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 Mn3Sn2 (Materials Project id mp-600428)

       160       64       35        0        0        0  
        64      164       22        0        0        0  
        35       22      122        0        0        0  
         0        0        0       60        0        0  
         0        0        0        0       63        0  
         0        0        0        0        0       49  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 76.444 GPaEV = 135.16 GPaGV = 56.067 GPaνV = 0.20533
ReussKR = 72.752 GPaER = 131.29 GPaGR = 54.74 GPaνR = 0.19922
HillKH = 74.598 GPaEH = 133.23 GPaGH = 55.404 GPaνH = 0.20234

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
49 GPa 60 GPa 63 GPa 92.45 GPa 113.75 GPa 239.8 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 113.88 GPa 139.39 GPa 3.2334 TPa–1 6.5557 TPa–1 48.594 GPa 63 GPa0.0514110.3847Value
Anisotropy 1.224 2.0275 1.296 7.4827Anisotropy
Axis 0.0000
0.0000
1.0000
0.7919
0.0000
0.6106
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
-0.7071
0.7071
0.0000
-0.0000
0.0000
-1.0000
0.0001
0.6264
0.7795
-0.0000
1.0000
-0.0000
Axis
-0.7071
-0.7071
-0.0000
-1.0000
0.0000
0.0000
-0.0001
0.7795
-0.6264
-1.0000
-0.0000
0.0000
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