# ZenGen, a tool to generate ordered configurations for systematic first-principles calculations: The Cr–Mo–Ni–Re system as a case study ☆

Abstract: “ZenGen” is a script-tool which helps us to automatically generate first-principles input files of all the ordered compounds of a given crystal structure in a given system. The complete set of heats of formation of each end-members can then easily be used in the thermodynamic phase modeling. “ZenGen” is a free and open source code, which can be downloaded from http://zengen.cnrs.fr . In order to test its applicability, we have chosen the quaternary system, Cr–Mo–Ni–Re as a case study to be investigated. The binary solid solution parameters have been estimated from special quasirandom structures (SQS) calculations. The σ-phase has been fully described without any adaptation to its crystal structure, i.e. with a 5-sublattice model, through first-principles calculation of the 4 5 = 1024 different ordered quaternary configurations. Several tentative ab initio phase diagrams are presented.

## Summary (1 min read)

### 1. Introduction

- The authors aim was not to assess thermodynamically this system, but rather to show that systematic DFT calculations can be run contently in this very complex system, that they allow the calculation of a preliminary ab initio computed phase diagram, and that they can be used as an input for a traditional Calphad assessment .
- The results are presented in the section 3.

### 2. The ZenGen workflow

- "ZenGen" is a free and open source code, governed by the CeCILL-B license under French law [7] , which is officially recognized by Open Source Initiative (OSI).
- Zengen can be installed on Unix-Linux machines and uses Bash, Perl and Python languages.
- It has been designed to run VASP program [8, 9] for the DFT calculations, but could be adapted to other first-principles codes.

### 2.1. Generation of ordered configurations

- $ zengen.pl the user should enter the name of the crystal structure (X= C14, chi−phase, SQS type, also known as After the command.
- Then, zengen.pl generates all the ordered configurations based on a simple algorithm which distributes atoms on all the inequivalent sites.
- Finally, zengen.pl creates a folder containing all the ordered configurations labeled into subfolders (one by configuration), including all the files (POSCAR and POTCAR) needed to perform DFT calculations.

### 2.4. Post-treatment

- At the moment, only the fcc, bcc, and hcp structures phases for binary systems are implemented.
- Generated structures have been taken from the literature [12, 13, 14] respectively.

### 3.2. DFT computational details

- In comparison with previous works, slight differences are observed and are explained by the different exchange-correlation functions and cut-off energy.
- The same most stable configurations are found for each system.
- Since the less stable quaternay configuration (Re:Ni:Cr:Mo:Cr, ∆ f H > 30 kJ/at) presents 6.6 valence electron and satisfies this electronic condition, it clearly shows that, even if the electronic argument may be important, the geometric one dominates strongly the σ−phase stability.

### 3.3.2. Ideal ternaries phase diagram

- Without any adjustable parameter and with DFT lattice stability of pure elements (only enthalpies no entropy terms), the four ternary phase diagrams have been calculated using the Thermo-Calc software package.
- With the exception of Cr-Mo-Ni, all the expected σ−phases appear in a reasonable range of compositions.

### 3.3.3. Additional interaction parameters

- Using the same hypothesis, the quaternary phase diagram is plotted in Figure 7 in the form of several constant Ni-composition sections.
- This plot allows to evaluate the quaternary extension of the σ−phase.
- The most striking feature is the shrinking of the homogeneity range as a function of the Ni-content.
- Thus, their result is in agreement with the empirical rule stating that the σ−phase forms for an average electron concentration range below the value of 8 [16, 26].

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