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 TiB2 (Materials Project id mp-1145)

       642       75      106        0        0        0  
        75      642      106        0        0        0  
       106      106      443        0        0        0  
         0        0        0      258        0        0  
         0        0        0        0      258        0  
         0        0        0        0        0      283  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 255.67 GPaEV = 575.47 GPaGV = 255.8 GPaνV = 0.12485
ReussKR = 250.35 GPaER = 562.48 GPaGR = 249.87 GPaνR = 0.12553
HillKH = 253.01 GPaEH = 568.98 GPaGH = 252.84 GPaνH = 0.12519

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
258 GPa 258 GPa 283 GPa 376.92 GPa 567 GPa 783.08 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 411.66 GPa 613.83 GPa 1.1418 TPa–1 1.7109 TPa–1 209.15 GPa 283.5 GPa0.0730080.22002Value
Anisotropy 1.491 1.4985 1.355 3.0136Anisotropy
Axis 0.0000
0.0000
1.0000
0.9700
0.0000
0.2431
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
-0.4999
0.5000
0.7071
-0.7071
0.7071
-0.0000
0.4824
0.4824
0.7312
1.0000
0.0002
0.0000
Axis
-0.4997
0.5003
-0.7071
-0.7071
-0.7071
-0.0000
0.5173
0.5167
-0.6822
-0.0000
0.0002
-1.0000
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