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 UNi5 (Materials Project id mp-2838)

       311      155      155        0        0        0  
       155      311      155        0        0        0  
       155      155      311        0        0        0  
         0        0        0      101        0        0  
         0        0        0        0      101        0  
         0        0        0        0        0      101  

Average properties

Averaging scheme	Bulk modulus	Young's modulus	Shear modulus	Poisson's ratio
Voigt	KV = 207 GPa	EV = 239.93 GPa	GV = 91.8 GPa	νV = 0.30682
Reuss	KR = 207 GPa	ER = 236.61 GPa	GR = 90.344 GPa	νR = 0.30949
Hill	KH = 207 GPa	EH = 238.27 GPa	GH = 91.072 GPa	νH = 0.30815

Eigenvalues of the stiffness matrix

λ1	λ2	λ3	λ4	λ5	λ6
101 GPa	101 GPa	101 GPa	156 GPa	156 GPa	621 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	207.89 GPa	260.61 GPa	1.6103 TPa–1	1.6103 TPa–1	78 GPa	101 GPa	0.21324	0.39212	Value
Anisotropy	1.254		1.0000		1.295		1.8388		Anisotropy
Axis	0.0000 0.0000 1.0000	0.5774 0.5774 0.5773	0.2500 0.9330 0.2588	0.0000 0.0000 1.0000	0.7071 -0.0003 0.7071	0.0000 0.0000 1.0000	0.7071 -0.0000 -0.7071	0.7071 -0.0005 0.7071	Axis
					0.7071 -0.0005 -0.7071	0.7660 0.6428 -0.0000	-0.7071 0.0002 -0.7071	0.0004 1.0000 0.0004	Second axis

Spatial dependence of Young's modulus

[[311.0, 155.0, 155.0, 0.0, 0.0, 0.0], [155.0, 311.0, 155.0, 0.0, 0.0, 0.0], [155.0, 155.0, 311.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 101.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 101.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 101.0]] UNi5 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-2838" target="_blank">mp-2838</a>) young

Spatial dependence of linear compressibility

[[311.0, 155.0, 155.0, 0.0, 0.0, 0.0], [155.0, 311.0, 155.0, 0.0, 0.0, 0.0], [155.0, 155.0, 311.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 101.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 101.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 101.0]] UNi5 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-2838" target="_blank">mp-2838</a>) lc

Spatial dependence of shear modulus

[[311.0, 155.0, 155.0, 0.0, 0.0, 0.0], [155.0, 311.0, 155.0, 0.0, 0.0, 0.0], [155.0, 155.0, 311.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 101.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 101.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 101.0]] UNi5 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-2838" target="_blank">mp-2838</a>) shear

Spatial dependence of Poisson's ratio

[[311.0, 155.0, 155.0, 0.0, 0.0, 0.0], [155.0, 311.0, 155.0, 0.0, 0.0, 0.0], [155.0, 155.0, 311.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 101.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 101.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 101.0]] UNi5 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-2838" target="_blank">mp-2838</a>) poisson

Code version: 2022.06.14 (running on Python 3.7.2)