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 Co3Mo (Materials Project id mp-1139)

       452      179      145        0        0        0  
       179      452      145        0        0        0  
       145      145      501        0        0        0  
         0        0        0      113        0        0  
         0        0        0        0      113        0  
         0        0        0        0        0      137  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 260.33 GPaEV = 345.31 GPaGV = 135 GPaνV = 0.27893
ReussKR = 260.29 GPaER = 337.64 GPaGR = 131.5 GPaνR = 0.2838
HillKH = 260.31 GPaEH = 341.48 GPaGH = 133.25 GPaνH = 0.28136

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
113 GPa 113 GPa 137 GPa 273 GPa 350.88 GPa 781.12 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 309.82 GPa 434.36 GPa 1.2442 TPa–1 1.2989 TPa–1 113 GPa 163.96 GPa0.19270.3805Value
Anisotropy 1.402 1.0440 1.451 1.9746Anisotropy
Axis 0.0000
0.7621
-0.6475
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.7934
0.6088
0.0000
0.0000
0.0000
1.0000
0.5000
0.5000
0.7071
1.0000
0.0002
0.0000
0.4750
0.4750
0.7408
Axis
1.0000
0.0001
-0.0000
0.5000
0.5000
-0.7071
-0.0000
0.0002
-1.0000
0.5238
0.5238
-0.6718
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