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 Re3N (Materials Project id mp-974435)

       611      171      247        0        0        0  
       171      611      247        0        0        0  
       247      247      727        0        0        0  
         0        0        0      174        0        0  
         0        0        0        0      174        0  
         0        0        0        0        0      220  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 364.33 GPaEV = 505.48 GPaGV = 199.2 GPaνV = 0.26877
ReussKR = 357.77 GPaER = 497.68 GPaGR = 196.22 GPaνR = 0.26815
HillKH = 361.05 GPaEH = 501.58 GPaGH = 197.71 GPaνH = 0.26846

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
174 GPa 174 GPa 220 GPa 404.11 GPa 440 GPa 1104.9 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 477.05 GPa 570.97 GPa 0.64502 TPa–1 1.075 TPa–1 174 GPa 220 GPa0.165210.37894Value
Anisotropy 1.197 1.6667 1.264 2.2937Anisotropy
Axis 0.7163
0.3048
-0.6277
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.8660
0.5000
0.0000
-0.0000
-0.0000
1.0000
0.3876
0.9218
-0.0000
0.7780
0.6283
-0.0000
0.6177
0.2320
-0.7514
Axis
1.0000
0.0002
0.0000
-0.9218
0.3876
0.0000
-0.6283
0.7780
0.0000
-0.7034
-0.2643
-0.6598
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