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 TeO2 (Materials Project id mp-2125)

        84       13       24        0        0        0  
        13       25       12        0        0        0  
        24       12       33        0        0        0  
         0        0        0       14        0        0  
         0        0        0        0       33        0  
         0        0        0        0        0       18  

Average properties

Averaging scheme	Bulk modulus	Young's modulus	Shear modulus	Poisson's ratio
Voigt	KV = 26.667 GPa	EV = 46.452 GPa	GV = 19.2 GPa	νV = 0.20968
Reuss	KR = 19.909 GPa	ER = 35.497 GPa	GR = 14.756 GPa	νR = 0.20283
Hill	KH = 23.288 GPa	EH = 40.976 GPa	GH = 16.978 GPa	νH = 0.20674

Eigenvalues of the stiffness matrix

λ1	λ2	λ3	λ4	λ5	λ6
14 GPa	16.042 GPa	18 GPa	28.643 GPa	33 GPa	97.315 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	20.362 GPa	76.092 GPa	2.1469 TPa–1	30.392 TPa–1	8.102 GPa	33 GPa	-0.12303	0.65198	Value
Anisotropy	3.737		14.1562		4.073		∞		Anisotropy
Axis	0.0000 1.0000 0.0000	0.8896 0.0000 0.4567	1.0000 0.0000 0.0000	0.0000 1.0000 0.0000	-0.0001 0.7071 0.7071	0.0000 0.0000 1.0000	0.7293 0.0001 -0.6841	1.0000 0.0002 0.0000	Axis
					0.0000 0.7071 -0.7071	1.0000 0.0000 -0.0000	-0.6841 -0.0000 -0.7293	-0.0000 0.0002 -1.0000	Second axis

Spatial dependence of Young's modulus

[[84.0, 13.0, 24.0, 0.0, 0.0, 0.0], [13.0, 25.0, 12.0, 0.0, 0.0, 0.0], [24.0, 12.0, 33.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 14.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 33.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 18.0]] TeO2 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-2125" target="_blank">mp-2125</a>) young

Spatial dependence of linear compressibility

[[84.0, 13.0, 24.0, 0.0, 0.0, 0.0], [13.0, 25.0, 12.0, 0.0, 0.0, 0.0], [24.0, 12.0, 33.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 14.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 33.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 18.0]] TeO2 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-2125" target="_blank">mp-2125</a>) lc

Spatial dependence of shear modulus

[[84.0, 13.0, 24.0, 0.0, 0.0, 0.0], [13.0, 25.0, 12.0, 0.0, 0.0, 0.0], [24.0, 12.0, 33.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 14.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 33.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 18.0]] TeO2 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-2125" target="_blank">mp-2125</a>) shear

Spatial dependence of Poisson's ratio

[[84.0, 13.0, 24.0, 0.0, 0.0, 0.0], [13.0, 25.0, 12.0, 0.0, 0.0, 0.0], [24.0, 12.0, 33.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 14.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 33.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 18.0]] TeO2 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-2125" target="_blank">mp-2125</a>) poisson

Code version: 2023.01.19 (running on Python 3.10.6)