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 VB (Materials Project id mp-9973)

       502      123      154        0        0        0  
       123      640       76        0        0        0  
       154       76      609        0        0        0  
         0        0        0      215        0        0  
         0        0        0        0      279        0  
         0        0        0        0        0      215  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 273 GPaEV = 547.81 GPaGV = 235 GPaνV = 0.16556
ReussKR = 272.3 GPaER = 537.39 GPaGR = 229.44 GPaνR = 0.17108
HillKH = 272.65 GPaEH = 542.61 GPaGH = 232.22 GPaνH = 0.16831

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
215 GPa 215 GPa 279 GPa 377.47 GPa 552.69 GPa 820.84 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 445.98 GPa 621.74 GPa 1.1546 TPa–1 1.3522 TPa–1 194.27 GPa 279 GPa0.0627470.2914Value
Anisotropy 1.394 1.1711 1.436 4.6440Anisotropy
Axis 1.0000
0.0000
0.0000
0.5893
0.0000
0.8079
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
-0.7071
0.3714
0.6017
0.0000
0.0000
1.0000
-0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
Axis
-0.7071
-0.3714
-0.6017
-1.0000
0.0000
0.0000
-0.0000
-1.0000
0.0000
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