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 Na3C (Materials Project id mp-977200)

        36       30       30        0        0        0  
        30       36       30        0        0        0  
        30       30       36        0        0        0  
         0        0        0        8        0        0  
         0        0        0        0        8        0  
         0        0        0        0        0        8  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 32 GPaEV = 16.941 GPaGV = 6 GPaνV = 0.41176
ReussKR = 32 GPaER = 13.714 GPaGR = 4.8 GPaνR = 0.42857
HillKH = 32 GPaEH = 15.337 GPaGH = 5.4 GPaνH = 0.42012

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
6 GPa 6 GPa 8 GPa 8 GPa 8 GPa 96 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 8.7273 GPa 22.154 GPa 10.417 TPa–1 10.417 TPa–1 3 GPa 8 GPa4.632e-080.83333Value
Anisotropy 2.538 1.0000 2.66717990715.2662Anisotropy
Axis 0.0000
0.0000
1.0000
-0.5774
0.5774
-0.5773
0.0000
0.0000
1.0000
0.9914
0.0000
0.1305
0.7071
-0.0003
0.7071
0.0000
0.0000
1.0000
0.7071
-0.0000
-0.7071
0.0000
0.7071
0.7071
Axis
0.7071
-0.0005
-0.7071
0.7660
0.6428
-0.0000
-0.7071
0.0002
-0.7071
-1.0000
-0.0000
0.0000
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