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 V (Materials Project id mp-146)

       276      131      131        0        0        0  
       131      276      131        0        0        0  
       131      131      276        0        0        0  
         0        0        0       16        0        0  
         0        0        0        0       16        0  
         0        0        0        0        0       16  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 179.33 GPaEV = 108.05 GPaGV = 38.6 GPaνV = 0.39958
ReussKR = 179.33 GPaER = 66.851 GPaGR = 23.246 GPaνR = 0.43787
HillKH = 179.33 GPaEH = 87.727 GPaGH = 30.923 GPaνH = 0.41847

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
16 GPa 16 GPa 16 GPa 145 GPa 145 GPa 538 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 46.614 GPa 191.67 GPa 1.8587 TPa–1 1.8587 TPa–1 16 GPa 72.5 GPa0.0965430.7966Value
Anisotropy 4.112 1.0000 4.531 8.2512Anisotropy
Axis -0.5774
0.5774
-0.5773
0.0000
1.0000
0.0000
0.4830
0.6294
0.6088
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.7071
0.0001
-0.7071
-0.7071
0.0000
0.7071
0.7071
-0.0000
-0.7071
Axis
1.0000
0.0000
-0.0000
-0.7071
-0.0002
-0.7071
-0.0000
-1.0000
0.0000
-0.7071
0.0002
-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