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 Si (Materials Project id mp-644693)

       115       35       44        8       16       26  
        35      103       39        7        3       14  
        44       39      122       20        4       16  
         8        7       20       16       -8        2  
        16        3        4       -8        5        4  
        26       14       16        2        4       11  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 64 GPaEV = 57.276 GPaGV = 21.2 GPaνV = 0.35084
ReussKR = 45.771 GPaER = -305.39 GPaGR = -58.459 GPaνR = 1.612
HillKH = 54.886 GPaEH = -63.018 GPaGH = -18.629 GPaνH = 0.69136

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
-2.3324 GPa 4.2722 GPa 17.269 GPa 72.89 GPa 77.948 GPa 201.95 GPa
Stiffness matrix is not definite positive, crystal is mechanically unstable
No further analysis will be performed.