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 TiO2 (Materials Project id mp-390)

       321      149      141        0        0        0  
       149      321      141        0        0        0  
       141      141      185        0        0        0  
         0        0        0       47        0        0  
         0        0        0        0       47        0  
         0        0        0        0        0       58  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 187.67 GPaEV = 154.78 GPaGV = 56.8 GPaνV = 0.36254
ReussKR = 170.97 GPaER = 142.81 GPaGR = 52.474 GPaνR = 0.36078
HillKH = 179.32 GPaEH = 148.8 GPaGH = 54.637 GPaνH = 0.3617

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
47 GPa 47 GPa 58 GPa 82.412 GPa 172 GPa 572.59 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 100.4 GPa 205.46 GPa 0.93244 TPa–1 3.9841 TPa–1 45.031 GPa 86 GPa0.194510.61391Value
Anisotropy 2.046 4.2727 1.91 3.1562Anisotropy
Axis 0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
-0.5001
0.4999
0.7071
-0.7071
0.7071
0.0000
1.0000
-0.0002
-0.0000
1.0000
-0.0003
0.0000
Axis
-0.4999
0.5001
-0.7071
-0.7071
-0.7071
0.0000
0.0002
1.0000
0.0000
0.0000
-0.0004
-1.0000
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