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 VF3 (Materials Project id mp-559931)

        58      -18       23      -28        0        0  
       -18       58       23       28        0        0  
        23       23       86        0        0        0  
       -28       28        0       50        0        0  
         0        0        0        0       50      -28  
         0        0        0        0      -28       38  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 28.667 GPaEV = 80.78 GPaGV = 39.2 GPaνV = 0.030351
ReussKR = 19.85 GPaER = 47.789 GPaGR = 21.747 GPaνR = 0.098746
HillKH = 24.258 GPaEH = 64.438 GPaGH = 30.474 GPaνH = 0.057278

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
15.364 GPa 21.323 GPa 23.163 GPa 72.636 GPa 102.84 GPa 104.68 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 30.916 GPa 112.06 GPa -2.5189 TPa–1 26.448 TPa–1 14.334 GPa 72.636 GPa-0.708040.7371Value
Anisotropy 3.625 5.067Anisotropy
Axis -0.8417
0.4859
0.2354
-0.0000
0.7078
0.7064
0.0000
0.0000
1.0000
0.9659
0.2588
0.0000
0.5007
-0.2891
-0.8159
-0.5445
0.3143
0.7777
-0.7073
0.4084
-0.5770
0.2845
0.1642
0.9445
Axis
-0.7066
0.4080
-0.5782
-0.5000
-0.8660
-0.0000
-0.5000
-0.8660
-0.0000
-0.5000
0.8660
-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