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 Si (Materials Project id mp-149)

       144       53       53        0        0        0  
        53      144       53        0        0        0  
        53       53      144        0        0        0  
         0        0        0       75        0        0  
         0        0        0        0       75        0  
         0        0        0        0        0       75  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 83.333 GPaEV = 151.34 GPaGV = 63.2 GPaνV = 0.19732
ReussKR = 83.333 GPaER = 144.29 GPaGR = 59.555 GPaνR = 0.21142
HillKH = 83.333 GPaEH = 147.84 GPaGH = 61.377 GPaνH = 0.20433

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
75 GPa 75 GPa 75 GPa 91 GPa 91 GPa 250 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 115.48 GPa 173.08 GPa 4 TPa–1 4 TPa–1 45.5 GPa 75 GPa0.025930.35851Value
Anisotropy 1.499 1.0000 1.648 13.8260Anisotropy
Axis 0.0000
0.0000
1.0000
0.5774
0.5774
0.5773
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.7071
-0.0003
0.7071
0.0000
0.0000
1.0000
0.7071
-0.0002
0.7071
0.7071
-0.0005
0.7071
Axis
0.7071
-0.0005
-0.7071
-0.7660
0.6428
-0.0000
0.7071
-0.0006
-0.7071
0.0004
1.0000
0.0004
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