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 LiB (Materials Project id mp-16726)

        41       32      -19        0        0        0  
        32       57      -27        0        0        0  
       -19      -27      400        0        0        0  
         0        0        0       14        0        0  
         0        0        0        0       20        0  
         0        0        0        0        0       40  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 52.222 GPaEV = 111.86 GPaGV = 48.933 GPaνV = 0.143
ReussKR = 31.168 GPaER = 44.93 GPaGR = 17.833 GPaνR = 0.25974
HillKH = 41.695 GPaEH = 79.052 GPaGH = 33.383 GPaνH = 0.18401

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
14 GPa 16.008 GPa 20 GPa 40 GPa 78.602 GPa 403.39 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 22.997 GPa 386.57 GPa 4.0015 TPa–1 19.708 TPa–1 8.0972 GPa 73.2 GPa-0.380050.76607Value
Anisotropy 16.81 4.9252 9.04Anisotropy
Axis 1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
-0.7071
0.7071
0.0000
0.4659
0.5320
-0.7071
-0.0000
-0.0000
1.0000
-0.0000
1.0000
-0.0000
Axis
-0.7071
-0.7071
-0.0000
0.4659
0.5320
0.7071
-0.0000
1.0000
0.0000
-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