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 Na2MoO4 (Materials Project id mp-18852)

        90       30       30        0        0        0  
        30       90       30        0        0        0  
        30       30       90        0        0        0  
         0        0        0       26        0        0  
         0        0        0        0       26        0  
         0        0        0        0        0       26  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 50 GPaEV = 69.932 GPaGV = 27.6 GPaνV = 0.26689
ReussKR = 50 GPaER = 69.643 GPaGR = 27.465 GPaνR = 0.26786
HillKH = 50 GPaEH = 69.788 GPaGH = 27.532 GPaνH = 0.26737

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
26 GPa 26 GPa 26 GPa 60 GPa 60 GPa 150 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 66.477 GPa 75 GPa 6.6667 TPa–1 6.6667 TPa–1 26 GPa 30 GPa0.228070.31579Value
Anisotropy 1.128 1.0000 1.154 1.3846Anisotropy
Axis 0.5774
0.5774
0.5773
0.0000
0.0000
1.0000
0.2244
0.8366
0.4997
0.6088
0.0000
0.7934
0.0000
0.0000
1.0000
0.7071
-0.0003
0.7071
0.7071
-0.0000
0.7071
0.7071
-0.0000
-0.7071
Axis
0.1735
0.9848
-0.0000
0.7071
-0.0005
-0.7071
0.0000
1.0000
0.0000
-0.7071
0.0002
-0.7071
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