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-1045)

       179       96       96        0        0        0  
        96      179       96        0        0        0  
        96       96      179        0        0        0  
         0        0        0       58        0        0  
         0        0        0        0       58        0  
         0        0        0        0        0       58  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 123.67 GPaEV = 135.44 GPaGV = 51.4 GPaνV = 0.31747
ReussKR = 123.67 GPaER = 132.28 GPaGR = 50.042 GPaνR = 0.32172
HillKH = 123.67 GPaEH = 133.86 GPaGH = 50.721 GPaνH = 0.31959

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
58 GPa 58 GPa 58 GPa 83 GPa 83 GPa 371 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 111.97 GPa 150.48 GPa 2.6954 TPa–1 2.6954 TPa–1 41.5 GPa 58 GPa0.194520.43199Value
Anisotropy 1.344 1.0000 1.398 2.2208Anisotropy
Axis 0.0000
0.0000
1.0000
0.5774
0.5774
0.5773
0.2053
0.7663
0.6088
0.9914
0.0000
-0.1305
0.7071
0.0001
-0.7071
0.0000
0.0000
1.0000
0.7071
-0.0002
0.7071
0.7071
-0.0001
0.7071
Axis
-0.7071
-0.0002
-0.7071
-0.1736
0.9848
-0.0000
0.7071
-0.0006
-0.7071
0.0001
1.0000
0.0001
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