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 Tl(CoSe)2 (Materials Project id mp-4475)

        93       36       33        0        0        0  
        36       93       33        0        0        0  
        33       33       51        0        0        0  
         0        0        0       15        0        0  
         0        0        0        0       15        0  
         0        0        0        0        0       36  

Average properties

Averaging scheme	Bulk modulus	Young's modulus	Shear modulus	Poisson's ratio
Voigt	KV = 49 GPa	EV = 57.862 GPa	GV = 22.2 GPa	νV = 0.30319
Reuss	KR = 44.455 GPa	ER = 49.918 GPa	GR = 19.011 GPa	νR = 0.31285
Hill	KH = 46.727 GPa	EH = 53.895 GPa	GH = 20.606 GPa	νH = 0.30777

Eigenvalues of the stiffness matrix

λ1	λ2	λ3	λ4	λ5	λ6
15 GPa	15 GPa	29.181 GPa	36 GPa	57 GPa	150.82 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	34.116 GPa	78.502 GPa	4.09 TPa–1	14.315 TPa–1	15 GPa	36 GPa	0.090301	0.58863	Value
Anisotropy	2.301		3.5000		2.4		6.5185		Anisotropy
Axis	0.0000 0.0000 1.0000	0.7071 0.7071 0.0000	0.1305 0.9914 0.0000	0.0000 0.0000 1.0000	0.0000 0.0000 1.0000	1.0000 -0.0003 -0.0000	0.7071 0.7071 -0.0000	-0.7071 0.7071 0.0000	Axis
					0.1736 0.9848 -0.0000	0.0003 1.0000 0.0000	-0.7071 0.7071 0.0000	0.0000 0.0000 1.0000	Second axis

Spatial dependence of Young's modulus

[[93.0, 36.0, 33.0, 0.0, 0.0, 0.0], [36.0, 93.0, 33.0, 0.0, 0.0, 0.0], [33.0, 33.0, 51.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 15.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 15.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 36.0]] Tl(CoSe)2 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-4475" target="_blank">mp-4475</a>) young

Spatial dependence of linear compressibility

[[93.0, 36.0, 33.0, 0.0, 0.0, 0.0], [36.0, 93.0, 33.0, 0.0, 0.0, 0.0], [33.0, 33.0, 51.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 15.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 15.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 36.0]] Tl(CoSe)2 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-4475" target="_blank">mp-4475</a>) lc

Spatial dependence of shear modulus

[[93.0, 36.0, 33.0, 0.0, 0.0, 0.0], [36.0, 93.0, 33.0, 0.0, 0.0, 0.0], [33.0, 33.0, 51.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 15.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 15.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 36.0]] Tl(CoSe)2 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-4475" target="_blank">mp-4475</a>) shear

Spatial dependence of Poisson's ratio

[[93.0, 36.0, 33.0, 0.0, 0.0, 0.0], [36.0, 93.0, 33.0, 0.0, 0.0, 0.0], [33.0, 33.0, 51.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 15.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 15.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 36.0]] Tl(CoSe)2 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-4475" target="_blank">mp-4475</a>) poisson

Code version: 2023.01.19 (running on Python 3.10.6)