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 Fe (Materials Project id mp-13)

       247      150      150        0        0        0  
       150      247      150        0        0        0  
       150      150      247        0        0        0  
         0        0        0       97        0        0  
         0        0        0        0       97        0  
         0        0        0        0        0       97  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 182.33 GPaEV = 203.88 GPaGV = 77.6 GPaνV = 0.31364
ReussKR = 182.33 GPaER = 184.49 GPaGR = 69.286 GPaνR = 0.33136
HillKH = 182.33 GPaEH = 194.25 GPaGH = 73.443 GPaνH = 0.32244

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
97 GPa 97 GPa 97 GPa 97 GPa 97 GPa 547 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 133.65 GPa 247.17 GPa 1.8282 TPa–1 1.8282 TPa–1 48.5 GPa 97 GPa0.0509130.57637Value
Anisotropy 1.849 1.0000 2 11.3207Anisotropy
Axis 1.0000
0.0000
0.0000
-0.5774
0.5774
0.5773
0.0000
0.0000
1.0000
0.9659
0.0000
0.2588
0.7071
-0.0003
0.7071
0.0000
0.0000
1.0000
0.7071
-0.0000
-0.7071
0.7071
-0.0001
0.7071
Axis
0.7071
-0.0005
-0.7071
0.7660
0.6428
-0.0000
-0.7071
0.0002
-0.7071
0.0001
1.0000
0.0001
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