Journal ArticleDOI

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

01 Dec 2015--Vol. 51, pp 233-240

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.

### 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.

• $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]. Did you find this useful? Give us your feedback ...read more Content maybe subject to copyright Report ZenGen I : a tool to generate ordered conﬁgurations for systematic ﬁrst-principles calculations, example of the Cr–Mo–Ni–Re system J.-C. Crivello a, , R. Souques a , N. Bourgeois a , A. Breidi a , J.-M. Joubert a a Chimie M´etallurgique des Terres Rares (CMTR), Institut de Chimie et des Mat´eriaux Paris-Est (ICMPE), CNRS UPEC UMR7182, 2–8 rue Henri Dunant, 94320 Thiais Cedex, France Abstract ”ZenGen” is a script-tool which helps 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-member 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 illustrate its possibilities, the quaternary system, Cr–Mo–Ni–Re, has been investigated. The binary solid solution parameters have been estimated from SQS calculations. The σphase has been considered according to its crystal structure, i.e. with a 5-sublattice model, by the DFT calculation of the 4 5 = 1024 dierent ordered quaternary conﬁgurations. Several tentative ab initio phase diagrams are presented. Keywords: Calphad, DFT, CEF, intermetallic, sigma-phase I Fully documented manual and program are available on http://zengen.cnrs.fr. Corresponding author Email address: crivello@icmpe.cnrs.fr (J.-C. Crivello) Preprint submitted to Calphad August 10, 2015 1. Introduction1 The ﬁeld of thermodynamic modeling has been recently stimulated by the progress of tech-2 niques allowing the calculation of thermodynamic quantities from ﬁrst-principles calculations,3 such as the Density Functional Theory (DFT) [1]. These methods allow the estimation of forma-4 tion enthalpies of fully ordered compounds, taking into account their crystal structures. These5 calculations can be done not only for stable compounds, but also for metastable ones which6 play an important role in the description of these phases within the Compound Energy Formal-7 ism (CEF) [2, 3]. By using the CEF, any intermetallic phase could be described by a sublattice8 model for which every ordered conﬁguration heat of formation has to be calculated. As an ex-9 ample, a binary phase with ve crystal sites, described in a 5-sublattice model generates 2 5 = 3210 dierent ordered conﬁgurations, a ternary 3 5 = 243 ... a huge number, but which can be calculated11 with today’s super-computers.12 Technically, performing calculations on a large number of end-members may cause two types13 of problems: (i) a mistake in the distribution of atoms among all dierent sites; (ii) a too fast14 relaxation of crystal structure, thus losing the initial symmetry. To avoid these kinds of errors,15 the ”ZenGen” code was created. This code is able to generate all the necessary input ﬁles for the16 DFT calculations of the ordered conﬁgurations considering a given system. It has been tested on17 several phases, such as Laves phases (C14, C15. . .), or other topologically close packed phases18 (A12, A13, D8 b , P, δ, . . . ). It can also be used to run Special Quasi-random Structures (SQS)19 calculations [4]. A basic introduction of Zengen workﬂow is given is section 2.20 Then, in order to illustrate the ZenGen capacity, we have investigated the challenging quater-21 nary Cr–Mo–Ni–Re system. Our aim was not to assess thermodynamically this system, but rather22 to show that systematic DFT calculations can be run contently in this very complex system, that23 they allow the calculation of a preliminary ab initio computed phase diagram, and that they can be24 used as an input for a traditional Calphad assessment . We have demonstrated this approach in our25 previous works [5, 6]. The results are presented in the section 3.26 2 2. The ZenGen workﬂow27 ”ZenGen” is a free and open source code, governed by the CeCILL-B license under French28 law [7], which is ocially recognized by Open Source Initiative (OSI). It can be downloaded from29 http://zengen.cnrs.fr. Zengen can be installed on Unix-Linux machines and uses Bash, Perl and30 Python languages. It has been designed to run VASP program [8, 9] for the DFT calculations, but31 could be adapted to other ﬁrst-principles codes.32 It requires as input the phase ϕ under consideration the crystallographic structure of which33 is constituted by m dierent sites, and the n dierent elements. Then, ZenGen decomposes the34 process into four steps:35 1. Automatic generation of the input ﬁles for the n m ordered conﬁgurations;36 2. Setup of the convergence criteria and relaxation steps of the ϕ phase;37 3. Job execution under the same conditions;38 4. Collection of output results (total energy, crystallographic parameters) and generation of a39 TDB ﬁle.40 These steps are shown schematically in the diagram of Figure 1 and are more detailed in the41 following paragraphs.42 2.1. Generation of ordered conﬁgurations43 After the command:44$ zengen.pl
the user should enter the name of the crystal structure (X= C14, chiphase, SQS type. . . ), and45
the name the chemical elements. The cut-o energy is also requested. For structures described by46
more than 2 nonequivalent sites, it is possible to merge sites in order to agree with a simpliﬁed sub-47
lattice description. Then, zengen.pl generates all the ordered conﬁgurations based on a simple48
algorithm which distributes atoms on all the inequivalent sites. The script separates the systems49
3

Figure 1: Schematic work ﬂow chart of ZenGen.
(unary, binary, ternary...) and sorts the whole conﬁgurations by ascending the elemental compo-50
sition. Finally, zengen.pl creates a folder containing all the ordered conﬁgurations labeled into51
subfolders (one by conﬁguration), including all the ﬁles (POSCAR and POTCAR) needed to perform52
DFT calculations.53
2.2. Setup of calculations54
The calculation is built into 2 interlinked loops: one on the conﬁgurations to be calculated, one55
on the relaxation step. The exe-X.sh ﬁle has to be modiﬁed by the user regarding the particular56
demand: numeration of conﬁguration and relaxation steps to be calculated . See the manual for57
more details.58
4

2.3. Execution of DFT calculations59
After the setup of the exe-X.sh ﬁle, its execution can be done in blind process mode by:60
$nohup ./exe-X.sh & 2.4. Post-treatment61 After the calculations, the post-treatment is made by the command:62$ ./fin-X.pl
This script generates several ﬁles: a summary ﬁle sum.out, and a database ﬁle: X.TDB. The63
sum.out ﬁle contains the total energy, cell parameters, internal positions and magnetic moment of64
every conﬁguration calculated by exe-X.sh. The X.TDB ﬁle can be used as an input ﬁle for ther-65
modynamic calculation softwares, such as Thermo-Calc [10] or Open-Calphad [11]. It contains,66
for each conﬁguration C in the ϕ phase, the corresponding formation energy, called
f
H
ϕ
(C),67
given in Joule per formula unit, obtained by the dierence between the total energies of E
ϕ
(C) and68
those of he weighted pure i elements in their standard element reference state (SER), E
SER
i
:69
f
H
ϕ
(C) = E
ϕ
(C)
X
i
x
i
· E
SER
i
(1)
The E
SER
i
and E
ϕ
i
(ϕ = A1, A2, A3) have already been calculated with and without spin-polarization.70
They are provided for several cut-o energies (5 sets: 300, 400, 500, 600, and 800 eV) in the folder71
pure of the Zengen installation directory. Figure 2 shows the available i elements of the current72
version.73
A user guide is available on the website http://zengen.cnrs.fr (”Documentation” page), includ-74
ing: the installation procedure, a tutorial, additional explanation, algorithm details, appendices...75
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