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 OsN2 (Materials Project id mp-973935)

       279       94       21        0        0        0  
        94      279       21        0        0        0  
        21       21     1425        0        0        0  
         0        0        0       47        0        0  
         0        0        0        0       47        0  
         0        0        0        0        0       92  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 250.56 GPaEV = 396.44 GPaGV = 160.33 GPaνV = 0.23629
ReussKR = 169.05 GPaER = 194.99 GPaGR = 74.553 GPaνR = 0.30775
HillKH = 209.8 GPaEH = 296.92 GPaGH = 117.44 GPaνH = 0.26412

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
47 GPa 47 GPa 92 GPa 185 GPa 372.16 GPa 1425.8 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 150.11 GPa 1422.6 GPa 0.62377 TPa–1 2.6458 TPa–1 47 GPa 207.15 GPa0.05630.67729Value
Anisotropy 9.477 4.2417 4.407 12.0300Anisotropy
Axis 0.5487
0.5487
0.6308
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.5000
0.8660
0.0000
0.0000
0.0000
1.0000
0.7071
0.0001
-0.7071
0.0000
0.0000
1.0000
0.5355
-0.0000
-0.8445
Axis
0.4998
0.8662
-0.0000
-0.7071
-0.0002
-0.7071
-0.7660
0.6428
0.0000
-0.8445
-0.0001
-0.5355
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