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 Th3N4 (Materials Project id mp-467)

       272      167       91       38        0        0  
       167      272       91      -38        0        0  
        91       91      167        0        0        0  
        38      -38        0       65        0        0  
         0        0        0        0       65       38  
         0        0        0        0       38       53  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 156.56 GPaEV = 161.34 GPaGV = 60.733 GPaνV = 0.32824
ReussKR = 138.76 GPaER = 101.89 GPaGR = 36.979 GPaνR = 0.37762
HillKH = 147.66 GPaEH = 132.01 GPaGH = 48.856 GPaνH = 0.35099

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
20.529 GPa 27.659 GPa 97.471 GPa 115.76 GPa 142.34 GPa 490.24 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 60.134 GPa 245.81 GPa 1.3392 TPa–1 4.5286 TPa–1 20.31 GPa 97.471 GPa-0.182690.99428Value
Anisotropy 4.088 3.3816 4.799Anisotropy
Axis -0.0000
0.8584
0.5130
-0.7589
0.4393
0.4807
-0.3798
0.9250
-0.0000
0.0000
0.0000
1.0000
-0.6587
0.3829
0.6477
-0.0000
0.6496
0.7603
0.0000
0.5602
-0.8283
-1.0000
-0.0000
-0.0000
Axis
-0.5052
-0.8630
-0.0037
-1.0000
-0.0000
0.0000
-1.0000
-0.0000
-0.0000
0.0000
-0.8582
-0.5134
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