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 Mg2Al4Si5O18 (Materials Project id mp-6174)

       195       91       90        0        0        0  
        91      202       85        0        0        0  
        90       85      175        0        0        0  
         0        0        0       42        0        0  
         0        0        0        0       48        0  
         0        0        0        0        0       60  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 122.67 GPaEV = 132.99 GPaGV = 50.4 GPaνV = 0.31931
ReussKR = 122.11 GPaER = 131.03 GPaGR = 49.59 GPaνR = 0.32115
HillKH = 122.39 GPaEH = 132.01 GPaGH = 49.995 GPaνH = 0.32023

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
42 GPa 48 GPa 60 GPa 94.134 GPa 109.27 GPa 368.6 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 114.7 GPa 151.35 GPa 2.4701 TPa–1 3.2387 TPa–1 42 GPa 60 GPa0.239410.40388Value
Anisotropy 1.319 1.3112 1.429 1.6869Anisotropy
Axis -0.0000
0.5871
0.8095
0.6001
0.7999
-0.0000
0.0000
1.0000
0.0000
0.0000
0.0000
1.0000
-0.0003
-0.0000
1.0000
1.0000
-0.0001
0.0000
-0.6781
0.5798
0.4518
-0.6167
0.5929
0.5177
Axis
0.0000
1.0000
0.0000
0.0001
1.0000
0.0000
-0.7190
-0.6507
-0.2441
0.1837
-0.5312
0.8271
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