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 BeSe (Materials Project id mp-1008524)

       149       94       40        0        0        0  
        94      149       40        0        0        0  
        40       40      189        0        0        0  
         0        0        0        5        0        0  
         0        0        0        0        5        0  
         0        0        0        0        0       28  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 92.778 GPaEV = 77.476 GPaGV = 28.467 GPaνV = 0.36082
ReussKR = 92.683 GPaER = 29.816 GPaGR = 10.307 GPaνR = 0.44638
HillKH = 92.731 GPaEH = 54.371 GPaGH = 19.387 GPaνH = 0.40228

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
5 GPa 5 GPa 28 GPa 55 GPa 153.32 GPa 278.68 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 18.579 GPa 175.83 GPa 3.4873 TPa–1 3.8149 TPa–1 5 GPa 53.472 GPa0.0579940.86509Value
Anisotropy 9.464 1.0940 10.69 14.9168Anisotropy
Axis 0.7180
0.0000
0.6961
0.0000
0.0000
1.0000
0.2390
0.9710
-0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.5236
0.4753
-0.7071
-0.3465
0.3465
-0.8717
-0.4492
0.4492
-0.7723
Axis
-0.7660
0.6428
-0.0000
-0.5235
-0.4753
-0.7071
-0.7071
-0.7071
-0.0000
-0.5461
0.5461
0.6353
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