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-2739)

        33      -10      -17        0        0        0  
       -10       33      -17        0        0        0  
       -17      -17       69        0        0        0  
         0        0        0       35        0        0  
         0        0        0        0       35        0  
         0        0        0        0        0       56  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 5.2222 GPaEV = 33.054 GPaGV = 37.133 GPaνV = -0.55492
ReussKR = 4.4061 GPaER = 28.258 GPaGR = 32.773 GPaνR = -0.56888
HillKH = 4.8142 GPaEH = 30.659 GPaGH = 34.953 GPaνH = -0.56142

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
12.728 GPa 35 GPa 35 GPa 43 GPa 56 GPa 79.272 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 21.824 GPa 43.87 GPa 56.492 TPa–1 85.233 TPa–1 21.5 GPa 56 GPa-0.76903-0.36771Value
Anisotropy 2.01 1.5088 2.605 0.4781Anisotropy
Axis 1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
-0.7071
0.7071
-0.0000
1.0000
-0.0000
0.0000
0.7071
0.7071
0.0000
1.0000
0.0002
0.0000
Axis
-0.7071
-0.7071
0.0000
0.0000
1.0000
0.0000
-0.7071
0.7071
-0.0000
0.0000
0.0003
-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