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 Mg2Ga5 (Materials Project id mp-27668)

       101       16       16        0        0        0  
        16       89       31        0        0        0  
        16       31       89        0        0        0  
         0        0        0       36        0        0  
         0        0        0        0       31        0  
         0        0        0        0        0       31  

Average properties

Averaging scheme	Bulk modulus	Young's modulus	Shear modulus	Poisson's ratio
Voigt	KV = 45 GPa	EV = 81.479 GPa	GV = 34 GPa	νV = 0.19822
Reuss	KR = 44.992 GPa	ER = 80.18 GPa	GR = 33.325 GPa	νR = 0.20299
Hill	KH = 44.996 GPa	EH = 80.831 GPa	GH = 33.663 GPa	νH = 0.2006

Eigenvalues of the stiffness matrix

λ1	λ2	λ3	λ4	λ5	λ6
31 GPa	31 GPa	36 GPa	58 GPa	85.959 GPa	135.04 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	74.17 GPa	96.733 GPa	7.3225 TPa–1	7.581 TPa–1	29 GPa	41.002 GPa	0.10626	0.32921	Value
Anisotropy	1.304		1.0353		1.414		3.0981		Anisotropy
Axis	0.5361 -0.0000 0.8442	1.0000 0.0000 0.0000	0.0000 0.9659 0.2588	1.0000 0.0000 0.0000	0.0002 0.7071 -0.7071	-0.7071 0.5000 0.5000	0.0000 0.0000 1.0000	-0.0004 -0.0002 1.0000	Axis
					0.0002 -0.7071 -0.7071	-0.7071 -0.5000 -0.5000	-1.0000 0.0000 0.0000	0.0000 1.0000 0.0002	Second axis

Spatial dependence of Young's modulus

[[101.0, 16.0, 16.0, 0.0, 0.0, 0.0], [16.0, 89.0, 31.0, 0.0, 0.0, 0.0], [16.0, 31.0, 89.0, 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, 31.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 31.0]] Mg2Ga5 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-27668" target="_blank">mp-27668</a>) young

Spatial dependence of linear compressibility

[[101.0, 16.0, 16.0, 0.0, 0.0, 0.0], [16.0, 89.0, 31.0, 0.0, 0.0, 0.0], [16.0, 31.0, 89.0, 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, 31.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 31.0]] Mg2Ga5 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-27668" target="_blank">mp-27668</a>) lc

Spatial dependence of shear modulus

[[101.0, 16.0, 16.0, 0.0, 0.0, 0.0], [16.0, 89.0, 31.0, 0.0, 0.0, 0.0], [16.0, 31.0, 89.0, 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, 31.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 31.0]] Mg2Ga5 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-27668" target="_blank">mp-27668</a>) shear

Spatial dependence of Poisson's ratio

[[101.0, 16.0, 16.0, 0.0, 0.0, 0.0], [16.0, 89.0, 31.0, 0.0, 0.0, 0.0], [16.0, 31.0, 89.0, 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, 31.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 31.0]] Mg2Ga5 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-27668" target="_blank">mp-27668</a>) poisson

Code version: 2020.07.26 (running on Python 3.7.2)