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 CeTe (Materials Project id mp-1525)

       109       25       25        0        0        0  
        25      109       25        0        0        0  
        25       25      109        0        0        0  
         0        0        0        1        0        0  
         0        0        0        0        1        0  
         0        0        0        0        0        1  

Average properties

Averaging scheme	Bulk modulus	Young's modulus	Shear modulus	Poisson's ratio
Voigt	KV = 53 GPa	EV = 47.051 GPa	GV = 17.4 GPa	νV = 0.35204
Reuss	KR = 53 GPa	ER = 4.8716 GPa	GR = 1.6406 GPa	νR = 0.48468
Hill	KH = 53 GPa	EH = 26.947 GPa	GH = 9.5203 GPa	νH = 0.41526

Eigenvalues of the stiffness matrix

λ1	λ2	λ3	λ4	λ5	λ6
1 GPa	1 GPa	1 GPa	84 GPa	84 GPa	159 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	2.9813 GPa	99.672 GPa	6.2893 TPa–1	6.2893 TPa–1	1 GPa	42 GPa	0.007367	0.96788	Value
Anisotropy	33.43		1.0000		42		131.3800		Anisotropy
Axis	0.5774 0.5773 -0.5774	1.0000 0.0000 0.0000	0.9659 0.0000 0.2588	0.3036 0.7330 0.6088	0.0000 0.0000 1.0000	0.7071 0.0001 -0.7071	-0.7071 0.0000 0.7071	0.7071 0.0000 -0.7071	Axis
					1.0000 0.0000 -0.0000	-0.7071 -0.0002 -0.7071	0.0000 -1.0000 0.0000	-0.7071 0.0001 -0.7071	Second axis

Spatial dependence of Young's modulus

[[109.0, 25.0, 25.0, 0.0, 0.0, 0.0], [25.0, 109.0, 25.0, 0.0, 0.0, 0.0], [25.0, 25.0, 109.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 1.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 1.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 1.0]] CeTe (Materials Project id <a href="https://www.materialsproject.org/materials/mp-1525" target="_blank">mp-1525</a>) young

Spatial dependence of linear compressibility

[[109.0, 25.0, 25.0, 0.0, 0.0, 0.0], [25.0, 109.0, 25.0, 0.0, 0.0, 0.0], [25.0, 25.0, 109.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 1.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 1.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 1.0]] CeTe (Materials Project id <a href="https://www.materialsproject.org/materials/mp-1525" target="_blank">mp-1525</a>) lc

Spatial dependence of shear modulus

[[109.0, 25.0, 25.0, 0.0, 0.0, 0.0], [25.0, 109.0, 25.0, 0.0, 0.0, 0.0], [25.0, 25.0, 109.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 1.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 1.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 1.0]] CeTe (Materials Project id <a href="https://www.materialsproject.org/materials/mp-1525" target="_blank">mp-1525</a>) shear

Spatial dependence of Poisson's ratio

[[109.0, 25.0, 25.0, 0.0, 0.0, 0.0], [25.0, 109.0, 25.0, 0.0, 0.0, 0.0], [25.0, 25.0, 109.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 1.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 1.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 1.0]] CeTe (Materials Project id <a href="https://www.materialsproject.org/materials/mp-1525" target="_blank">mp-1525</a>) poisson

Code version: 2020.07.26 (running on Python 3.7.2)