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 PuO (Materials Project id mp-806)

       221       64       64        0        0        0  
        64      221       64        0        0        0  
        64       64      221        0        0        0  
         0        0        0       35        0        0  
         0        0        0        0       35        0  
         0        0        0        0        0       35  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 116.33 GPaEV = 136.68 GPaGV = 52.4 GPaνV = 0.30419
ReussKR = 116.33 GPaER = 119.5 GPaGR = 44.967 GPaνR = 0.32879
HillKH = 116.33 GPaEH = 128.17 GPaGH = 48.684 GPaνH = 0.31637

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
35 GPa 35 GPa 35 GPa 157 GPa 157 GPa 349 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 95.43 GPa 192.26 GPa 2.8653 TPa–1 2.8653 TPa–1 35 GPa 78.5 GPa0.127520.55965Value
Anisotropy 2.015 1.0000 2.243 4.3887Anisotropy
Axis -0.5774
0.5774
-0.5773
0.0000
0.0000
1.0000
0.5000
0.0000
0.8660
0.4619
0.8001
0.3827
0.0000
0.0000
1.0000
0.7071
0.0001
-0.7071
-0.7071
-0.0000
0.7071
0.7071
-0.0002
0.7071
Axis
-0.9397
0.3420
0.0000
-0.7071
-0.0002
-0.7071
0.0000
-1.0000
0.0000
0.7071
-0.0005
-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