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 Sn4Bi2Se7 (Materials Project id mp-675477)

        64        6        7        0       15        0  
         6      113       11        0       -2        0  
         7       11       67        0       -8        0  
         0        0        0       13        0        1  
        15       -2       -8        0       21        0  
         0        0        0        1        0        6  

Average properties

Averaging scheme	Bulk modulus	Young's modulus	Shear modulus	Poisson's ratio
Voigt	KV = 32.444 GPa	EV = 55.156 GPa	GV = 22.667 GPa	νV = 0.21667
Reuss	KR = 29.91 GPa	ER = 34.613 GPa	GR = 13.24 GPa	νR = 0.30713
Hill	KH = 31.177 GPa	EH = 45.186 GPa	GH = 17.953 GPa	νH = 0.25844

Eigenvalues of the stiffness matrix

λ1	λ2	λ3	λ4	λ5	λ6
5.8599 GPa	13.14 GPa	14.44 GPa	63.967 GPa	70.013 GPa	116.58 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	19.387 GPa	110.6 GPa	6.8246 TPa–1	16.654 TPa–1	5.8599 GPa	37.177 GPa	-0.12971	0.79639	Value
Anisotropy	5.705		2.4404		6.344		∞		Anisotropy
Axis	0.7270 0.6517 -0.2163	0.0000 1.0000 0.0000	0.0000 1.0000 0.0000	-0.8729 0.0000 0.4880	-0.9903 0.0000 0.1387	0.8861 0.0001 -0.4635	-0.2733 0.2754 0.9217	-0.6383 0.6935 -0.3341	Axis
					-0.0000 -1.0000 0.0000	-0.4635 -0.0001 -0.8861	-0.8273 0.4216 -0.3713	-0.7211 -0.6906 -0.0559	Second axis

Spatial dependence of Young's modulus

[[64.0, 6.0, 7.0, 0.0, 15.0, 0.0], [6.0, 113.0, 11.0, 0.0, -2.0, 0.0], [7.0, 11.0, 67.0, 0.0, -8.0, 0.0], [0.0, 0.0, 0.0, 13.0, 0.0, 1.0], [15.0, -2.0, -8.0, 0.0, 21.0, 0.0], [0.0, 0.0, 0.0, 1.0, 0.0, 6.0]] Sn4Bi2Se7 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-675477" target="_blank">mp-675477</a>) young

Spatial dependence of linear compressibility

[[64.0, 6.0, 7.0, 0.0, 15.0, 0.0], [6.0, 113.0, 11.0, 0.0, -2.0, 0.0], [7.0, 11.0, 67.0, 0.0, -8.0, 0.0], [0.0, 0.0, 0.0, 13.0, 0.0, 1.0], [15.0, -2.0, -8.0, 0.0, 21.0, 0.0], [0.0, 0.0, 0.0, 1.0, 0.0, 6.0]] Sn4Bi2Se7 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-675477" target="_blank">mp-675477</a>) lc

Spatial dependence of shear modulus

[[64.0, 6.0, 7.0, 0.0, 15.0, 0.0], [6.0, 113.0, 11.0, 0.0, -2.0, 0.0], [7.0, 11.0, 67.0, 0.0, -8.0, 0.0], [0.0, 0.0, 0.0, 13.0, 0.0, 1.0], [15.0, -2.0, -8.0, 0.0, 21.0, 0.0], [0.0, 0.0, 0.0, 1.0, 0.0, 6.0]] Sn4Bi2Se7 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-675477" target="_blank">mp-675477</a>) shear

Spatial dependence of Poisson's ratio

[[64.0, 6.0, 7.0, 0.0, 15.0, 0.0], [6.0, 113.0, 11.0, 0.0, -2.0, 0.0], [7.0, 11.0, 67.0, 0.0, -8.0, 0.0], [0.0, 0.0, 0.0, 13.0, 0.0, 1.0], [15.0, -2.0, -8.0, 0.0, 21.0, 0.0], [0.0, 0.0, 0.0, 1.0, 0.0, 6.0]] Sn4Bi2Se7 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-675477" target="_blank">mp-675477</a>) poisson

Code version: 2020.07.26 (running on Python 3.7.2)