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 FeSi2 (Materials Project id mp-20738)

       333       76       99        0        0        0  
        76      333       99        0        0        0  
        99       99      452        0        0        0  
         0        0        0      112        0        0  
         0        0        0        0      112        0  
         0        0        0        0        0      118  

Average properties

Averaging scheme	Bulk modulus	Young's modulus	Shear modulus	Poisson's ratio
Voigt	KV = 185.11 GPa	EV = 305.43 GPa	GV = 124.67 GPa	νV = 0.225
Reuss	KR = 180.22 GPa	ER = 299.51 GPa	GR = 122.45 GPa	νR = 0.22302
Hill	KH = 182.67 GPa	EH = 302.47 GPa	GH = 123.56 GPa	νH = 0.22402

Eigenvalues of the stiffness matrix

λ1	λ2	λ3	λ4	λ5	λ6
112 GPa	112 GPa	118 GPa	257 GPa	288.85 GPa	572.15 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	280.32 GPa	404.07 GPa	1.2767 TPa–1	2.136 TPa–1	112 GPa	143.15 GPa	0.1682	0.32515	Value
Anisotropy	1.441		1.6730		1.278		1.9331		Anisotropy
Axis	0.6268 0.6268 0.4628	0.0000 0.0000 1.0000	0.0000 0.0000 1.0000	1.0000 0.0000 0.0000	-0.0000 -0.0000 1.0000	0.7071 -0.0003 0.7071	-0.8648 -0.0000 -0.5021	0.6293 0.0001 0.7772	Axis
					1.0000 0.0002 0.0000	0.7071 -0.0005 -0.7071	0.0000 -1.0000 -0.0000	0.7772 0.0001 -0.6293	Second axis

Spatial dependence of Young's modulus

[[333.0, 76.0, 99.0, 0.0, 0.0, 0.0], [76.0, 333.0, 99.0, 0.0, 0.0, 0.0], [99.0, 99.0, 452.0, 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, 118.0]] FeSi2 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-20738" target="_blank">mp-20738</a>) young

Spatial dependence of linear compressibility

[[333.0, 76.0, 99.0, 0.0, 0.0, 0.0], [76.0, 333.0, 99.0, 0.0, 0.0, 0.0], [99.0, 99.0, 452.0, 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, 118.0]] FeSi2 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-20738" target="_blank">mp-20738</a>) lc

Spatial dependence of shear modulus

[[333.0, 76.0, 99.0, 0.0, 0.0, 0.0], [76.0, 333.0, 99.0, 0.0, 0.0, 0.0], [99.0, 99.0, 452.0, 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, 118.0]] FeSi2 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-20738" target="_blank">mp-20738</a>) shear

Spatial dependence of Poisson's ratio

[[333.0, 76.0, 99.0, 0.0, 0.0, 0.0], [76.0, 333.0, 99.0, 0.0, 0.0, 0.0], [99.0, 99.0, 452.0, 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, 118.0]] FeSi2 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-20738" target="_blank">mp-20738</a>) poisson

Code version: 2020.07.26 (running on Python 3.7.2)