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 Bi2Se3 (Materials Project id mp-541837)

        64       17        3       -1        0        0  
        17       64        3        1        0        0  
         3        3        5        0        0        0  
        -1        1        0        2        0        0  
         0        0        0        0        2       -1  
         0        0        0        0       -1       23  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 19.889 GPaEV = 31.482 GPaGV = 12.733 GPaνV = 0.23619
ReussKR = 4.8987 GPaER = 8.5301 GPaGR = 3.5255 GPaνR = 0.20979
HillKH = 12.394 GPaEH = 20.013 GPaGH = 8.1294 GPaνH = 0.23088

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
1.9525 GPa 1.9556 GPa 4.7639 GPa 23.048 GPa 47.044 GPa 81.236 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 4.6289 GPa 58.571 GPa 5.168 TPa–1 193.8 TPa–1 1.955 GPa 23.546 GPa0.00289370.679Value
Anisotropy 12.65 37.5000 12.04234.6496Anisotropy
Axis 0.3514
0.2027
0.9140
-0.0000
0.9997
0.0236
0.2430
0.9700
0.0000
0.0000
0.0000
1.0000
0.0190
0.0083
0.9998
0.7071
0.7063
0.0328
-0.6763
0.3867
-0.6270
1.0000
0.0000
-0.0000
Axis
0.8576
0.5139
-0.0205
-0.7071
0.7064
0.0328
-0.4964
-0.8681
0.0001
-0.0000
0.5942
-0.8044
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