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 P2O5 (Materials Project id mp-2452)

       108       39       42        0        0        0  
        39      145       16        0        0        0  
        42       16       31        0        0        0  
         0        0        0        8        0        0  
         0        0        0        0       42        0  
         0        0        0        0        0       32  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 53.111 GPaEV = 73.317 GPaGV = 28.867 GPaνV = 0.26993
ReussKR = 26.659 GPaER = 36.571 GPaGR = 14.382 GPaνR = 0.27136
HillKH = 39.885 GPaEH = 54.944 GPaGH = 21.625 GPaνH = 0.27041

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
8 GPa 12.515 GPa 32 GPa 42 GPa 92.596 GPa 178.89 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 14.661 GPa 130.87 GPa -8.5095 TPa–1 41.404 TPa–1 7.0726 GPa 42 GPa-0.262071.2895Value
Anisotropy 8.926 5.938Anisotropy
Axis 0.0000
0.0000
1.0000
0.0000
1.0000
0.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.7071
-0.0002
0.7071
0.0000
0.0000
-1.0000
0.7473
0.2661
0.6089
1.0000
-0.0004
-0.0000
Axis
0.7071
-0.0006
-0.7071
-1.0000
0.0000
-0.0000
-0.6575
0.4286
0.6197
-0.0000
-0.0003
-1.0000
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