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 Si3Pt2 (Materials Project id mp-10744)

       213      155       96        0        0        0  
       155      213       96        0        0        0  
        96       96      335        0        0        0  
         0        0        0        7        0        0  
         0        0        0        0        7        0  
         0        0        0        0        0       29  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 161.67 GPaEV = 101.06 GPaGV = 36.2 GPaνV = 0.39582
ReussKR = 160.32 GPaER = 40.072 GPaGR = 13.739 GPaνR = 0.45834
HillKH = 160.99 GPaEH = 71.226 GPaGH = 24.969 GPaνH = 0.42626

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
7 GPa 7 GPa 29 GPa 58 GPa 214.74 GPa 488.26 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 25.789 GPa 284.91 GPa 1.6786 TPa–1 2.2795 TPa–1 7 GPa 64.27 GPa0.0840330.8581Value
Anisotropy 11.05 1.3580 9.181 10.2115Anisotropy
Axis 0.6772
0.2604
0.6882
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
-0.0000
-0.0000
1.0000
0.3283
0.6263
-0.7071
0.3611
0.3323
-0.8713
-0.4931
0.3122
0.8120
Axis
1.0000
0.0002
0.0000
-0.3282
-0.6263
-0.7071
-0.6772
0.7358
0.0000
0.6860
-0.4344
0.5837
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