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 TePb (Materials Project id mp-20943)

        53       34       34        0        0        0  
        34       53       34        0        0        0  
        34       34       53        0        0        0  
         0        0        0       11        0        0  
         0        0        0        0       11        0  
         0        0        0        0        0       11  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 40.333 GPaEV = 28.731 GPaGV = 10.4 GPaνV = 0.38128
ReussKR = 40.333 GPaER = 28.595 GPaGR = 10.347 GPaνR = 0.38184
HillKH = 40.333 GPaEH = 28.663 GPaGH = 10.373 GPaνH = 0.38156

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
11 GPa 11 GPa 11 GPa 19 GPa 19 GPa 121 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 26.425 GPa 30.25 GPa 8.2645 TPa–1 8.2645 TPa–1 9.5 GPa 11 GPa0.326980.43175Value
Anisotropy 1.145 1.0000 1.158 1.3204Anisotropy
Axis 0.0000
0.0000
1.0000
0.5774
0.5774
0.5773
0.8660
0.0000
0.5000
0.0000
0.0000
1.0000
0.7071
-0.0003
0.7071
0.0000
0.0000
1.0000
0.7071
-0.0000
-0.7071
0.7071
0.0004
-0.7071
Axis
0.7071
-0.0005
-0.7071
-0.9397
-0.3420
0.0000
-0.7071
0.0002
-0.7071
-0.0003
1.0000
0.0003
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