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-2133)

       188      109       92        0        0        0  
       109      188       92        0        0        0  
        92       92      205        0        0        0  
         0        0        0       37        0        0  
         0        0        0        0       37        0  
         0        0        0        0        0       39  

Average properties

Averaging scheme	Bulk modulus	Young's modulus	Shear modulus	Poisson's ratio
Voigt	KV = 129.67 GPa	EV = 113.23 GPa	GV = 41.8 GPa	νV = 0.35446
Reuss	KR = 129.67 GPa	ER = 110.65 GPa	GR = 40.746 GPa	νR = 0.35778
Hill	KH = 129.67 GPa	EH = 111.94 GPa	GH = 41.273 GPa	νH = 0.35612

Eigenvalues of the stiffness matrix

λ1	λ2	λ3	λ4	λ5	λ6
37 GPa	37 GPa	39 GPa	79 GPa	113 GPa	389 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	102.89 GPa	148 GPa	2.5707 TPa–1	2.5707 TPa–1	37 GPa	51.011 GPa	0.23941	0.46653	Value
Anisotropy	1.438		1.0000		1.379		1.9486		Anisotropy
Axis	0.5636 0.5636 -0.6040	0.0000 0.0000 1.0000	0.2391 0.8924 -0.3827	0.9659 0.0000 0.2588	0.0000 0.0000 1.0000	0.7071 -0.0003 0.7071	0.7071 0.7071 0.0000	-0.7071 0.7071 -0.0000	Axis
					-0.7662 0.6426 -0.0000	0.7071 -0.0005 -0.7071	0.0004 -0.0004 -1.0000	-0.7071 -0.7071 -0.0000	Second axis

Spatial dependence of Young's modulus

[[188.0, 109.0, 92.0, 0.0, 0.0, 0.0], [109.0, 188.0, 92.0, 0.0, 0.0, 0.0], [92.0, 92.0, 205.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 37.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 37.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 39.0]] ZnO (Materials Project id <a href="https://www.materialsproject.org/materials/mp-2133" target="_blank">mp-2133</a>) young

Spatial dependence of linear compressibility

[[188.0, 109.0, 92.0, 0.0, 0.0, 0.0], [109.0, 188.0, 92.0, 0.0, 0.0, 0.0], [92.0, 92.0, 205.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 37.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 37.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 39.0]] ZnO (Materials Project id <a href="https://www.materialsproject.org/materials/mp-2133" target="_blank">mp-2133</a>) lc

Spatial dependence of shear modulus

[[188.0, 109.0, 92.0, 0.0, 0.0, 0.0], [109.0, 188.0, 92.0, 0.0, 0.0, 0.0], [92.0, 92.0, 205.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 37.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 37.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 39.0]] ZnO (Materials Project id <a href="https://www.materialsproject.org/materials/mp-2133" target="_blank">mp-2133</a>) shear

Spatial dependence of Poisson's ratio

[[188.0, 109.0, 92.0, 0.0, 0.0, 0.0], [109.0, 188.0, 92.0, 0.0, 0.0, 0.0], [92.0, 92.0, 205.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 37.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 37.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 39.0]] ZnO (Materials Project id <a href="https://www.materialsproject.org/materials/mp-2133" target="_blank">mp-2133</a>) poisson

Code version: 2023.01.19 (running on Python 3.10.6)