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 AlV3 (Materials Project id mp-1387)

       211      133      133        0        0        0  
       133      211      133        0        0        0  
       133      133      211        0        0        0  
         0        0        0        2        0        0  
         0        0        0        0        2        0  
         0        0        0        0        0        2

Average properties

Averaging scheme	Bulk modulus	Young's modulus	Shear modulus	Poisson's ratio
Voigt	K_V = 159 GPa	E_V = 48.685 GPa	G_V = 16.8 GPa	ν_V = 0.44897
Reuss	K_R = 159 GPa	E_R = 9.6045 GPa	G_R = 3.2231 GPa	ν_R = 0.48993
Hill	K_H = 159 GPa	E_H = 29.417 GPa	G_H = 10.012 GPa	ν_H = 0.46916

Eigenvalues of the stiffness matrix

λ₁	λ₂	λ₃	λ₄	λ₅	λ₆
2 GPa	2 GPa	2 GPa	78 GPa	78 GPa	477 GPa

Variations of the elastic moduli

	Young's modulus		Linear compressibility		Shear modulus		Poisson's ratio
	E_min	E_max	β_min	β_max	G_min	G_max	ν_min	ν_max
Value	5.9749 GPa	108.16 GPa	2.0964 TPa^–1	2.0964 TPa^–1	2 GPa	39 GPa	0.027963	0.95564	Value
Anisotropy	18.1		1.0000		19.5		34.1748		Anisotropy
Axis	0.5774 0.5773 -0.5774	0.0000 1.0000 0.0000	0.8660 0.0000 0.5000	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 -0.0000 -0.7071	Axis
					1.0000 0.0000 -0.0000	-0.7071 -0.0002 -0.7071	0.0000 -1.0000 0.0000	-0.7071 0.0002 -0.7071	Second axis

Spatial dependence of Young's modulus

Young's modulus in (xy) plane

Young's modulus in (xz) plane

Young's modulus in (yz) plane

Spatial dependence of linear compressibility

linear compressibility in (xy) plane

linear compressibility in (xz) plane

linear compressibility in (yz) plane

Spatial dependence of shear modulus

Shear modulus in (xy) plane

Shear modulus in (xz) plane

Shear modulus in (yz) plane

Spatial dependence of Poisson's ratio

Poisson's ratio in (xy) plane

Poisson's ratio in (xz) plane

Poisson's ratio in (yz) plane