1 31 MyElas An automatized tool -kit for high -throughput calculation post -processing and visualization of elastic ity and

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MyElas: An automatized tool-kit for high-throughput

calculation, post-processing and visualization of elasticity and

related properties of solids

Hao Wang1, 2, Y. C. Gan2, Hua Y. Geng2, 3, Xiang-Rong Chen1*

1 College of Physics, Sichuan University, Chengdu 610065, People’s Republic of China

2 National Key Laboratory of Shock Wave and Detonation Physics, Institute of Fluid Physics,

CAEP, Mianyang 621900, People’s Republic of China

3 HEDPS, Center for Applied Physics and Technology, and college of Engineering, Peking

University, Beijing 100871, People’s Republic of China

Abstract: Elasticity is one of the most fundamental mechanical properties of solid. In

high-throughput design of advanced materials, there is an imperative demand for the

capability to quickly calculate and screen a massive pool of candidate structures. A

fully automatized pipeline with minimal human intervention is the key to provide high

efficiency to achieve the goal. Here, we introduce a tool-kit MyElas that aims to address

this problem by forging all pre-processing, elastic constant and other related property

calculations, and post-processing into an integrated framework that automatically

performs the assigned tasks to drive data flowing through parallelized pipelines from

input to output. The core of MyElas is to calculate the second and third order elastic

constants of a solid with the energy-strain method from first-principles. MyElas can

auto-analyze the elastic constants, to derive other related physical quantities.

Furthermore, the tool-kit also integrates a visualization function, which can, for

example, plot the spatial anisotropy of elastic modulus and sound velocity of

monocrystalline. The validity and efficiency of the toolkit are tested and bench-marked

on several typical systems.

Key words: Elastic properties; sound velocity; high-throughput computing;

automatization; post-processing analysis

 Corresponding authors. E-mail: xrchen@scu.edu.cn, s102genghy@caep.cn

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PROGRAM SUMMARY 
Program title: MyElas 
CPC Library link to program files: (to be added by Technical Editor)   
Code Ocean capsule: (to be added by Technical Editor)   
Licensing provisions: GNU General Public License 3 (GPL) 
Programming language: Python 3.X 
External routines/libraries: Numpy [1], Spglib [2], Matplotlib [3] 
Nature of problem: Through the first-principal calculation, the second-order and third-
order elastic constants of solid materials are automatically calculated, and the post-
processing and visualization of single crystal and polycrystalline physical properties 
are carried out. 
Solution  method:  Firstly,  the  required  strain  structure  is  automatically  generated 
through the space group of materials and the corresponding strain matrix. Secondly, the 
energy of the structure is calculated by first-principles calculation software such as 
VASP [4]. Thirdly, the relationship between energy and strain is polynomial fitted to 
deduce the elastic constant of the material. Fourth, automatically derive the relevant 
physical properties. Finally, the distribution of mechanical modulus and sound velocity 
in spherical space is visualized. 
Additional comments including Restrictions and Unusual features: Many modules of 
the software can be embedded into other software through simple modification, such as 
visualization  module.  The  software  supports  finite  temperature  calculation  with 
electronic  temperature.  In  addition,  the  software  supports  the  derivation  of 
corresponding elastic constants from phonon spectrum data generated by Phonopy [5], 
Alamode  [6]  and  TDEP  [7]  software  through  long-wave  limit  approximation  and 
Christoffel equation. 
 
References: 
[1]  C.R.  Harris,  K.J.  Millman,  S.J.  van  der  Walt,  R.  Gommers,  P.  Virtanen,  D. 
Cournapeau, E. Wieser, J. Taylor, S. Berg, N.J. Smith, R. Kern, M. Picus, S. Hoyer, 

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M.H. van Kerkwijk, M. Brett, A. Haldane, J.F. Del Rio, M. Wiebe, P. Peterson, P.

Gerard-Marchant, K. Sheppard, T. Reddy, W. Weckesser, H. Abbasi, C. Gohlke, T.E.

Oliphant, Nature 585 (2020) 357-362.

[2] A. Togo, I. Tanaka, arXiv preprint arXiv:1808.01590 DOI (2018).

[3] J.D. Hunter, Computing in Science & Engineering 9 (2007) 90-95.

[4] G. Kresse, J. Furthmuller, Comput. Mater. Sci. 6 (1996) 15-50.

[5] A. Togo, I. Tanaka, Scripta Mater. 108 (2015) 1-5.

[6] T. Tadano, Y. Gohda, S. Tsuneyuki, J. Phys.: Condens. Matter 26 (2014) 225402.

[7] O. Hellman, I.A. Abrikosov, S.I. Simak, Phys. Rev. B 84 (2011) 180301.

 4 /  31 
 
1. Introduction 
For solid materials, elasticity describes the reversible strain response to external 
forces within the elastic limit, and is the fundament for understanding the mechanical 
properties [1-3], which plays a vital role in design of advanced materials. Therefore, to 
compute and screen elastic constants has become one of the most frequent routine-tasks 
in modern material science. 
So far, most calculations are limited to calculate the second-order elastic constants 
(SOEC) of a single crystal. However, with SOEC, we can further derive other related 
mechanical properties straightforwardly, such as Young's modulus, shear modulus, and 
corresponding sound velocity in polycrystalline samples[4-6], which are more relevant 
for practical applications. The spatial anisotropy distribution of mechanical modulus 
(and sound velocity) in single crystals[7, 8] also can be obtained, as well as, other 
important  parameters  such  as  the  Debye  temperature  and  the  lowest  thermal 
conductivity. 
On the other hand, first-principles methods are in-dispensable to calculate elastic 
constants accurately across a wide pressure range, in which SOEC can be obtained by 
fitting to the energy-strain or stress-strain relations[4, 9]. The elastic constants are then 
extracted from the second order derivatives of the energy function in the former case, 
and from the first order derivatives of the stress in the latter case, with respect to strains. 
At first glance, the stress-strain method seems simpler and easier than the former one. 
But in actual applications, the algorithm based on energy is much more robust than that 
of  stress,  mainly  because  the  larger  uncertainty  in  the  numerical  value  of  the 
commutated stress. 
There are already several tools that can calculate the SOEC for solids, including 
ElaStic[10], AELAS[11], ELATE[8], Elastic3rd[12], etc. However, they all are for the 
ground state at zero kelvin, and are not equipped for finite temperatures. Furthermore, 
they  suffer  other  limitations,  especially  in  high-throughput  non-intervention 
calculations. For example, AELAS can only deal with polycrystalline modulus. Many 
other important  physical  properties  that  are  relevant in  experiments  or  engineering 

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applications, e.g., the sound velocity, Debye temperature and anisotropic distribution

of monocrystalline modulus, are not evaluated. On the other hand, ELATE is only for

online analysis and visualization of the anisotropy of SOEC, and it cannot calculate the

elastic constants by itself. Elastic3rd devotes mainly to the computation of the third-

order elastic constants (TOEC), but does not have a feature for post-processing and

analysis of these quantities. For all of these tools, frequent manual interventions are

often requisite.

In this article, we present an efficient and integrated elasticity computation and

processing toolkit, MyElas, for both zero kelvin and finite temperature cases. It

combines the computation of SOEC, TOEC and other elastic properties, the pre-

processing of the input, the post-processing and visualization of the output into single

package. MyElas is designed with parallelized high-throughput computation in mind,

and forges these operations into automatic pipelines so that can deal with massive

candidate structures simultaneously without hanuman intervention. In next section, we

present the theory for SOEC and TOEC computation, as well as the derivation of other

relevant physical quantities. In the third section, the implementation and workflow of

the toolkit are described, as well as a brief introduction to the control parameters and

an example of Si. The fourth section discusses testing and benchmarking of the toolkit,

with the fifth section concludes the full text.

2. Theoretical methods

2.1. Elasticity theory

Elastic constants can be calculated with the energy-strain method. In the spatial

coordinate system, if the initial coordinate of the material element is aj, and the

coordinate after a uniform elastic deformation is marked as xi, then this material

deformation can be represented by a deformation gradient of



=

(1)

The associated Lagrangian strain tensor is defined as follows[2, 13],

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1/31MyElas:Anautomatizedtool-kitforhigh-throughputcalculation,post-processingandvisualizationofelasticityandrelatedpropertiesofsolidsHaoWang1,2,Y.C.Gan2,HuaY.Geng2,3,Xiang-RongChen1*1CollegeofPhysics,SichuanUniversity,Chengdu610065,People’sRepublicofChina2NationalKeyLaboratoryofShockWaveandDetonati...

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