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 Ge (Materials Project id mp-12093)

        58       69       69        0        0        0  
        69       58       69        0        0        0  
        69       69       58        0        0        0  
         0        0        0       22        0        0  
         0        0        0        0       22        0  
         0        0        0        0        0       22  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 65.333 GPaEV = 31.246 GPaGV = 11 GPaνV = 0.42029
ReussKR = 65.333 GPaER = -74.345 GPaGR = -22 GPaνR = 0.68966
HillKH = 65.333 GPaEH = -16.976 GPaGH = -5.5 GPaνH = 0.54331

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
-11 GPa -11 GPa 22 GPa 22 GPa 22 GPa 196 GPa
Stiffness matrix is not definite positive, crystal is mechanically unstable
No further analysis will be performed.