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 Li3Sb (Materials Project id mp-7955)

        73       15        1        0        0        0  
        15       73        1        0        0        0  
         1        1       71        0        0        0  
         0        0        0       16        0        0  
         0        0        0        0       16        0  
         0        0        0        0        0       29  

Average properties

Averaging scheme	Bulk modulus	Young's modulus	Shear modulus	Poisson's ratio
Voigt	KV = 27.889 GPa	EV = 58.689 GPa	GV = 25.533 GPa	νV = 0.14927
Reuss	KR = 27.637 GPa	ER = 53.369 GPa	GR = 22.649 GPa	νR = 0.17816
Hill	KH = 27.763 GPa	EH = 56.059 GPa	GH = 24.091 GPa	νH = 0.16347

Eigenvalues of the stiffness matrix

λ1	λ2	λ3	λ4	λ5	λ6
16 GPa	16 GPa	29 GPa	58 GPa	70.883 GPa	88.117 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	44.163 GPa	70.977 GPa	11.207 TPa–1	13.769 TPa–1	16 GPa	34.827 GPa	0.011364	0.3801	Value
Anisotropy	1.607		1.2286		2.177		33.4491		Anisotropy
Axis	0.7094 0.0005 0.7049	0.0000 0.0000 1.0000	0.8660 0.5000 0.0000	0.0000 0.0000 1.0000	0.0000 0.0000 1.0000	-0.1699 0.6864 -0.7071	0.0000 0.0000 1.0000	0.3367 0.6202 -0.7085	Axis
					1.0000 0.0000 -0.0000	0.1700 -0.6864 -0.7071	0.1736 0.9848 -0.0000	0.3381 0.6226 0.7057	Second axis

Spatial dependence of Young's modulus

[[73.0, 15.0, 1.0, 0.0, 0.0, 0.0], [15.0, 73.0, 1.0, 0.0, 0.0, 0.0], [1.0, 1.0, 71.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 16.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 16.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 29.0]] Li3Sb (Materials Project id <a href="https://www.materialsproject.org/materials/mp-7955" target="_blank">mp-7955</a>) young

Spatial dependence of linear compressibility

[[73.0, 15.0, 1.0, 0.0, 0.0, 0.0], [15.0, 73.0, 1.0, 0.0, 0.0, 0.0], [1.0, 1.0, 71.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 16.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 16.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 29.0]] Li3Sb (Materials Project id <a href="https://www.materialsproject.org/materials/mp-7955" target="_blank">mp-7955</a>) lc

Spatial dependence of shear modulus

[[73.0, 15.0, 1.0, 0.0, 0.0, 0.0], [15.0, 73.0, 1.0, 0.0, 0.0, 0.0], [1.0, 1.0, 71.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 16.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 16.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 29.0]] Li3Sb (Materials Project id <a href="https://www.materialsproject.org/materials/mp-7955" target="_blank">mp-7955</a>) shear

Spatial dependence of Poisson's ratio

[[73.0, 15.0, 1.0, 0.0, 0.0, 0.0], [15.0, 73.0, 1.0, 0.0, 0.0, 0.0], [1.0, 1.0, 71.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 16.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 16.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 29.0]] Li3Sb (Materials Project id <a href="https://www.materialsproject.org/materials/mp-7955" target="_blank">mp-7955</a>) poisson

Code version: 2020.07.26 (running on Python 3.7.2)