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 Ti2O3 (Materials Project id mp-458)

       334      162      160       -6        0        0  
       162      334      160        6        0        0  
       160      160      310        0        0        0  
        -6        6        0       93        0        0  
         0        0        0        0       93       -6  
         0        0        0        0       -6       86  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 215.78 GPaEV = 231.17 GPaGV = 87.467 GPaνV = 0.32145
ReussKR = 215.46 GPaER = 229.63 GPaGR = 86.825 GPaνR = 0.32237
HillKH = 215.62 GPaEH = 230.4 GPaGH = 87.146 GPaνH = 0.32191

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
82.554 GPa 92.099 GPa 96.446 GPa 158.36 GPa 172.9 GPa 647.64 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 206.77 GPa 251.47 GPa 1.4626 TPa–1 1.7161 TPa–1 80.175 GPa 96.446 GPa0.256760.37929Value
Anisotropy 1.216 1.1733 1.203 1.4772Anisotropy
Axis 0.0000
0.0000
1.0000
0.0000
0.8231
0.5679
0.3807
0.9247
0.0000
0.0000
0.0000
1.0000
-0.5409
0.3123
0.7810
0.0000
0.4981
-0.8671
0.5214
0.3015
0.7983
0.5609
0.3238
0.7619
Axis
0.6764
-0.3905
0.6245
-1.0000
0.0000
-0.0000
0.6915
0.3989
-0.6023
-0.5000
0.8660
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