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 Sn (Materials Project id mp-117)

        59       28       28        0        0        0  
        28       59       28        0        0        0  
        28       28       59        0        0        0  
         0        0        0       26        0        0  
         0        0        0        0       26        0  
         0        0        0        0        0       26  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 38.333 GPaEV = 54.978 GPaGV = 21.8 GPaνV = 0.26096
ReussKR = 38.333 GPaER = 52.102 GPaGR = 20.457 GPaνR = 0.27347
HillKH = 38.333 GPaEH = 53.547 GPaGH = 21.128 GPaνH = 0.26719

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
26 GPa 26 GPa 26 GPa 31 GPa 31 GPa 115 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 40.977 GPa 63.617 GPa 8.6957 TPa–1 8.6957 TPa–1 15.5 GPa 26 GPa0.0749290.43902Value
Anisotropy 1.553 1.0000 1.677 5.8591Anisotropy
Axis 0.0000
0.0000
1.0000
-0.5774
0.5774
-0.5773
0.0000
0.0000
1.0000
0.5624
0.7330
0.3827
0.7071
-0.0003
0.7071
-0.0000
0.0000
1.0000
0.7071
-0.0002
0.7071
-0.7071
0.0000
0.7071
Axis
0.7071
-0.0005
-0.7071
-0.5000
0.8660
-0.0000
0.7071
-0.0006
-0.7071
-0.0001
-1.0000
-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