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 Ni3Hg (Materials Project id mp-973884)

       195      152      151        0        0        0  
       152      195      152        0        0        0  
       151      152      194        0        0        0  
         0        0        0       72        0        0  
         0        0        0        0       72        0  
         0        0        0        0        0       72  

Average properties

Averaging scheme	Bulk modulus	Young's modulus	Shear modulus	Poisson's ratio
Voigt	KV = 166 GPa	EV = 140.76 GPa	GV = 51.8 GPa	νV = 0.35868
Reuss	KR = 165.99 GPa	ER = 103.63 GPa	GR = 37.117 GPa	νR = 0.39595
Hill	KH = 166 GPa	EH = 122.44 GPa	GH = 44.459 GPa	νH = 0.37706

Eigenvalues of the stiffness matrix

λ1	λ2	λ3	λ4	λ5	λ6
42.421 GPa	43.577 GPa	72 GPa	72 GPa	72 GPa	498 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	61.255 GPa	188.72 GPa	1.9607 TPa–1	2.0552 TPa–1	21.248 GPa	72 GPa	-0.14046	0.88897	Value
Anisotropy	3.081		1.0482		3.388		∞		Anisotropy
Axis	0.0000 1.0000 0.0000	-0.5773 0.5782 0.5766	0.0000 1.0000 0.0000	0.0000 0.0000 1.0000	-0.0001 0.7071 0.7071	0.0000 0.0000 1.0000	0.7074 0.0001 -0.7068	-0.7074 0.0000 0.7068	Axis
					0.0001 0.7071 -0.7071	0.4962 0.8682 -0.0000	-0.7068 -0.0002 -0.7074	-0.0000 -1.0000 -0.0000	Second axis

Spatial dependence of Young's modulus

[[195.0, 152.0, 151.0, 0.0, 0.0, 0.0], [152.0, 195.0, 152.0, 0.0, 0.0, 0.0], [151.0, 152.0, 194.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 72.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 72.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 72.0]] Ni3Hg (Materials Project id <a href="https://www.materialsproject.org/materials/mp-973884" target="_blank">mp-973884</a>) young

Spatial dependence of linear compressibility

[[195.0, 152.0, 151.0, 0.0, 0.0, 0.0], [152.0, 195.0, 152.0, 0.0, 0.0, 0.0], [151.0, 152.0, 194.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 72.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 72.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 72.0]] Ni3Hg (Materials Project id <a href="https://www.materialsproject.org/materials/mp-973884" target="_blank">mp-973884</a>) lc

Spatial dependence of shear modulus

[[195.0, 152.0, 151.0, 0.0, 0.0, 0.0], [152.0, 195.0, 152.0, 0.0, 0.0, 0.0], [151.0, 152.0, 194.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 72.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 72.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 72.0]] Ni3Hg (Materials Project id <a href="https://www.materialsproject.org/materials/mp-973884" target="_blank">mp-973884</a>) shear

Spatial dependence of Poisson's ratio

[[195.0, 152.0, 151.0, 0.0, 0.0, 0.0], [152.0, 195.0, 152.0, 0.0, 0.0, 0.0], [151.0, 152.0, 194.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 72.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 72.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 72.0]] Ni3Hg (Materials Project id <a href="https://www.materialsproject.org/materials/mp-973884" target="_blank">mp-973884</a>) poisson

Code version: 2020.07.26 (running on Python 3.7.2)