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-2657)

       472      149      149        0        0        0  
       149      262      168        0        0        0  
       149      168      262        0        0        0  
         0        0        0      212        0        0  
         0        0        0        0      113        0  
         0        0        0        0        0      113  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 214.22 GPaEV = 309.58 GPaGV = 122.93 GPaνV = 0.25914
ReussKR = 203.8 GPaER = 250.1 GPaGR = 96.527 GPaνR = 0.29547
HillKH = 209.01 GPaEH = 280.16 GPaGH = 109.73 GPaνH = 0.2766

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
94 GPa 113 GPa 113 GPa 212 GPa 239.24 GPa 662.76 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 146.9 GPa 374.86 GPa 0.8325 TPa–1 2.0371 TPa–1 47 GPa 212 GPa-0.11590.58803Value
Anisotropy 2.552 2.4470 4.511Anisotropy
Axis 0.0000
1.0000
0.0000
0.0000
0.7071
0.7071
1.0000
0.0000
0.0000
0.0000
0.9239
0.3827
0.0002
0.7071
-0.7071
0.0004
0.0003
1.0000
-0.0000
0.7071
-0.7071
-0.5822
-0.0000
0.8130
Axis
0.0002
-0.7071
-0.7071
0.0000
1.0000
-0.0003
0.0000
0.7071
0.7071
0.0000
-1.0000
-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