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 V2N (Materials Project id mp-684903)

       452      166      182        0      -24        0  
       166      452      182        0       24        0  
       182      182      442        0        0        0  
         0        0        0      152        0       24  
       -24       24        0        0      152        0  
         0        0        0       24        0      143  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 267.33 GPaEV = 365.81 GPaGV = 143.8 GPaνV = 0.27194
ReussKR = 267.32 GPaER = 358.25 GPaGR = 140.31 GPaνR = 0.27664
HillKH = 267.33 GPaEH = 362.04 GPaGH = 142.06 GPaνH = 0.27429

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
123.08 GPa 143.89 GPa 171.92 GPa 257.99 GPa 294.11 GPa 802.01 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 320.68 GPa 424.11 GPa 1.2276 TPa–1 1.2566 TPa–1 123.08 GPa 171.92 GPa0.178120.37377Value
Anisotropy 1.323 1.0236 1.397 2.0984Anisotropy
Axis 0.9153
-0.0000
0.4027
-0.4155
0.7196
-0.5564
0.0000
0.0000
1.0000
0.7934
0.6088
0.0000
-0.7695
0.0000
0.6386
-0.3193
0.5531
0.7695
0.0000
1.0000
0.0000
0.2780
0.4814
-0.8312
Axis
-0.0000
-1.0000
0.0000
-0.8660
-0.5000
-0.0000
-0.7933
-0.0000
0.6088
-0.8660
0.5000
-0.0000
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