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 Co(PtO2)3 (Materials Project id mp-19238)

       309      139      122        0        0        0  
       139      335      139        0        0        0  
       122      139      311        0        0        0  
         0        0        0       34        0        0  
         0        0        0        0       67        0  
         0        0        0        0        0      109  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 195 GPaEV = 208.8 GPaGV = 79 GPaνV = 0.32154
ReussKR = 194.28 GPaER = 179.09 GPaGR = 66.507 GPaνR = 0.34637
HillKH = 194.64 GPaEH = 194.08 GPaGH = 72.754 GPaνH = 0.33381

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
34 GPa 67 GPa 109 GPa 180.98 GPa 188.05 GPa 585.97 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 113.96 GPa 269.38 GPa 1.4517 TPa–1 1.8576 TPa–1 34 GPa 109 GPa0.048310.67597Value
Anisotropy 2.364 1.2795 3.206 13.9923Anisotropy
Axis 0.0000
0.7043
0.7099
0.6700
0.7424
0.0000
0.0000
1.0000
0.0000
1.0000
0.0000
0.0000
-0.0003
-0.0000
1.0000
1.0000
-0.0002
0.0000
0.6842
0.5593
0.4681
0.0011
0.7130
-0.7011
Axis
0.0000
1.0000
0.0000
0.0002
1.0000
-0.0000
-0.7284
0.5569
0.3993
-0.0006
-0.7011
-0.7130
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