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 MnSi (Materials Project id mp-1431)

       399      115      115        0        0        0  
       115      399      115        0        0        0  
       115      115      399        0        0        0  
         0        0        0      141        0        0  
         0        0        0        0      141        0  
         0        0        0        0        0      141  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 209.67 GPaEV = 346.34 GPaGV = 141.4 GPaνV = 0.22469
ReussKR = 209.67 GPaER = 346.34 GPaGR = 141.4 GPaνR = 0.22469
HillKH = 209.67 GPaEH = 346.34 GPaGH = 141.4 GPaνH = 0.22469

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
141 GPa 141 GPa 141 GPa 284 GPa 284 GPa 629 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 345.54 GPa 347.54 GPa 1.5898 TPa–1 1.5898 TPa–1 141 GPa 142 GPa0.222770.22709Value
Anisotropy 1.006 1.0000 1.007 1.0194Anisotropy
Axis -0.5774
0.5774
0.5773
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.8660
0.0000
0.5000
0.0000
0.0000
1.0000
0.7071
-0.0002
0.7071
-0.7071
0.0000
-0.7071
0.7071
-0.0002
0.7071
Axis
1.0000
0.0000
-0.0000
0.7071
-0.0006
-0.7071
-0.0000
-1.0000
-0.0000
0.7071
-0.0006
-0.7071
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