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-13150)

       739      166        0        0        0        0  
       166      739        0       -0        0        0  
         0        0        4        0        0        0  
         0       -0        0        2        0        0  
         0        0        0        0        2        0  
         0        0        0        0        0      287  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 201.56 GPaEV = 352.68 GPaGV = 145.93 GPaνV = 0.20837
ReussKR = 3.965 GPaER = 8.516 GPaGR = 3.7284 GPaνR = 0.14203
HillKH = 102.76 GPaEH = 180.64 GPaGH = 74.831 GPaνH = 0.20701

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
2 GPa 2 GPa 4 GPa 287 GPa 573 GPa 905 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 4 GPa 702.46 GPa 1.105 TPa–1 250 TPa–1 2 GPa 287 GPa00.46227Value
Anisotropy 175.6226.2500 143.5Anisotropy
Axis 0.0000
0.0000
1.0000
-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
0.6818
0.6819
-0.2649
Axis
1.0000
0.0000
-0.0000
-0.0007
1.0000
0.0000
1.0000
0.0000
-0.0000
-0.1873
-0.1873
-0.9643
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