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 Eu2O3 (Materials Project id mp-647924)

       144       90       62        0       11        0  
        90      183       67        0        6        0  
        62       67      199        0        4        0  
         0        0        0       27        0       -1  
        11        6        4        0       45        0  
         0        0        0       -1        0       61  

Average properties

Averaging scheme	Bulk modulus	Young's modulus	Shear modulus	Poisson's ratio
Voigt	KV = 107.11 GPa	EV = 123.16 GPa	GV = 47.067 GPa	νV = 0.30836
Reuss	KR = 104.23 GPa	ER = 110.69 GPa	GR = 41.834 GPa	νR = 0.323
Hill	KH = 105.67 GPa	EH = 116.95 GPa	GH = 44.45 GPa	νH = 0.31554

Eigenvalues of the stiffness matrix

λ1	λ2	λ3	λ4	λ5	λ6
26.971 GPa	43.508 GPa	61.029 GPa	71.823 GPa	132.45 GPa	323.21 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	81.881 GPa	166.02 GPa	2.2962 TPa–1	4.7435 TPa–1	26.971 GPa	65.046 GPa	0.055345	0.58422	Value
Anisotropy	2.028		2.0658		2.412		10.5561		Anisotropy
Axis	0.0250 0.7439 0.6679	-0.0103 -0.0000 0.9999	0.0000 1.0000 0.0000	-0.9123 -0.0000 0.4095	0.0294 -0.0000 0.9996	-0.3820 0.5794 -0.7199	0.5965 0.4761 -0.6461	-0.5812 0.5282 -0.6191	Axis
					-0.0000 1.0000 0.0000	-0.4823 0.5395 0.6901	-0.7749 0.5512 -0.3094	0.1244 -0.6941 -0.7090	Second axis

Spatial dependence of Young's modulus

[[144.0, 90.0, 62.0, 0.0, 11.0, 0.0], [90.0, 183.0, 67.0, 0.0, 6.0, 0.0], [62.0, 67.0, 199.0, 0.0, 4.0, 0.0], [0.0, 0.0, 0.0, 27.0, 0.0, -1.0], [11.0, 6.0, 4.0, 0.0, 45.0, 0.0], [0.0, 0.0, 0.0, -1.0, 0.0, 61.0]] Eu2O3 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-647924" target="_blank">mp-647924</a>) young

Spatial dependence of linear compressibility

[[144.0, 90.0, 62.0, 0.0, 11.0, 0.0], [90.0, 183.0, 67.0, 0.0, 6.0, 0.0], [62.0, 67.0, 199.0, 0.0, 4.0, 0.0], [0.0, 0.0, 0.0, 27.0, 0.0, -1.0], [11.0, 6.0, 4.0, 0.0, 45.0, 0.0], [0.0, 0.0, 0.0, -1.0, 0.0, 61.0]] Eu2O3 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-647924" target="_blank">mp-647924</a>) lc

Spatial dependence of shear modulus

[[144.0, 90.0, 62.0, 0.0, 11.0, 0.0], [90.0, 183.0, 67.0, 0.0, 6.0, 0.0], [62.0, 67.0, 199.0, 0.0, 4.0, 0.0], [0.0, 0.0, 0.0, 27.0, 0.0, -1.0], [11.0, 6.0, 4.0, 0.0, 45.0, 0.0], [0.0, 0.0, 0.0, -1.0, 0.0, 61.0]] Eu2O3 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-647924" target="_blank">mp-647924</a>) shear

Spatial dependence of Poisson's ratio

[[144.0, 90.0, 62.0, 0.0, 11.0, 0.0], [90.0, 183.0, 67.0, 0.0, 6.0, 0.0], [62.0, 67.0, 199.0, 0.0, 4.0, 0.0], [0.0, 0.0, 0.0, 27.0, 0.0, -1.0], [11.0, 6.0, 4.0, 0.0, 45.0, 0.0], [0.0, 0.0, 0.0, -1.0, 0.0, 61.0]] Eu2O3 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-647924" target="_blank">mp-647924</a>) poisson

Code version: 2020.07.26 (running on Python 3.7.2)