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 C (Materials Project id mp-606949)

       884      155       -1        0        0        0  
       155      884       -1        0        0        0  
        -1       -1        7        0        0        0  
         0        0        0        2        0        0  
         0        0        0        0        2        0  
         0        0        0        0        0      365  

Average properties

Averaging scheme	Bulk modulus	Young's modulus	Shear modulus	Poisson's ratio
Voigt	KV = 231.22 GPa	EV = 432.39 GPa	GV = 181.93 GPa	νV = 0.18833
Reuss	KR = 6.8789 GPa	ER = 10.427 GPa	GR = 4.1796 GPa	νR = 0.24737
Hill	KH = 119.05 GPa	EH = 221.47 GPa	GH = 93.056 GPa	νH = 0.18996

Eigenvalues of the stiffness matrix

λ1	λ2	λ3	λ4	λ5	λ6
2 GPa	2 GPa	6.9981 GPa	365 GPa	729 GPa	1039 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	5.7083 GPa	857.42 GPa	1.1003 TPa–1	143.17 TPa–1	2 GPa	365 GPa	-0.00096246	0.67376	Value
Anisotropy	150.2		130.1250		182.5		∞		Anisotropy
Axis	0.5487 0.0000 -0.8360	0.7071 0.7071 0.0000	1.0000 0.0000 0.0000	0.0000 0.0000 1.0000	0.0000 0.0000 1.0000	1.0000 0.0007 0.0000	0.0000 0.0000 -1.0000	0.7104 0.6373 -0.2986	Axis
					1.0000 0.0000 -0.0000	-0.0007 1.0000 0.0000	0.9397 0.3420 0.0000	-0.2221 -0.1995 -0.9544	Second axis

Spatial dependence of Young's modulus

[[884.0, 155.0, -1.0, 0.0, 0.0, 0.0], [155.0, 884.0, -1.0, 0.0, 0.0, 0.0], [-1.0, -1.0, 7.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 2.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 2.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 365.0]] C (Materials Project id <a href="https://www.materialsproject.org/materials/mp-606949" target="_blank">mp-606949</a>) young

Spatial dependence of linear compressibility

[[884.0, 155.0, -1.0, 0.0, 0.0, 0.0], [155.0, 884.0, -1.0, 0.0, 0.0, 0.0], [-1.0, -1.0, 7.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 2.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 2.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 365.0]] C (Materials Project id <a href="https://www.materialsproject.org/materials/mp-606949" target="_blank">mp-606949</a>) lc

Spatial dependence of shear modulus

[[884.0, 155.0, -1.0, 0.0, 0.0, 0.0], [155.0, 884.0, -1.0, 0.0, 0.0, 0.0], [-1.0, -1.0, 7.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 2.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 2.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 365.0]] C (Materials Project id <a href="https://www.materialsproject.org/materials/mp-606949" target="_blank">mp-606949</a>) shear

Spatial dependence of Poisson's ratio

[[884.0, 155.0, -1.0, 0.0, 0.0, 0.0], [155.0, 884.0, -1.0, 0.0, 0.0, 0.0], [-1.0, -1.0, 7.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 2.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 2.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 365.0]] C (Materials Project id <a href="https://www.materialsproject.org/materials/mp-606949" target="_blank">mp-606949</a>) poisson

Code version: 2022.06.14 (running on Python 3.7.2)