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-7459)

         6        4        2        0       -0        0  
         4       81       42        0        1        0  
         2       42      125        0       -0        0  
         0        0        0       42        0        0  
        -0        1       -0        0        1        0  
         0        0        0        0        0        3  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 34.222 GPaEV = 50.497 GPaGV = 20.133 GPaνV = 0.25407
ReussKR = 5.8669 GPaER = 7.7371 GPaGR = 3.0218 GPaνR = 0.2802
HillKH = 20.045 GPaEH = 29.125 GPaGH = 11.578 GPaνH = 0.25783

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
0.98427 GPa 3 GPa 5.7873 GPa 42 GPa 55.715 GPa 150.51 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 3.1789 GPa 111.25 GPa 1.8004 TPa–1 163.88 TPa–1 0.98461 GPa 42 GPa-0.82441.5514Value
Anisotropy 35 91.0261 42.66Anisotropy
Axis -0.7733
-0.0000
-0.6341
0.0000
0.4986
0.8668
0.0000
1.0000
0.0000
1.0000
-0.0000
-0.0056
0.0021
0.0000
1.0000
-0.0000
0.0000
-1.0000
-0.1196
0.7714
0.6251
-0.1206
0.7925
0.5979
Axis
1.0000
0.0000
-0.0021
0.0000
-1.0000
-0.0000
-0.6217
-0.5491
0.5586
-0.7730
0.3029
-0.5575
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