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 Fe2N (Materials Project id mp-21476)

       379      163      202        0        0        0  
       163      357      198        0        0        0  
       202      198      336        0        0        0  
         0        0        0       92        0        0  
         0        0        0        0      102        0  
         0        0        0        0        0       87  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 244.22 GPaEV = 240.78 GPaGV = 90.133 GPaνV = 0.33568
ReussKR = 244.02 GPaER = 235.61 GPaGR = 87.974 GPaνR = 0.33908
HillKH = 244.12 GPaEH = 238.2 GPaGH = 89.053 GPaνH = 0.33738

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
87 GPa 92 GPa 102 GPa 134.09 GPa 205.02 GPa 732.89 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 185.3 GPa 271.9 GPa 1.2972 TPa–1 1.4717 TPa–1 70.996 GPa 102 GPa0.17070.49339Value
Anisotropy 1.467 1.1345 1.437 2.8904Anisotropy
Axis 0.0000
0.0000
1.0000
0.8339
-0.0000
-0.5519
1.0000
0.0000
0.0000
0.0000
1.0000
0.0000
0.4190
0.5696
0.7071
-0.0000
0.0000
1.0000
0.0000
1.0000
0.0000
1.0000
0.0003
0.0000
Axis
0.4191
0.5695
-0.7071
-1.0000
0.0000
-0.0000
-1.0000
0.0000
-0.0000
0.0000
0.0002
-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