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 FeS (Materials Project id mp-505531)

       137       81        3        0        0        0  
        81      137        3        0        0        0  
         3        3        9        0        0        0  
         0        0        0        2        0        0  
         0        0        0        0        2        0  
         0        0        0        0        0       99  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 50.778 GPaEV = 82.719 GPaGV = 33.667 GPaνV = 0.22849
ReussKR = 8.6786 GPaER = 10.756 GPaGR = 4.1579 GPaνR = 0.29344
HillKH = 29.728 GPaEH = 46.81 GPaGH = 18.912 GPaνH = 0.23756

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
2 GPa 2 GPa 8.9139 GPa 56 GPa 99 GPa 218.09 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 6.1771 GPa 206.61 GPa 3.0864 TPa–1 109.05 TPa–1 2 GPa 99 GPa0.0137610.72081Value
Anisotropy 33.45 35.3333 49.5 52.3788Anisotropy
Axis 0.6041
-0.0000
0.7969
0.7071
0.7071
0.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
1.0000
0.0007
0.0000
0.0000
0.0000
1.0000
-0.6575
0.6575
0.3680
Axis
1.0000
0.0000
-0.0000
-0.0007
1.0000
0.0000
0.1736
0.9848
-0.0000
0.2602
-0.2602
0.9298
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