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 Fe (Materials Project id mp-13)

       247      150      150        0        0        0  
       150      247      150        0        0        0  
       150      150      247        0        0        0  
         0        0        0       97        0        0  
         0        0        0        0       97        0  
         0        0        0        0        0       97  

Average properties

Averaging scheme	Bulk modulus	Young's modulus	Shear modulus	Poisson's ratio
Voigt	KV = 182.33 GPa	EV = 203.88 GPa	GV = 77.6 GPa	νV = 0.31364
Reuss	KR = 182.33 GPa	ER = 184.49 GPa	GR = 69.286 GPa	νR = 0.33136
Hill	KH = 182.33 GPa	EH = 194.25 GPa	GH = 73.443 GPa	νH = 0.32244

Eigenvalues of the stiffness matrix

λ1	λ2	λ3	λ4	λ5	λ6
97 GPa	97 GPa	97 GPa	97 GPa	97 GPa	547 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	133.65 GPa	247.17 GPa	1.8282 TPa–1	1.8282 TPa–1	48.5 GPa	97 GPa	0.050913	0.57637	Value
Anisotropy	1.849		1.0000		2		11.3207		Anisotropy
Axis	1.0000 0.0000 0.0000	-0.5774 0.5774 0.5773	0.0000 0.0000 1.0000	0.9659 0.0000 0.2588	0.7071 -0.0003 0.7071	0.0000 0.0000 1.0000	0.7071 -0.0000 -0.7071	0.7071 -0.0001 0.7071	Axis
					0.7071 -0.0005 -0.7071	0.7660 0.6428 -0.0000	-0.7071 0.0002 -0.7071	0.0001 1.0000 0.0001	Second axis

Spatial dependence of Young's modulus

[[247.0, 150.0, 150.0, 0.0, 0.0, 0.0], [150.0, 247.0, 150.0, 0.0, 0.0, 0.0], [150.0, 150.0, 247.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 97.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 97.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 97.0]] Fe (Materials Project id <a href="https://www.materialsproject.org/materials/mp-13" target="_blank">mp-13</a>) young

Spatial dependence of linear compressibility

[[247.0, 150.0, 150.0, 0.0, 0.0, 0.0], [150.0, 247.0, 150.0, 0.0, 0.0, 0.0], [150.0, 150.0, 247.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 97.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 97.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 97.0]] Fe (Materials Project id <a href="https://www.materialsproject.org/materials/mp-13" target="_blank">mp-13</a>) lc

Spatial dependence of shear modulus

[[247.0, 150.0, 150.0, 0.0, 0.0, 0.0], [150.0, 247.0, 150.0, 0.0, 0.0, 0.0], [150.0, 150.0, 247.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 97.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 97.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 97.0]] Fe (Materials Project id <a href="https://www.materialsproject.org/materials/mp-13" target="_blank">mp-13</a>) shear

Spatial dependence of Poisson's ratio

[[247.0, 150.0, 150.0, 0.0, 0.0, 0.0], [150.0, 247.0, 150.0, 0.0, 0.0, 0.0], [150.0, 150.0, 247.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 97.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 97.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 97.0]] Fe (Materials Project id <a href="https://www.materialsproject.org/materials/mp-13" target="_blank">mp-13</a>) poisson

Code version: 2023.01.19 (running on Python 3.10.6)