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 Al2O3 (Materials Project id mp-782035)

       176       10      -23        0      -19        0  
        10      244      -82        0       -9        0  
       -23      -82      111        0      -63        0  
         0        0        0       30        0        1  
       -19       -9      -63        0       50        0  
         0        0        0        1        0       80  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 37.889 GPaEV = 134.17 GPaGV = 73.733 GPaνV = -0.090181
ReussKR = -6.3125 GPaER = -42.844 GPaGR = -58.084 GPaνR = -0.63119
HillKH = 15.788 GPaEH = 20.146 GPaGH = 7.8248 GPaνH = 0.28733

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
-5.2831 GPa 29.98 GPa 80.02 GPa 121.77 GPa 176.94 GPa 287.57 GPa
Stiffness matrix is not definite positive, crystal is mechanically unstable
No further analysis will be performed.