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 Eu2O3 (Materials Project id mp-647924)

       144       90       62        0       11        0  
        90      183       67        0        6        0  
        62       67      199        0        4        0  
         0        0        0       27        0       -1  
        11        6        4        0       45        0  
         0        0        0       -1        0       61  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 107.11 GPaEV = 123.16 GPaGV = 47.067 GPaνV = 0.30836
ReussKR = 104.23 GPaER = 110.69 GPaGR = 41.834 GPaνR = 0.323
HillKH = 105.67 GPaEH = 116.95 GPaGH = 44.45 GPaνH = 0.31554

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
26.971 GPa 43.508 GPa 61.029 GPa 71.823 GPa 132.45 GPa 323.21 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 81.881 GPa 166.02 GPa 2.2962 TPa–1 4.7435 TPa–1 26.971 GPa 65.046 GPa0.0553450.58422Value
Anisotropy 2.028 2.0658 2.412 10.5561Anisotropy
Axis 0.0250
0.7439
0.6679
-0.0103
-0.0000
0.9999
0.0000
1.0000
0.0000
-0.9123
-0.0000
0.4095
0.0294
-0.0000
0.9996
-0.3820
0.5794
-0.7199
0.5965
0.4761
-0.6461
-0.5812
0.5282
-0.6191
Axis
-0.0000
1.0000
0.0000
-0.4823
0.5395
0.6901
-0.7749
0.5512
-0.3094
0.1244
-0.6941
-0.7090
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