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 Mo2C (Materials Project id mp-1552)

       488      169      226        0        0        0  
       169      489      216        0        0        0  
       226      216      453        0        0        0  
         0        0        0      179        0        0  
         0        0        0        0      167        0  
         0        0        0        0        0      139  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 294.67 GPaEV = 388.22 GPaGV = 151.6 GPaνV = 0.28042
ReussKR = 294.57 GPaER = 379.48 GPaGR = 147.63 GPaνR = 0.28529
HillKH = 294.62 GPaEH = 383.86 GPaGH = 149.61 GPaνH = 0.28285

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
139 GPa 167 GPa 179 GPa 226.02 GPa 319.86 GPa 884.12 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 304.27 GPa 431.51 GPa 1.0771 TPa–1 1.1739 TPa–1 118.36 GPa 179 GPa0.158650.42325Value
Anisotropy 1.418 1.0899 1.512 2.6679Anisotropy
Axis 0.0000
0.0000
1.0000
-0.0000
0.7920
0.6105
0.0000
0.0000
1.0000
0.0000
1.0000
0.0000
0.5723
0.4153
0.7071
-0.0000
0.0000
1.0000
-1.0000
-0.0001
-0.0000
1.0000
0.0003
0.0000
Axis
0.5724
0.4151
-0.7071
0.0000
-1.0000
0.0000
0.0001
-1.0000
-0.0000
0.0000
0.0002
-1.0000
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