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 BeCu (Materials Project id mp-2323)

       183      122      122        0        0        0  
       122      183      122        0        0        0  
       122      122      183        0        0        0  
         0        0        0      121        0        0  
         0        0        0        0      121        0  
         0        0        0        0        0      121  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 142.33 GPaEV = 212.25 GPaGV = 84.8 GPaνV = 0.25147
ReussKR = 142.33 GPaER = 146.95 GPaGR = 55.33 GPaνR = 0.32793
HillKH = 142.33 GPaEH = 180.57 GPaGH = 70.065 GPaνH = 0.28856

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
61 GPa 61 GPa 121 GPa 121 GPa 121 GPa 427 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 85.4 GPa 282.85 GPa 2.3419 TPa–1 2.3419 TPa–1 30.5 GPa 121 GPa-0.259320.83955Value
Anisotropy 3.312 1.0000 3.967Anisotropy
Axis 0.0000
0.0000
1.0000
0.5774
0.5773
-0.5774
0.0000
0.0000
1.0000
0.4330
0.7500
0.5000
0.7071
-0.0003
0.7071
0.0000
0.0000
1.0000
0.7071
0.0001
-0.7071
0.0000
0.7071
0.7071
Axis
0.7071
-0.0005
-0.7071
1.0000
0.0002
-0.0000
-0.7071
-0.0002
-0.7071
-1.0000
-0.0000
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