sxrd solver

sxrd is a Solver that uses sxrdcalc to calculate the Rocking curve by giving atomic positions \(x\) , atomic occupancies, and Debye-Waller factor and finally returnes the error \(f(x)\) from the experimental Rocking curve.

Preparation

The sxrdcalc is called from py2dmat. You will need to install sxrdcalc beforehand. sxrdcalc is available on GitHub at the following URL:

https://github.com/sxrdcalc/sxrdcalc

Access the site and download the source code from “Code” - “Download zip”. After unzipping the zip file, edit the Makefile to fit your computing environment, and then type make to create the sxrdcalc executable.

It is noted that the bulk data must be prepared in advance before running py2dmat (see the auxiliary file for solvers below for the format).

Input parameters

Input parameters are specified in subsections in the solver section (config, post, param, and reference).

[config] section

• sxrd_exec_file

  Format: string

  Description: Path to the solver sxrdcalc.

• bulk_struc_in_file

  Format: string

  Description: Input file name of the bulk structure.

An example of the input input is given as follows:

[config]
sxrd_exec_file = "../../sxrdcalc"
bulk_struc_in_file = "sic111-r3xr3.blk"

[param] section

• scale_factor

  Format: float (default: 1.0)

  Description: The value of the target Rocking Curve and the scale of the Rocking Curve obtained from the simulation.

• opt_scale_factor

  Format: bool (default: false)

  Description: Flag whether scale_factor should be optimized or not.

• type_vector

  Format: list

  Description: A list of positive numbers which specifies the type of variables to be optimized. This list corresponds to the types specified in the [param.atom] subsection. If the type is the same, they are treated as the same variable.

[param.domain] subsection

In this section, parameters to create domains are specified. You will need to define the domains you want to create. In the [param.domain.atom] sub-subsection, paramters of the information in the domain are specified.

• domain_occupancy

  Format: float

  Description: Occupancy of the whole domain.

[param.domain.atom] subsection

This section needs to be defined as many times as the number of atoms you want to optimize belonging to the domain. Note that the type, which represents the type of variable, must be a positive number.

• name

  Format: string (can be duplicated)

  Description: The name of the atom to be optimized.

• pos_center

  Format: list

  Description: Center coordinates of the atom. Describe in format of [\(x_0, y_0, z_0\)](\(x_0, y_0, z_0\) はfloat).

• DWfactor

  Format: float

  Description: Debye-Waller factor (in the unit of \(\text{Å}^{2}\) ).

• occupancy

  Format: float (default: 1.0)

  Description: Atom occupancy.

• displace_vector (can be omitted)

  Format: list of lists

  Description: A vector that defines the direction in which the atoms are moved. A maximum of three directions can be specified. Define displacement vectors and initial values in each list as [type, \(D_{i1}, D_{i2}, D_{i3}\) ](type is int, \(D_{i1}, D_{i2}, D_{i3}\) is float type). Follwing the specified information, \(l_{type}\) is varied as \(dr_i = (D_{i1} \vec{a} + D_{i2} \vec{b} + D_{i3} \vec{c}) * l_{type}\) ( \(\vec{a}, \vec{b}, \vec{c}\) is a unit lattice vector defined in bulk_struc_in_file or struc_in_file).

• opt_DW (can be omitted)

  Format: list

  Description: Sets the scale at which the Debye-Waller coefficient is varied. It is defined as [type, scale].

• opt_occupancy

  Format: int

  Description: If defined, the occupancy changes. The specified variable represents the type.

An example of an input file is given as follows:

[param]
scale_factor = 1.0
type_vector = [1, 2]

[[param.domain]]
domain_occupancy = 1.0
 [[param.domain.atom]]
   name = "Si"
   pos_center = [0.00000000, 0.00000000, 1.00000000]
   DWfactor = 0.0
   occupancy = 1.0
   displace_vector = [[1, 0.0, 0.0, 1.0]]
 [[param.domain.atom]]
   name = "Si"
   pos_center = [0.33333333, 0.66666667, 1.00000000]
   DWfactor = 0.0
   occupancy = 1.0
   displace_vector = [[1, 0.0, 0.0, 1.0]]
 [[param.domain.atom]]
   name = "Si"
   pos_center = [0.66666667, 0.33333333, 1.00000000]
   DWfactor = 0.0
   occupancy = 1.0
   displace_vector = [[1, 0.0, 0.0, 1.0]]
 [[param.domain.atom]]
   name = "Si"
   pos_center = [0.33333333, 0.33333333, 1.00000000]
   DWfactor = 0.0
   occupancy = 1.0
   displace_vector = [[2, 0.0, 0.0, 1.0]]

[reference] section

• f_in_file

  Format: string

  Description: Path to the input file for the target locking curve.

Reference file for Solver

Target reference file

The file containing the data to be targeted to fit. The path is specified by f_in_file in the [reference] section. For each line, h k l F sigma is written. Here, h, k, l are the wavenumbers, F is the intensity, and sigma is the uncertainty of F. An example file is shown below.

0.000000 0.000000 0.050000 572.805262 0.1
0.000000 0.000000 0.150000 190.712559 0.1
0.000000 0.000000 0.250000 114.163340 0.1
0.000000 0.000000 0.350000 81.267319 0.1
0.000000 0.000000 0.450000 62.927325 0.1
...

Bulk structure file

The file containing the bulk structure data. The path is specified by bulk_struc_in_file in the [config] section. The first line is a comment, the second line is a b c alpha beta gamma. Here, a , b, and c are the lattice constants of the unit cells, and alpha, beta , and gamma are their angles. The third and subsequent lines specify the atomsymbol r1 r2 r3 DWfactor occupancy. Here, atomsymbol is the atom species, r1, r2, and r3 are the position coordinates of the atom, DWfactor is the Debye-Waller factor, and occupancy is the occupancy rate. An example file is given below.

# SiC(111) bulk
5.33940 5.33940  7.5510487  90.000000 90.000000 120.000000
Si 0.00000000   0.00000000   0.00000000 0.0 1.0
Si 0.33333333   0.66666667   0.00000000 0.0 1.0
Si 0.66666667   0.33333333   0.00000000 0.0 1.0
C  0.00000000   0.00000000   0.25000000 0.0 1.0
...

Output files

In sxrd, the output files are stored in the folder with the rank number. Here is a description of the files that are output by py2dmat.

stdout

The standard output by sxrd is described. For sxrd’s Least square fitting, we give variables as initial parameters and calculate the Rfactor for a 1-shot calculation (number of iterations = 0). The Rfactor is written in R under Fit results. Here is an example of the output.

---------------------------------------
Program py2dmat/mapper_sxrd/sxrdcalc for surface x-ray diffraction calculations.
Version 3.3.3 - August 2019


 Inputfile: lsfit.in
Least-squares fit of model to experimental structure factors.

...

Fit results:
Fit not converged after 0 iterations.
Consider increasing the maximum number of iterations or find better starting values.
chi^2 = 10493110.323318, chi^2 / (degree of freedom) = 223257.666454 (Intensities)
chi^2 = 3707027.897897, chi^2 / (degree of freedom) = 78872.933998 (Structure factors)
R = 0.378801

Scale factor:   1.00000000000000 +/- 0.000196
Parameter Nr. 1:   3.500000 +/- 299467640982.406067
Parameter Nr. 2:   3.500000 +/- 898402922947.218384

Covariance matrix:
          0            1            2
 0  0.0000000383 20107160.3315223120 -60321480.9945669472
 1  20107160.3315223120 89680867995567253356544.0000000000 -269042603986701827178496.0000000000
 2  -60321480.9945669472 -269042603986701827178496.0000000000 807127811960105615753216.0000000000