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 Nd (Materials Project id mp-123)

        63       23       16        0        0        0  
        23       63       16        0        0        0  
        16       16       70        0        0        0  
         0        0        0       18        0        0  
         0        0        0        0       18        0  
         0        0        0        0        0       20  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 34 GPaEV = 51.416 GPaGV = 20.6 GPaνV = 0.24796
ReussKR = 34 GPaER = 50.477 GPaGR = 20.149 GPaνR = 0.25257
HillKH = 34 GPaEH = 50.947 GPaGH = 20.375 GPaνH = 0.25026

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
18 GPa 18 GPa 20 GPa 40 GPa 54 GPa 102 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 47.114 GPa 64.047 GPa 9.8039 TPa–1 9.8039 TPa–1 18 GPa 24.828 GPa0.154070.32063Value
Anisotropy 1.359 1.0000 1.379 2.0811Anisotropy
Axis 0.7116
0.3157
0.6276
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.0847
0.7020
-0.7071
0.9439
0.3302
0.0000
-0.1280
0.6585
-0.7417
Axis
1.0000
0.0000
-0.0000
-0.0846
-0.7020
-0.7071
-0.0000
-0.0000
1.0000
-0.1415
0.7280
0.6708
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