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 SiO2 (Materials Project id mp-9258)

       622      169      169        0        0        0  
       169      622      169        0        0        0  
       169      169      622        0        0        0  
         0        0        0      193        0        0  
         0        0        0        0      193        0  
         0        0        0        0        0      193  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 320 GPaEV = 509.63 GPaGV = 206.4 GPaνV = 0.23457
ReussKR = 320 GPaER = 507.06 GPaGR = 205.14 GPaνR = 0.23591
HillKH = 320 GPaEH = 508.34 GPaGH = 205.77 GPaνH = 0.23524

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
193 GPa 193 GPa 193 GPa 453 GPa 453 GPa 960 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 482.08 GPa 549.79 GPa 1.0417 TPa–1 1.0417 TPa–1 193 GPa 226.5 GPa0.193290.28859Value
Anisotropy 1.14 1.0000 1.174 1.4930Anisotropy
Axis 0.5774
0.5774
0.5773
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.5000
0.0000
0.8660
0.0000
0.0000
1.0000
0.7071
-0.0003
0.7071
-0.7071
-0.0000
0.7071
0.7071
-0.0002
0.7071
Axis
0.1734
0.9849
-0.0000
0.7071
-0.0005
-0.7071
0.0000
-1.0000
-0.0000
0.7071
-0.0006
-0.7071
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