lpa-input 0.9.19

Tools for the generation and analysis of dislocation distributions.

Line Profile Analysis - Input

This repository is related to the analysis of crystals containing dislocations by X-ray diffraction. It is part of a project conducted during a research internship at the laboratory of material and structural sciences of the École Nationale Supérieure des Mines de Saint-Étienne. Three python packages have been developed to conduct line profile analyses based on simulation results:

• lpa.input (line profile analysis input generator)
• lpa.xrd (line profile analysis x-ray diffraction simulation program)
• lpa.output (line profile analysis output analyzer)

Features

The package lpa.input can be used to:

• generate dislocation distributions according to different models
• export the distributions in standardized files for input to an X-ray diffraction simulation program
• export the distributions in dislocation maps
• export a spatial analysis of the distributions

Installation

The package is indexed on PyPI and installable directly via pip:

pip install -U lpa-input

Examples

Distribution maps

Input data files

# please keep the structure of this file unchanged
 1  1  0 # z: direction of 'l' (line vector) [uvw]
-1  1  0 # x: direction of 'L' (Fourier variable) [uvw]
 1  1  0 # b: Burgers vector direction [uvw]
 2  0  0 # g: diffraction vector direction (hkl)
0.250000 # C: contrast coefficient [1]
0.404940 # a: cell parameter [nm]
     400 # s: Cylinder radius [nm]
    11.8 # a3: step size of 'L' along x [nm]
   0.345 # nu: Poisson's number [1]
      25 # number of dislocations
# Burgers vector and dislocation (x,y) coordinates
 1 -1.61548011465209754078E+02 -1.87858054587866405427E+02
 1 -4.95321847603491747236E+01  3.96358615901232042233E+02
 1  3.83092997789296475730E+02  1.00863319641021547568E+02
 1  3.29405674347048261552E+02  3.43310242328645074394E+01
 1  1.24896256845976836303E+02 -2.97446481284809294721E+02
 1  2.83261500112922590233E+02 -1.72957796716792046254E+02
 1 -1.95525742141039444277E+02 -1.54910012577794219624E+02
 1 -1.88880305594950499426E+01 -1.45803577134339775512E+02
 1 -3.27077937109537572269E+02 -9.19682417317111031707E+01
 1  2.66132672811368365728E+02 -1.15022137253631683507E+02
 1  8.95788549895187458105E+01 -2.03995903949563853530E+02
 1  2.78766292014808357180E+02  4.79706674967438928547E+00
-1  2.35696079304986938041E+02 -2.94559691227597113539E+02
-1  3.78008065264777542325E+02  8.09744721982159489926E+01
-1 -3.05015488147403850405E+01 -2.37311792781886936154E+02
-1  1.36174901645258700000E+02  2.70002164951812687832E+02
-1  1.48116703651397642716E+02 -1.71931802385698262015E+02
-1 -2.97958976321769398510E+02 -7.94257720216477167696E+01
-1 -7.14523593672500396679E+01  2.21269872377589337020E+02
-1 -2.21359970901484132355E+02  1.16870883315733863128E+02
-1  3.71458286581792890502E+02  6.68029763594811925032E+01
-1  1.35411516921856758700E+02  1.34197377210817563764E+02
-1 -1.51035996503921097656E+02 -2.77305014216898598534E+02
-1 -6.97944269504084076061E+01 -9.25807374125183457636E+01
 1 -2.73203683148690629423E+02 -2.42038862868204574852E+02

Spatial analysis

Physical aspects

Two geometries are proposed:

• circle (intersection of a plane with a cylinder) centered in (0, 0)
• square (intersection of a plane with a cuboid) bottom left corner at (0, 0)

A dislocation associates:

• a Burgers vector sense b
• a position p

A distribution is mainly characterized by the following elements:

• the shape of the region of interest
• the model used for the random generation of dislocations
• the generated dislocations

A sample is a set of distribution and is mainly characterized by:

• the number of generated distribution stored
• the shape of the region of interest
• the model used for the random generation of dislocations
• the stored distributions

Abbreviations

Some abbreviations are used in the program:

Models

• RDD random dislocation distribution
• RRDD restrictedly random dislocation distribution
• RCDD random cell dislocation distribution

Model variants

• R randomly distributed Burgers vectors
• E evenly distributed Burgers vectors
• D dipolar Burgers vectors

Boundary conditions

• PBCG periodic boundary conditions applied when generating the distribution
• PBCR periodic boundary conditions applied when running the simulation
• IDBC image dislocations boundary conditions

User guide

The directory tests/ contains several examples of package module usage. The docstrings are carefully written and it is recommended to refer to the documentation with the help() command.