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 TeO3 (Materials Project id mp-2552)

       189      -21       74      -70        0        0  
       -21      189       74       70        0        0  
        74       74      242        0        0        0  
       -70       70        0      156        0        0  
         0        0        0        0      156      -70  
         0        0        0        0      -70      105  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 97.111 GPaEV = 249.31 GPaGV = 116.27 GPaνV = 0.07213
ReussKR = 83.438 GPaER = 176.34 GPaGR = 76.821 GPaνR = 0.14776
HillKH = 90.275 GPaEH = 213.52 GPaGH = 96.544 GPaνH = 0.1058

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
56 GPa 80.389 GPa 94 GPa 205 GPa 285.61 GPa 316 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 121.67 GPa 361.36 GPa 0.67331 TPa–1 5.6558 TPa–1 52.5 GPa 205 GPa-0.364060.60876Value
Anisotropy 2.97 8.4000 3.905Anisotropy
Axis -0.0000
0.9718
-0.2356
0.6419
0.3706
-0.6712
0.0000
0.0000
1.0000
-0.1305
0.9914
0.0000
0.5144
-0.2970
-0.8045
0.4967
0.2867
0.8192
0.7298
0.4213
-0.5384
0.3592
0.2074
0.9099
Axis
-0.6967
0.4022
-0.5940
-0.5000
0.8660
-0.0000
-0.5000
0.8660
-0.0000
-0.5000
0.8660
-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