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 TiSe (Materials Project id mp-571651)

       165       94       56        0        0        0  
        94      166       79        0        0        0  
        56       79      160        0        0        0  
         0        0        0      102        0        0  
         0        0        0        0       58        0  
         0        0        0        0        0       80  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 105.44 GPaEV = 162.72 GPaGV = 65.467 GPaνV = 0.2428
ReussKR = 104.06 GPaER = 143.69 GPaGR = 56.58 GPaνR = 0.26985
HillKH = 104.75 GPaEH = 153.3 GPaGH = 61.023 GPaνH = 0.25609

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
58 GPa 66.026 GPa 80 GPa 102 GPa 107.26 GPa 317.72 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 96.716 GPa 189.71 GPa 2.1675 TPa–1 3.9613 TPa–1 34.714 GPa 102 GPa-0.0873380.55619Value
Anisotropy 1.962 1.8276 2.938Anisotropy
Axis 0.0000
1.0000
0.0000
-0.3640
0.6548
-0.6624
0.0000
1.0000
0.0000
0.0000
0.0000
1.0000
-0.7071
0.7071
0.0000
-0.0000
0.0000
-1.0000
-0.0000
0.7033
-0.7109
0.0000
0.8100
0.5865
Axis
-0.7071
-0.7071
0.0000
0.0000
-1.0000
-0.0000
-0.0000
0.7109
0.7033
-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