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 BeGeN2 (Materials Project id mp-1019550)

       409      102       71        0        0        0  
       102      392       64        0        0        0  
        71       64      444        0        0        0  
         0        0        0      126        0        0  
         0        0        0        0      121        0  
         0        0        0        0        0      148  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 191 GPaEV = 349.44 GPaGV = 146.2 GPaνV = 0.19508
ReussKR = 190.88 GPaER = 342.87 GPaGR = 142.79 GPaνR = 0.20062
HillKH = 190.94 GPaEH = 346.16 GPaGH = 144.49 GPaνH = 0.19784

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
121 GPa 126 GPa 148 GPa 298.14 GPa 373.43 GPa 573.44 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 316.32 GPa 425.83 GPa 1.6902 TPa–1 1.8307 TPa–1 121 GPa 176.12 GPa0.126290.31146Value
Anisotropy 1.346 1.0832 1.456 2.4662Anisotropy
Axis 0.7488
0.0000
-0.6628
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
0.0000
1.0000
0.7071
0.0001
-0.7071
0.0000
0.0000
1.0000
0.6875
0.0001
-0.7262
Axis
-1.0000
0.0000
0.0000
-0.7071
-0.0002
-0.7071
-0.0000
1.0000
-0.0000
-0.7262
-0.0000
-0.6875
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