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 LiC (Materials Project id mp-1378)

       162       16        6        0        0        0  
        16       85       14        0        0        0  
         6       14       77        0        0        0  
         0        0        0       27        0        0  
         0        0        0        0       16        0  
         0        0        0        0        0       20  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 44 GPaEV = 76.879 GPaGV = 31.8 GPaνV = 0.20879
ReussKR = 40.195 GPaER = 62.899 GPaGR = 25.379 GPaνR = 0.23919
HillKH = 42.098 GPaEH = 69.937 GPaGH = 28.59 GPaνH = 0.22312

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
16 GPa 20 GPa 27 GPa 66.169 GPa 91.786 GPa 166.05 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 48.295 GPa 158.84 GPa 4.8738 TPa–1 10.963 TPa–1 16 GPa 49.349 GPa0.0211630.54063Value
Anisotropy 3.289 2.2494 3.084 25.5457Anisotropy
Axis 0.6449
0.0000
-0.7643
1.0000
0.0000
0.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.7071
-0.0000
-0.7071
0.0000
0.0000
1.0000
0.7740
0.0001
0.6332
Axis
1.0000
0.0000
-0.0000
-0.7071
0.0002
-0.7071
-1.0000
0.0000
0.0000
0.6332
0.0003
-0.7740
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