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 Zr3N4 (Materials Project id mp-11661)

       352      117      117        0        0        0  
       117      352      117        0        0        0  
       117      117      352        0        0        0  
         0        0        0      107        0        0  
         0        0        0        0      107        0  
         0        0        0        0        0      107  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 195.33 GPaEV = 280.39 GPaGV = 111.2 GPaνV = 0.26076
ReussKR = 195.33 GPaER = 279.9 GPaGR = 110.97 GPaνR = 0.26118
HillKH = 195.33 GPaEH = 280.14 GPaGH = 111.08 GPaνH = 0.26097

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
107 GPa 107 GPa 107 GPa 235 GPa 235 GPa 586 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 271.44 GPa 293.62 GPa 1.7065 TPa–1 1.7065 TPa–1 107 GPa 117.5 GPa0.235060.29282Value
Anisotropy 1.082 1.0000 1.098 1.2457Anisotropy
Axis 0.5774
0.5774
0.5773
1.0000
0.0000
0.0000
0.9670
0.0000
0.2549
0.1122
0.8596
0.4986
0.0000
0.0000
1.0000
0.7071
0.0001
-0.7071
-0.7071
-0.0000
-0.7071
0.7071
-0.0002
0.7071
Axis
-0.9404
0.3400
-0.0000
-0.7071
-0.0002
-0.7071
0.0000
-1.0000
-0.0000
0.7071
-0.0006
-0.7071
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