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 Fe3N (Materials Project id mp-673635)

       312      141      142        0        3        0  
       141      312      142        0       -3        0  
       142      142      323        0        0        0  
         0        0        0      104        0       -3  
         3       -3        0        0      104        0  
         0        0        0       -3        0       86  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 199.67 GPaEV = 242.85 GPaGV = 93.6 GPaνV = 0.29729
ReussKR = 199.61 GPaER = 240.96 GPaGR = 92.764 GPaνR = 0.2988
HillKH = 199.64 GPaEH = 241.91 GPaGH = 93.182 GPaνH = 0.29804

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
85.513 GPa 103.73 GPa 104.49 GPa 171.27 GPa 176.92 GPa 599.08 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 223.96 GPa 261.08 GPa 1.5945 TPa–1 1.7077 TPa–1 85.027 GPa 104.48 GPa0.223270.36412Value
Anisotropy 1.166 1.0710 1.229 1.6308Anisotropy
Axis 0.9964
0.0000
-0.0847
-0.3596
0.6098
0.7063
0.0000
0.0000
1.0000
0.2588
0.9659
-0.0000
-0.6984
0.7071
0.1109
0.0781
-0.1364
0.9876
-0.6841
-0.0001
0.7294
-0.6776
0.0000
0.7354
Axis
-0.6983
-0.7071
0.1109
0.8672
0.4979
0.0002
-0.7294
0.0001
-0.6841
-0.0000
-1.0000
0.0000
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