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 WS (Materials Project id mp-1004526)

       270      153       80        0        0        0  
       153      270       80        0        0        0  
        80       80      468        0        0        0  
         0        0        0       70        0        0  
         0        0        0        0       70        0  
         0        0        0        0        0       59  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 181.56 GPaEV = 223.12 GPaGV = 86.133 GPaνV = 0.29518
ReussKR = 178.21 GPaER = 192.68 GPaGR = 72.995 GPaνR = 0.31981
HillKH = 179.88 GPaEH = 208.02 GPaGH = 79.564 GPaνH = 0.30726

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
59 GPa 70 GPa 70 GPa 117 GPa 330.15 GPa 560.85 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 172.91 GPa 437.74 GPa 1.4204 TPa–1 2.0954 TPa–1 58.5 GPa 115.61 GPa0.0780260.54355Value
Anisotropy 2.532 1.4753 1.976 6.9662Anisotropy
Axis 0.8891
-0.0000
0.4578
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.5000
0.8660
0.0000
-0.7071
0.7071
0.0000
0.5000
0.5000
-0.7071
1.0000
0.0003
0.0000
1.0000
-0.0000
-0.0000
Axis
-0.7071
-0.7071
0.0000
-0.5002
-0.4998
-0.7071
0.0000
0.0002
-1.0000
0.0000
1.0000
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