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-569416)

         3       -1       -1        0        0        0  
        -1      849      152        0       -0        0  
        -1      152      849        0        0        0  
         0        0        0      349        0       -0  
         0       -0        0        0        1        0  
         0        0        0       -0        0        1  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 222.33 GPaEV = 413.24 GPaGV = 173.6 GPaνV = 0.19022
ReussKR = 2.9683 GPaER = 4.9805 GPaGR = 2.0406 GPaνR = 0.22035
HillKH = 112.65 GPaEH = 209.12 GPaGH = 87.82 GPaνH = 0.19061

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
1 GPa 1 GPa 2.998 GPa 349 GPa 697 GPa 1001 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 2.6643 GPa 822.26 GPa 1.3329 TPa–1 334.22 TPa–1 1 GPa 348.5 GPa-0.273760.63421Value
Anisotropy 308.6250.7500 348.5Anisotropy
Axis 0.8658
0.5005
0.0000
0.0000
0.7071
0.7071
0.0000
0.6088
0.7934
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.0000
0.6967
0.7174
0.0000
0.0000
1.0000
0.2595
0.6829
0.6829
Axis
1.0000
0.0000
-0.0000
-0.0000
-0.7174
0.6967
1.0000
0.0000
-0.0000
-0.9657
0.1835
0.1835
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