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 LiCrO2 (Materials Project id mp-18793)

       351      106       69       -9        0        0  
       106      351       69        9        0        0  
        69       69      203        0        0        0  
        -9        9        0       54        0        0  
         0        0        0        0       54       -9  
         0        0        0        0       -9      122  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 154.78 GPaEV = 226.3 GPaGV = 90.067 GPaνV = 0.25631
ReussKR = 141.82 GPaER = 194.89 GPaGR = 76.669 GPaνR = 0.27097
HillKH = 148.3 GPaEH = 210.63 GPaGH = 83.368 GPaνH = 0.26328

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
52.829 GPa 53.156 GPa 123.17 GPa 169.84 GPa 245.84 GPa 490.16 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 145.4 GPa 308.58 GPa 1.6096 TPa–1 3.8319 TPa–1 53.175 GPa 123.65 GPa0.0787220.47928Value
Anisotropy 2.122 2.3806 2.325 6.0882Anisotropy
Axis 0.5573
0.3226
0.7651
0.0000
0.9979
0.0647
0.0948
0.9955
0.0000
0.0000
0.0000
1.0000
0.0358
0.0203
0.9992
0.7070
0.7013
0.0907
-0.0000
0.6377
0.7703
-0.0000
0.7590
0.6510
Axis
0.8638
0.5022
-0.0412
-0.7072
0.7012
0.0907
-1.0000
-0.0000
0.0000
0.0000
0.6510
-0.7590
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