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 NdFe5 (Materials Project id mp-11382)

       169       60       77        0        0       -0  
        60      169       77        0        0        0  
        77       77      213        0        0        0  
         0        0        0       64       -0        0  
         0        0        0       -0       64        0  
        -0        0        0        0        0       54  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 108.78 GPaEV = 149.61 GPaGV = 58.867 GPaνV = 0.27077
ReussKR = 106.39 GPaER = 147.84 GPaGR = 58.278 GPaνR = 0.26841
HillKH = 107.59 GPaEH = 148.73 GPaGH = 58.572 GPaνH = 0.2696

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
54 GPa 64 GPa 64 GPa 109 GPa 111.81 GPa 330.19 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 133.08 GPa 163.91 GPa 2.0315 TPa–1 3.6837 TPa–1 54 GPa 64 GPa0.227850.33624Value
Anisotropy 1.232 1.8133 1.185 1.4757Anisotropy
Axis 0.7071
0.7071
0.0000
0.4629
0.0000
0.8864
0.0000
0.0000
1.0000
0.6088
0.7934
0.0000
1.0000
-0.0002
0.0000
0.0000
0.0000
1.0000
-1.0000
-0.0000
0.0000
-0.0000
-0.0000
1.0000
Axis
0.0002
1.0000
0.0000
0.7660
0.6428
-0.0000
0.0000
-1.0000
-0.0000
0.7585
0.6517
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