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 VOs (Materials Project id mp-12778)

       399      226      226        0        0        0  
       226      399      226        0        0        0  
       226      226      399        0        0        0  
         0        0        0      139        0        0  
         0        0        0        0      139        0  
         0        0        0        0        0      139  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 283.67 GPaEV = 310.89 GPaGV = 118 GPaνV = 0.31734
ReussKR = 283.67 GPaER = 296.56 GPaGR = 111.85 GPaνR = 0.32576
HillKH = 283.67 GPaEH = 303.75 GPaGH = 114.92 GPaνH = 0.32153

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
139 GPa 139 GPa 139 GPa 173 GPa 173 GPa 851 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 235.56 GPa 358.45 GPa 1.1751 TPa–1 1.1751 TPa–1 86.5 GPa 139 GPa0.140620.48677Value
Anisotropy 1.522 1.0000 1.607 3.4615Anisotropy
Axis 1.0000
0.0000
0.0000
0.5774
0.5774
0.5773
0.0000
0.0000
1.0000
0.9239
0.0000
0.3827
0.7071
-0.0003
0.7071
0.0000
0.0000
1.0000
0.7071
-0.0000
-0.7071
-0.7071
-0.0000
0.7071
Axis
0.7071
-0.0005
-0.7071
1.0000
0.0000
-0.0000
-0.7071
0.0002
-0.7071
-0.0000
-1.0000
-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