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 Nb (Materials Project id mp-75)

       233      145      145        0        0        0  
       145      233      145        0        0        0  
       145      145      233        0        0        0  
         0        0        0       11        0        0  
         0        0        0        0       11        0  
         0        0        0        0        0       11  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 174.33 GPaEV = 69.389 GPaGV = 24.2 GPaνV = 0.43366
ReussKR = 174.33 GPaER = 45.768 GPaGR = 15.714 GPaνR = 0.45625
HillKH = 174.33 GPaEH = 57.671 GPaGH = 19.957 GPaνH = 0.44487

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
11 GPa 11 GPa 11 GPa 88 GPa 88 GPa 523 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 32.32 GPa 121.76 GPa 1.912 TPa–1 1.912 TPa–1 11 GPa 44 GPa0.124730.79957Value
Anisotropy 3.767 1.0000 4 6.4103Anisotropy
Axis -0.5774
0.5774
0.5773
1.0000
0.0000
0.0000
0.9659
0.0000
0.2588
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.7071
0.0001
-0.7071
0.7071
0.0000
-0.7072
0.7071
-0.0002
0.7071
Axis
-0.7880
0.6157
-0.0000
-0.7071
-0.0002
-0.7071
-0.0000
1.0000
0.0000
0.7071
-0.0001
-0.7071
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