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 Ti2Zn (Materials Project id mp-1014229)

       156       33       94        0        0        0  
        33      156       94        0        0        0  
        94       94      123        0        0        0  
         0        0        0      112        0        0  
         0        0        0        0      112        0  
         0        0        0        0        0       30  

Average properties

Averaging scheme	Bulk modulus	Young's modulus	Shear modulus	Poisson's ratio
Voigt	KV = 97.444 GPa	EV = 159.66 GPa	GV = 65.067 GPa	νV = 0.22692
Reuss	KR = 94.492 GPa	ER = 78.963 GPa	GR = 29.015 GPa	νR = 0.36072
Hill	KH = 95.968 GPa	EH = 121.3 GPa	GH = 47.041 GPa	νH = 0.28933

Eigenvalues of the stiffness matrix

λ1	λ2	λ3	λ4	λ5	λ6
19.029 GPa	30 GPa	112 GPa	112 GPa	123 GPa	292.97 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	29.497 GPa	206.06 GPa	0.17937 TPa–1	5.2018 TPa–1	11.496 GPa	112 GPa	-0.46272	1.1169	Value
Anisotropy	6.986		29.0000		9.743		∞		Anisotropy
Axis	0.0000 0.0000 1.0000	0.7921 0.0000 -0.6104	0.0000 0.0000 1.0000	0.3827 0.9239 0.0000	0.5001 0.4999 -0.7071	-0.0000 0.0000 1.0000	0.9881 0.0003 0.1538	1.0000 0.0002 0.0000	Axis
					-0.5000 -0.5001 -0.7071	-0.5000 0.8660 -0.0000	-0.0003 1.0000 0.0000	0.0000 -0.0000 -1.0000	Second axis

Spatial dependence of Young's modulus

[[156.0, 33.0, 94.0, 0.0, 0.0, 0.0], [33.0, 156.0, 94.0, 0.0, 0.0, 0.0], [94.0, 94.0, 123.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 112.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 112.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 30.0]] Ti2Zn (Materials Project id <a href="https://www.materialsproject.org/materials/mp-1014229" target="_blank">mp-1014229</a>) young

Spatial dependence of linear compressibility

[[156.0, 33.0, 94.0, 0.0, 0.0, 0.0], [33.0, 156.0, 94.0, 0.0, 0.0, 0.0], [94.0, 94.0, 123.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 112.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 112.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 30.0]] Ti2Zn (Materials Project id <a href="https://www.materialsproject.org/materials/mp-1014229" target="_blank">mp-1014229</a>) lc

Spatial dependence of shear modulus

[[156.0, 33.0, 94.0, 0.0, 0.0, 0.0], [33.0, 156.0, 94.0, 0.0, 0.0, 0.0], [94.0, 94.0, 123.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 112.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 112.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 30.0]] Ti2Zn (Materials Project id <a href="https://www.materialsproject.org/materials/mp-1014229" target="_blank">mp-1014229</a>) shear

Spatial dependence of Poisson's ratio

[[156.0, 33.0, 94.0, 0.0, 0.0, 0.0], [33.0, 156.0, 94.0, 0.0, 0.0, 0.0], [94.0, 94.0, 123.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 112.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 112.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 30.0]] Ti2Zn (Materials Project id <a href="https://www.materialsproject.org/materials/mp-1014229" target="_blank">mp-1014229</a>) poisson

Code version: 2020.07.26 (running on Python 3.7.2)