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 YN (Materials Project id mp-1017533)

       298       86       17        0        0        0  
        86      298       17        0        0        0  
        17       17      454        0        0        0  
         0        0        0       42        0        0  
         0        0        0        0       42        0  
         0        0        0        0        0      106  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 143.33 GPaEV = 243.4 GPaGV = 100 GPaνV = 0.21698
ReussKR = 141.96 GPaER = 180.34 GPaGR = 69.992 GPaνR = 0.28827
HillKH = 142.65 GPaEH = 212.74 GPaGH = 84.996 GPaνH = 0.25144

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
42 GPa 42 GPa 106 GPa 212 GPa 376.54 GPa 461.46 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 135.1 GPa 452.49 GPa 2.0143 TPa–1 2.515 TPa–1 42 GPa 164.73 GPa0.0442710.61889Value
Anisotropy 3.349 1.2486 3.922 13.9796Anisotropy
Axis 0.7093
0.1948
0.6775
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.0847
0.7020
-0.7071
0.0000
0.0000
1.0000
0.6584
0.0001
-0.7527
Axis
-0.7660
-0.6428
0.0000
-0.0846
-0.7020
-0.7071
-0.1736
0.9848
0.0000
-0.7527
-0.0003
-0.6584
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