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-1009838)

       444      150      100        0        0        0  
       150      444      100        0        0        0  
       100      100      576        0        0        0  
         0        0        0       81        0        0  
         0        0        0        0       81        0  
         0        0        0        0        0      147  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 240.44 GPaEV = 343.42 GPaGV = 136.07 GPaνV = 0.26195
ReussKR = 239.33 GPaER = 301.57 GPaGR = 116.89 GPaνR = 0.28999
HillKH = 239.89 GPaEH = 322.72 GPaGH = 126.48 GPaνH = 0.27579

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
81 GPa 81 GPa 147 GPa 294 GPa 443.29 GPa 726.71 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 246.29 GPa 542.33 GPa 1.2231 TPa–1 1.4776 TPa–1 81 GPa 197.65 GPa0.127550.53048Value
Anisotropy 2.202 1.2081 2.44 4.1591Anisotropy
Axis 0.7209
0.1785
0.6697
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.5291
0.4691
-0.7071
-0.5005
0.1844
0.8459
0.6232
0.2311
-0.7471
Axis
1.0000
0.0000
-0.0000
-0.5291
-0.4692
-0.7071
-0.3457
-0.9383
-0.0000
-0.7005
-0.2597
-0.6647
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