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 Nb5Ga3 (Materials Project id mp-570293)

       329      110      110        0        0        0  
       110      289       73        0        0        0  
       110       73      289        0        0        0  
         0        0        0       99        0        0  
         0        0        0        0       52        0  
         0        0        0        0        0       52  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 165.89 GPaEV = 210.17 GPaGV = 81.533 GPaνV = 0.28885
ReussKR = 163.62 GPaER = 191.09 GPaGR = 73.195 GPaνR = 0.30535
HillKH = 164.75 GPaEH = 200.68 GPaGH = 77.364 GPaνH = 0.29699

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
52 GPa 52 GPa 99 GPa 189.06 GPa 216 GPa 501.94 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 159.95 GPa 262.15 GPa 1.4963 TPa–1 2.3077 TPa–1 52 GPa 108 GPa0.12760.55258Value
Anisotropy 1.639 1.5423 2.077 4.3305Anisotropy
Axis 0.6891
0.5124
0.5124
1.0000
0.0000
0.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.0002
0.7071
-0.7071
0.4867
0.8736
-0.0002
-0.7183
0.6957
-0.0000
Axis
1.0000
0.0000
-0.0000
0.0002
-0.7071
-0.7071
0.0001
-0.0003
-1.0000
-0.6957
-0.7183
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