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 Mn3Si (Materials Project id mp-20211)

       284      164      164        0        0        0  
       164      284      164        0        0        0  
       164      164      284        0        0        0  
         0        0        0      138        0        0  
         0        0        0        0      138        0  
         0        0        0        0        0      138  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 204 GPaEV = 272.79 GPaGV = 106.8 GPaνV = 0.27713
ReussKR = 204 GPaER = 237.18 GPaGR = 90.789 GPaνR = 0.30622
HillKH = 204 GPaEH = 255.19 GPaGH = 98.795 GPaνH = 0.29151

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
120 GPa 120 GPa 138 GPa 138 GPa 138 GPa 612 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 163.93 GPa 337.82 GPa 1.634 TPa–1 1.634 TPa–1 60 GPa 138 GPa-0.0325640.59627Value
Anisotropy 2.061 1.0000 2.3Anisotropy
Axis 0.0000
0.0000
1.0000
0.5774
0.5774
0.5773
0.9239
0.0000
0.3827
0.0000
0.0000
1.0000
0.7071
0.0001
-0.7071
0.0000
0.0000
1.0000
0.7071
-0.0003
0.7071
0.0000
0.7071
0.7071
Axis
-0.7071
-0.0002
-0.7071
0.7660
0.6428
-0.0000
0.7071
-0.0005
-0.7071
-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