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 NaPF6 (Materials Project id mp-10474)

        40       10       10        0        0        0  
        10       40       10        0        0        0  
        10       10       40        0        0        0  
         0        0        0        8        0        0  
         0        0        0        0        8        0  
         0        0        0        0        0        8  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 20 GPaEV = 27.458 GPaGV = 10.8 GPaνV = 0.27119
ReussKR = 20 GPaER = 25.352 GPaGR = 9.8361 GPaνR = 0.28873
HillKH = 20 GPaEH = 26.412 GPaGH = 10.318 GPaνH = 0.2799

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
8 GPa 8 GPa 8 GPa 30 GPa 30 GPa 60 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 21.176 GPa 36 GPa 16.667 TPa–1 16.667 TPa–1 8 GPa 15 GPa0.131150.47541Value
Anisotropy 1.7 1.0000 1.875 3.6250Anisotropy
Axis 0.5774
0.5773
-0.5774
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.8660
0.0000
0.5000
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
1.0000
0.0000
-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