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-629015)

       722      161        0        0        0        0  
       161      722        0        0        0        0  
         0        0        4        0        0        0  
         0        0        0        1        0        0  
         0        0        0        0        1        0  
         0        0        0        0        0      281  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 196.67 GPaEV = 344.14 GPaGV = 142.4 GPaνV = 0.20836
ReussKR = 3.9641 GPaER = 5.4315 GPaGR = 2.1356 GPaνR = 0.27164
HillKH = 100.32 GPaEH = 174.82 GPaGH = 72.268 GPaνH = 0.20955

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
1 GPa 1 GPa 4 GPa 281 GPa 561 GPa 883 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 2.9985 GPa 686.85 GPa 1.1325 TPa–1 250 TPa–1 1 GPa 281 GPa00.72103Value
Anisotropy 229.1220.7500 281Anisotropy
Axis 0.5779
-0.0000
0.8161
0.7071
0.7071
0.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
1.0000
0.0007
-0.0000
0.0000
0.0000
1.0000
0.6816
0.6816
-0.2663
Axis
1.0000
0.0000
-0.0000
-0.0007
1.0000
-0.0000
1.0000
0.0000
-0.0000
-0.1883
-0.1883
-0.9639
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