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 TcN (Materials Project id mp-1019319)

       499      119      119        0        0        0  
       119      499      119        0        0        0  
       119      119      499        0        0        0  
         0        0        0      110        0        0  
         0        0        0        0      110        0  
         0        0        0        0        0      110  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 245.67 GPaEV = 357.18 GPaGV = 142 GPaνV = 0.25768
ReussKR = 245.67 GPaER = 336.45 GPaGR = 132.28 GPaνR = 0.27174
HillKH = 245.67 GPaEH = 346.87 GPaGH = 137.14 GPaνH = 0.26467

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
110 GPa 110 GPa 110 GPa 380 GPa 380 GPa 737 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 287.14 GPa 453.17 GPa 1.3569 TPa–1 1.3569 TPa–1 110 GPa 190 GPa0.134310.43679Value
Anisotropy 1.578 1.0000 1.727 3.2521Anisotropy
Axis -0.5774
0.5774
0.5773
1.0000
0.0000
0.0000
0.7934
0.0000
0.6088
0.3314
0.8001
0.5000
0.0000
0.0000
1.0000
0.7071
-0.0003
0.7071
0.7071
-0.0000
0.7071
0.7071
-0.0000
-0.7071
Axis
1.0000
0.0002
-0.0000
0.7071
-0.0005
-0.7071
0.0000
1.0000
0.0000
-0.7071
0.0002
-0.7071
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