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 MgIn (Materials Project id mp-2313)

        67       28       24        0        0        0  
        28       67       24        0        0        0  
        24       24       72        0        0        0  
         0        0        0       10        0        0  
         0        0        0        0       10        0  
         0        0        0        0        0       17  

Average properties

Averaging scheme	Bulk modulus	Young's modulus	Shear modulus	Poisson's ratio
Voigt	KV = 39.778 GPa	EV = 42.481 GPa	GV = 16.067 GPa	νV = 0.32201
Reuss	KR = 39.776 GPa	ER = 38.074 GPa	GR = 14.202 GPa	νR = 0.34046
Hill	KH = 39.777 GPa	EH = 40.293 GPa	GH = 15.134 GPa	νH = 0.33117

Eigenvalues of the stiffness matrix

λ1	λ2	λ3	λ4	λ5	λ6
10 GPa	10 GPa	17 GPa	39 GPa	47.664 GPa	119.34 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	30.853 GPa	59.874 GPa	8.263 TPa–1	8.4388 TPa–1	10 GPa	22.578 GPa	0.16515	0.57034	Value
Anisotropy	1.941		1.0213		2.258		3.4534		Anisotropy
Axis	0.5198 0.5197 -0.6780	0.0000 0.0000 1.0000	0.0000 0.0000 1.0000	0.9659 0.2588 0.0000	0.0000 0.0000 1.0000	0.7071 0.0001 -0.7071	-0.6313 -0.0000 0.7756	0.6862 0.0001 -0.7275	Axis
					-0.7660 0.6428 -0.0000	-0.7071 -0.0002 -0.7071	0.0000 -1.0000 -0.0000	-0.7275 -0.0000 -0.6862	Second axis

Spatial dependence of Young's modulus

[[67.0, 28.0, 24.0, 0.0, 0.0, 0.0], [28.0, 67.0, 24.0, 0.0, 0.0, 0.0], [24.0, 24.0, 72.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 10.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 10.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 17.0]] MgIn (Materials Project id <a href="https://www.materialsproject.org/materials/mp-2313" target="_blank">mp-2313</a>) young

Spatial dependence of linear compressibility

[[67.0, 28.0, 24.0, 0.0, 0.0, 0.0], [28.0, 67.0, 24.0, 0.0, 0.0, 0.0], [24.0, 24.0, 72.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 10.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 10.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 17.0]] MgIn (Materials Project id <a href="https://www.materialsproject.org/materials/mp-2313" target="_blank">mp-2313</a>) lc

Spatial dependence of shear modulus

[[67.0, 28.0, 24.0, 0.0, 0.0, 0.0], [28.0, 67.0, 24.0, 0.0, 0.0, 0.0], [24.0, 24.0, 72.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 10.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 10.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 17.0]] MgIn (Materials Project id <a href="https://www.materialsproject.org/materials/mp-2313" target="_blank">mp-2313</a>) shear

Spatial dependence of Poisson's ratio

[[67.0, 28.0, 24.0, 0.0, 0.0, 0.0], [28.0, 67.0, 24.0, 0.0, 0.0, 0.0], [24.0, 24.0, 72.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 10.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 10.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 17.0]] MgIn (Materials Project id <a href="https://www.materialsproject.org/materials/mp-2313" target="_blank">mp-2313</a>) poisson

Code version: 2020.07.26 (running on Python 3.7.2)