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 NdCo2 (Materials Project id mp-445)

       130      111      115        0        6        0  
       111      146      111        0        7        0  
       115      111      131        0        6        0  
         0        0        0       21        0        0  
         6        7        6        0       21        0  
         0        0        0        0        0       21  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 120.11 GPaEV = 49.431 GPaGV = 17.267 GPaνV = 0.43141
ReussKR = 117.93 GPaER = 42.705 GPaGR = 14.832 GPaνR = 0.43965
HillKH = 119.02 GPaEH = 46.077 GPaGH = 16.049 GPaνH = 0.43548

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
15.494 GPa 20.607 GPa 21 GPa 21 GPa 31.122 GPa 360.78 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 25.503 GPa 61.243 GPa 1.8803 TPa–1 4.4152 TPa–1 7.7484 GPa 21 GPa0.0712330.8127Value
Anisotropy 2.401 2.3482 2.71 11.4090Anisotropy
Axis 1.0000
-0.0000
-0.0055
0.5631
0.6043
0.5636
0.6782
0.0000
0.7349
-0.7349
0.0000
0.6782
0.7070
-0.0000
-0.7072
-0.0000
-0.0000
1.0000
-0.0200
0.6929
0.7208
0.0223
0.6765
0.7361
Axis
-0.7072
0.0002
-0.7070
-0.0000
1.0000
0.0000
-0.0161
-0.7210
0.6927
-0.9994
0.0341
-0.0010
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