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 GdO2 (Materials Project id mp-21149)

       275       64       78        0        0        0  
        64      275       78        0        0        0  
        78       78      204        0        0        0  
         0        0        0       74        0        0  
         0        0        0        0       74        0  
         0        0        0        0        0       44  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 132.67 GPaEV = 187.19 GPaGV = 74 GPaνV = 0.26483
ReussKR = 131.01 GPaER = 174.58 GPaGR = 68.305 GPaνR = 0.27791
HillKH = 131.84 GPaEH = 180.91 GPaGH = 71.153 GPaνH = 0.27129

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
44 GPa 74 GPa 74 GPa 142.18 GPa 211 GPa 400.82 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 133.84 GPa 240.41 GPa 2.211 TPa–1 3.2112 TPa–1 44 GPa 105.5 GPa0.116430.5209Value
Anisotropy 1.796 1.4524 2.398 4.4739Anisotropy
Axis 0.7071
0.7071
0.0000
1.0000
0.0000
0.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
1.0000
-0.0002
-0.0000
-0.7071
0.7071
-0.0000
0.5186
0.5186
-0.6797
-0.7071
0.7071
0.0000
Axis
0.0002
1.0000
-0.0000
-0.7071
-0.7071
0.0000
0.4807
0.4806
0.7335
-0.7071
-0.7071
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