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 Mg5Hg3 (Materials Project id mp-11465)

        81       36       21        0        0        0  
        36       81       21        0        0        0  
        21       21       70        0        0        0  
         0        0        0       18        0        0  
         0        0        0        0       18        0  
         0        0        0        0        0       23  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 43.111 GPaEV = 56.551 GPaGV = 22.067 GPaνV = 0.28137
ReussKR = 42.243 GPaER = 54.768 GPaGR = 21.328 GPaνR = 0.28392
HillKH = 42.677 GPaEH = 55.66 GPaGH = 21.698 GPaνH = 0.28263

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
18 GPa 18 GPa 23 GPa 45 GPa 55.629 GPa 131.37 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 48.948 GPa 63.862 GPa 6.705 TPa–1 10.263 TPa–1 18 GPa 26.727 GPa0.179490.39759Value
Anisotropy 1.305 1.5306 1.485 2.2151Anisotropy
Axis 0.7049
-0.0000
0.7093
0.7071
0.7071
0.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.4999
0.5001
-0.7071
-0.0000
-0.0000
1.0000
1.0000
-0.0007
-0.0000
Axis
1.0000
0.0000
-0.0000
-0.5001
-0.4999
-0.7071
-0.7669
0.6418
-0.0000
0.0007
1.0000
-0.0001
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