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-984)

       734      164        1        0        0        0  
       164      734        1        0        0        0  
         1        1        5        0        0        0  
         0        0        0        2        0        0  
         0        0        0        0        2        0  
         0        0        0        0        0      285  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 200.56 GPaEV = 350.39 GPaGV = 144.93 GPaνV = 0.20881
ReussKR = 4.9646 GPaER = 9.3119 GPaGR = 3.9211 GPaνR = 0.18739
HillKH = 102.76 GPaEH = 179.86 GPaGH = 74.427 GPaνH = 0.20829

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
2 GPa 2 GPa 4.9978 GPa 285 GPa 570 GPa 898 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 4.7991 GPa 697.24 GPa 0.89127 TPa–1 199.64 TPa–1 2 GPa 285 GPa0.00111360.5649Value
Anisotropy 145.3224.0000 142.5507.2771Anisotropy
Axis -0.1963
0.3580
0.9128
0.9239
0.3827
0.0000
0.4972
0.8677
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
-0.6863
0.7273
0.0000
0.0000
0.0000
1.0000
0.7382
0.6228
-0.2594
Axis
1.0000
0.0000
-0.0000
-0.7273
-0.6863
0.0000
0.1736
0.9848
-0.0000
-0.1983
-0.1673
-0.9658
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