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 NaO3 (Materials Project id mp-22464)

        70       -3       12        0        0        0  
        -3       35        6        0        0        0  
        12        6       48        0        0        0  
         0        0        0        7        0        0  
         0        0        0        0       16        0  
         0        0        0        0        0       13  

Average properties

Averaging scheme	Bulk modulus	Young's modulus	Shear modulus	Poisson's ratio
Voigt	KV = 20.333 GPa	EV = 38.775 GPa	GV = 16.4 GPa	νV = 0.18217
Reuss	KR = 18.364 GPa	ER = 31.882 GPa	GR = 13.167 GPa	νR = 0.21065
Hill	KH = 19.349 GPa	EH = 35.348 GPa	GH = 14.784 GPa	νH = 0.19552

Eigenvalues of the stiffness matrix

λ1	λ2	λ3	λ4	λ5	λ6
7 GPa	13 GPa	16 GPa	31.126 GPa	46.592 GPa	75.282 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	21.399 GPa	66.409 GPa	13.025 TPa–1	27.259 TPa–1	7 GPa	24.656 GPa	-0.13139	0.53549	Value
Anisotropy	3.103		2.0928		3.522		∞		Anisotropy
Axis	0.0000 0.7368 0.6761	1.0000 0.0000 0.0000	1.0000 0.0000 0.0000	0.0000 1.0000 0.0000	-0.0003 -0.0000 1.0000	0.7071 0.7071 0.0000	1.0000 0.0006 -0.0000	0.0002 0.6712 -0.7412	Axis
					0.0000 1.0000 0.0000	-0.7071 0.7071 -0.0001	-0.0006 1.0000 0.0000	0.0001 -0.7412 -0.6712	Second axis

Spatial dependence of Young's modulus

[[70.0, -3.0, 12.0, 0.0, 0.0, 0.0], [-3.0, 35.0, 6.0, 0.0, 0.0, 0.0], [12.0, 6.0, 48.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 7.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 16.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 13.0]] NaO3 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-22464" target="_blank">mp-22464</a>) young

Spatial dependence of linear compressibility

[[70.0, -3.0, 12.0, 0.0, 0.0, 0.0], [-3.0, 35.0, 6.0, 0.0, 0.0, 0.0], [12.0, 6.0, 48.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 7.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 16.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 13.0]] NaO3 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-22464" target="_blank">mp-22464</a>) lc

Spatial dependence of shear modulus

[[70.0, -3.0, 12.0, 0.0, 0.0, 0.0], [-3.0, 35.0, 6.0, 0.0, 0.0, 0.0], [12.0, 6.0, 48.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 7.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 16.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 13.0]] NaO3 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-22464" target="_blank">mp-22464</a>) shear

Spatial dependence of Poisson's ratio

[[70.0, -3.0, 12.0, 0.0, 0.0, 0.0], [-3.0, 35.0, 6.0, 0.0, 0.0, 0.0], [12.0, 6.0, 48.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 7.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 16.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 13.0]] NaO3 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-22464" target="_blank">mp-22464</a>) poisson

Code version: 2020.07.26 (running on Python 3.7.2)