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-644751)

       657      284      126        0        0        0  
       284      372      113        0        0        0  
       126      113      763        0        0        0  
         0        0        0      183        0        0  
         0        0        0        0      295        0  
         0        0        0        0        0      274  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 315.33 GPaEV = 564.72 GPaGV = 235 GPaνV = 0.20152
ReussKR = 290.41 GPaER = 476.97 GPaGR = 194.48 GPaνR = 0.22626
HillKH = 302.87 GPaEH = 521.07 GPaGH = 214.74 GPaνH = 0.21326

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
183 GPa 195.04 GPa 274 GPa 295 GPa 628.74 GPa 968.22 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 244.6 GPa 725.09 GPa 0.4534 TPa–1 2.0593 TPa–1 102.23 GPa 304.68 GPa-0.00343710.74688Value
Anisotropy 2.964 4.5419 2.98Anisotropy
Axis 0.0000
1.0000
0.0000
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
0.0000
1.0000
0.0000
-0.7071
0.7071
-0.0000
0.5830
0.4002
0.7071
0.7050
-0.0002
0.7092
1.0000
-0.0002
-0.0000
Axis
-0.7071
-0.7071
-0.0000
0.5830
0.4002
-0.7071
0.7092
-0.0005
-0.7050
0.0002
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