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 ThSi2 (Materials Project id mp-7497)

       145       93       72        0        0        0  
        93      145       72        0        0        0  
        72       72      195        0        0        0  
         0        0        0       78        0        0  
         0        0        0        0       78        0  
         0        0        0        0        0       26  

Average properties

Averaging scheme	Bulk modulus	Young's modulus	Shear modulus	Poisson's ratio
Voigt	KV = 106.56 GPa	EV = 136.24 GPa	GV = 52.933 GPa	νV = 0.2869
Reuss	KR = 106.01 GPa	ER = 110.27 GPa	GR = 41.562 GPa	νR = 0.32662
Hill	KH = 106.28 GPa	EH = 123.45 GPa	GH = 47.248 GPa	νH = 0.30641

Eigenvalues of the stiffness matrix

λ1	λ2	λ3	λ4	λ5	λ6
26 GPa	52 GPa	78 GPa	78 GPa	112.43 GPa	320.57 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	81.165 GPa	163.18 GPa	2.6081 TPa–1	3.4127 TPa–1	26 GPa	78 GPa	-0.076606	0.6499	Value
Anisotropy	2.01		1.3085		3		∞		Anisotropy
Axis	0.3827 0.9239 0.0000	0.4320 0.1741 0.8849	0.0000 0.0000 1.0000	0.3827 0.9239 0.0000	1.0000 -0.0002 0.0000	0.0000 0.0000 1.0000	-0.1680 0.6720 -0.7212	0.7225 0.2629 -0.6394	Axis
					0.0002 1.0000 0.0000	-0.7660 0.6428 -0.0000	0.1750 -0.6997 -0.6927	-0.3420 0.9397 -0.0000	Second axis

Spatial dependence of Young's modulus

[[145.0, 93.0, 72.0, 0.0, 0.0, 0.0], [93.0, 145.0, 72.0, 0.0, 0.0, 0.0], [72.0, 72.0, 195.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 78.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 78.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 26.0]] ThSi2 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-7497" target="_blank">mp-7497</a>) young

Spatial dependence of linear compressibility

[[145.0, 93.0, 72.0, 0.0, 0.0, 0.0], [93.0, 145.0, 72.0, 0.0, 0.0, 0.0], [72.0, 72.0, 195.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 78.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 78.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 26.0]] ThSi2 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-7497" target="_blank">mp-7497</a>) lc

Spatial dependence of shear modulus

[[145.0, 93.0, 72.0, 0.0, 0.0, 0.0], [93.0, 145.0, 72.0, 0.0, 0.0, 0.0], [72.0, 72.0, 195.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 78.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 78.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 26.0]] ThSi2 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-7497" target="_blank">mp-7497</a>) shear

Spatial dependence of Poisson's ratio

[[145.0, 93.0, 72.0, 0.0, 0.0, 0.0], [93.0, 145.0, 72.0, 0.0, 0.0, 0.0], [72.0, 72.0, 195.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 78.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 78.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 26.0]] ThSi2 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-7497" target="_blank">mp-7497</a>) poisson

Code version: 2020.07.26 (running on Python 3.7.2)