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 MgC2 (Materials Project id mp-29771)

       139      106       36        0        0        0  
       106      139       36        0        0        0  
        36       36      102        0        0        0  
         0        0        0       13        0        0  
         0        0        0        0       13        0  
         0        0        0        0        0       98

Average properties

Averaging scheme	Bulk modulus	Young's modulus	Shear modulus	Poisson's ratio
Voigt	K_V = 81.778 GPa	E_V = 99.31 GPa	G_V = 38.267 GPa	ν_V = 0.2976
Reuss	K_R = 73.436 GPa	E_R = 55.709 GPa	G_R = 20.279 GPa	ν_R = 0.37357
Hill	K_H = 77.607 GPa	E_H = 78.01 GPa	G_H = 29.273 GPa	ν_H = 0.33247

Eigenvalues of the stiffness matrix

λ₁	λ₂	λ₃	λ₄	λ₅	λ₆
13 GPa	13 GPa	33 GPa	85.726 GPa	98 GPa	261.27 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	38.833 GPa	207.12 GPa	2.9467 TPa^–1	7.7239 TPa^–1	13 GPa	97.999 GPa	0.035201	0.73402	Value
Anisotropy	5.334		2.6212		7.538		20.8520		Anisotropy
Axis	0.7560 0.0000 0.6545	0.7071 0.7071 0.0000	0.2588 0.9659 0.0000	0.0000 0.0000 1.0000	0.0000 0.0000 1.0000	1.0000 0.0007 0.0000	-0.6221 0.6221 0.4753	-0.5681 0.5681 0.5954	Axis
					0.1735 0.9848 -0.0000	-0.0007 1.0000 -0.0000	-0.7071 -0.7071 -0.0000	0.4210 -0.4210 0.8035	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