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 FeN (Materials Project id mp-1008929)

       362      112      112        0        0        0  
       112      362      112        0        0        0  
       112      112      362        0        0        0  
         0        0        0       71        0        0  
         0        0        0        0       71        0  
         0        0        0        0        0       71  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 195.33 GPaEV = 239.89 GPaGV = 92.6 GPaνV = 0.29531
ReussKR = 195.33 GPaER = 224.6 GPaGR = 85.832 GPaνR = 0.30836
HillKH = 195.33 GPaEH = 232.28 GPaGH = 89.216 GPaνH = 0.30181

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
71 GPa 71 GPa 71 GPa 250 GPa 250 GPa 586 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 189.98 GPa 309.07 GPa 1.7065 TPa–1 1.7065 TPa–1 71 GPa 125 GPa0.160720.48052Value
Anisotropy 1.627 1.0000 1.761 2.9897Anisotropy
Axis -0.5774
0.5774
-0.5773
0.0000
1.0000
0.0000
0.4830
0.6294
0.6088
0.9239
0.0000
0.3827
0.0000
0.0000
1.0000
0.7071
0.0001
-0.7071
0.7071
-0.0001
0.7071
0.7071
-0.0000
-0.7071
Axis
0.7660
0.6428
-0.0000
-0.7071
-0.0002
-0.7071
0.0001
1.0000
0.0000
-0.7071
0.0002
-0.7071
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