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 Mg2Ga5 (Materials Project id mp-27668)

       101       16       16        0        0        0  
        16       89       31        0        0        0  
        16       31       89        0        0        0  
         0        0        0       36        0        0  
         0        0        0        0       31        0  
         0        0        0        0        0       31  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 45 GPaEV = 81.479 GPaGV = 34 GPaνV = 0.19822
ReussKR = 44.992 GPaER = 80.18 GPaGR = 33.325 GPaνR = 0.20299
HillKH = 44.996 GPaEH = 80.831 GPaGH = 33.663 GPaνH = 0.2006

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
31 GPa 31 GPa 36 GPa 58 GPa 85.959 GPa 135.04 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 74.17 GPa 96.733 GPa 7.3225 TPa–1 7.581 TPa–1 29 GPa 41.002 GPa0.106260.32921Value
Anisotropy 1.304 1.0353 1.414 3.0981Anisotropy
Axis 0.5361
-0.0000
0.8442
1.0000
0.0000
0.0000
0.0000
0.9659
0.2588
1.0000
0.0000
0.0000
0.0002
0.7071
-0.7071
-0.7071
0.5000
0.5000
0.0000
0.0000
1.0000
-0.0004
-0.0002
1.0000
Axis
0.0002
-0.7071
-0.7071
-0.7071
-0.5000
-0.5000
-1.0000
0.0000
0.0000
0.0000
1.0000
0.0002
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