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 Li2CO3 (Materials Project id mp-3054)

       137       58       33        0      -12        0  
        58      146       23        0       -2        0  
        33       23       56        0       -4        0  
         0        0        0       16        0        1  
       -12       -2       -4        0       12        0  
         0        0        0        1        0       57  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 63 GPaEV = 82.1 GPaGV = 32 GPaνV = 0.28281
ReussKR = 46.153 GPaER = 54.687 GPaGR = 20.993 GPaνR = 0.30252
HillKH = 54.577 GPaEH = 68.417 GPaGH = 26.496 GPaνH = 0.29107

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
10.712 GPa 15.976 GPa 44.181 GPa 57.024 GPa 85.802 GPa 210.31 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 28.931 GPa 137.29 GPa 1.5762 TPa–1 16.703 TPa–1 10.756 GPa 57.024 GPa-0.0306090.76281Value
Anisotropy 4.745 10.5971 5.302Anisotropy
Axis -0.6797
0.0000
-0.7335
0.6204
0.7842
-0.0120
-0.9546
-0.0000
0.2979
0.2979
-0.0000
0.9546
0.0557
-0.0006
0.9984
-0.0000
1.0000
-0.0000
0.6464
0.7138
0.2697
-0.8144
0.0001
0.5803
Axis
0.9984
0.0004
-0.0557
-0.9997
-0.0000
-0.0244
-0.6052
0.6948
-0.3885
-0.5803
-0.0000
-0.8144
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