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 NbZn3 (Materials Project id mp-953)

       187       85       85        0        0        0  
        85      187       85        0        0        0  
        85       85      187        0        0        0  
         0        0        0       90        0        0  
         0        0        0        0       90        0  
         0        0        0        0        0       90  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 119 GPaEV = 184.71 GPaGV = 74.4 GPaνV = 0.24131
ReussKR = 119 GPaER = 173.3 GPaGR = 68.919 GPaνR = 0.25728
HillKH = 119 GPaEH = 179.04 GPaGH = 71.659 GPaνH = 0.24924

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
90 GPa 90 GPa 90 GPa 102 GPa 102 GPa 357 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 133.88 GPa 215.64 GPa 2.8011 TPa–1 2.8011 TPa–1 51 GPa 90 GPa0.0393010.43668Value
Anisotropy 1.611 1.0000 1.765 11.1111Anisotropy
Axis 0.0000
0.0000
1.0000
0.5774
0.5773
-0.5774
0.8001
0.4619
0.3827
0.0000
0.0000
1.0000
0.7071
-0.0003
0.7071
-0.0000
0.0000
1.0000
0.7071
-0.0000
-0.7071
-0.7071
0.0000
0.7071
Axis
0.7071
-0.0005
-0.7071
-1.0000
0.0000
-0.0000
-0.7071
0.0002
-0.7071
-0.0001
-1.0000
-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