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 Nb4N3 (Materials Project id mp-569167)

       606      104      135        0        0        0  
       104      606      135        0        0        0  
       135      135      564        0        0        0  
         0        0        0       92        0        0  
         0        0        0        0       92        0  
         0        0        0        0        0      112  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 280.44 GPaEV = 387.66 GPaGV = 152.67 GPaνV = 0.26962
ReussKR = 280.42 GPaER = 331.73 GPaGR = 127.31 GPaνR = 0.30284
HillKH = 280.43 GPaEH = 360.05 GPaGH = 139.99 GPaνH = 0.28601

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
92 GPa 92 GPa 112 GPa 432.6 GPa 502 GPa 841.4 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 261.42 GPa 564.73 GPa 1.1786 TPa–1 1.2088 TPa–1 92 GPa 251 GPa0.0830540.56998Value
Anisotropy 2.16 1.0256 2.728 6.8628Anisotropy
Axis 0.5487
0.5487
-0.6308
1.0000
0.0000
0.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.7071
0.7071
-0.0000
0.7916
0.0004
0.6111
0.7201
0.0000
-0.6938
Axis
0.1734
0.9849
-0.0000
-0.7071
0.7071
0.0000
-0.0003
1.0000
-0.0003
-0.6938
0.0001
-0.7201
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