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 AlN (Materials Project id mp-661)

       376      129       98        0        0        0  
       129      376       98        0        0        0  
        98       98      353        0        0        0  
         0        0        0      113        0        0  
         0        0        0        0      113        0  
         0        0        0        0        0      124  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 195 GPaEV = 302.84 GPaGV = 122 GPaνV = 0.24116
ReussKR = 194.21 GPaER = 301.21 GPaGR = 121.31 GPaνR = 0.2415
HillKH = 194.6 GPaEH = 302.03 GPaGH = 121.66 GPaνH = 0.24133

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
113 GPa 113 GPa 124 GPa 247 GPa 270.94 GPa 587.06 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 287.2 GPa 319.92 GPa 1.6032 TPa–1 1.9427 TPa–1 113 GPa 132.75 GPa0.194060.29184Value
Anisotropy 1.114 1.2118 1.175 1.5039Anisotropy
Axis 0.6959
0.0000
0.7181
0.7071
0.7071
0.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.5000
0.5000
-0.7071
0.0000
0.0000
1.0000
1.0000
-0.0002
0.0000
Axis
1.0000
0.0001
-0.0000
-0.5000
-0.5000
-0.7071
-0.7660
0.6428
0.0000
0.0002
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