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 CN2 (Materials Project id mp-1009818)

       941       46       53        0        0        0  
        46      941       53        0        0        0  
        53       53     1548        0        0        0  
         0        0        0      213        0        0  
         0        0        0        0      213        0  
         0        0        0        0        0      138  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 414.89 GPaEV = 785.02 GPaGV = 331.33 GPaνV = 0.18464
ReussKR = 393.25 GPaER = 606.2 GPaGR = 243.83 GPaνR = 0.24308
HillKH = 404.07 GPaEH = 697.32 GPaGH = 287.58 GPaνH = 0.21238

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
138 GPa 213 GPa 213 GPa 895 GPa 977.16 GPa 1557.8 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 431.03 GPa 1542.3 GPa 0.57875 TPa–1 0.98209 TPa–1 138 GPa 560.18 GPa0.0150070.56169Value
Anisotropy 3.578 1.6969 4.059 37.4286Anisotropy
Axis 0.7071
0.7071
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.3827
0.9239
0.0000
1.0000
-0.0002
0.0001
0.7071
-0.0000
-0.7071
0.7071
0.7071
0.0000
0.7071
0.7071
-0.0000
Axis
0.0002
1.0000
-0.0000
-0.7071
0.0002
-0.7071
0.0001
-0.0001
-1.0000
-0.7071
0.7071
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