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 BC5 (Materials Project id mp-1018649)

       827      193       86      102        0        0  
       193      827       86     -102        0        0  
        86       86     1017        0        0        0  
       102     -102        0      366        0        0  
         0        0        0        0      366      102  
         0        0        0        0      102      317  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 377.89 GPaEV = 825.79 GPaGV = 363.53 GPaνV = 0.13579
ReussKR = 377.32 GPaER = 766.57 GPaGR = 330.02 GPaνR = 0.1614
HillKH = 377.61 GPaEH = 796.5 GPaGH = 346.78 GPaνH = 0.14844

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
236.6 GPa 303.11 GPa 446.4 GPa 696.89 GPa 896.87 GPa 1140.1 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 596.61 GPa 1002.5 GPa 0.8293 TPa–1 0.91047 TPa–1 236.6 GPa 448.86 GPa-0.0501170.37174Value
Anisotropy 1.68 1.0979 1.897Anisotropy
Axis 0.7641
0.4412
-0.4707
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
-0.7934
0.6088
0.0000
0.6801
0.3927
0.6191
0.0000
0.4850
-0.8745
-0.0000
0.4941
-0.8694
0.5000
0.8660
-0.0000
Axis
-0.5000
0.8660
-0.0000
-0.0000
0.8745
0.4850
-1.0000
-0.0000
0.0000
-0.7521
0.4342
-0.4959
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