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 Sc2S3 (Materials Project id mp-401)

       113       22       31        0        0        0  
        22      117       37        0        0        0  
        31       37       93        0        0        0  
         0        0        0       42        0        0  
         0        0        0        0       36        0  
         0        0        0        0        0       33  

Average properties

Averaging scheme	Bulk modulus	Young's modulus	Shear modulus	Poisson's ratio
Voigt	KV = 55.889 GPa	EV = 92.404 GPa	GV = 37.733 GPa	νV = 0.22444
Reuss	KR = 55.705 GPa	ER = 90.609 GPa	GR = 36.866 GPa	νR = 0.2289
Hill	KH = 55.797 GPa	EH = 91.508 GPa	GH = 37.3 GPa	νH = 0.22666

Eigenvalues of the stiffness matrix

λ1	λ2	λ3	λ4	λ5	λ6
33 GPa	36 GPa	42 GPa	61.922 GPa	92.99 GPa	168.09 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	75.989 GPa	105.49 GPa	5.3209 TPa–1	6.6383 TPa–1	31.47 GPa	46.403 GPa	0.094512	0.36646	Value
Anisotropy	1.388		1.2476		1.475		3.8774		Anisotropy
Axis	0.0000 0.0000 1.0000	-0.0000 0.8692 -0.4944	0.0000 1.0000 0.0000	0.0000 0.0000 1.0000	-0.4566 0.5399 0.7071	0.7071 0.7071 -0.0000	-1.0000 -0.0000 -0.0000	-0.0000 1.0000 -0.0000	Axis
					-0.4565 0.5400 -0.7071	-0.7071 0.7071 -0.0000	0.0000 -1.0000 0.0000	-0.0000 0.0000 1.0000	Second axis

Spatial dependence of Young's modulus

[[113.0, 22.0, 31.0, 0.0, 0.0, 0.0], [22.0, 117.0, 37.0, 0.0, 0.0, 0.0], [31.0, 37.0, 93.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 42.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 36.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 33.0]] Sc2S3 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-401" target="_blank">mp-401</a>) young

Spatial dependence of linear compressibility

[[113.0, 22.0, 31.0, 0.0, 0.0, 0.0], [22.0, 117.0, 37.0, 0.0, 0.0, 0.0], [31.0, 37.0, 93.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 42.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 36.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 33.0]] Sc2S3 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-401" target="_blank">mp-401</a>) lc

Spatial dependence of shear modulus

[[113.0, 22.0, 31.0, 0.0, 0.0, 0.0], [22.0, 117.0, 37.0, 0.0, 0.0, 0.0], [31.0, 37.0, 93.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 42.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 36.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 33.0]] Sc2S3 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-401" target="_blank">mp-401</a>) shear

Spatial dependence of Poisson's ratio

[[113.0, 22.0, 31.0, 0.0, 0.0, 0.0], [22.0, 117.0, 37.0, 0.0, 0.0, 0.0], [31.0, 37.0, 93.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 42.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 36.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 33.0]] Sc2S3 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-401" target="_blank">mp-401</a>) poisson

Code version: 2020.07.26 (running on Python 3.7.2)