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 ZrN (Materials Project id mp-1017546)

       397      115      144        0        0        0  
       115      397      144        0        0        0  
       144      144      541        0        0        0  
         0        0        0       57        0        0  
         0        0        0        0       57        0  
         0        0        0        0        0      141  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 237.89 GPaEV = 292.96 GPaGV = 113.13 GPaνV = 0.29475
ReussKR = 231.36 GPaER = 239.86 GPaGR = 90.363 GPaνR = 0.32721
HillKH = 234.62 GPaEH = 266.69 GPaGH = 101.75 GPaνH = 0.31055

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
57 GPa 57 GPa 141 GPa 282 GPa 322.34 GPa 730.66 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 186.34 GPa 460 GPa 0.95109 TPa–1 1.6856 TPa–1 57 GPa 158.27 GPa0.115230.64101Value
Anisotropy 2.469 1.7723 2.777 5.5630Anisotropy
Axis 0.4811
0.5494
-0.6832
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
-0.4023
0.5815
-0.7071
0.5710
0.4497
0.6869
0.3215
0.5807
-0.7480
Axis
1.0000
0.0002
-0.0000
0.4024
-0.5815
-0.7071
-0.6187
0.7856
0.0000
-0.3623
-0.6544
-0.6637
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