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-568390)

        32       48       34        8        0        0  
        48       32       34       -8        0        0  
        34       34       61        0        0        0  
         8       -8        0       21        0        0  
         0        0        0        0       21        8  
         0        0        0        0        8       -8  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 39.667 GPaEV = 20.9 GPaGV = 7.4 GPaνV = 0.41218
ReussKR = 38.909 GPaER = 639.79 GPaGR = -257.87 GPaνR = -2.2405
HillKH = 39.288 GPaEH = 6008.4 GPaGH = -125.23 GPaνH = -24.989

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
-19.185 GPa -10.06 GPa 21.487 GPa 23.06 GPa 24.185 GPa 119.51 GPa
Stiffness matrix is not definite positive, crystal is mechanically unstable
No further analysis will be performed.