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 Mo2N (Materials Project id mp-27953)

       501      204      231        0        0        0  
       204      501      231        0        0        0  
       231      231      381        0        0        0  
         0        0        0       51        0        0  
         0        0        0        0       51        0  
         0        0        0        0        0      144  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 301.67 GPaEV = 262.83 GPaGV = 97 GPaνV = 0.35479
ReussKR = 298.13 GPaER = 215.31 GPaGR = 78.033 GPaνR = 0.37963
HillKH = 299.9 GPaEH = 239.27 GPaGH = 87.517 GPaνH = 0.36702

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
51 GPa 51 GPa 144 GPa 178.35 GPa 297 GPa 907.65 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 165.01 GPa 349.62 GPa 0.9266 TPa–1 1.5011 TPa–1 51 GPa 148.5 GPa0.14670.64772Value
Anisotropy 2.119 1.6200 2.912 4.4154Anisotropy
Axis -0.4604
0.4604
-0.7590
0.0000
1.0000
0.0000
-0.0393
0.9992
-0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.7071
0.7071
-0.0000
0.8663
0.0002
0.4996
0.8025
0.0001
0.5966
Axis
-0.7660
0.6428
-0.0000
-0.7071
0.7071
0.0000
-0.0002
1.0000
-0.0000
0.5966
0.0003
-0.8025
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