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 KNbO3 (Materials Project id mp-7375)

       196       73       49      -28        0        0  
        73      196       49       28        0        0  
        49       49      191        0        0        0  
       -28       28        0       32        0        0  
         0        0        0        0       32      -28  
         0        0        0        0      -28       61  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 102.78 GPaEV = 134.51 GPaGV = 52.467 GPaνV = 0.28187
ReussKR = 102.37 GPaER = 79.739 GPaGR = 29.098 GPaνR = 0.37017
HillKH = 102.57 GPaEH = 108.03 GPaGH = 40.782 GPaνH = 0.32447

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
14.968 GPa 17.182 GPa 78.032 GPa 137.82 GPa 150.48 GPa 309.52 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 43 GPa 190.25 GPa 3.0487 TPa–1 3.6713 TPa–1 14.968 GPa 76.53 GPa-0.306030.99054Value
Anisotropy 4.425 1.2042 5.113Anisotropy
Axis -0.6934
0.4010
0.5986
-0.0000
0.9578
0.2873
0.9659
0.2588
0.0000
0.0000
0.0000
1.0000
-0.0000
0.5197
0.8544
0.6490
0.0001
-0.7608
0.5254
0.3031
-0.7950
0.5298
0.3049
-0.7914
Axis
-1.0000
-0.0000
-0.0000
0.7070
0.3691
0.6032
-0.5002
0.8659
-0.0003
-0.6848
-0.3968
-0.6113
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