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-2701)

       566      210      168        0        0        0  
       210      566      168        0        0        0  
       168      168      613        0        0        0  
         0        0        0      185        0        0  
         0        0        0        0      185        0  
         0        0        0        0        0      178  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 315.22 GPaEV = 473.67 GPaGV = 189.53 GPaνV = 0.24956
ReussKR = 315.22 GPaER = 471.02 GPaGR = 188.27 GPaνR = 0.25095
HillKH = 315.22 GPaEH = 472.35 GPaGH = 188.9 GPaνH = 0.25026

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
178 GPa 185 GPa 185 GPa 356 GPa 443.32 GPa 945.68 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 458.63 GPa 540.26 GPa 1.0495 TPa–1 1.0614 TPa–1 178 GPa 208.86 GPa0.187640.31533Value
Anisotropy 1.178 1.0114 1.173 1.6805Anisotropy
Axis -0.6590
0.5442
0.5191
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
-0.1305
0.9914
0.0000
1.0000
-0.0008
-0.0000
0.6046
0.3667
0.7071
0.2910
0.9567
0.0000
-0.9183
0.3959
0.0000
Axis
0.0008
1.0000
-0.0000
0.6046
0.3667
-0.7071
-0.0000
-0.0000
1.0000
-0.3959
-0.9183
-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