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-569304)

       849      148       -1        0        0        0  
       148      849       -1       -0        0        0  
        -1       -1        5        0        0        0  
         0       -0        0        1        0        0  
         0        0        0        0        1        0  
         0        0        0        0        0      351  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 221.67 GPaEV = 414.5 GPaGV = 174.4 GPaνV = 0.18835
ReussKR = 4.9288 GPaER = 5.7455 GPaGR = 2.2001 GPaνR = 0.30572
HillKH = 113.3 GPaEH = 210.27 GPaGH = 88.3 GPaνH = 0.19068

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
1 GPa 1 GPa 4.998 GPa 351 GPa 701 GPa 997 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 3.197 GPa 823.75 GPa 1.2041 TPa–1 200.48 TPa–1 1 GPa 351 GPa-0.0010030.77187Value
Anisotropy 257.7166.5000 351Anisotropy
Axis 0.6128
0.0000
0.7902
0.7071
0.7071
0.0000
0.6088
0.7934
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
1.0000
0.0007
-0.0000
-0.0000
-0.0000
1.0000
0.7237
0.6303
-0.2811
Axis
1.0000
0.0000
-0.0000
-0.0007
1.0000
0.0000
0.7585
0.6517
0.0000
-0.2119
-0.1847
-0.9597
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