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 BN (Materials Project id mp-2653)

       929      130       57        0        0        0  
       130      929       57        0        0        0  
        57       57     1013        0        0        0  
         0        0        0      329        0        0  
         0        0        0        0      329        0  
         0        0        0        0        0      400  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 373.22 GPaEV = 862.35 GPaGV = 386.73 GPaνV = 0.11491
ReussKR = 373.21 GPaER = 849.95 GPaGR = 379.3 GPaνR = 0.12043
HillKH = 373.22 GPaEH = 856.16 GPaGH = 383.01 GPaνH = 0.11767

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
329 GPa 329 GPa 400 GPa 799 GPa 952.17 GPa 1119.8 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 793.59 GPa 1006.9 GPa 0.88627 TPa–1 0.89658 TPa–1 329 GPa 454.52 GPa0.0538240.20971Value
Anisotropy 1.269 1.0116 1.382 3.8963Anisotropy
Axis 0.7511
-0.0000
0.6602
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
-0.0000
-0.0000
1.0000
0.5000
0.5000
0.7071
0.0000
0.0000
1.0000
-0.4916
0.4914
-0.7189
Axis
0.1717
0.9851
0.0000
0.5000
0.5000
-0.7071
0.1736
0.9848
-0.0000
0.5083
-0.5085
-0.6951
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