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 DyN (Materials Project id mp-1410)

       330       90       90        0        0        0  
        90      330       90        0        0        0  
        90       90      330        0        0        0  
         0        0        0      123        0        0  
         0        0        0        0      123        0  
         0        0        0        0        0      123  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 170 GPaEV = 294.96 GPaGV = 121.8 GPaνV = 0.21083
ReussKR = 170 GPaER = 294.92 GPaGR = 121.78 GPaνR = 0.21086
HillKH = 170 GPaEH = 294.94 GPaGH = 121.79 GPaνH = 0.21084

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
123 GPa 123 GPa 123 GPa 240 GPa 240 GPa 510 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 291.43 GPa 297.3 GPa 1.9608 TPa–1 1.9608 TPa–1 120 GPa 123 GPa0.202480.21751Value
Anisotropy 1.02 1.0000 1.025 1.0742Anisotropy
Axis 0.0000
0.0000
1.0000
0.5774
0.5774
0.5773
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.7071
-0.0003
0.7071
0.0000
0.0000
1.0000
0.7071
-0.0002
0.7071
0.7071
-0.0003
-0.7071
Axis
0.7071
-0.0005
-0.7071
0.7660
0.6428
-0.0000
0.7071
-0.0006
-0.7071
0.0002
1.0000
-0.0002
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