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 VFe3 (Materials Project id mp-866134)

       274      153      153        0        0        0  
       153      274      153        0        0        0  
       153      153      274        0        0        0  
         0        0        0      118        0        0  
         0        0        0        0      118        0  
         0        0        0        0        0      118  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 193.33 GPaEV = 244.89 GPaGV = 95 GPaνV = 0.28889
ReussKR = 193.33 GPaER = 223.54 GPaGR = 85.497 GPaνR = 0.30729
HillKH = 193.33 GPaEH = 234.29 GPaGH = 90.249 GPaνH = 0.29803

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
118 GPa 118 GPa 118 GPa 121 GPa 121 GPa 580 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 164.36 GPa 294.15 GPa 1.7241 TPa–1 1.7241 TPa–1 60.5 GPa 118 GPa0.0409070.53555Value
Anisotropy 1.79 1.0000 1.95 13.0920Anisotropy
Axis 0.0000
0.0000
1.0000
0.5774
0.5773
-0.5774
0.0000
0.0000
1.0000
0.3794
0.9160
0.1305
0.7071
-0.0003
0.7071
0.0000
0.0000
1.0000
0.7071
-0.0002
0.7071
0.7071
-0.0001
0.7071
Axis
0.7071
-0.0005
-0.7071
-0.1736
0.9848
-0.0000
0.7071
-0.0006
-0.7071
0.0001
1.0000
0.0001
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