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 MoS2 (Materials Project id mp-1434)

       179       45        1        0        0        0  
        45      179        1       -0        0        0  
         1        1        3        0        0        0  
         0       -0        0        1        0        0  
         0        0        0        0        1        0  
         0        0        0        0        0       67  

Average properties

Averaging scheme	Bulk modulus	Young's modulus	Shear modulus	Poisson's ratio
Voigt	KV = 50.556 GPa	EV = 84.784 GPa	GV = 34.733 GPa	νV = 0.22049
Reuss	KR = 2.9646 GPa	ER = 4.9265 GPa	GR = 2.014 GPa	νR = 0.22304
Hill	KH = 26.76 GPa	EH = 44.855 GPa	GH = 18.374 GPa	νH = 0.22063

Eigenvalues of the stiffness matrix

λ1	λ2	λ3	λ4	λ5	λ6
1 GPa	1 GPa	2.991 GPa	67 GPa	134 GPa	224.01 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	2.664 GPa	167.5 GPa	2.9851 TPa–1	331.34 TPa–1	1 GPa	67 GPa	0.0044643	0.619	Value
Anisotropy	62.88		111.0000		67		138.6559		Anisotropy
Axis	0.3044 0.3967 0.8660	0.6088 0.7934 0.0000	0.7934 0.6088 0.0000	0.0000 0.0000 1.0000	0.0000 0.0000 1.0000	1.0000 0.0006 0.0000	0.0000 0.0000 1.0000	-0.5981 0.7405 0.3063	Axis
					1.0000 0.0000 -0.0000	-0.0006 1.0000 0.0000	0.5000 0.8660 -0.0000	0.1925 -0.2383 0.9519	Second axis

Spatial dependence of Young's modulus

[[179.0, 45.0, 1.0, 0.0, 0.0, 0.0], [45.0, 179.0, 1.0, -0.0, 0.0, 0.0], [1.0, 1.0, 3.0, 0.0, 0.0, 0.0], [0.0, -0.0, 0.0, 1.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 1.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 67.0]] MoS2 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-1434" target="_blank">mp-1434</a>) young

Spatial dependence of linear compressibility

[[179.0, 45.0, 1.0, 0.0, 0.0, 0.0], [45.0, 179.0, 1.0, -0.0, 0.0, 0.0], [1.0, 1.0, 3.0, 0.0, 0.0, 0.0], [0.0, -0.0, 0.0, 1.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 1.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 67.0]] MoS2 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-1434" target="_blank">mp-1434</a>) lc

Spatial dependence of shear modulus

[[179.0, 45.0, 1.0, 0.0, 0.0, 0.0], [45.0, 179.0, 1.0, -0.0, 0.0, 0.0], [1.0, 1.0, 3.0, 0.0, 0.0, 0.0], [0.0, -0.0, 0.0, 1.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 1.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 67.0]] MoS2 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-1434" target="_blank">mp-1434</a>) shear

Spatial dependence of Poisson's ratio

[[179.0, 45.0, 1.0, 0.0, 0.0, 0.0], [45.0, 179.0, 1.0, -0.0, 0.0, 0.0], [1.0, 1.0, 3.0, 0.0, 0.0, 0.0], [0.0, -0.0, 0.0, 1.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 1.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 67.0]] MoS2 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-1434" target="_blank">mp-1434</a>) poisson

Code version: 2023.01.19 (running on Python 3.10.6)