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 YbCu2 (Materials Project id mp-567538)

        95       42       29        0        0        0  
        42      101       55        0        0        0  
        29       55       99        0        0        0  
         0        0        0       37        0        0  
         0        0        0        0       24        0  
         0        0        0        0        0       24  

Average properties

Averaging scheme	Bulk modulus	Young's modulus	Shear modulus	Poisson's ratio
Voigt	KV = 60.778 GPa	EV = 73.418 GPa	GV = 28.267 GPa	νV = 0.29867
Reuss	KR = 59.719 GPa	ER = 70.044 GPa	GR = 26.847 GPa	νR = 0.30452
Hill	KH = 60.248 GPa	EH = 71.733 GPa	GH = 27.557 GPa	νH = 0.30156

Eigenvalues of the stiffness matrix

λ1	λ2	λ3	λ4	λ5	λ6
24 GPa	24 GPa	37 GPa	42.454 GPa	68.85 GPa	183.7 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	59.568 GPa	94.04 GPa	3.7137 TPa–1	7.0623 TPa–1	21.762 GPa	37 GPa	0.079045	0.51168	Value
Anisotropy	1.579		1.9017		1.7		6.4733		Anisotropy
Axis	0.6575 0.0000 0.7534	-0.0000 0.6804 0.7328	0.0000 1.0000 0.0000	1.0000 0.0000 0.0000	0.3195 0.7071 0.6308	-0.0006 -0.0006 1.0000	0.0000 0.0000 1.0000	-0.0004 -0.0002 1.0000	Axis
					-0.3195 0.7071 -0.6308	-0.0000 1.0000 0.0006	-1.0000 0.0000 0.0000	0.0000 1.0000 0.0002	Second axis

Spatial dependence of Young's modulus

[[95.0, 42.0, 29.0, 0.0, 0.0, 0.0], [42.0, 101.0, 55.0, 0.0, 0.0, 0.0], [29.0, 55.0, 99.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 37.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 24.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 24.0]] YbCu2 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-567538" target="_blank">mp-567538</a>) young

Spatial dependence of linear compressibility

[[95.0, 42.0, 29.0, 0.0, 0.0, 0.0], [42.0, 101.0, 55.0, 0.0, 0.0, 0.0], [29.0, 55.0, 99.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 37.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 24.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 24.0]] YbCu2 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-567538" target="_blank">mp-567538</a>) lc

Spatial dependence of shear modulus

[[95.0, 42.0, 29.0, 0.0, 0.0, 0.0], [42.0, 101.0, 55.0, 0.0, 0.0, 0.0], [29.0, 55.0, 99.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 37.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 24.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 24.0]] YbCu2 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-567538" target="_blank">mp-567538</a>) shear

Spatial dependence of Poisson's ratio

[[95.0, 42.0, 29.0, 0.0, 0.0, 0.0], [42.0, 101.0, 55.0, 0.0, 0.0, 0.0], [29.0, 55.0, 99.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 37.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 24.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 24.0]] YbCu2 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-567538" target="_blank">mp-567538</a>) poisson

Code version: 2020.07.26 (running on Python 3.7.2)