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 Li (Materials Project id mp-10173)

        22       11        8        0        0        0  
        11       22        8        0        0        0  
         8        8       26        0        0        0  
         0        0        0        6        0        0  
         0        0        0        0        6        0  
         0        0        0        0        0        5  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 13.778 GPaEV = 16.325 GPaGV = 6.2667 GPaνV = 0.30252
ReussKR = 13.774 GPaER = 15.799 GPaGR = 6.0358 GPaνR = 0.30882
HillKH = 13.776 GPaEH = 16.063 GPaGH = 6.1512 GPaνH = 0.30566

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
5 GPa 6 GPa 6 GPa 11 GPa 17.657 GPa 41.343 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 14.606 GPa 22.121 GPa 23.288 TPa–1 24.658 TPa–1 5 GPa 7.6695 GPa0.161620.47475Value
Anisotropy 1.515 1.0588 1.534 2.9375Anisotropy
Axis 0.6543
0.6542
0.3794
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.3827
0.9239
0.0000
1.0000
-0.0002
0.0000
0.7071
0.0001
-0.7071
-0.7071
0.7071
0.0000
-0.7071
0.7071
0.0000
Axis
0.0002
1.0000
0.0000
-0.7071
-0.0002
-0.7071
0.0000
0.0000
1.0000
-0.7071
-0.7071
-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