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 TiS2 (Materials Project id mp-2156)

       121       25        1       -1        0        0  
        25      121        1        1        0        0  
         1        1        4        0        0        0  
        -1        1        0        2        0        0  
         0        0        0        0        2       -1  
         0        0        0        0       -1       48  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 33.333 GPaEV = 60 GPaGV = 25 GPaνV = 0.2
ReussKR = 3.88 GPaER = 8.2155 GPaGR = 3.581 GPaνR = 0.1471
HillKH = 18.607 GPaEH = 34.133 GPaGH = 14.29 GPaνH = 0.19426

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
1.9783 GPa 1.9787 GPa 3.9859 GPa 48.022 GPa 96.021 GPa 146.01 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 3.9863 GPa 115.71 GPa 5.1546 TPa–1 247.42 TPa–1 1.9783 GPa 48.022 GPa-0.00497790.43271Value
Anisotropy 29.03 48.0000 24.27Anisotropy
Axis 0.0332
0.0192
0.9993
0.8660
0.4999
-0.0109
0.1127
0.9936
-0.0000
0.0000
0.0000
1.0000
-0.0188
-0.0109
0.9998
-0.0000
0.9998
-0.0217
-0.6880
0.3972
-0.6074
0.9427
-0.0224
-0.3330
Axis
-0.5000
0.8660
-0.0000
-1.0000
-0.0000
-0.0000
-0.5000
-0.8660
-0.0000
0.3304
-0.0769
0.9407
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