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 NbNi3 (Materials Project id mp-1451)

       328      150      149        0        0        0  
       150      372      128        0        0        0  
       149      128      344        0        0        0  
         0        0        0       53        0        0  
         0        0        0        0       61        0  
         0        0        0        0        0       81  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 210.89 GPaEV = 213.37 GPaGV = 80.133 GPaνV = 0.33137
ReussKR = 210.66 GPaER = 199.26 GPaGR = 74.219 GPaνR = 0.34236
HillKH = 210.78 GPaEH = 206.34 GPaGH = 77.176 GPaνH = 0.33684

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
53 GPa 61 GPa 81 GPa 180.19 GPa 230.75 GPa 633.05 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 162.53 GPa 290.43 GPa 1.4615 TPa–1 1.6584 TPa–1 53 GPa 114.74 GPa0.175110.53426Value
Anisotropy 1.787 1.1348 2.165 3.0511Anisotropy
Axis -0.0000
0.6952
0.7188
0.0000
1.0000
0.0000
0.0000
1.0000
0.0000
0.0000
0.0000
1.0000
0.0002
0.0001
1.0000
0.0002
0.7071
-0.7071
-0.5404
0.0000
0.8414
-0.0003
0.7205
-0.6935
Axis
-0.0000
1.0000
-0.0001
0.0001
-0.7071
-0.7071
-0.0000
-1.0000
-0.0000
-0.0003
-0.6935
-0.7205
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