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 FeP (Materials Project id mp-1005)

       431      125      126        0        0        0  
       125      405      155        0        0        0  
       126      155      285        0        0        0  
         0        0        0      153        0        0  
         0        0        0        0      148        0  
         0        0        0        0        0      142  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 214.78 GPaEV = 337.44 GPaGV = 136.27 GPaνV = 0.23815
ReussKR = 209.13 GPaER = 322.47 GPaGR = 129.71 GPaνR = 0.243
HillKH = 211.95 GPaEH = 329.96 GPaGH = 132.99 GPaνH = 0.24054

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
142 GPa 148 GPa 153 GPa 172.24 GPa 297.85 GPa 650.91 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 210.11 GPa 370.18 GPa 1.1921 TPa–1 2.2825 TPa–1 90.742 GPa 153 GPa0.0923820.47733Value
Anisotropy 1.762 1.9146 1.686 5.1670Anisotropy
Axis 0.0000
0.0000
1.0000
0.9400
-0.0000
0.3411
0.0000
1.0000
0.0000
0.0000
0.0000
1.0000
0.0002
0.7071
-0.7071
0.0000
-0.0000
1.0000
0.6789
-0.0001
0.7342
-0.0000
1.0000
0.0000
Axis
0.0002
-0.7071
-0.7071
0.0000
-1.0000
-0.0000
0.7342
-0.0002
-0.6789
-0.0002
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