ELATE: Elastic tensor analysis

Welcome to ELATE, the online tool for analysis of elastic tensors, developed by Romain Gaillac and Fran├žois-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 Mg (Materials Project id mp-153)

        58       30       22        0        0        0  
        30       58       22        0        0        0  
        22       22       66        0        0        0  
         0        0        0       20        0        0  
         0        0        0        0       20        0  
         0        0        0        0        0       14  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 36.667 GPaEV = 46.406 GPaGV = 18 GPaνV = 0.28906
ReussKR = 36.667 GPaER = 44.942 GPaGR = 17.342 GPaνR = 0.29572
HillKH = 36.667 GPaEH = 45.676 GPaGH = 17.671 GPaνH = 0.29238

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
14 GPa 20 GPa 20 GPa 28 GPa 44 GPa 110 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 40.526 GPa 55 GPa 9.0909 TPa–1 9.0909 TPa–1 14 GPa 20 GPa0.183180.44737Value
Anisotropy 1.357 1.0000 1.429 2.4422Anisotropy
Axis 0.8660
0.5000
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.4330
0.7500
0.5000
0.6375
0.7705
-0.0000
-0.0000
0.0000
1.0000
-0.9090
0.2178
0.3553
0.6373
0.7706
0.0000
Axis
-0.7705
0.6375
0.0000
-0.5000
0.8660
-0.0000
-0.3455
0.0828
-0.9348
-0.7706
0.6373
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