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

doi:10.1016/j.calphad.2015.09.005

Calphad

Volume 51, December 2015, Pages 233-240

https://doi.org/10.1016/j.calphad.2015.09.005 Get rights and content

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.

Graphical abstract

Introduction

The field of thermodynamic modeling has been recently stimulated by the progress of techniques allowing the calculation of thermodynamic quantities from first-principles calculations, such as the Density Functional Theory (DFT) [1]. These methods allow the estimation of formation enthalpies of fully ordered compounds, taking into account their crystal structures. These calculations can be done not only for stable compounds, but also for metastable ones which play an important role in the description of these phases within the Compound Energy Formalism (CEF) [2], [3]. By using the CEF, any intermetallic phase could be described by a sublattice model for which every ordered configuration heat of formation has to be calculated. As an example, a binary phase with five crystal sites described in a 5-sublattice model generates $2^{5} = 32$ different ordered configurations, a ternary $3^{5} = 243$ a huge number, but which can be calculated with today's super-computers.

Technically, performing calculations on a large number of end-members may cause two types of problems: (i) a mistake in the distribution of atoms among all different sites; (ii) a too fast relaxation of crystal structure, thus losing the initial symmetry. To avoid these problematics, “ZenGen” code was created. This code is able to generate the necessary input files required to start DFT calculations of the corresponding ordered configurations for a given system. It has been tested on several phases, such as Laves phases (C14, C15, etc.), or other topologically close packed phases ( $A 12$ , $A 13$ , D8_b, P, δ, etc.). It can also be used to run Special Quasi-random Structures (SQS) calculations [4]. A basic introduction of ZenGen workflow is given is Section 2.

Thereafter, in order to illustrate ZenGen capacity, we have investigated the challenging quaternary Cr–Mo–Ni–Re system. Our 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. We have demonstrated this approach in our previous works [5], [6]. The results are presented in Section 3.

Section snippets

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). It can be downloaded from http://zengen.cnrs.fr. ZenGen can be installed on Unix–Linux machines and uses Bash, Perl and Python languages. In its present version, it is compatible with VASP program [8], [9] for DFT calculations; however it can be adapted to be compatible with other first-principles codes, as well.

φ, the conventional name

Known phase diagrams

The quaternary Cr–Mo–Ni–Re system is well suited for an automatic investigation of phase stability. Solid solutions with three different structures exist: $A 1 - fcc$ (Ni), $A 2 - bcc$ (Cr, Mo) and $A 3 - hcp$ (Re), and two of elements are magnetic. The σ-phase is stable in the four ternaries. This phase is a hard brittle intermetallic compound and has a deleterious effect on the mechanical properties of many technologically important systems, like Cr–Mo–Ni–Re, a key system for Ni-based superalloys. The

Conclusions

ZenGen is a tool to automate the construction of the input files required for systematic DFT calculations of all the ordered configurations of a multicomponent phase. This approach can be used in parallel with a thermodynamic assessment by the Calphad method. It has been illustrated through the calculation of the quaternary Cr–Mo–Ni–Re system for which all the binary solid solutions and every end-member of the quaternary σ-phase have been calculated for the first time.

Many improvements will be

Acknowledgments

DFT calculations were performed using HPC resources from GENCI-CINES (Grant 2014-96175). Financial support, from the Agence Nationale de la Recherche (ANR), Project Armide ANR-10-BLAN-912-01 is acknowledged. N. Bourgeois is thankful to the French ANR agency for financial support from the National Program Investments for Future ANR-11-LABX-022-01. The authors wish to thank Nathalie Dupin for useful and fruitful discussions.

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^☆: Fully documented manual and program are available on http://zengen.cnrs.fr

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

Abstract

Graphical abstract

Introduction

Section snippets

The ZenGen workflow

Known phase diagrams

Conclusions

Acknowledgments

J. Phys. Chem. Solids

Acta Metall.

Acta Mater.

Calphad

Acta Mater.

J. Alloys Compd.

Prog. Mater. Sci.

Calphad

Comput. Mater. Sci.

Acta Mater.

Calphad

Calphad

Comput. Mater. Sci.

Comput. Mater. Sci.

J. Alloys Compd.

Nobel Lectures, Chemistry 1996–2000

Special quasirandom structures

Phys. Rev. Lett.