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 Ni3N (Materials Project id mp-2033)

       282      151      156        0        0        0  
       151      282      156        0        0        0  
       156      156      283        0        0        0  
         0        0        0       89        0        0  
         0        0        0        0       89        0  
         0        0        0        0        0       66  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 197 GPaEV = 198.24 GPaGV = 74.4 GPaνV = 0.33228
ReussKR = 196.98 GPaER = 193.91 GPaGR = 72.577 GPaνR = 0.33593
HillKH = 196.99 GPaEH = 196.08 GPaGH = 73.489 GPaνH = 0.3341

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
66 GPa 89 GPa 89 GPa 124.98 GPa 131 GPa 591.02 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 170.59 GPa 215.38 GPa 1.6381 TPa–1 1.7193 TPa–1 63.219 GPa 89 GPa0.207740.43202Value
Anisotropy 1.263 1.0496 1.408 2.0796Anisotropy
Axis 0.0000
0.0000
1.0000
0.5086
0.5086
0.6947
0.0000
0.0000
1.0000
0.3827
0.9239
0.0000
0.7071
-0.0003
0.7071
-0.0000
0.0000
1.0000
0.7045
-0.0002
0.7097
0.6789
-0.0003
0.7342
Axis
0.7071
-0.0005
-0.7071
-0.7660
0.6428
-0.0000
0.7097
-0.0005
-0.7045
0.0005
1.0000
-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