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 CeY3 (Materials Project id mp-985551)

        52       32       35        0        0        0  
        32       52       35        0        0        0  
        35       35       56        0        0        0  
         0        0        0       31        0        0  
         0        0        0        0       31        0  
         0        0        0        0        0       31  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 40.444 GPaEV = 56.87 GPaGV = 22.467 GPaνV = 0.26565
ReussKR = 40.25 GPaER = 43.372 GPaGR = 16.424 GPaνR = 0.3204
HillKH = 40.347 GPaEH = 50.261 GPaGH = 19.445 GPaνH = 0.29238

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
18.561 GPa 20 GPa 31 GPa 31 GPa 31 GPa 121.44 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 26.722 GPa 74.106 GPa 6.2112 TPa–1 9.3168 TPa–1 9.4567 GPa 31 GPa-0.212710.74295Value
Anisotropy 2.773 1.5000 3.278Anisotropy
Axis 1.0000
0.0000
0.0000
0.5694
0.5693
-0.5930
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
0.7071
-0.0003
0.7071
-0.0000
0.0000
1.0000
0.7071
0.7071
-0.0000
0.0000
0.6870
0.7267
Axis
0.7071
-0.0005
-0.7071
-1.0000
0.0000
-0.0000
-0.7071
0.7071
0.0000
-1.0000
0.0000
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