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 NbSe2 (Materials Project id mp-643063)

       119       32        2        0        0        0  
        32      119        2        0        0        0  
         2        2       11        0        0        0  
         0        0        0        3        0        0  
         0        0        0        0        3        0  
         0        0        0        0        0       43  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 35.667 GPaEV = 58.809 GPaGV = 24 GPaνV = 0.22519
ReussKR = 10.018 GPaER = 14.87 GPaGR = 5.9356 GPaνR = 0.25262
HillKH = 22.842 GPaEH = 36.854 GPaGH = 14.968 GPaνH = 0.2311

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
3 GPa 3 GPa 10.943 GPa 43 GPa 87 GPa 151.06 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 8.6818 GPa 110.2 GPa 5.4446 TPa–1 88.929 TPa–1 3 GPa 43.5 GPa0.0132450.61088Value
Anisotropy 12.69 16.3333 14.5 46.1213Anisotropy
Axis -0.4010
0.4010
0.8236
1.0000
0.0000
0.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.7071
0.7071
0.0000
0.0000
0.0000
1.0000
0.8833
0.0001
0.4688
Axis
0.1735
0.9848
-0.0000
-0.7071
0.7071
0.0000
-0.7660
0.6428
0.0000
0.4688
-0.0001
-0.8833
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