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 Mg3Pa (Materials Project id mp-978291)

        59       24       24        0        0        0  
        24       59       24        0        0        0  
        24       24       59        0        0        0  
         0        0        0       46        0        0  
         0        0        0        0       46        0  
         0        0        0        0        0       46  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 35.667 GPaEV = 78.436 GPaGV = 34.6 GPaνV = 0.13347
ReussKR = 35.667 GPaER = 66.304 GPaGR = 27.855 GPaνR = 0.19017
HillKH = 35.667 GPaEH = 72.518 GPaGH = 31.227 GPaνH = 0.16113

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
35 GPa 35 GPa 46 GPa 46 GPa 46 GPa 107 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 45.12 GPa 96.51 GPa 9.3458 TPa–1 9.3458 TPa–1 17.5 GPa 46 GPa-0.183470.48141Value
Anisotropy 2.139 1.0000 2.629Anisotropy
Axis 0.0000
0.0000
1.0000
0.5774
0.5773
-0.5774
0.4830
0.6294
0.6088
0.0000
0.0000
1.0000
0.7071
0.0001
-0.7071
-0.0000
0.0000
1.0000
0.7071
0.0001
-0.7071
0.7071
-0.0004
-0.7071
Axis
-0.7071
-0.0002
-0.7071
-0.1736
0.9848
-0.0000
-0.7071
-0.0002
-0.7071
0.0002
1.0000
-0.0003
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