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 Sn3Pd (Materials Project id mp-1371)

       119       43       48        0        0        0  
        43       92       37        0        0        0  
        48       37      116        0        0        0  
         0        0        0       15        0        0  
         0        0        0        0       34        0  
         0        0        0        0        0       19  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 64.778 GPaEV = 70.81 GPaGV = 26.867 GPaνV = 0.31781
ReussKR = 63.372 GPaER = 63.491 GPaGR = 23.815 GPaνR = 0.33302
HillKH = 64.075 GPaEH = 67.167 GPaGH = 25.341 GPaνH = 0.32529

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
15 GPa 19 GPa 34 GPa 60.297 GPa 70.407 GPa 196.3 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 46.512 GPa 91.586 GPa 3.9192 TPa–1 7.1387 TPa–1 15 GPa 34.647 GPa0.167080.55637Value
Anisotropy 1.969 1.8215 2.31 3.3301Anisotropy
Axis 0.0000
0.7346
0.6785
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
0.0000
1.0000
0.0000
-0.0000
0.0000
-1.0000
0.7071
-0.0000
0.7071
0.4172
0.7065
-0.5716
-0.0000
0.6710
0.7414
Axis
-0.0000
-1.0000
-0.0000
0.7071
0.0000
-0.7071
-0.8576
0.0980
-0.5049
0.0000
0.7414
-0.6710
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