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 Sm (Materials Project id mp-86)

        68       21       18        3        0        0  
        21       68       18       -3        0        0  
        18       18       74        0        0        0  
         3       -3        0       20        0        0  
         0        0        0        0       20        3  
         0        0        0        0        3       23  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 36 GPaEV = 56.477 GPaGV = 22.8 GPaνV = 0.23853
ReussKR = 35.988 GPaER = 55.068 GPaGR = 22.116 GPaνR = 0.24497
HillKH = 35.994 GPaEH = 55.774 GPaGH = 22.458 GPaνH = 0.24174

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
18.146 GPa 19.349 GPa 24.854 GPa 47.651 GPa 54.962 GPa 108.04 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 46.725 GPa 66.719 GPa 8.9256 TPa–1 9.4308 TPa–1 18.146 GPa 26.773 GPa0.115570.36578Value
Anisotropy 1.428 1.0566 1.475 3.1650Anisotropy
Axis 0.6976
0.4125
-0.5858
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
-0.9659
0.2588
0.0000
0.0000
0.5257
-0.8507
0.0005
0.6196
-0.7849
0.0000
0.5660
-0.8244
-0.0002
0.6019
-0.7986
Axis
-1.0000
0.0000
-0.0000
-0.0001
-0.7849
-0.6196
-1.0000
0.0000
0.0000
-0.0002
-0.7986
-0.6019
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