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 LaBi3 (Materials Project id mp-867248)

        59       49       49       -0       -0       -0  
        49       59       49       -0       -0       -0  
        49       49       59       -0       -0       -0  
        -0       -0       -0       21       -0       -0  
        -0       -0       -0       -0       21       -0  
        -0       -0       -0       -0       -0       21  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 52.333 GPaEV = 40.073 GPaGV = 14.6 GPaνV = 0.37238
ReussKR = 52.333 GPaER = 26.1 GPaGR = 9.2105 GPaνR = 0.41688
HillKH = 52.333 GPaEH = 33.198 GPaGH = 11.905 GPaνH = 0.39427

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
10 GPa 10 GPa 21 GPa 21 GPa 21 GPa 157 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 14.537 GPa 55.567 GPa 6.3694 TPa–1 6.3694 TPa–1 5 GPa 21 GPa-0.224311.0168Value
Anisotropy 3.822 1.0000 4.2Anisotropy
Axis 0.0000
0.0000
1.0000
0.5774
0.5773
-0.5774
0.0000
0.0000
1.0000
0.9916
0.0000
0.1294
0.7071
-0.0003
0.7071
0.0000
0.0000
1.0000
0.7071
-0.0003
0.7071
-0.0000
0.7071
-0.7071
Axis
0.7071
-0.0005
-0.7071
0.1736
0.9848
-0.0000
0.7071
-0.0005
-0.7071
-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