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 FeF2 (Materials Project id mp-556911)

       160       78       78        0        0        0  
        78      116       87        0        0        0  
        78       87      116        0        0        0  
         0        0        0       77        0        0  
         0        0        0        0       32        0  
         0        0        0        0        0       32  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 97.556 GPaEV = 101.21 GPaGV = 38.133 GPaνV = 0.32709
ReussKR = 96.265 GPaER = 78.706 GPaGR = 28.857 GPaνR = 0.36373
HillKH = 96.91 GPaEH = 90.104 GPaGH = 33.495 GPaνH = 0.34504

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
29 GPa 32 GPa 32 GPa 69.116 GPa 77 GPa 293.88 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 47.214 GPa 139.17 GPa 2.3139 TPa–1 4.037 TPa–1 14.5 GPa 77 GPa-0.096280.64509Value
Anisotropy 2.948 1.7447 5.31Anisotropy
Axis 0.0000
0.0000
1.0000
0.0000
0.7071
0.7071
1.0000
0.0000
0.0000
0.0000
0.8660
0.5000
-0.0001
0.7071
0.7071
0.0004
0.0003
1.0000
-0.0002
0.7071
-0.7071
0.5205
-0.0013
0.8538
Axis
0.0001
0.7071
-0.7071
0.0000
1.0000
-0.0003
-0.0002
-0.7071
-0.7071
0.0017
1.0000
0.0005
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