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 Al2O3 (Materials Project id mp-776475)

       410      118      118        0        0        0  
       118      410      118        0        0        0  
       118      118      410        0        0        0  
         0        0        0      116        0        0  
         0        0        0        0      116        0  
         0        0        0        0        0      116  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 215.33 GPaEV = 320.5 GPaGV = 128 GPaνV = 0.25194
ReussKR = 215.33 GPaER = 317.12 GPaGR = 126.39 GPaνR = 0.25455
HillKH = 215.33 GPaEH = 318.81 GPaGH = 127.19 GPaνH = 0.25324

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
116 GPa 116 GPa 116 GPa 292 GPa 292 GPa 646 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 295.02 GPa 357.26 GPa 1.548 TPa–1 1.548 TPa–1 116 GPa 146 GPa0.192960.32956Value
Anisotropy 1.211 1.0000 1.259 1.7079Anisotropy
Axis 0.5774
0.5773
-0.5774
0.0000
0.0000
1.0000
0.2241
0.8365
0.5000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.7071
-0.0003
0.7071
-0.7071
-0.0000
0.7071
0.7071
-0.0000
-0.7071
Axis
1.0000
0.0000
-0.0000
0.7071
-0.0005
-0.7071
0.0000
-1.0000
-0.0000
-0.7071
0.0002
-0.7071
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