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 SmF3 (Materials Project id mp-7384)

       189       86      102        0        0        0  
        86      211       58        0        0        0  
       102       58      139        0        0        0  
         0        0        0       47        0        0  
         0        0        0        0       54        0  
         0        0        0        0        0       49  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 114.56 GPaEV = 129.88 GPaGV = 49.533 GPaνV = 0.31104
ReussKR = 108.98 GPaER = 120.58 GPaGR = 45.829 GPaνR = 0.31558
HillKH = 111.77 GPaEH = 125.23 GPaGH = 47.681 GPaνH = 0.31325

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
47 GPa 49 GPa 54 GPa 58.436 GPa 133.03 GPa 347.53 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 83.171 GPa 170.27 GPa 1.2559 TPa–1 5.0928 TPa–1 29.521 GPa 62.918 GPa0.067420.63678Value
Anisotropy 2.047 4.0551 2.131 9.4450Anisotropy
Axis 0.0000
0.0000
1.0000
0.0000
1.0000
0.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.7071
-0.0000
-0.7071
-0.4929
0.7071
0.5070
0.0000
-0.0000
1.0000
1.0000
0.0003
0.0000
Axis
-0.7071
0.0002
-0.7071
-0.4929
-0.7071
0.5070
-0.0000
-1.0000
-0.0000
0.0000
0.0002
-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