IRelakit Overview

IRelakit enables the representation of elastic properties in both 3D and 2D visual formats, making them easier to visualize. This allows for the conversion of the elastic stiffness matrix into a function of spherical coordinates (either 3D or 2D representations). To achieve this, the system transitions to spherical coordinates, where the unit vectors are perpendicular, similar to principal axes. To facilitate this, IRelakit defines two unit spherical vectors, a and b, in the new basis set and transitions from the original basis set to the new one in spherical coordinates. In this way, IRelakit connects elastic properties with spherical coordinates as functions of θ, φ, and γ, making them visualizable.

Program Structure

The IRelakit package consists of several scripts, each with a specific purpose:

•	IRelakit: This is the primary script responsible for preparing the entire calculation. It must be executed in a directory that contains a valid elastic constants matrix (Cij-matrix file) and mass density (.rho file). Alternatively, the program can calculate the mass density of the compound based on the number of atoms and the unit cell volume. The script takes in the number of mesh points for θ and φ, as well as the Miller index for the 2D cut. The mesh number controls the scanning loops during which elastic properties are calculated, and it determines the grid used for graphical representations. From this, the program calculates the optimum values and averages. It creates forth main types of files:

o	*.dat (e.g., Shear-Rati.dat)
o	*2D.dat (e.g., Poisson-Rati2D.dat)
o	*2DB.dat (e.g., Young-Modu2DB.dat)
o	ThPhCalP.dat file

The *.dat and *2D.dat files are used for 3D and 2D-cut plots, respectively. The *2DB.dat file is used for plotting the convex hull (edge border) of the 2D-cut, while the ThPhCalP.dat file is for generating color/gray maps and heat maps using the Gnuplot program. At the end of the process, the calculated parameters are stored in the IRelakit.dat file.

If the convex hull is not sufficiently accurate, the -d/-D ds option (default value of ds = 4 degrees) can be used to improve the convex hull by reducing the polar angle rotation parameter ( for example: IRelakit -d 3). For further details on how to use the program, execute the following:

IRelakit -h

•	xyz2wrl: This Fortran-based program is used to generate 3D representations of elastic properties in the wrl format. This format can be visualized in a VRML browser, such as the well-known View3dscene program. It reads data from either *.dat (for 3D) or *2D.dat (for 2D-cut) files, depending on the input parameters. The output file will be in the wrl format (e.g., *.wrl or *2D.wrl). For more details on how to use the program, execute:

xyz2wrl -h

•	Heatmap_lapw: This shell script is used for generating palette-mapped 3D color/gray maps or 2D polar heat maps (for 2D-cut plots) in which each "pixel" corresponds to a pre-determined range of θ and r for the elastic properties. The program uses Gnuplot for plotting. It reads from the ThPhCalP.dat or *2DB.dat files and outputs png images (e.g., *HM.png or *HM2DC.png). For further details, run:

Heatmap_lapw -h

•	Polarplot_lapw: This script provides an interface for plotting 2D-cut elastic properties (convex hull) as polar or Cartesian coordinates using Gnuplot. It uses data from *2DB.dat and generates output images such as *2DB.png (r vs. θ)  for polar coordinates, and  *2DBrxy.png ( -rxy option, r vs. θ) as well as *2DBxy.png (-xy option, ry vs. rx) for Cartesian coordinates. For more information on options, use:

Polarplot_lapw -h

•	xyz2gnu: This program is an interface for plotting elastic properties in 3D (x, y, z) or as Pm3d plots, including monochrome options (-mc). The -mv option can be used to project the 3D plot onto a 2D map view, effectively flattening the Z coordinate onto the XY plane. The program reads data from the ThPhCalP.dat file and outputs png or pdf images. For details, run:

xyz2gnu -h

•	IRelakit_lapw: This shell script automates the process of calling all the necessary programs (IRelakit, xyz2wrl, xyz2gnu, Heatmap_lapw, and Polarplot_lapw) for all elastic properties. It organizes the output files in appropriate subdirectories, generating png and wrl formatted output.