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 Be4B (Materials Project id mp-27757)

       368      -10       52        0        0        0  
       -10      368       52        0        0        0  
        52       52      314        0        0        0  
         0        0        0      170        0        0  
         0        0        0        0      170        0  
         0        0        0        0        0      109  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 137.56 GPaEV = 335.7 GPaGV = 153.53 GPaνV = 0.093253
ReussKR = 137.54 GPaER = 325.65 GPaGR = 147.31 GPaνR = 0.10537
HillKH = 137.55 GPaEH = 330.71 GPaGH = 150.42 GPaνH = 0.09928

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
109 GPa 170 GPa 170 GPa 259.24 GPa 378 GPa 412.76 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 265.9 GPa 370.57 GPa 2.3737 TPa–1 2.4485 TPa–1 109 GPa 189 GPa-0.0517860.22841Value
Anisotropy 1.394 1.0315 1.734Anisotropy
Axis -0.7071
0.7071
0.0000
0.8525
-0.0000
0.5227
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
1.0000
-0.0002
-0.0000
0.7071
0.7071
0.0000
1.0000
0.0007
0.0000
-0.6102
0.6102
0.5052
Axis
0.0002
1.0000
-0.0000
-0.7071
0.7071
0.0000
-0.0007
1.0000
-0.0000
-0.7071
-0.7071
0.0000
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