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-1986)

       152      114      114        0        0        0  
       114      152      114        0        0        0  
       114      114      152        0        0        0  
         0        0        0       65        0        0  
         0        0        0        0       65        0  
         0        0        0        0        0       65  

Average properties

Averaging scheme	Bulk modulus	Young's modulus	Shear modulus	Poisson's ratio
Voigt	KV = 126.67 GPa	EV = 124.53 GPa	GV = 46.6 GPa	νV = 0.33615
Reuss	KR = 126.67 GPa	ER = 91.144 GPa	GR = 33.021 GPa	νR = 0.38007
Hill	KH = 126.67 GPa	EH = 108.11 GPa	GH = 39.811 GPa	νH = 0.35775

Eigenvalues of the stiffness matrix

λ1	λ2	λ3	λ4	λ5	λ6
38 GPa	38 GPa	65 GPa	65 GPa	65 GPa	380 GPa

Variations of the elastic moduli

	Young's modulus		Linear compressibility		Shear modulus		Poisson's ratio
	Emin	Emax	βmin	βmax	Gmin	Gmax	νmin	νmax
Value	54.286 GPa	166.52 GPa	2.6316 TPa–1	2.6316 TPa–1	19 GPa	65 GPa	-0.15556	0.86667	Value
Anisotropy	3.067		1.0000		3.421		∞		Anisotropy
Axis	1.0000 0.0000 0.0000	0.5774 0.5774 0.5773	0.0000 0.0000 1.0000	0.9659 0.0000 0.2588	0.7071 -0.0003 0.7071	0.0000 0.0000 1.0000	0.7071 0.0001 -0.7071	0.0000 0.7071 0.7071	Axis
					0.7071 -0.0005 -0.7071	0.7660 0.6428 -0.0000	-0.7071 -0.0002 -0.7071	-1.0000 0.0000 -0.0000	Second axis

Spatial dependence of Young's modulus

[[152.0, 114.0, 114.0, 0.0, 0.0, 0.0], [114.0, 152.0, 114.0, 0.0, 0.0, 0.0], [114.0, 114.0, 152.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 65.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 65.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 65.0]] ZnO (Materials Project id <a href="https://www.materialsproject.org/materials/mp-1986" target="_blank">mp-1986</a>) young

Spatial dependence of linear compressibility

[[152.0, 114.0, 114.0, 0.0, 0.0, 0.0], [114.0, 152.0, 114.0, 0.0, 0.0, 0.0], [114.0, 114.0, 152.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 65.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 65.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 65.0]] ZnO (Materials Project id <a href="https://www.materialsproject.org/materials/mp-1986" target="_blank">mp-1986</a>) lc

Spatial dependence of shear modulus

[[152.0, 114.0, 114.0, 0.0, 0.0, 0.0], [114.0, 152.0, 114.0, 0.0, 0.0, 0.0], [114.0, 114.0, 152.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 65.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 65.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 65.0]] ZnO (Materials Project id <a href="https://www.materialsproject.org/materials/mp-1986" target="_blank">mp-1986</a>) shear

Spatial dependence of Poisson's ratio

[[152.0, 114.0, 114.0, 0.0, 0.0, 0.0], [114.0, 152.0, 114.0, 0.0, 0.0, 0.0], [114.0, 114.0, 152.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 65.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 65.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 65.0]] ZnO (Materials Project id <a href="https://www.materialsproject.org/materials/mp-1986" target="_blank">mp-1986</a>) poisson

Code version: 2023.01.19 (running on Python 3.10.6)