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 Te2Mo (Materials Project id mp-602)

       106       26        1        0        0        0  
        26      106        1        0        0        0  
         1        1        2        0        0        0  
         0        0        0        4        0        0  
         0        0        0        0        4        0  
         0        0        0        0        0       40  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 30 GPaEV = 53.036 GPaGV = 22 GPaνV = 0.20536
ReussKR = 1.9848 GPaER = 7.2229 GPaGR = 4.042 GPaνR = -0.10651
HillKH = 15.992 GPaEH = 30.724 GPaGH = 13.021 GPaνH = 0.1798

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
1.9846 GPa 4 GPa 4 GPa 40 GPa 80 GPa 132.02 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 1.9848 GPa 99.336 GPa 3.8168 TPa–1 496.18 TPa–1 1.9175 GPa 40 GPa-0.622130.37915Value
Anisotropy 50.05130.0000 20.86Anisotropy
Axis 0.0000
0.0000
1.0000
1.0000
0.0001
0.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
-0.4023
0.5815
-0.7071
-0.7021
0.7121
-0.0000
-0.8851
0.2557
-0.3889
0.8052
0.5930
0.0000
Axis
0.4024
-0.5815
-0.7071
-0.7121
-0.7021
0.0000
0.3736
-0.1080
-0.9213
0.0000
-0.0000
-1.0000
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