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 SnPd (Materials Project id mp-2369)

       139       78      105        0        0        0  
        78      114       86        0        0        0  
       105       86      132        0        0        0  
         0        0        0       42        0        0  
         0        0        0        0       69        0  
         0        0        0        0        0       62  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 102.56 GPaEV = 111.64 GPaGV = 42.333 GPaνV = 0.31857
ReussKR = 99.294 GPaER = 81.311 GPaGR = 29.817 GPaνR = 0.36352
HillKH = 100.93 GPaEH = 96.703 GPaGH = 36.075 GPaνH = 0.34031

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
27.932 GPa 42 GPa 47.725 GPa 62 GPa 69 GPa 309.34 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 42.242 GPa 145.03 GPa 1.7848 TPa–1 5.5605 TPa–1 14.76 GPa 69 GPa-0.303370.95253Value
Anisotropy 3.433 3.1155 4.675Anisotropy
Axis 0.0000
0.0000
1.0000
0.6503
0.4607
0.6041
0.0000
0.0000
1.0000
0.0000
1.0000
0.0000
0.7071
0.0001
-0.7071
-0.0000
0.0000
1.0000
0.7046
0.7096
0.0000
-0.7465
0.6653
-0.0000
Axis
-0.7071
-0.0002
-0.7071
-1.0000
0.0000
-0.0000
-0.7096
0.7046
-0.0000
-0.0000
0.0000
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