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 OsN2 (Materials Project id mp-21264)

       736      175      265        0        0        0  
       175      901       79        0        0        0  
       265       79      593        0        0        0  
         0        0        0      131        0        0  
         0        0        0        0      332        0  
         0        0        0        0        0      169  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 363.11 GPaEV = 590.95 GPaGV = 240.47 GPaνV = 0.22876
ReussKR = 354.34 GPaER = 515.59 GPaGR = 205.01 GPaνR = 0.25749
HillKH = 358.72 GPaEH = 553.63 GPaGH = 222.74 GPaνH = 0.24278

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
131 GPa 169 GPa 332 GPa 385.8 GPa 735.09 GPa 1109.1 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 367.06 GPa 858.88 GPa 0.7003 TPa–1 1.2584 TPa–1 131 GPa 359.55 GPa0.0186070.51982Value
Anisotropy 2.34 1.7969 2.745 27.9370Anisotropy
Axis -0.0000
0.6351
-0.7724
0.0000
1.0000
0.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.0002
0.0001
1.0000
0.4856
0.7071
0.5140
-0.0000
0.0000
1.0000
0.5510
0.7081
-0.4416
Axis
-0.0000
1.0000
-0.0001
-0.4856
0.7071
-0.5140
0.0000
-1.0000
0.0000
-0.4712
0.7007
0.5357
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