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 Al13Os4 (Materials Project id mp-567929)

       229       84      108        0       -2        0  
        84      285      107        0      -19        0  
       108      107      218        0       11        0  
         0        0        0       86        0       -3  
        -2      -19       11        0      114        0  
         0        0        0       -3        0       57  

Average properties

Averaging scheme	Bulk modulus	Young's modulus	Shear modulus	Poisson's ratio
Voigt	KV = 147.78 GPa	EV = 203.89 GPa	GV = 80.267 GPa	νV = 0.27005
Reuss	KR = 146.69 GPa	ER = 188.96 GPa	GR = 73.508 GPa	νR = 0.28531
Hill	KH = 147.24 GPa	EH = 196.46 GPa	GH = 76.888 GPa	νH = 0.27761

Eigenvalues of the stiffness matrix

λ1	λ2	λ3	λ4	λ5	λ6
56.693 GPa	86.307 GPa	97.132 GPa	123.96 GPa	179.33 GPa	445.57 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	144.5 GPa	266.31 GPa	1.863 TPa–1	2.5737 TPa–1	54.444 GPa	112.94 GPa	0.045668	0.48518	Value
Anisotropy	1.843		1.3815		2.074		10.6242		Anisotropy
Axis	0.1013 0.0000 -0.9949	0.6973 -0.0000 0.7167	0.0000 1.0000 0.0000	0.9407 -0.0000 0.3391	-0.5344 0.3740 -0.7580	-0.0692 0.0000 0.9976	0.5457 0.3485 0.7621	-0.5466 0.5656 0.6175	Axis
					0.6570 -0.3804 -0.6509	-0.9976 0.0000 -0.0692	-0.6281 -0.4318 0.6473	-0.6409 -0.7572 0.1261	Second axis

Spatial dependence of Young's modulus

[[229.0, 84.0, 108.0, 0.0, -2.0, 0.0], [84.0, 285.0, 107.0, 0.0, -19.0, 0.0], [108.0, 107.0, 218.0, 0.0, 11.0, 0.0], [0.0, 0.0, 0.0, 86.0, 0.0, -3.0], [-2.0, -19.0, 11.0, 0.0, 114.0, 0.0], [0.0, 0.0, 0.0, -3.0, 0.0, 57.0]] Al13Os4 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-567929" target="_blank">mp-567929</a>) young

Spatial dependence of linear compressibility

[[229.0, 84.0, 108.0, 0.0, -2.0, 0.0], [84.0, 285.0, 107.0, 0.0, -19.0, 0.0], [108.0, 107.0, 218.0, 0.0, 11.0, 0.0], [0.0, 0.0, 0.0, 86.0, 0.0, -3.0], [-2.0, -19.0, 11.0, 0.0, 114.0, 0.0], [0.0, 0.0, 0.0, -3.0, 0.0, 57.0]] Al13Os4 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-567929" target="_blank">mp-567929</a>) lc

Spatial dependence of shear modulus

[[229.0, 84.0, 108.0, 0.0, -2.0, 0.0], [84.0, 285.0, 107.0, 0.0, -19.0, 0.0], [108.0, 107.0, 218.0, 0.0, 11.0, 0.0], [0.0, 0.0, 0.0, 86.0, 0.0, -3.0], [-2.0, -19.0, 11.0, 0.0, 114.0, 0.0], [0.0, 0.0, 0.0, -3.0, 0.0, 57.0]] Al13Os4 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-567929" target="_blank">mp-567929</a>) shear

Spatial dependence of Poisson's ratio

[[229.0, 84.0, 108.0, 0.0, -2.0, 0.0], [84.0, 285.0, 107.0, 0.0, -19.0, 0.0], [108.0, 107.0, 218.0, 0.0, 11.0, 0.0], [0.0, 0.0, 0.0, 86.0, 0.0, -3.0], [-2.0, -19.0, 11.0, 0.0, 114.0, 0.0], [0.0, 0.0, 0.0, -3.0, 0.0, 57.0]] Al13Os4 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-567929" target="_blank">mp-567929</a>) poisson

Code version: 2020.07.26 (running on Python 3.7.2)