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 CoPtO2 (Materials Project id mp-19210)

       211      115      135        0        0        0  
       115      211      135       -0        0        0  
       135      135      571        0        0        0  
         0       -0        0       41        0        0  
         0        0        0        0       41        0  
         0        0        0        0        0       48  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 195.89 GPaEV = 179.3 GPaGV = 66.533 GPaνV = 0.34745
ReussKR = 161.31 GPaER = 138.08 GPaGR = 50.865 GPaνR = 0.35733
HillKH = 178.6 GPaEH = 158.71 GPaGH = 58.699 GPaνH = 0.35189

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
41 GPa 41 GPa 48 GPa 96 GPa 221.66 GPa 675.34 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 118.65 GPa 459.19 GPa 0.37409 TPa–1 2.9126 TPa–1 41 GPa 90.115 GPa0.126740.57485Value
Anisotropy 3.87 7.7857 2.198 4.5357Anisotropy
Axis 0.7602
0.3284
-0.5606
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.9239
0.3827
0.0000
-0.0000
-0.0000
1.0000
0.5644
0.4260
0.7071
-0.8373
0.5468
0.0000
0.4658
0.1787
0.8667
Axis
1.0000
0.0002
0.0000
0.5646
0.4258
-0.7071
-0.0000
-0.0000
-1.0000
0.8090
0.3108
-0.4989
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