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 Mo (Materials Project id mp-129)

       472      158      158        0        0        0  
       158      472      158        0        0        0  
       158      158      472        0        0        0  
         0        0        0      106        0        0  
         0        0        0        0      106        0  
         0        0        0        0        0      106  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 262.67 GPaEV = 326.78 GPaGV = 126.4 GPaνV = 0.29265
ReussKR = 262.67 GPaER = 316.55 GPaGR = 121.83 GPaνR = 0.29914
HillKH = 262.67 GPaEH = 321.68 GPaGH = 124.12 GPaνH = 0.29589

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
106 GPa 106 GPa 106 GPa 314 GPa 314 GPa 788 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 280.3 GPa 392.75 GPa 1.269 TPa–1 1.269 TPa–1 106 GPa 157 GPa0.192780.42409Value
Anisotropy 1.401 1.0000 1.481 2.1998Anisotropy
Axis -0.5774
0.5774
0.5773
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.7934
0.0000
0.6088
-0.0000
-0.0000
1.0000
0.7071
-0.0003
0.7071
-0.7071
-0.0000
0.7071
0.7071
-0.0000
-0.7071
Axis
1.0000
0.0002
0.0000
0.7071
-0.0005
-0.7071
0.0000
-1.0000
-0.0000
-0.7071
0.0002
-0.7071
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