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 V2O3 (Materials Project id mp-18937)

       308      162      143        8        0        0  
       162      308      143       -8        0        0  
       143      143      308        0        0        0  
         8       -8        0       86        0        0  
         0        0        0        0       86        8  
         0        0        0        0        8       73  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 202.22 GPaEV = 213.75 GPaGV = 80.733 GPaνV = 0.32383
ReussKR = 202.07 GPaER = 210.96 GPaGR = 79.546 GPaνR = 0.326
HillKH = 202.14 GPaEH = 212.36 GPaGH = 80.14 GPaνH = 0.32491

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
69.192 GPa 83.938 GPa 89.808 GPa 148.06 GPa 171.15 GPa 606.85 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 191.88 GPa 233.47 GPa 1.5886 TPa–1 1.7716 TPa–1 69.192 GPa 89.808 GPa0.245120.42834Value
Anisotropy 1.217 1.1152 1.298 1.7475Anisotropy
Axis -0.0000
0.9309
0.3653
0.0000
0.7663
-0.6425
0.3797
0.9251
0.0000
0.0000
0.0000
1.0000
0.7820
0.4515
0.4298
0.3722
0.2149
-0.9029
0.4598
0.2658
-0.8473
-1.0000
-0.0000
-0.0000
Axis
-0.5000
0.8660
-0.0000
-0.5000
0.8660
0.0000
-0.7339
-0.4234
-0.5311
0.0000
-0.9171
-0.3988
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