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 RuN2 (Materials Project id mp-607371)

       606      161      216        0        0        0  
       161      745       98        0        0        0  
       216       98      439        0        0        0  
         0        0        0       92        0        0  
         0        0        0        0      259        0  
         0        0        0        0        0       90  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 304.44 GPaEV = 442.41 GPaGV = 175.87 GPaνV = 0.2578
ReussKR = 292.17 GPaER = 358.51 GPaGR = 138.37 GPaνR = 0.29549
HillKH = 298.31 GPaEH = 400.96 GPaGH = 157.12 GPaνH = 0.27598

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
90 GPa 92 GPa 259 GPa 290.65 GPa 561.48 GPa 937.88 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 265.81 GPa 697.67 GPa 0.80232 TPa–1 1.6713 TPa–1 90 GPa 259 GPa0.0578360.62382Value
Anisotropy 2.625 2.0831 2.878 10.7861Anisotropy
Axis 0.0000
0.6274
-0.7787
0.0000
1.0000
0.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
1.0000
-0.0000
-0.0000
-0.0000
0.0000
1.0000
-0.0000
0.0000
1.0000
-0.5698
0.7262
-0.3847
Axis
0.0000
1.0000
0.0000
-1.0000
0.0000
-0.0000
-0.0000
-1.0000
0.0000
-0.6074
-0.6875
-0.3981
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