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 ZrV2 (Materials Project id mp-258)

       159      131      131        0        0        0  
       131      159      131        0        0        0  
       131      131      159        0        0        0  
         0        0        0       10        0        0  
         0        0        0        0       10        0  
         0        0        0        0        0       10  

Average properties

Averaging scheme	Bulk modulus	Young's modulus	Shear modulus	Poisson's ratio
Voigt	KV = 140.33 GPa	EV = 33.867 GPa	GV = 11.6 GPa	νV = 0.45978
Reuss	KR = 140.33 GPa	ER = 32.986 GPa	GR = 11.29 GPa	νR = 0.46082
Hill	KH = 140.33 GPa	EH = 33.427 GPa	GH = 11.445 GPa	νH = 0.4603

Eigenvalues of the stiffness matrix

λ1	λ2	λ3	λ4	λ5	λ6
10 GPa	10 GPa	10 GPa	28 GPa	28 GPa	421 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	29.304 GPa	40.648 GPa	2.3753 TPa–1	2.3753 TPa–1	10 GPa	14 GPa	0.35008	0.57509	Value
Anisotropy	1.387		1.0000		1.4		1.6427		Anisotropy
Axis	0.5774 0.5773 -0.5774	0.0000 0.0000 1.0000	0.0000 0.0000 1.0000	0.0000 0.0000 1.0000	0.0000 0.0000 1.0000	0.7071 0.0001 -0.7071	-0.7071 -0.0000 0.7071	0.7071 -0.0002 0.7071	Axis
					-0.7660 0.6428 -0.0000	-0.7071 -0.0002 -0.7071	-0.0000 -1.0000 -0.0000	0.7071 -0.0005 -0.7071	Second axis

Spatial dependence of Young's modulus

[[159.0, 131.0, 131.0, 0.0, 0.0, 0.0], [131.0, 159.0, 131.0, 0.0, 0.0, 0.0], [131.0, 131.0, 159.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 10.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 10.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 10.0]] ZrV2 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-258" target="_blank">mp-258</a>) young

Spatial dependence of linear compressibility

[[159.0, 131.0, 131.0, 0.0, 0.0, 0.0], [131.0, 159.0, 131.0, 0.0, 0.0, 0.0], [131.0, 131.0, 159.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 10.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 10.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 10.0]] ZrV2 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-258" target="_blank">mp-258</a>) lc

Spatial dependence of shear modulus

[[159.0, 131.0, 131.0, 0.0, 0.0, 0.0], [131.0, 159.0, 131.0, 0.0, 0.0, 0.0], [131.0, 131.0, 159.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 10.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 10.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 10.0]] ZrV2 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-258" target="_blank">mp-258</a>) shear

Spatial dependence of Poisson's ratio

[[159.0, 131.0, 131.0, 0.0, 0.0, 0.0], [131.0, 159.0, 131.0, 0.0, 0.0, 0.0], [131.0, 131.0, 159.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 10.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 10.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 10.0]] ZrV2 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-258" target="_blank">mp-258</a>) poisson

Code version: 2020.07.26 (running on Python 3.7.2)