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 Tc3N (Materials Project id mp-1017987)

       552      172      211        0        0        0  
       172      552      211        0        0        0  
       211      211      630        0        0        0  
         0        0        0      171        0        0  
         0        0        0        0      171        0  
         0        0        0        0        0      190  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 324.67 GPaEV = 460.89 GPaGV = 182.4 GPaνV = 0.2634
ReussKR = 322 GPaER = 458.65 GPaGR = 181.63 GPaνR = 0.2626
HillKH = 323.33 GPaEH = 459.77 GPaGH = 182.01 GPaνH = 0.26301

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
171 GPa 171 GPa 190 GPa 374.92 GPa 380 GPa 979.08 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 448.52 GPa 507.01 GPa 0.82271 TPa–1 1.1414 TPa–1 171 GPa 190 GPa0.210520.32367Value
Anisotropy 1.13 1.3874 1.111 1.5374Anisotropy
Axis 0.4036
0.7209
-0.5634
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.5000
0.8660
0.0000
0.0000
0.0000
1.0000
0.3876
0.9218
-0.0000
-0.7521
0.6590
0.0000
-0.1450
0.6258
-0.7664
Axis
0.9397
0.3420
-0.0000
-0.9218
0.3876
0.0000
-0.6590
-0.7521
0.0000
-0.1730
0.7466
0.6424
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