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 TiFe2Sn (Materials Project id mp-19963)

       318      113      113        0        0        0  
       113      318      113        0        0        0  
       113      113      318        0        0        0  
         0        0        0      108        0        0  
         0        0        0        0      108        0  
         0        0        0        0        0      108

Average properties

Averaging scheme	Bulk modulus	Young's modulus	Shear modulus	Poisson's ratio
Voigt	K_V = 181.33 GPa	E_V = 265.72 GPa	G_V = 105.8 GPa	ν_V = 0.25577
Reuss	K_R = 181.33 GPa	E_R = 265.58 GPa	G_R = 105.73 GPa	ν_R = 0.25591
Hill	K_H = 181.33 GPa	E_H = 265.65 GPa	G_H = 105.77 GPa	ν_H = 0.25584

Eigenvalues of the stiffness matrix

λ₁	λ₂	λ₃	λ₄	λ₅	λ₆
108 GPa	108 GPa	108 GPa	205 GPa	205 GPa	544 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	258.75 GPa	270.33 GPa	1.8382 TPa^–1	1.8382 TPa^–1	102.5 GPa	108 GPa	0.23768	0.27089	Value
Anisotropy	1.045		1.0000		1.054		1.1397		Anisotropy
Axis	1.0000 0.0000 0.0000	-0.5774 0.5774 0.5773	0.0000 0.0000 1.0000	-0.4830 0.6294 0.6088	0.7071 -0.0003 0.7071	0.0000 0.0000 1.0000	0.7071 -0.0002 0.7071	-0.7071 -0.0000 0.7071	Axis
					0.7071 -0.0005 -0.7071	0.5000 0.8660 -0.0000	0.7071 -0.0006 -0.7071	0.0000 -1.0000 -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