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-554089)

        68        6        0        0        0        0  
         6       50       -8        0        0        0  
         0       -8       69        0        0        0  
         0        0        0       69        0        0  
         0        0        0        0       25        0  
         0        0        0        0        0       32  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 20.333 GPaEV = 70.014 GPaGV = 37.8 GPaνV = -0.073887
ReussKR = 19.625 GPaER = 63.245 GPaGR = 32.842 GPaνR = -0.037125
HillKH = 19.979 GPaEH = 66.673 GPaGH = 35.321 GPaνH = -0.056189

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
25 GPa 32 GPa 45.649 GPa 68.32 GPa 69 GPa 73.031 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 48.543 GPa 76.15 GPa 12.838 TPa–1 21.171 TPa–1 25 GPa 69 GPa-0.475430.17079Value
Anisotropy 1.569 1.6491 2.76Anisotropy
Axis 0.0000
1.0000
0.0000
-0.0000
0.5647
0.8253
1.0000
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
0.0000
-1.0000
-0.0000
0.0000
1.0000
-0.0000
0.6646
0.7472
0.6849
0.3788
0.6224
Axis
-1.0000
0.0000
-0.0000
-0.0000
-1.0000
0.0000
0.0000
0.7472
-0.6646
-0.7269
0.2959
0.6197
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