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 VO2 (Materials Project id mp-19094)

       407      170      170        0        0        0  
       170      314      194        0        0        0  
       170      194      314        0        0        0  
         0        0        0      225        0        0  
         0        0        0        0      127        0  
         0        0        0        0        0      127  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 233.67 GPaEV = 327.28 GPaGV = 129.2 GPaνV = 0.26656
ReussKR = 232.02 GPaER = 280.61 GPaGR = 108.06 GPaνR = 0.29843
HillKH = 232.84 GPaEH = 304.22 GPaGH = 118.63 GPaνH = 0.28224

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
120 GPa 127 GPa 127 GPa 211.84 GPa 225 GPa 703.16 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 180.74 GPa 403.67 GPa 1.1278 TPa–1 1.5911 TPa–1 60 GPa 225 GPa-0.102960.5513Value
Anisotropy 2.233 1.4107 3.75Anisotropy
Axis 0.0000
0.0000
1.0000
0.0000
0.7071
0.7071
1.0000
0.0000
0.0000
0.0000
0.7934
0.6088
0.0002
0.7071
-0.7071
0.0002
0.0001
1.0000
0.0002
0.7071
-0.7071
-0.6064
0.0000
0.7952
Axis
0.0002
-0.7071
-0.7071
-0.0000
1.0000
-0.0001
0.0001
-0.7071
-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