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 CoN (Materials Project id mp-448)

       296      228      228        0        0        0  
       228      296      228        0        0        0  
       228      228      296        0        0        0  
         0        0        0       62        0        0  
         0        0        0        0       62        0  
         0        0        0        0        0       62  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 250.67 GPaEV = 142.76 GPaGV = 50.8 GPaνV = 0.40508
ReussKR = 250.67 GPaER = 131.74 GPaGR = 46.637 GPaνR = 0.41241
HillKH = 250.67 GPaEH = 137.26 GPaGH = 48.719 GPaνH = 0.40873

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
62 GPa 62 GPa 62 GPa 68 GPa 68 GPa 752 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 97.588 GPa 171.83 GPa 1.3298 TPa–1 1.3298 TPa–1 34 GPa 62 GPa0.16430.64372Value
Anisotropy 1.761 1.0000 1.824 3.9180Anisotropy
Axis 0.0000
0.0000
1.0000
-0.5774
0.5774
0.5773
0.2728
0.9554
0.1127
0.0000
0.0000
1.0000
0.7071
-0.0003
0.7071
-0.0000
0.0000
1.0000
0.7071
-0.0002
0.7071
0.0000
0.7071
0.7071
Axis
0.7071
-0.0005
-0.7071
-1.0000
0.0000
-0.0000
0.7071
-0.0006
-0.7071
-1.0000
0.0000
-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