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 KRbO (Materials Project id mp-755480)

        42       20       32        0        0        0  
        20       42       32        0        0        0  
        32       32       76        0        0        0  
         0        0        0        4        0        0  
         0        0        0        0        4        0  
         0        0        0        0        0        6  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 36.444 GPaEV = 22.016 GPaGV = 7.8667 GPaνV = 0.39932
ReussKR = 30.977 GPaER = 16.789 GPaGR = 5.9548 GPaνR = 0.40967
HillKH = 33.711 GPaEH = 19.406 GPaGH = 6.9107 GPaνH = 0.40406

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
4 GPa 4 GPa 6 GPa 22 GPa 23.207 GPa 114.79 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 12.802 GPa 42.968 GPa-0.75075 TPa–1 16.517 TPa–1 4 GPa 11.864 GPa0.138540.75608Value
Anisotropy 3.356 2.966 5.4574Anisotropy
Axis 0.5529
0.5528
0.6235
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.7071
0.0001
-0.7071
-0.7866
0.0000
0.6175
0.6097
0.0001
-0.7926
Axis
1.0000
0.0000
-0.0000
-0.7071
-0.0002
-0.7071
0.0000
-1.0000
0.0000
-0.7926
-0.0003
-0.6097
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