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 Mg3Hg (Materials Project id mp-731)

        62       47       18        0        0        0  
        47       62       18        0        0        0  
        18       18      100        0        0        0  
         0        0        0       18        0        0  
         0        0        0        0       18        0  
         0        0        0        0        0        7  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 43.333 GPaEV = 47.432 GPaGV = 18 GPaνV = 0.31757
ReussKR = 43.257 GPaER = 33.245 GPaGR = 12.116 GPaνR = 0.37191
HillKH = 43.295 GPaEH = 40.481 GPaGH = 15.058 GPaνH = 0.34417

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
7 GPa 15 GPa 18 GPa 18 GPa 78.649 GPa 130.35 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 24.636 GPa 94.055 GPa 7.1206 TPa–1 7.9984 TPa–1 7 GPa 19.101 GPa0.0432540.7597Value
Anisotropy 3.818 1.1233 2.729 17.5635Anisotropy
Axis 0.7071
0.7071
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
1.0000
-0.0002
-0.0000
0.7071
-0.0003
0.7071
-0.7071
0.7071
-0.0000
0.7071
0.7071
-0.0000
Axis
0.0002
1.0000
-0.0000
0.7071
-0.0005
-0.7071
0.0000
-0.0000
-1.0000
-0.7071
0.7071
0.0000
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