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 Nb2O5 (Materials Project id mp-776896)

        65       53       39        0        0        0  
        53       64       40        0        0        0  
        39       40      114        0        0        0  
         0        0        0       39        0        0  
         0        0        0        0       34        0  
         0        0        0        0        0       41  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 56.333 GPaEV = 76.864 GPaGV = 30.2 GPaνV = 0.27259
ReussKR = 54.796 GPaER = 47.335 GPaGR = 17.454 GPaνR = 0.35603
HillKH = 55.565 GPaEH = 62.541 GPaGH = 23.827 GPaνH = 0.31241

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
11.485 GPa 34 GPa 39 GPa 41 GPa 59.876 GPa 171.64 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 20.042 GPa 93.329 GPa 3.7448 TPa–1 7.4049 TPa–1 5.7438 GPa 41 GPa-0.388121.0664Value
Anisotropy 4.657 1.9774 7.138Anisotropy
Axis 0.0000
1.0000
0.0000
0.4687
0.4878
0.7364
0.0000
0.0000
1.0000
0.0000
1.0000
0.0000
-0.7071
0.7071
0.0000
-1.0000
-0.0000
0.0000
0.0000
0.6163
0.7875
0.0000
0.6594
0.7517
Axis
-0.7071
-0.7071
-0.0000
0.0000
-1.0000
0.0000
0.0000
0.7875
-0.6163
-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