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 BeAu (Materials Project id mp-30365)

       201      121      121        0        0        0  
       121      201      121        0        0        0  
       121      121      201        0        0        0  
         0        0        0       42        0        0  
         0        0        0        0       42        0  
         0        0        0        0        0       42  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 147.67 GPaEV = 113.08 GPaGV = 41.2 GPaνV = 0.37237
ReussKR = 147.67 GPaER = 113.02 GPaGR = 41.176 GPaνR = 0.37243
HillKH = 147.67 GPaEH = 113.05 GPaGH = 41.188 GPaνH = 0.3724

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
42 GPa 42 GPa 42 GPa 80 GPa 80 GPa 443 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 110.06 GPa 115.09 GPa 2.2573 TPa–1 2.2573 TPa–1 40 GPa 42 GPa0.354640.3885Value
Anisotropy 1.046 1.0000 1.05 1.0955Anisotropy
Axis 1.0000
0.0000
0.0000
0.5774
0.5774
0.5773
0.0000
0.0000
1.0000
0.9239
0.0000
0.3827
0.7071
-0.0003
0.7071
0.0000
0.0000
1.0000
0.7071
-0.0002
0.7071
-0.7071
-0.0000
0.7071
Axis
0.7071
-0.0005
-0.7071
0.1736
0.9848
-0.0000
0.7071
-0.0005
-0.7071
0.0000
-1.0000
-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