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 Al6C3N2 (Materials Project id mp-5798)

       313      122       58        0        0        0  
       122      313       58       -0        0        0  
        58       58      382        0        0        0  
         0       -0        0       94        0        0  
         0        0        0        0       94        0  
         0        0        0        0        0       95  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 164.89 GPaEV = 265.8 GPaGV = 107.93 GPaνV = 0.23133
ReussKR = 164.88 GPaER = 256.03 GPaGR = 103.14 GPaνR = 0.2412
HillKH = 164.89 GPaEH = 260.94 GPaGH = 105.54 GPaνH = 0.23625

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
94 GPa 94 GPa 95 GPa 191 GPa 322.3 GPa 494.7 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 237.67 GPa 366.53 GPa 2.0007 TPa–1 2.0321 TPa–1 94 GPa 137.52 GPa0.0949910.37437Value
Anisotropy 1.542 1.0157 1.463 3.9411Anisotropy
Axis -0.5763
0.5763
-0.5795
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.6088
0.7934
0.0000
0.0000
0.0000
1.0000
0.7071
-0.0003
0.7071
-0.7071
0.7071
0.0000
-0.7071
0.7071
-0.0000
Axis
0.4998
0.8662
-0.0000
0.7071
-0.0005
-0.7071
0.0000
-0.0000
1.0000
-0.7071
-0.7071
-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