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 Si2W (Materials Project id mp-8939)

       422       80      144        0        0        0  
        80      422      144        0        0        0  
       144      144      412        0        0        0  
         0        0        0      138        0        0  
         0        0        0        0      138        0  
         0        0        0        0        0      171  

Average properties

Averaging scheme	Bulk modulus	Young's modulus	Shear modulus	Poisson's ratio
Voigt	KV = 221.33 GPa	EV = 364.28 GPa	GV = 148.6 GPa	νV = 0.2257
Reuss	KR = 220.47 GPa	ER = 359.03 GPa	GR = 146.11 GPa	νR = 0.22859
Hill	KH = 220.9 GPa	EH = 361.65 GPa	GH = 147.36 GPa	νH = 0.22714

Eigenvalues of the stiffness matrix

λ1	λ2	λ3	λ4	λ5	λ6
138 GPa	138 GPa	171 GPa	248.44 GPa	342 GPa	665.56 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	329.39 GPa	369.3 GPa	1.2942 TPa–1	1.6208 TPa–1	133.59 GPa	171 GPa	0.079829	0.32161	Value
Anisotropy	1.121		1.2523		1.28		4.0288		Anisotropy
Axis	0.0000 0.0000 1.0000	0.9243 0.3815 -0.0000	0.0000 0.0000 1.0000	1.0000 0.0000 0.0000	0.7071 -0.0003 0.7071	0.8329 0.5534 0.0000	0.7325 0.6808 0.0000	0.7434 0.6688 -0.0000	Axis
					0.7071 -0.0005 -0.7071	-0.5534 0.8329 0.0000	-0.6808 0.7325 -0.0000	-0.0000 0.0000 -1.0000	Second axis

Spatial dependence of Young's modulus

[[422.0, 80.0, 144.0, 0.0, 0.0, 0.0], [80.0, 422.0, 144.0, 0.0, 0.0, 0.0], [144.0, 144.0, 412.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 138.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 138.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 171.0]] Si2W (Materials Project id <a href="https://www.materialsproject.org/materials/mp-8939" target="_blank">mp-8939</a>) young

Spatial dependence of linear compressibility

[[422.0, 80.0, 144.0, 0.0, 0.0, 0.0], [80.0, 422.0, 144.0, 0.0, 0.0, 0.0], [144.0, 144.0, 412.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 138.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 138.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 171.0]] Si2W (Materials Project id <a href="https://www.materialsproject.org/materials/mp-8939" target="_blank">mp-8939</a>) lc

Spatial dependence of shear modulus

[[422.0, 80.0, 144.0, 0.0, 0.0, 0.0], [80.0, 422.0, 144.0, 0.0, 0.0, 0.0], [144.0, 144.0, 412.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 138.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 138.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 171.0]] Si2W (Materials Project id <a href="https://www.materialsproject.org/materials/mp-8939" target="_blank">mp-8939</a>) shear

Spatial dependence of Poisson's ratio

[[422.0, 80.0, 144.0, 0.0, 0.0, 0.0], [80.0, 422.0, 144.0, 0.0, 0.0, 0.0], [144.0, 144.0, 412.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 138.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 138.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 171.0]] Si2W (Materials Project id <a href="https://www.materialsproject.org/materials/mp-8939" target="_blank">mp-8939</a>) poisson

Code version: 2020.07.26 (running on Python 3.7.2)