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 VO (Materials Project id mp-714885)

       354       67       67        0       -0        0  
        67      354       67        0       -0        0  
        67       67      354        0       -0        0  
         0        0        0       68        0       -0  
        -0       -0       -0        0       68        0  
         0        0        0       -0        0       68  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 162.67 GPaEV = 245.25 GPaGV = 98.2 GPaνV = 0.24872
ReussKR = 162.67 GPaER = 219.62 GPaGR = 86.125 GPaνR = 0.27498
HillKH = 162.67 GPaEH = 232.57 GPaGH = 92.163 GPaνH = 0.26172

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
68 GPa 68 GPa 68 GPa 287 GPa 287 GPa 488 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 179.05 GPa 332.67 GPa 2.0492 TPa–1 2.0492 TPa–1 68 GPa 143.5 GPa0.0968330.48837Value
Anisotropy 1.858 1.0000 2.11 5.0435Anisotropy
Axis 0.5774
0.5773
-0.5774
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
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
-0.1736
0.9848
-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