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 Na2CO3 (Materials Project id mp-20495)

       109       40       24        0        0        0  
        40      109       24        0        0        0  
        24       24       45        0        0        0  
         0        0        0      -18        0        0  
         0        0        0        0      -18        0  
         0        0        0        0        0       35  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 48.778 GPaEV = 31.9 GPaGV = 11.467 GPaνV = 0.391
ReussKR = 38.832 GPaER = 356.55 GPaGR = -5882.8 GPaνR = -1.0303
HillKH = 43.805 GPaEH = 412.72 GPaGH = -2935.7 GPaνH = -1.0703

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
-18 GPa -18 GPa 34.903 GPa 35 GPa 69 GPa 159.1 GPa
Stiffness matrix is not definite positive, crystal is mechanically unstable
No further analysis will be performed.