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 LaN (Materials Project id mp-256)

       204       81       81        0        0        0  
        81      204       81        0        0        0  
        81       81      204        0        0        0  
         0        0        0       71        0        0  
         0        0        0        0       71        0  
         0        0        0        0        0       71  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 122 GPaEV = 170.33 GPaGV = 67.2 GPaνV = 0.26731
ReussKR = 122 GPaER = 169.62 GPaGR = 66.868 GPaνR = 0.26828
HillKH = 122 GPaEH = 169.97 GPaGH = 67.034 GPaνH = 0.2678

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
71 GPa 71 GPa 71 GPa 123 GPa 123 GPa 366 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 157.96 GPa 178.39 GPa 2.7322 TPa–1 2.7322 TPa–1 61.5 GPa 71 GPa0.216930.31092Value
Anisotropy 1.129 1.0000 1.154 1.4333Anisotropy
Axis 1.0000
0.0000
0.0000
-0.5774
0.5774
0.5773
0.0000
0.0000
1.0000
0.9239
0.0000
0.3827
0.7071
-0.0003
0.7071
0.0000
0.0000
1.0000
0.7071
-0.0002
0.7071
0.7071
-0.0005
0.7071
Axis
0.7071
-0.0005
-0.7071
0.9397
0.3420
-0.0000
0.7071
-0.0006
-0.7071
0.0004
1.0000
0.0003
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