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 Mg13Ir3 (Materials Project id mp-16860)

        99       39       42        2        0        0  
        39       99       42       -2        0        0  
        42       42       98        0        0        0  
         2       -2        0       27        0        0  
         0        0        0        0       27        2  
         0        0        0        0        2       30  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 60.222 GPaEV = 73.477 GPaGV = 28.333 GPaνV = 0.29665
ReussKR = 60.217 GPaER = 73.076 GPaGR = 28.155 GPaνR = 0.29774
HillKH = 60.22 GPaEH = 73.277 GPaGH = 28.244 GPaνH = 0.2972

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
26 GPa 26.759 GPa 31 GPa 55.326 GPa 60.241 GPa 180.67 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 68.333 GPa 78.043 GPa 5.4022 TPa–1 5.6022 TPa–1 26 GPa 31 GPa0.234830.35101Value
Anisotropy 1.142 1.0370 1.192 1.4948Anisotropy
Axis -0.6734
0.3888
-0.6288
0.0000
0.9409
-0.3386
0.0000
0.0000
1.0000
0.9201
0.3917
0.0000
0.3873
0.2236
0.8944
-0.5000
0.8660
-0.0000
0.5000
0.8660
-0.0000
0.5077
0.2928
0.8103
Axis
-0.5000
0.8660
0.0000
-0.7746
-0.4472
0.4472
-0.7516
0.4340
0.4967
0.7016
0.4054
-0.5861
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