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 KHO (Materials Project id mp-626785)

        55       10       17        0        0        0  
        10       35       20        0        0        0  
        17       20       47        0        0        0  
         0        0        0       19        0        0  
         0        0        0        0       18        0  
         0        0        0        0        0        1  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 25.667 GPaEV = 34.675 GPaGV = 13.6 GPaνV = 0.27483
ReussKR = 24.617 GPaER = 11.31 GPaGR = 3.9726 GPaνR = 0.42343
HillKH = 25.142 GPaEH = 23.609 GPaGH = 8.7863 GPaνH = 0.3435

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
1 GPa 18 GPa 19 GPa 19.945 GPa 38.675 GPa 78.38 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 3.7929 GPa 48.562 GPa 8.2699 TPa–1 20.443 TPa–1 1 GPa 19 GPa-0.986841.737Value
Anisotropy 12.8 2.4720 19Anisotropy
Axis 0.7005
0.7136
0.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.0000
1.0000
0.0000
1.0000
-0.0002
-0.0000
0.0000
-0.0000
1.0000
-0.3055
0.4446
0.8420
0.3780
0.3985
0.8357
Axis
0.0002
1.0000
-0.0000
0.0000
-1.0000
-0.0000
-0.6233
0.5752
-0.5298
-0.7044
0.7096
-0.0197
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