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 Lu(FeB)2 (Materials Project id mp-12061)

       216      199       67        0        0        0  
       199      216       67        0        0        0  
        67       67      252        0        0        0  
         0        0        0      128        0        0  
         0        0        0        0      128        0  
         0        0        0        0        0      170  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 150 GPaEV = 262.46 GPaGV = 108.6 GPaνV = 0.20838
ReussKR = 146.85 GPaER = 93.798 GPaGR = 33.655 GPaνR = 0.39355
HillKH = 148.43 GPaEH = 183.99 GPaGH = 71.127 GPaνH = 0.2934

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
17 GPa 128 GPa 128 GPa 170 GPa 208.52 GPa 458.48 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 32.542 GPa 358.61 GPa 1.9351 TPa–1 2.9393 TPa–1 8.5 GPa 170 GPa-0.853561.4596Value
Anisotropy 11.02 1.5189 20Anisotropy
Axis 0.0000
1.0000
0.0000
0.7071
0.7071
0.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
-0.7071
0.7071
0.0000
-1.0000
0.0000
0.0000
0.5367
-0.0000
0.8438
-0.0000
0.6058
0.7956
Axis
-0.7071
-0.7071
-0.0000
-0.0000
-1.0000
0.0000
-0.8438
0.0000
0.5367
-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