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 PuN (Materials Project id mp-1719)

       292       85       85        0        0        0  
        85      292       85        0        0        0  
        85       85      292        0        0        0  
         0        0        0       83        0        0  
         0        0        0        0       83        0  
         0        0        0        0        0       83  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 154 GPaEV = 228.49 GPaGV = 91.2 GPaνV = 0.25271
ReussKR = 154 GPaER = 226.28 GPaGR = 90.142 GPaνR = 0.25511
HillKH = 154 GPaEH = 227.39 GPaGH = 90.671 GPaνH = 0.25391

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
83 GPa 83 GPa 83 GPa 207 GPa 207 GPa 462 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 211.08 GPa 253.67 GPa 2.1645 TPa–1 2.1645 TPa–1 83 GPa 103.5 GPa0.195830.32727Value
Anisotropy 1.202 1.0000 1.247 1.6712Anisotropy
Axis -0.5774
0.5774
-0.5773
0.0000
0.0000
1.0000
0.2500
0.9330
0.2588
-0.2391
0.8924
0.3827
0.0000
0.0000
1.0000
0.7071
0.0001
-0.7071
0.7071
0.0000
-0.7071
0.7071
-0.0000
-0.7071
Axis
-0.7660
0.6428
-0.0000
-0.7071
-0.0002
-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