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 Pm2O3 (Materials Project id mp-547622)

       222      130       87       40        0        0  
       130      222       87      -40        0        0  
        87       87      151        0        0        0  
        40      -40        0       67        0        0  
         0        0        0        0       67       40  
         0        0        0        0       40       46  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 133.67 GPaEV = 146.03 GPaGV = 55.4 GPaνV = 0.31792
ReussKR = 124.23 GPaER = 80.21 GPaGR = 28.803 GPaνR = 0.39239
HillKH = 128.95 GPaEH = 113.91 GPaGH = 42.101 GPaνH = 0.35277

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
15.145 GPa 21.567 GPa 92.634 GPa 97.855 GPa 137.43 GPa 410.37 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 45.869 GPa 236.78 GPa 1.6836 TPa–1 4.6825 TPa–1 15.145 GPa 97.855 GPa-0.239491.0092Value
Anisotropy 5.162 2.7813 6.461Anisotropy
Axis -0.0000
0.8772
0.4802
-0.7369
0.4254
0.5254
0.3484
0.9373
0.0000
0.0000
0.0000
1.0000
0.6857
0.3959
0.6108
0.0000
0.6108
0.7918
0.5067
0.2925
0.8110
-0.5000
0.8660
-0.0000
Axis
-0.5000
0.8660
-0.0000
-1.0000
-0.0000
0.0000
-0.5000
0.8660
-0.0000
-0.7404
-0.4275
0.5187
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