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-1580)

       674      120      120        0        0        0  
       120      674      120        0        0        0  
       120      120      674        0        0        0  
         0        0        0       74        0        0  
         0        0        0        0       74        0  
         0        0        0        0        0       74  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 304.67 GPaEV = 398.02 GPaGV = 155.2 GPaνV = 0.28227
ReussKR = 304.67 GPaER = 281.79 GPaGR = 104.69 GPaνR = 0.34585
HillKH = 304.67 GPaEH = 341.31 GPaGH = 129.94 GPaνH = 0.31329

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
74 GPa 74 GPa 74 GPa 554 GPa 554 GPa 914 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 205.37 GPa 637.73 GPa 1.0941 TPa–1 1.0941 TPa–1 74 GPa 277 GPa0.0586030.67084Value
Anisotropy 3.105 1.0000 3.743 11.4472Anisotropy
Axis 0.5774
0.5773
-0.5774
1.0000
0.0000
0.0000
0.8660
0.0000
0.5000
0.3536
0.8536
0.3827
-0.0000
-0.0000
1.0000
0.7071
0.0001
-0.7071
-0.7071
-0.0000
0.7071
0.7071
-0.0000
-0.7071
Axis
-0.7648
0.6443
0.0000
-0.7071
-0.0002
-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