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 SbF3 (Materials Project id mp-1880)

        41       10       18        0        0        0  
        10       21        3        0        0        0  
        18        3       24        0        0        0  
         0        0        0        7        0        0  
         0        0        0        0        7        0  
         0        0        0        0        0        6  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 16.444 GPaEV = 19.906 GPaGV = 7.6667 GPaνV = 0.29825
ReussKR = 12.652 GPaER = 17.725 GPaGR = 6.9976 GPaνR = 0.2665
HillKH = 14.548 GPaEH = 18.833 GPaGH = 7.3321 GPaνH = 0.28425

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
6 GPa 7 GPa 7 GPa 11.469 GPa 19.168 GPa 55.363 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 14.765 GPa 24.588 GPa -3.2043 TPa–1 43.628 TPa–1 6 GPa 9.3122 GPa-0.0749010.70303Value
Anisotropy 1.665 1.552Anisotropy
Axis -0.0000
0.6189
-0.7855
1.0000
0.0000
0.0000
1.0000
0.0000
0.0000
0.0000
1.0000
0.0000
1.0000
-0.0000
0.0000
0.0000
0.7071
0.7071
-0.0002
0.0001
1.0000
1.0000
-0.0003
-0.0000
Axis
0.0000
1.0000
0.0000
0.0000
0.7071
-0.7071
0.0000
-1.0000
0.0001
-0.0000
-0.0004
-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