ELATE: Elastic tensor analysis

Welcome to ELATE, the online tool for analysis of elastic tensors, developed by Romain Gaillac and Fran├žois-Xavier Coudert at CNRS / Chimie ParisTech.
If you use the software in published results (paper, conference, etc.), please cite the corresponding paper (J. Phys. Condens. Matter, 2016, 28, 275201) and give the website URL.

ELATE is open source software. Any queries or comments are welcome at

Summary of the properties

Input: stiffness matrix (coefficients in GPa) of CsErS2 (Materials Project id mp-561751)

        81       22       21        8        0        0  
        22       81       21       -8        0        0  
        21       21       81        0        0        0  
         8       -8        0       24        0        0  
         0        0        0        0       24        8  
         0        0        0        0        8       29  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 41.222 GPaEV = 67.157 GPaGV = 27.333 GPaνV = 0.22848
ReussKR = 41.221 GPaER = 62.365 GPaGR = 24.989 GPaνR = 0.24784
HillKH = 41.222 GPaEH = 64.78 GPaGH = 26.161 GPaνH = 0.23808

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
18.118 GPa 20.661 GPa 34.882 GPa 60.33 GPa 62.339 GPa 123.67 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 47.51 GPa 81.279 GPa 8.0418 TPa–1 8.1758 TPa–1 18.118 GPa 35.13 GPa0.0145030.44531Value
Anisotropy 1.711 1.0167 1.939 30.7040Anisotropy
Axis 0.7073
0.4124
-0.5742
-0.0000
0.9324
-0.3614
0.0948
0.9955
0.0000
0.0000
0.0000
1.0000
-0.0000
0.5923
-0.8057
0.5151
0.8569
-0.0162
-0.5504
0.3143
0.7734
0.5021
0.8648
0.0021
Axis
-1.0000
0.0000
0.0000
-0.7010
0.4103
-0.5834
-0.4980
-0.8672
-0.0020
-0.6659
0.3881
-0.6371
Second axis

Spatial dependence of Young's modulus



Young's modulus in (xy) plane

Young's modulus in (xz) plane

Young's modulus in (yz) plane

Spatial dependence of linear compressibility



linear compressibility in (xy) plane

linear compressibility in (xz) plane

linear compressibility in (yz) plane

Spatial dependence of shear modulus



Shear modulus in (xy) plane

Shear modulus in (xz) plane

Shear modulus in (yz) plane

Spatial dependence of Poisson's ratio



Poisson's ratio in (xy) plane

Poisson's ratio in (xz) plane

Poisson's ratio in (yz) plane