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 TeO2 (Materials Project id mp-2125)

        84       13       24        0        0        0  
        13       25       12        0        0        0  
        24       12       33        0        0        0  
         0        0        0       14        0        0  
         0        0        0        0       33        0  
         0        0        0        0        0       18  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 26.667 GPaEV = 46.452 GPaGV = 19.2 GPaνV = 0.20968
ReussKR = 19.909 GPaER = 35.497 GPaGR = 14.756 GPaνR = 0.20283
HillKH = 23.288 GPaEH = 40.976 GPaGH = 16.978 GPaνH = 0.20674

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
14 GPa 16.042 GPa 18 GPa 28.643 GPa 33 GPa 97.315 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 20.362 GPa 76.092 GPa 2.1469 TPa–1 30.392 TPa–1 8.102 GPa 33 GPa-0.123030.65198Value
Anisotropy 3.737 14.1562 4.073Anisotropy
Axis 0.0000
1.0000
0.0000
0.8896
-0.0000
-0.4567
1.0000
0.0000
0.0000
0.0000
1.0000
0.0000
-0.0001
0.7071
0.7071
0.0000
0.0000
1.0000
0.7293
0.0001
-0.6841
1.0000
0.0002
0.0000
Axis
0.0000
0.7071
-0.7071
1.0000
0.0000
-0.0000
-0.6841
-0.0000
-0.7293
-0.0000
0.0002
-1.0000
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