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 YMg2 (Materials Project id mp-11499)

        77       29       23        0        0        0  
        29       77       23        0        0        0  
        23       23       82        0        0        0  
         0        0        0       19        0        0  
         0        0        0        0       19        0  
         0        0        0        0        0       24

Average properties

Averaging scheme	Bulk modulus	Young's modulus	Shear modulus	Poisson's ratio
Voigt	K_V = 42.889 GPa	E_V = 58.824 GPa	G_V = 23.133 GPa	ν_V = 0.27141
Reuss	K_R = 42.888 GPa	E_R = 57.435 GPa	G_R = 22.492 GPa	ν_R = 0.2768
Hill	K_H = 42.888 GPa	E_H = 58.131 GPa	G_H = 22.812 GPa	ν_H = 0.2741

Eigenvalues of the stiffness matrix

λ₁	λ₂	λ₃	λ₄	λ₅	λ₆
19 GPa	19 GPa	24 GPa	48 GPa	59.33 GPa	128.67 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	52.293 GPa	72.019 GPa	7.7286 TPa^–1	7.8596 TPa^–1	19 GPa	28.013 GPa	0.20079	0.38064	Value
Anisotropy	1.377		1.0169		1.474		1.8957		Anisotropy
Axis	0.7229 0.1834 -0.6662	0.0000 0.0000 1.0000	1.0000 0.0000 0.0000	0.0000 0.0000 1.0000	0.0000 0.0000 1.0000	0.0847 0.7020 -0.7071	0.5071 -0.0002 0.8619	0.3252 0.5998 -0.7311	Axis
					1.0000 0.0000 -0.0000	-0.0846 -0.7020 -0.7071	0.0005 1.0000 -0.0000	0.3485 0.6427 0.6823	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