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 TiO (Materials Project id mp-2664)

       531       71       71        0        0        0  
        71      531       71        0        0        0  
        71       71      531        0        0        0  
         0        0        0       17        0        0  
         0        0        0        0       17        0  
         0        0        0        0        0       17  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 224.33 GPaEV = 266.18 GPaGV = 102.2 GPaνV = 0.30224
ReussKR = 224.33 GPaER = 77.883 GPaGR = 27.003 GPaνR = 0.44214
HillKH = 224.33 GPaEH = 176.83 GPaGH = 64.601 GPaνH = 0.36863

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
17 GPa 17 GPa 17 GPa 460 GPa 460 GPa 673 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 49.743 GPa 514.25 GPa 1.4859 TPa–1 1.4859 TPa–1 17 GPa 230 GPa0.0147360.88979Value
Anisotropy 10.34 1.0000 13.53 60.3824Anisotropy
Axis 0.5774
0.5773
-0.5774
0.0000
0.0000
1.0000
0.2241
0.8365
0.5000
0.7934
0.0000
0.6088
0.0000
0.0000
1.0000
0.7071
0.0001
-0.7071
-0.7071
-0.0000
0.7071
0.7071
-0.0000
0.7071
Axis
-0.1736
0.9848
-0.0000
-0.7071
-0.0002
-0.7071
-0.0000
-1.0000
-0.0000
0.7071
0.0000
-0.7071
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