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 LiI (Materials Project id mp-570935)

        22       12       11        0        0        0  
        12       22       11        0        0        0  
        11       11       24        0        0        0  
         0        0        0        5        0        0  
         0        0        0        0        5        0  
         0        0        0        0        0        5  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 15.111 GPaEV = 14.155 GPaGV = 5.2667 GPaνV = 0.34387
ReussKR = 15.105 GPaER = 14.041 GPaGR = 5.2194 GPaνR = 0.34508
HillKH = 15.108 GPaEH = 14.098 GPaGH = 5.2431 GPaνH = 0.34447

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
5 GPa 5 GPa 5 GPa 10 GPa 12.66 GPa 45.34 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 13.507 GPa 16.882 GPa 20.906 TPa–1 22.648 TPa–1 5 GPa 5.9359 GPa0.270270.41032Value
Anisotropy 1.25 1.0833 1.187 1.5182Anisotropy
Axis -0.3496
0.7502
-0.5612
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.4986
0.8668
0.0000
0.0000
0.0000
1.0000
0.1037
0.6995
0.7071
0.4515
0.8923
0.0000
-0.4645
0.8856
0.0000
Axis
-0.7660
0.6428
-0.0000
0.1037
0.6995
-0.7071
0.0000
-0.0000
1.0000
-0.8856
-0.4645
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