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 KNb4O5F (Materials Project id mp-549490)

       376       55       64        0        0        0  
        55      376       64        0        0        0  
        64       64      186        0        0        0  
         0        0        0       56        0        0  
         0        0        0        0       56        0  
         0        0        0        0        0       89  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 144.89 GPaEV = 224.78 GPaGV = 90.533 GPaνV = 0.24143
ReussKR = 131.58 GPaER = 192.49 GPaGR = 76.618 GPaνR = 0.25618
HillKH = 138.23 GPaEH = 208.67 GPaGH = 83.575 GPaνH = 0.24841

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
56 GPa 56 GPa 89 GPa 156.19 GPa 321 GPa 460.81 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 149.46 GPa 350.91 GPa 1.6951 TPa–1 4.2099 TPa–1 56 GPa 160.5 GPa0.0841730.45395Value
Anisotropy 2.348 2.4836 2.866 5.3930Anisotropy
Axis 0.4138
0.4138
0.8109
1.0000
0.0000
0.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
-0.0000
-0.0000
1.0000
0.7071
0.7071
-0.0000
-0.8916
0.0000
0.4528
0.8247
0.0000
0.5656
Axis
1.0000
0.0002
0.0000
-0.7071
0.7071
0.0000
-0.0000
-1.0000
0.0000
0.5656
0.0001
-0.8247
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