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 σ−phase

has been considered according to its crystal structure, i.e. with a 5-sublattice model, by the DFT

calculation of the 4

5

= 1024 diﬀerent 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 ﬁve crystal sites, described in a 5-sublattice model generates 2

5

= 3210

diﬀerent 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 diﬀerent 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 oﬃcially 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 diﬀerent sites, and the n diﬀerent 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, chi−phase, SQS type. . . ), and45

the name the chemical elements. The cut-oﬀ 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 diﬀerence 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-oﬀ 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

5