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 YHg3 (Materials Project id mp-30726)

        80       50       43        0        0        0  
        50       80       43        0        0        0  
        43       43      103        0        0        0  
         0        0        0       19        0        0  
         0        0        0        0       19        0  
         0        0        0        0        0       15  

Average properties

Averaging scheme	Bulk modulus	Young's modulus	Shear modulus	Poisson's ratio
Voigt	KV = 59.444 GPa	EV = 51.675 GPa	GV = 19.067 GPa	νV = 0.35512
Reuss	KR = 59.098 GPa	ER = 49.407 GPa	GR = 18.156 GPa	νR = 0.36066
Hill	KH = 59.271 GPa	EH = 50.543 GPa	GH = 18.611 GPa	νH = 0.35788

Eigenvalues of the stiffness matrix

λ1	λ2	λ3	λ4	λ5	λ6
15 GPa	19 GPa	19 GPa	30 GPa	54.208 GPa	178.79 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	45.495 GPa	74.554 GPa	4.5398 TPa–1	6.1907 TPa–1	15 GPa	22.59 GPa	0.20185	0.51651	Value
Anisotropy	1.639		1.3636		1.506		2.5589		Anisotropy
Axis	1.0000 0.0001 -0.0000	0.0000 0.0000 1.0000	0.0000 0.0000 1.0000	1.0000 0.0000 0.0000	1.0000 -0.0008 -0.0000	-0.1699 0.6864 -0.7071	0.9337 0.3580 -0.0000	0.1047 0.9945 -0.0000	Axis
					0.0008 1.0000 -0.0000	0.1700 -0.6864 -0.7071	-0.0000 0.0000 -1.0000	-0.9945 0.1047 0.0000	Second axis

Spatial dependence of Young's modulus

[[80.0, 50.0, 43.0, 0.0, 0.0, 0.0], [50.0, 80.0, 43.0, 0.0, 0.0, 0.0], [43.0, 43.0, 103.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 19.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 19.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 15.0]] YHg3 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-30726" target="_blank">mp-30726</a>) young

Spatial dependence of linear compressibility

[[80.0, 50.0, 43.0, 0.0, 0.0, 0.0], [50.0, 80.0, 43.0, 0.0, 0.0, 0.0], [43.0, 43.0, 103.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 19.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 19.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 15.0]] YHg3 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-30726" target="_blank">mp-30726</a>) lc

Spatial dependence of shear modulus

[[80.0, 50.0, 43.0, 0.0, 0.0, 0.0], [50.0, 80.0, 43.0, 0.0, 0.0, 0.0], [43.0, 43.0, 103.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 19.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 19.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 15.0]] YHg3 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-30726" target="_blank">mp-30726</a>) shear

Spatial dependence of Poisson's ratio

[[80.0, 50.0, 43.0, 0.0, 0.0, 0.0], [50.0, 80.0, 43.0, 0.0, 0.0, 0.0], [43.0, 43.0, 103.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 19.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 19.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 15.0]] YHg3 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-30726" target="_blank">mp-30726</a>) poisson

Code version: 2020.07.26 (running on Python 3.7.2)