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 Na2O (Materials Project id mp-2352)

       102       18       18        0        0        0  
        18      102       18        0        0        0  
        18       18      102        0        0        0  
         0        0        0       24        0        0  
         0        0        0        0       24        0  
         0        0        0        0        0       24  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 46 GPaEV = 76.34 GPaGV = 31.2 GPaνV = 0.2234
ReussKR = 46 GPaER = 71.822 GPaGR = 28.966 GPaνR = 0.23978
HillKH = 46 GPaEH = 74.096 GPaGH = 30.083 GPaνH = 0.23154

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
24 GPa 24 GPa 24 GPa 84 GPa 84 GPa 138 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 61.333 GPa 96.6 GPa 7.2464 TPa–1 7.2464 TPa–1 24 GPa 42 GPa0.10480.40611Value
Anisotropy 1.575 1.0000 1.75 3.8750Anisotropy
Axis 0.5774
0.5774
0.5773
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
-0.2500
0.9330
-0.2588
0.0000
0.0000
1.0000
0.7071
0.0001
-0.7071
-0.7071
-0.0000
-0.7071
0.7071
-0.0000
-0.7071
Axis
0.1735
0.9848
-0.0000
-0.7071
-0.0002
-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