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 NpN (Materials Project id mp-2596)

       306       65       65        0        0        0  
        65      306       65        0        0        0  
        65       65      306        0        0        0  
         0        0        0       61        0        0  
         0        0        0        0       61        0  
         0        0        0        0        0       61  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 145.33 GPaEV = 212.98 GPaGV = 84.8 GPaνV = 0.25576
ReussKR = 145.33 GPaER = 194.19 GPaGR = 76.013 GPaνR = 0.27731
HillKH = 145.33 GPaEH = 203.66 GPaGH = 80.407 GPaνH = 0.26644

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
61 GPa 61 GPa 61 GPa 241 GPa 241 GPa 436 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 160.54 GPa 283.22 GPa 2.2936 TPa–1 2.2936 TPa–1 61 GPa 120.5 GPa0.111370.4757Value
Anisotropy 1.764 1.0000 1.975 4.2714Anisotropy
Axis -0.5774
0.5774
-0.5773
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.9239
0.0000
0.3827
-0.0000
-0.0000
1.0000
0.7071
0.0001
-0.7071
0.7071
-0.0000
0.7071
0.7071
-0.0002
0.7071
Axis
1.0000
0.0002
0.0000
-0.7071
-0.0002
-0.7071
0.0000
1.0000
0.0000
0.7071
-0.0005
-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