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(CoP)2 (Materials Project id mp-573563)

       256       41       64        0        0        0  
        41      256       64        0        0        0  
        64       64      156        0        0        0  
         0        0        0      111        0        0  
         0        0        0        0      111        0  
         0        0        0        0        0      101  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 111.78 GPaEV = 227.27 GPaGV = 97.867 GPaνV = 0.16113
ReussKR = 108.05 GPaER = 213.58 GPaGR = 91.231 GPaνR = 0.17054
HillKH = 109.91 GPaEH = 220.44 GPaGH = 94.549 GPaνH = 0.16573

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
101 GPa 111 GPa 111 GPa 111.77 GPa 215 GPa 341.23 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 128.42 GPa 249.74 GPa 2.4122 TPa–1 4.431 TPa–1 63.843 GPa 111 GPa0.00320730.38393Value
Anisotropy 1.945 1.8370 1.739119.7046Anisotropy
Axis 0.0000
0.0000
1.0000
0.8733
0.0000
-0.4872
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
-0.5001
0.4998
0.7071
0.0000
0.0000
1.0000
0.4996
0.4996
-0.7077
1.0000
0.0002
0.0000
Axis
-0.4999
0.5002
-0.7071
-0.9397
0.3420
0.0000
0.5004
0.5004
0.7065
-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