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 FeN (Materials Project id mp-6988)

       302      250      250        0        0        0  
       250      302      250        0        0        0  
       250      250      302        0        0        0  
         0        0        0      105        0        0  
         0        0        0        0      105        0  
         0        0        0        0        0      105  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 267.33 GPaEV = 201.74 GPaGV = 73.4 GPaνV = 0.37423
ReussKR = 267.33 GPaER = 134.25 GPaGR = 47.396 GPaνR = 0.4163
HillKH = 267.33 GPaEH = 168.5 GPaGH = 60.398 GPaνH = 0.39495

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
52 GPa 52 GPa 105 GPa 105 GPa 105 GPa 802 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 75.551 GPa 278.53 GPa 1.2469 TPa–1 1.2469 TPa–1 26 GPa 105 GPa-0.206580.99882Value
Anisotropy 3.687 1.0000 4.038Anisotropy
Axis 0.0000
0.0000
1.0000
0.5774
0.5773
-0.5774
0.0000
0.0000
1.0000
0.9659
0.0000
0.2588
0.7071
0.0001
-0.7071
0.0000
0.0000
1.0000
0.7071
0.0001
-0.7071
-0.0000
0.7071
-0.7071
Axis
-0.7071
-0.0002
-0.7071
-1.0000
0.0000
0.0000
-0.7071
-0.0002
-0.7071
-1.0000
0.0000
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