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 Nd2O3 (Materials Project id mp-7954)

       123       75       39        0        0        0  
        75      123       39        0        0        0  
        39       39      310        0        0        0  
         0        0        0       31        0        0  
         0        0        0        0       31        0  
         0        0        0        0        0       24  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 95.778 GPaEV = 114.62 GPaGV = 44.067 GPaνV = 0.30054
ReussKR = 88.124 GPaER = 84.932 GPaGR = 31.706 GPaνR = 0.33937
HillKH = 91.951 GPaEH = 99.934 GPaGH = 37.886 GPaνH = 0.31886

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
24 GPa 31 GPa 31 GPa 48 GPa 175.4 GPa 332.6 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 74.251 GPa 294.64 GPa 2.057 TPa–1 4.6453 TPa–1 24 GPa 56.165 GPa0.0511350.59354Value
Anisotropy 3.968 2.2583 2.34 11.6074Anisotropy
Axis 0.9137
0.0001
0.4064
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
0.6375
0.7705
-0.0000
0.6081
0.3608
0.7071
1.0000
0.0003
0.0000
0.5064
0.8623
0.0000
Axis
-0.7705
0.6375
0.0000
0.6081
0.3608
-0.7071
0.0000
0.0002
-1.0000
-0.8623
0.5064
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