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 MgAl2O4 (Materials Project id mp-3536)

       252      145      145        0        0        0  
       145      252      145        0        0        0  
       145      145      252        0        0        0  
         0        0        0      142        0        0  
         0        0        0        0      142        0  
         0        0        0        0        0      142  

Average properties

Averaging scheme	Bulk modulus	Young's modulus	Shear modulus	Poisson's ratio
Voigt	KV = 180.67 GPa	EV = 267.24 GPa	GV = 106.6 GPa	νV = 0.25347
Reuss	KR = 180.67 GPa	ER = 221.45 GPa	GR = 85.456 GPa	νR = 0.29571
Hill	KH = 180.67 GPa	EH = 244.72 GPa	GH = 96.028 GPa	νH = 0.27424

Eigenvalues of the stiffness matrix

λ1	λ2	λ3	λ4	λ5	λ6
107 GPa	107 GPa	142 GPa	142 GPa	142 GPa	542 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	146.08 GPa	337.56 GPa	1.845 TPa–1	1.845 TPa–1	53.5 GPa	142 GPa	-0.10477	0.63568	Value
Anisotropy	2.311		1.0000		2.654		∞		Anisotropy
Axis	0.0000 0.0000 1.0000	0.5774 0.5773 -0.5774	0.2391 0.8924 0.3827	0.8660 0.0000 0.5000	0.7071 0.0001 -0.7071	0.0000 0.0000 1.0000	0.7071 0.0001 -0.7071	0.0000 0.7071 0.7071	Axis
					-0.7071 -0.0002 -0.7071	0.9397 0.3420 -0.0000	-0.7071 -0.0002 -0.7071	-1.0000 0.0000 -0.0000	Second axis

Spatial dependence of Young's modulus

[[252.0, 145.0, 145.0, 0.0, 0.0, 0.0], [145.0, 252.0, 145.0, 0.0, 0.0, 0.0], [145.0, 145.0, 252.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 142.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 142.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 142.0]] MgAl2O4 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-3536" target="_blank">mp-3536</a>) young

Spatial dependence of linear compressibility

[[252.0, 145.0, 145.0, 0.0, 0.0, 0.0], [145.0, 252.0, 145.0, 0.0, 0.0, 0.0], [145.0, 145.0, 252.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 142.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 142.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 142.0]] MgAl2O4 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-3536" target="_blank">mp-3536</a>) lc

Spatial dependence of shear modulus

[[252.0, 145.0, 145.0, 0.0, 0.0, 0.0], [145.0, 252.0, 145.0, 0.0, 0.0, 0.0], [145.0, 145.0, 252.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 142.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 142.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 142.0]] MgAl2O4 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-3536" target="_blank">mp-3536</a>) shear

Spatial dependence of Poisson's ratio

[[252.0, 145.0, 145.0, 0.0, 0.0, 0.0], [145.0, 252.0, 145.0, 0.0, 0.0, 0.0], [145.0, 145.0, 252.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 142.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 142.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 142.0]] MgAl2O4 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-3536" target="_blank">mp-3536</a>) poisson

Code version: 2023.01.19 (running on Python 3.10.6)