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 NaMgF3 (Materials Project id mp-2955)

       130       40       48        0        0        0  
        40      130       37        0        0        0  
        48       37      119        0        0        0  
         0        0        0       38        0        0  
         0        0        0        0       44        0  
         0        0        0        0        0       42  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 69.889 GPaEV = 104.42 GPaGV = 41.733 GPaνV = 0.25099
ReussKR = 69.735 GPaER = 103.8 GPaGR = 41.456 GPaνR = 0.25192
HillKH = 69.812 GPaEH = 104.11 GPaGH = 41.595 GPaνH = 0.25146

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
38 GPa 42 GPa 44 GPa 76.144 GPa 92.912 GPa 209.94 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 94.735 GPa 112.81 GPa 4.28 TPa–1 5.1505 TPa–1 38 GPa 45.842 GPa0.188890.33756Value
Anisotropy 1.191 1.2034 1.206 1.7871Anisotropy
Axis -0.0000
0.5287
0.8488
0.0000
1.0000
0.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
-0.0003
-0.0000
1.0000
0.5468
0.7071
0.4484
-0.0006
-0.0006
1.0000
1.0000
0.0002
0.0000
Axis
0.0000
1.0000
0.0000
-0.5468
0.7071
-0.4484
0.0000
1.0000
0.0006
0.0000
0.0003
-1.0000
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