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 FeSe (Materials Project id mp-1090)

       118       46       26       -1        0        0  
        46      118       26        1        0        0  
        26       26      144        0        0        0  
        -1        1        0       33        0        0  
         0        0        0        0       33       -1  
         0        0        0        0       -1       36  

Average properties

Averaging scheme	Bulk modulus	Young's modulus	Shear modulus	Poisson's ratio
Voigt	KV = 64 GPa	EV = 97.661 GPa	GV = 39.2 GPa	νV = 0.24567
Reuss	KR = 63.977 GPa	ER = 94.01 GPa	GR = 37.451 GPa	νR = 0.2551
Hill	KH = 63.989 GPa	EH = 95.842 GPa	GH = 38.326 GPa	νH = 0.25037

Eigenvalues of the stiffness matrix

λ1	λ2	λ3	λ4	λ5	λ6
32.697 GPa	32.949 GPa	36.303 GPa	72.051 GPa	115.89 GPa	192.11 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	84.496 GPa	135.76 GPa	5.0305 TPa–1	5.3 TPa–1	32.697 GPa	50.33 GPa	0.11297	0.36661	Value
Anisotropy	1.607		1.0536		1.539		3.2452		Anisotropy
Axis	0.6962 0.4019 0.5948	0.0000 0.0000 1.0000	0.0000 0.0000 1.0000	-0.9239 0.3827 0.0000	-0.0000 0.2898 0.9571	0.0000 0.6927 0.7212	0.4999 0.8661 0.0000	-0.5000 0.8660 -0.0000	Axis
					-1.0000 -0.0000 -0.0000	-0.0000 -0.7212 0.6927	0.0709 -0.0409 0.9966	-0.8631 -0.4984 -0.0818	Second axis

Spatial dependence of Young's modulus

[[118.0, 46.0, 26.0, -1.0, 0.0, 0.0], [46.0, 118.0, 26.0, 1.0, 0.0, 0.0], [26.0, 26.0, 144.0, 0.0, 0.0, 0.0], [-1.0, 1.0, 0.0, 33.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 33.0, -1.0], [0.0, 0.0, 0.0, 0.0, -1.0, 36.0]] FeSe (Materials Project id <a href="https://www.materialsproject.org/materials/mp-1090" target="_blank">mp-1090</a>) young

Spatial dependence of linear compressibility

[[118.0, 46.0, 26.0, -1.0, 0.0, 0.0], [46.0, 118.0, 26.0, 1.0, 0.0, 0.0], [26.0, 26.0, 144.0, 0.0, 0.0, 0.0], [-1.0, 1.0, 0.0, 33.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 33.0, -1.0], [0.0, 0.0, 0.0, 0.0, -1.0, 36.0]] FeSe (Materials Project id <a href="https://www.materialsproject.org/materials/mp-1090" target="_blank">mp-1090</a>) lc

Spatial dependence of shear modulus

[[118.0, 46.0, 26.0, -1.0, 0.0, 0.0], [46.0, 118.0, 26.0, 1.0, 0.0, 0.0], [26.0, 26.0, 144.0, 0.0, 0.0, 0.0], [-1.0, 1.0, 0.0, 33.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 33.0, -1.0], [0.0, 0.0, 0.0, 0.0, -1.0, 36.0]] FeSe (Materials Project id <a href="https://www.materialsproject.org/materials/mp-1090" target="_blank">mp-1090</a>) shear

Spatial dependence of Poisson's ratio

[[118.0, 46.0, 26.0, -1.0, 0.0, 0.0], [46.0, 118.0, 26.0, 1.0, 0.0, 0.0], [26.0, 26.0, 144.0, 0.0, 0.0, 0.0], [-1.0, 1.0, 0.0, 33.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 33.0, -1.0], [0.0, 0.0, 0.0, 0.0, -1.0, 36.0]] FeSe (Materials Project id <a href="https://www.materialsproject.org/materials/mp-1090" target="_blank">mp-1090</a>) poisson

Code version: 2020.07.26 (running on Python 3.7.2)