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 Bi2Te3 (Materials Project id mp-34202)

        55       14        8       -4        0        0  
        14       55        8        4        0        0  
         8        8       10        0        0        0  
        -4        4        0        8        0        0  
         0        0        0        0        8       -4  
         0        0        0        0       -4       20  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 20 GPaEV = 32.459 GPaGV = 13.2 GPaνV = 0.22951
ReussKR = 9.8596 GPaER = 19.491 GPaGR = 8.3259 GPaνR = 0.17052
HillKH = 14.93 GPaEH = 26.033 GPaGH = 10.763 GPaνH = 0.20938

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
6.7889 GPa 7.0572 GPa 7.9049 GPa 21.211 GPa 41.943 GPa 71.095 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 8.1449 GPa 50.185 GPa 3.5587 TPa–1 94.306 TPa–1 5.5956 GPa 21.57 GPa0.0377120.79067Value
Anisotropy 6.161 26.5000 3.855 20.9658Anisotropy
Axis 0.0000
0.0000
1.0000
-0.0000
0.9848
0.1737
0.9659
0.2587
0.0000
0.0000
0.0000
1.0000
-0.4968
0.2999
0.8144
-0.8139
0.5089
0.2804
-0.7264
0.4122
-0.5500
1.0000
-0.0004
0.0001
Axis
-0.7019
0.4130
-0.5803
-0.5354
-0.8444
-0.0216
-0.4907
-0.8713
-0.0049
0.0002
0.4583
-0.8888
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