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 C (Materials Project id mp-48)

       904      159       -1        0        0        0  
       159      904       -1        0        0        0  
        -1       -1        8        0        0        0  
         0        0        0        2        0        0  
         0        0        0        0        2        0  
         0        0        0        0        0      372  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 236.67 GPaEV = 441.79 GPaGV = 185.8 GPaνV = 0.18888
ReussKR = 7.8504 GPaER = 10.833 GPaGR = 4.2648 GPaνR = 0.27002
HillKH = 122.26 GPaEH = 226.43 GPaGH = 95.032 GPaνH = 0.19133

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
2 GPa 2 GPa 7.9981 GPa 372 GPa 745 GPa 1063 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 5.9931 GPa 875.95 GPa 1.0586 TPa–1 125.26 TPa–1 2 GPa 372.5 GPa-0.000940730.71095Value
Anisotropy 146.2118.3333 186.2Anisotropy
Axis 0.4089
0.4089
0.8158
0.0000
1.0000
0.0000
0.7071
0.7071
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
-0.7071
0.7071
0.0000
0.0000
0.0000
1.0000
0.9525
-0.0006
0.3045
Axis
1.0000
0.0000
-0.0000
-0.7071
-0.7071
0.0000
0.1736
0.9848
-0.0000
0.3045
-0.0006
-0.9525
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