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-1700)

       284      150      150        0        0        0  
       150      284      150        0        0        0  
       150      150      284        0        0        0  
         0        0        0      179        0        0  
         0        0        0        0      179        0  
         0        0        0        0        0      179  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 194.67 GPaEV = 327.37 GPaGV = 134.2 GPaνV = 0.21972
ReussKR = 194.67 GPaER = 271.88 GPaGR = 107.27 GPaνR = 0.26723
HillKH = 194.67 GPaEH = 300.15 GPaGH = 120.74 GPaνH = 0.24302

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
134 GPa 134 GPa 179 GPa 179 GPa 179 GPa 584 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 180.31 GPa 411.02 GPa 1.7123 TPa–1 1.7123 TPa–1 67 GPa 179 GPa-0.130140.59691Value
Anisotropy 2.279 1.0000 2.672Anisotropy
Axis 1.0000
0.0000
0.0000
0.5774
0.5774
0.5773
0.0000
0.0000
1.0000
0.7934
0.0000
0.6088
0.7071
-0.0003
0.7071
0.0000
0.0000
1.0000
0.7071
-0.0003
0.7071
-0.0000
0.7071
-0.7071
Axis
0.7071
-0.0005
-0.7071
0.7660
0.6428
-0.0000
0.7071
-0.0005
-0.7071
-1.0000
-0.0000
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