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 Mn3Si (Materials Project id mp-20211)

       284      164      164        0        0        0  
       164      284      164        0        0        0  
       164      164      284        0        0        0  
         0        0        0      138        0        0  
         0        0        0        0      138        0  
         0        0        0        0        0      138

Average properties

Averaging scheme	Bulk modulus	Young's modulus	Shear modulus	Poisson's ratio
Voigt	K_V = 204 GPa	E_V = 272.79 GPa	G_V = 106.8 GPa	ν_V = 0.27713
Reuss	K_R = 204 GPa	E_R = 237.18 GPa	G_R = 90.789 GPa	ν_R = 0.30622
Hill	K_H = 204 GPa	E_H = 255.19 GPa	G_H = 98.795 GPa	ν_H = 0.29151

Eigenvalues of the stiffness matrix

λ₁	λ₂	λ₃	λ₄	λ₅	λ₆
120 GPa	120 GPa	138 GPa	138 GPa	138 GPa	612 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	163.93 GPa	337.82 GPa	1.634 TPa^–1	1.634 TPa^–1	60 GPa	138 GPa	-0.032564	0.59627	Value
Anisotropy	2.061		1.0000		2.3		∞		Anisotropy
Axis	0.0000 0.0000 1.0000	0.5774 0.5774 0.5773	0.9239 0.0000 0.3827	0.0000 0.0000 1.0000	0.7071 0.0001 -0.7071	0.0000 0.0000 1.0000	0.7071 -0.0003 0.7071	0.0000 0.7071 0.7071	Axis
					-0.7071 -0.0002 -0.7071	0.7660 0.6428 -0.0000	0.7071 -0.0005 -0.7071	-1.0000 0.0000 -0.0000	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