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-556464)

       243       77       74        0       -8        0  
        77      243       74        0        8        0  
        74       74      286        0        0        0  
         0        0        0       53        0        8  
        -8        8        0        0       53        0  
         0        0        0        8        0       83  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 135.78 GPaEV = 188.44 GPaGV = 74.267 GPaνV = 0.26869
ReussKR = 135.18 GPaER = 176.09 GPaGR = 68.628 GPaνR = 0.2829
HillKH = 135.48 GPaEH = 182.3 GPaGH = 71.447 GPaνH = 0.27574

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
51 GPa 51.878 GPa 85 GPa 167.12 GPa 196.98 GPa 409.02 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 141.4 GPa 251.77 GPa 2.1348 TPa–1 2.6313 TPa–1 51 GPa 94.866 GPa0.102010.50882Value
Anisotropy 1.781 1.2326 1.86 4.9877Anisotropy
Axis -0.3846
0.6663
0.6389
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.9651
0.2620
0.0000
0.1213
0.2100
0.9701
0.3342
0.5788
0.7438
0.3139
0.5437
0.7783
0.3190
0.5524
0.7701
Axis
-0.8660
0.5000
0.0000
-0.3719
-0.6442
0.6683
-0.8660
0.5000
-0.0000
0.3850
0.6670
-0.6379
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