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 ErN (Materials Project id mp-19830)

       343       85       85        0        0        0  
        85      343       85        0        0        0  
        85       85      343        0        0        0  
         0        0        0      133        0        0  
         0        0        0        0      133        0  
         0        0        0        0        0      133  

Average properties

Averaging scheme	Bulk modulus	Young's modulus	Shear modulus	Poisson's ratio
Voigt	KV = 171 GPa	EV = 313.82 GPa	GV = 131.4 GPa	νV = 0.19413
Reuss	KR = 171 GPa	ER = 313.76 GPa	GR = 131.37 GPa	νR = 0.19419
Hill	KH = 171 GPa	EH = 313.79 GPa	GH = 131.39 GPa	νH = 0.19416

Eigenvalues of the stiffness matrix

λ1	λ2	λ3	λ4	λ5	λ6
133 GPa	133 GPa	133 GPa	258 GPa	258 GPa	513 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	309.24 GPa	316.85 GPa	1.9493 TPa–1	1.9493 TPa–1	129 GPa	133 GPa	0.18389	0.20224	Value
Anisotropy	1.025		1.0000		1.031		1.0998		Anisotropy
Axis	0.0000 1.0000 0.0000	0.5774 0.5774 0.5773	0.9659 0.0000 0.2588	0.4330 0.7500 0.5000	0.7071 -0.0003 0.7071	0.0000 0.0000 1.0000	0.7071 -0.0002 0.7071	0.7071 -0.0004 0.7071	Axis
					0.7071 -0.0005 -0.7071	0.5000 0.8660 -0.0000	0.7071 -0.0006 -0.7071	0.0003 1.0000 0.0003	Second axis

Spatial dependence of Young's modulus

[[343.0, 85.0, 85.0, 0.0, 0.0, 0.0], [85.0, 343.0, 85.0, 0.0, 0.0, 0.0], [85.0, 85.0, 343.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 133.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 133.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 133.0]] ErN (Materials Project id <a href="https://www.materialsproject.org/materials/mp-19830" target="_blank">mp-19830</a>) young

Spatial dependence of linear compressibility

[[343.0, 85.0, 85.0, 0.0, 0.0, 0.0], [85.0, 343.0, 85.0, 0.0, 0.0, 0.0], [85.0, 85.0, 343.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 133.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 133.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 133.0]] ErN (Materials Project id <a href="https://www.materialsproject.org/materials/mp-19830" target="_blank">mp-19830</a>) lc

Spatial dependence of shear modulus

[[343.0, 85.0, 85.0, 0.0, 0.0, 0.0], [85.0, 343.0, 85.0, 0.0, 0.0, 0.0], [85.0, 85.0, 343.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 133.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 133.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 133.0]] ErN (Materials Project id <a href="https://www.materialsproject.org/materials/mp-19830" target="_blank">mp-19830</a>) shear

Spatial dependence of Poisson's ratio

[[343.0, 85.0, 85.0, 0.0, 0.0, 0.0], [85.0, 343.0, 85.0, 0.0, 0.0, 0.0], [85.0, 85.0, 343.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 133.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 133.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 133.0]] ErN (Materials Project id <a href="https://www.materialsproject.org/materials/mp-19830" target="_blank">mp-19830</a>) poisson

Code version: 2020.07.26 (running on Python 3.7.2)