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 MoN (Materials Project id mp-2811)

       499      177      235        0        0        0  
       177      499      235        0        0        0  
       235      235      714        0        0        0  
         0        0        0      241        0        0  
         0        0        0        0      241        0  
         0        0        0        0        0      161  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 334 GPaEV = 499.33 GPaGV = 199.6 GPaνV = 0.25083
ReussKR = 319.77 GPaER = 478.97 GPaGR = 191.53 GPaνR = 0.25036
HillKH = 326.89 GPaEH = 489.15 GPaGH = 195.57 GPaνH = 0.2506

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
161 GPa 241 GPa 241 GPa 322 GPa 362.12 GPa 1027.9 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 398.1 GPa 581.49 GPa 0.55345 TPa–1 1.2869 TPa–1 161 GPa 241 GPa0.149030.36185Value
Anisotropy 1.461 2.3252 1.497 2.4280Anisotropy
Axis 0.9914
0.1305
0.0000
0.4686
0.1976
0.8610
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
0.6375
0.7705
-0.0000
0.0000
0.0000
1.0000
0.6900
0.2572
-0.6766
-0.3914
0.2634
-0.8817
Axis
-0.7705
0.6375
0.0000
0.7660
0.6428
-0.0000
0.6340
0.2363
0.7364
-0.5583
-0.8296
-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