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-9173)

       108       70       44        0        0        0  
        70      146       46        0        0        0  
        44       46      334        0        0        0  
         0        0        0       81        0        0  
         0        0        0        0       44        0  
         0        0        0        0        0       38  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 100.89 GPaEV = 152.58 GPaGV = 61.133 GPaνV = 0.24794
ReussKR = 87.782 GPaER = 118.43 GPaGR = 46.436 GPaνR = 0.27515
HillKH = 94.336 GPaEH = 135.59 GPaGH = 53.785 GPaνH = 0.26045

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
38 GPa 44 GPa 54.273 GPa 81 GPa 174.5 GPa 359.23 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 72.931 GPa 313.04 GPa 1.6978 TPa–1 6.4925 TPa–1 27.548 GPa 81 GPa0.00920660.62639Value
Anisotropy 4.292 3.8241 2.94 68.0370Anisotropy
Axis 1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
-0.7071
0.7071
0.0001
0.0003
0.0003
1.0000
0.0000
0.7183
0.6957
0.0000
0.9598
0.2807
Axis
-0.7071
-0.7071
0.0000
-0.0000
1.0000
-0.0003
0.0000
-0.6957
0.7183
-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