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 RhN2 (Materials Project id mp-20304)

       400      115      183        0        0        0  
       115      561       78        0        0        0  
       183       78      254        0        0        0  
         0        0        0       71        0        0  
         0        0        0        0      184        0  
         0        0        0        0        0      108  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 218.56 GPaEV = 322.4 GPaGV = 128.53 GPaνV = 0.25414
ReussKR = 200.42 GPaER = 262.9 GPaGR = 102.58 GPaνR = 0.28138
HillKH = 209.49 GPaEH = 292.83 GPaGH = 115.56 GPaνH = 0.26703

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
71 GPa 108 GPa 129.98 GPa 184 GPa 402.33 GPa 682.69 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 165.57 GPa 524.15 GPa 0.77817 TPa–1 3.0063 TPa–1 66.734 GPa 199.85 GPa0.0480880.68685Value
Anisotropy 3.166 3.8633 2.995 14.2831Anisotropy
Axis 0.0000
0.3847
0.9230
0.0000
1.0000
0.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.7071
-0.0002
0.7071
0.5457
0.7071
0.4496
-0.0000
0.0000
1.0000
1.0000
0.0001
0.0000
Axis
0.7071
-0.0006
-0.7071
-0.5457
0.7071
-0.4496
-0.0000
-1.0000
0.0000
0.0000
0.0002
-1.0000
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