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-1017539)

       236      158        0        0        0        0  
       158      236        0        0        0        0  
         0        0        4        0        0        0  
         0        0        0       -2        0        0  
         0        0        0        0       -2        0  
         0        0        0        0        0       39

Average properties

Averaging scheme	Bulk modulus	Young's modulus	Shear modulus	Poisson's ratio
Voigt	K_V = 88 GPa	E_V = 76.435 GPa	G_V = 28.2 GPa	ν_V = 0.35524
Reuss	K_R = 3.9204 GPa	E_R = -79.548 GPa	G_R = -8.1474 GPa	ν_R = 3.8818
Hill	K_H = 45.96 GPa	E_H = 28.04 GPa	G_H = 10.026 GPa	ν_H = 0.39832

Eigenvalues of the stiffness matrix

λ₁	λ₂	λ₃	λ₄	λ₅	λ₆
-2 GPa	-2 GPa	4 GPa	39 GPa	78 GPa	394 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)