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 MoS2 (Materials Project id mp-1434)

       179       45        1        0        0        0  
        45      179        1       -0        0        0  
         1        1        3        0        0        0  
         0       -0        0        1        0        0  
         0        0        0        0        1        0  
         0        0        0        0        0       67  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 50.556 GPaEV = 84.784 GPaGV = 34.733 GPaνV = 0.22049
ReussKR = 2.9646 GPaER = 4.9265 GPaGR = 2.014 GPaνR = 0.22304
HillKH = 26.76 GPaEH = 44.855 GPaGH = 18.374 GPaνH = 0.22063

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
1 GPa 1 GPa 2.991 GPa 67 GPa 134 GPa 224.01 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 2.664 GPa 167.5 GPa 2.9851 TPa–1 331.34 TPa–1 1 GPa 67 GPa0.00446430.619Value
Anisotropy 62.88111.0000 67138.6559Anisotropy
Axis 0.3044
0.3967
0.8660
0.6088
0.7934
0.0000
0.7934
0.6088
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
1.0000
0.0006
0.0000
0.0000
0.0000
1.0000
-0.5981
0.7405
0.3063
Axis
1.0000
0.0000
-0.0000
-0.0006
1.0000
0.0000
0.5000
0.8660
-0.0000
0.1925
-0.2383
0.9519
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