there are 7 allowed values of the lattice string:
- cubic
- tetragonal
- orthorhombic
- hexagonal
- rhombohedral
- monoclinic
- triclinic
For 2D systems, the allowed lattice systems are:
- square
- rectangular
- hexagonal
- rhombic
- oblique
For 1D systems, there is only one allowed lattice system identifier, which must be "lamellar".
The lattice system parameter is initialized by the parameter file and is immutable thereafter.
groupName
The "groupName" is an optional string parameter that, if present, identifies a crystallographic space group for a 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.
All allowed identifiers for 1D, 2D, and 3D crystallographic space groups are listed on the following page:
The space group identifier may only be given a value in the parameter file, and may not be initialized or modified after the parameter file has been read.
The "groupName" parameter is used primarily for SCFT calculations of structures with a known space group symmetry. A "groupName" parameter must be present in order to allow PSCF to read or write files using the symmetry-adapted basis file format that is designed to be used for this purpose. This parameter is also required to enable use of SCFT iteration algorithms that are designed search for a solution with a specific space group, such as the AmIteratorBasis algorithm that is used by default by both pscf_pc and pscf_pg. SCFT calculations that are initialized with a parameter file that does not contain a groupName must instead import and export fields in the real-space grid file format, and must use an iteration algorithm that does not impose any symmetry, such as the AmIteratorGrid algorithm.
The groupName parameter is usually omitted from parameter files that are used to initialize stochastic field theoretic simulations. The random changes imposed during the course of such a simulation generate fields that do not exactly preserve any nontrivial symmetry.
Unit cell parameters
To completely describe the Bravais lattice for a crystal with a known crystal system, values must be assigned to a list of unit cell parameters that give the lengths of the edges of the unit cell and (for some lattice systems) angles between some non-orthogonal edges. Values for unit cell parameters are not given in the parameter file. These parameter values must instead either be read from information contains in a field file or set by an explicit command, as discussed below.
Values for unit cell parameters are given within the header section of all field files that contain either chemical potential fields (w-fields) or monomer concentration fields (c-cields) for periodic structures. The unit cell parameter values that are stored in memory by the pscf_pc or pscf_pg program may be set to the values given in such a field file by executing the READ_W_BASIS and READ_W_RGRID command in a command file. Each of these commands causes the program to read in a set of w-fields, and also sets a corresponding list of unit cell parameters. This is the most common method of setting initial values for unit cell parameters.
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 iteratively 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 the field file that contains the converged w-fields.
Unit cell parameters may also be explicitly initialized or reset by executing a command named SET_UNIT_CELL. This command takes a list of unit parameters as arguments, and may be invoked anywhere within a command file.
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 instead required to describe an 3D 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. The same conventions for the number, order and meaning of unit cell parameters for each lattice type are used in a list of parameters given in the header of a field file and for a list given as arguments of a SET_UNIT_CELL command in a command file. Conventions used for each lattice system are described in a separate page of documentation about unit cells.
Symmetry-adapted bases
When the groupName parameter appears in a parameter file used by pscf_pc or pscf_pg, the program will construct a symmetry-adapted Fourier basis appropriate to the specified space group. A symmetry-adapted Fourier basis is a set of periodic functions of position that are all eigenfunctions of the Laplacian that are invariant under all symmetry operations of an associated space group. Such a basis can be used to construct a Fourier series expansion of fields that are required to exhibit a specified space group symmetry. The type of basis used by pscf_pc and pscf_pg contains basis functions that are defined on the nodes of the computational mesh described by the "mesh" parameter, and provides a complete basis for periodic functions of the specified space-group symmetry that are defined on the associated mesh.
The algorithm used by PSCF to construct a symmetry-adapted basis requires access to a set of values for the unit cell parameters, in addition to the information that is provided in the parameter file. If the Domain block of the parameter file contains a groupName parameter, a symmetry-adapted Fourier basis is constructed immediately after the first time that unit cell parameters are initial values by a command in the command file.
This initial assignment of unit cell parameters and construction of a basis may occur during execution of a READ_W_BASIS, READ_W_RGID, SET_UNIT_CELL command, whichever of these appears first in the command file.
The content of the set of basis functions generated by PSCF depends only on the space group and the mesh dimensions, but not on the unit cell parameter values. Unit cell parameter values are actually used during basis construction only in order to determine the order in which basis functions are indexed in internal data structures: By convention, basis functions are indexed internally in order of increasing absolute magnitude for the associated eigenvalue of the Laplacian or (equivalently) in order of increasing wavenumber, using eigenvalues that are computed during basis construction using the initial unit cell parameter values. The use of this convention for the indexing of basis functions has no effect on the result of any calculation.
See also:
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