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 VSi2 (Materials Project id mp-11190)

       365       58       76        0        0        0  
        58      365       76        0        0        0  
        76       76      428        0        0        0  
         0        0        0      134        0        0  
         0        0        0        0      134        0  
         0        0        0        0        0      153  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 175.33 GPaEV = 345.41 GPaGV = 147.4 GPaνV = 0.17167
ReussKR = 173.84 GPaER = 342.7 GPaGR = 146.27 GPaνR = 0.17144
HillKH = 174.59 GPaEH = 344.05 GPaGH = 146.84 GPaνH = 0.17155

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
134 GPa 134 GPa 153 GPa 307 GPa 317.99 GPa 533.01 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 330.71 GPa 400.69 GPa 1.5989 TPa–1 2.0768 TPa–1 134 GPa 159.14 GPa0.126450.24961Value
Anisotropy 1.212 1.2989 1.188 1.9740Anisotropy
Axis 0.5791
0.5791
-0.5738
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.6088
0.7934
0.0000
0.0000
0.0000
1.0000
0.7071
0.0001
-0.7071
0.9716
-0.0001
0.2368
0.6665
0.0001
-0.7455
Axis
1.0000
0.0000
-0.0000
-0.7071
-0.0002
-0.7071
0.0001
1.0000
-0.0000
-0.7455
-0.0002
-0.6665
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