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 UN (Materials Project id mp-1865)

       403      125      125        0        0        0  
       125      403      125        0        0        0  
       125      125      403        0        0        0  
         0        0        0       53        0        0  
         0        0        0        0       53        0  
         0        0        0        0        0       53  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 217.67 GPaEV = 231.25 GPaGV = 87.4 GPaνV = 0.32293
ReussKR = 217.67 GPaER = 190.72 GPaGR = 70.43 GPaνR = 0.35397
HillKH = 217.67 GPaEH = 211.22 GPaGH = 78.915 GPaνH = 0.33827

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
53 GPa 53 GPa 53 GPa 278 GPa 278 GPa 653 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 147.06 GPa 343.81 GPa 1.5314 TPa–1 1.5314 TPa–1 53 GPa 139 GPa0.118170.61902Value
Anisotropy 2.338 1.0000 2.623 5.2383Anisotropy
Axis 0.5774
0.5773
-0.5774
0.0000
0.0000
1.0000
0.4830
0.3706
0.7934
0.5000
0.0000
0.8660
-0.0000
-0.0000
1.0000
0.7071
-0.0003
0.7071
0.7071
-0.0000
0.7071
0.7071
-0.0000
-0.7071
Axis
1.0000
0.0002
0.0000
0.7071
-0.0005
-0.7071
0.0000
1.0000
0.0000
-0.7071
0.0002
-0.7071
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