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-604884)

       736      163       -1        0        0        0  
       163      736       -1        0        0        0  
        -1       -1        4        0        0        0  
         0        0        0        2        0        0  
         0        0        0        0        2        0  
         0        0        0        0        0      286  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 199.78 GPaEV = 351.56 GPaGV = 145.67 GPaνV = 0.20671
ReussKR = 3.9451 GPaER = 8.5084 GPaGR = 3.7299 GPaνR = 0.14055
HillKH = 101.86 GPaEH = 180.08 GPaGH = 74.698 GPaνH = 0.20536

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
2 GPa 2 GPa 3.9978 GPa 286 GPa 573 GPa 899 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 3.9978 GPa 699.75 GPa 1.3912 TPa–1 250.7 TPa–1 2 GPa 286.5 GPa-0.00111230.45517Value
Anisotropy 175180.2000 143.2Anisotropy
Axis 0.0236
-0.0003
0.9997
1.0000
0.0000
0.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
-0.7071
0.7071
-0.0000
-0.0000
-0.0000
1.0000
0.9577
0.0002
0.2876
Axis
1.0000
0.0000
-0.0000
-0.7071
-0.7071
0.0000
0.1735
0.9848
0.0000
0.2876
0.0002
-0.9577
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