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 MoC (Materials Project id mp-567925)

       488      147      292        0        0        0  
       147      488      292        0        0        0  
       292      292      459        0        0        0  
         0        0        0      103        0        0  
         0        0        0        0      103        0  
         0        0        0        0        0      171  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 321.89 GPaEV = 325.73 GPaGV = 122.33 GPaνV = 0.33134
ReussKR = 314.12 GPaER = 286.23 GPaGR = 106.16 GPaνR = 0.34813
HillKH = 318.01 GPaEH = 306.08 GPaGH = 114.24 GPaνH = 0.33958

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
103 GPa 103 GPa 124.78 GPa 171 GPa 341 GPa 969.22 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 190.45 GPa 319.19 GPa 0.42171 TPa–1 1.3809 TPa–1 74.385 GPa 171 GPa-0.129680.71867Value
Anisotropy 1.676 3.2745 2.299Anisotropy
Axis 0.0000
0.0000
1.0000
0.6138
0.6138
0.4965
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
0.7071
-0.0003
0.7071
1.0000
0.0006
-0.0000
-0.7071
0.7071
-0.0000
-0.7071
0.7071
0.0000
Axis
0.7071
-0.0005
-0.7071
-0.0006
1.0000
-0.0000
-0.7071
-0.7071
-0.0000
-0.0000
0.0000
-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