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 NbN (Materials Project id mp-2634)

       562      200      137        0        0        0  
       200      562      137        0        0        0  
       137      137      753        0        0        0  
         0        0        0      210        0        0  
         0        0        0        0      210        0  
         0        0        0        0        0      181  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 313.89 GPaEV = 522.59 GPaGV = 213.73 GPaνV = 0.22252
ReussKR = 311.77 GPaER = 509.66 GPaGR = 207.59 GPaνR = 0.22755
HillKH = 312.83 GPaEH = 516.13 GPaGH = 210.66 GPaνH = 0.22502

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
181 GPa 210 GPa 210 GPa 362 GPa 563.7 GPa 951.3 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 479.46 GPa 703.74 GPa 0.91003 TPa–1 1.1487 TPa–1 181 GPa 249.05 GPa0.122630.32598Value
Anisotropy 1.468 1.2623 1.376 2.6582Anisotropy
Axis 0.9631
0.1265
0.2376
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
1.0000
-0.0002
-0.0000
-0.4023
0.5815
-0.7071
-0.7779
0.6284
-0.0000
0.5486
0.8361
-0.0000
Axis
0.0002
1.0000
-0.0000
0.4024
-0.5815
-0.7071
0.0000
0.0000
1.0000
-0.8361
0.5486
-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