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 TiCo3 (Materials Project id mp-608)

       258      162      162        0        0        0  
       162      258      162        0        0        0  
       162      162      258        0        0        0  
         0        0        0      119        0        0  
         0        0        0        0      119        0  
         0        0        0        0        0      119  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 194 GPaEV = 235.19 GPaGV = 90.6 GPaνV = 0.29795
ReussKR = 194 GPaER = 198.76 GPaGR = 74.764 GPaνR = 0.32924
HillKH = 194 GPaEH = 217.19 GPaGH = 82.682 GPaνH = 0.31341

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
96 GPa 96 GPa 119 GPa 119 GPa 119 GPa 582 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 133.03 GPa 296.4 GPa 1.7182 TPa–1 1.7182 TPa–1 48 GPa 119 GPa-0.0471710.65753Value
Anisotropy 2.228 1.0000 2.479Anisotropy
Axis 0.0000
0.0000
1.0000
0.5774
0.5774
0.5773
0.9983
0.0000
0.0589
0.0000
0.0000
1.0000
0.7071
0.0001
-0.7071
0.0000
0.0000
1.0000
0.7071
0.0001
-0.7071
0.0000
0.7071
0.7071
Axis
-0.7071
-0.0002
-0.7071
0.7660
0.6428
-0.0000
-0.7071
-0.0002
-0.7071
-1.0000
0.0000
0.0000
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