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 ZnO (Materials Project id mp-13161)

       408       31       31        0        0        0  
        31      408       31        0        0        0  
        31       31      408        0        0        0  
         0        0        0      -60        0        0  
         0        0        0        0      -60        0  
         0        0        0        0        0      -60  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 156.67 GPaEV = 109.06 GPaGV = 39.4 GPaνV = 0.38398
ReussKR = 156.67 GPaER = -521.71 GPaGR = -126.94 GPaνR = 1.055
HillKH = 156.67 GPaEH = -144.79 GPaGH = -43.768 GPaνH = 0.65403

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
-60 GPa -60 GPa -60 GPa 377 GPa 377 GPa 470 GPa
Stiffness matrix is not definite positive, crystal is mechanically unstable
No further analysis will be performed.