ELATE: Elastic tensor analysis

Welcome to ELATE, the online tool for analysis of elastic tensors, developed by Romain Gaillac and François-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-997630)

       263      123      109        0        0        0  
       123      263      109        0        0        0  
       109      109      299        0        0        0  
         0        0        0      -16        0        0  
         0        0        0        0      -16        0  
         0        0        0        0        0       70

Average properties

Averaging scheme	Bulk modulus	Young's modulus	Shear modulus	Poisson's ratio
Voigt	K_V = 167.44 GPa	E_V = 110.81 GPa	G_V = 39.867 GPa	ν_V = 0.38971
Reuss	K_R = 167.25 GPa	E_R = -198.67 GPa	G_R = -58.502 GPa	ν_R = 0.69798
Hill	K_H = 167.35 GPa	E_H = -28.482 GPa	G_H = -9.3178 GPa	ν_H = 0.52837

Eigenvalues of the stiffness matrix

λ₁	λ₂	λ₃	λ₄	λ₅	λ₆
-16 GPa	-16 GPa	70 GPa	140 GPa	182.33 GPa	502.67 GPa

Stiffness matrix is not definite positive, crystal is mechanically unstable
No further analysis will be performed.

Code version: 2023.01.19 (running on Python 3.10.6)