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 Sm2O (Materials Project id mp-33104)

       149       64       55        0        0       -0  
        64      149       55        0        0       -0  
        55       55      121        0        0        0  
         0        0        0       43        0        0  
         0        0        0        0       43        0  
        -0       -0        0        0        0       48  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 85.222 GPaEV = 110.72 GPaGV = 43.133 GPaνV = 0.28347
ReussKR = 83.928 GPaER = 109.76 GPaGR = 42.808 GPaνR = 0.28203
HillKH = 84.575 GPaEH = 110.24 GPaGH = 42.971 GPaνH = 0.28275

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
43 GPa 43 GPa 48 GPa 76.634 GPa 85 GPa 257.37 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 92.596 GPa 120.83 GPa 3.3463 TPa–1 5.2223 TPa–1 39.484 GPa 48 GPa0.239370.33696Value
Anisotropy 1.305 1.5606 1.216 1.4077Anisotropy
Axis 0.0000
0.0000
1.0000
0.7071
0.7071
0.0000
0.3827
0.9239
0.0000
0.0000
0.0000
1.0000
0.7071
-0.0003
0.7071
1.0000
0.0000
0.0000
0.5996
0.0000
0.8003
0.7071
0.7071
0.0000
Axis
0.7071
-0.0005
-0.7071
-0.0000
1.0000
-0.0000
0.8003
0.0003
-0.5996
0.0001
-0.0000
-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