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 TaN (Materials Project id mp-1279)

       525      210      160        0        0        0  
       210      525      160        0        0        0  
       160      160      657        0        0        0  
         0        0        0      186        0        0  
         0        0        0        0      186        0  
         0        0        0        0        0      157  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 307.44 GPaEV = 460.75 GPaGV = 184.27 GPaνV = 0.25023
ReussKR = 306.38 GPaER = 452.02 GPaGR = 180.22 GPaνR = 0.25411
HillKH = 306.91 GPaEH = 456.39 GPaGH = 182.24 GPaνH = 0.25216

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
157 GPa 186 GPa 186 GPa 315 GPa 466.39 GPa 925.61 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 424.93 GPa 587.34 GPa 0.96133 TPa–1 1.1513 TPa–1 157 GPa 208.68 GPa0.157490.35329Value
Anisotropy 1.382 1.1976 1.329 2.2432Anisotropy
Axis 0.7071
0.7071
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
1.0000
-0.0002
-0.0000
0.7071
0.0001
-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
0.0000
-0.0000
-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