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 Ge3N4 (Materials Project id mp-13852)

       283      143       83        0        0        0  
       143      283       83        0        0        0  
        83       83      392        0        0        0  
         0        0        0       66        0        0  
         0        0        0        0       66        0  
         0        0        0        0        0       70  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 175.11 GPaEV = 216.52 GPaGV = 83.667 GPaνV = 0.29392
ReussKR = 174.5 GPaER = 199.25 GPaGR = 76.066 GPaνR = 0.3097
HillKH = 174.81 GPaEH = 207.93 GPaGH = 79.867 GPaνH = 0.30175

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
66 GPa 66 GPa 70 GPa 140 GPa 290.4 GPa 527.6 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 178.85 GPa 359.66 GPa 1.697 TPa–1 2.0168 TPa–1 66 GPa 114.75 GPa0.111680.47255Value
Anisotropy 2.011 1.1885 1.739 4.2312Anisotropy
Axis 0.5598
0.5895
0.5824
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.7071
0.0001
-0.7071
0.9336
0.3584
-0.0000
1.0000
-0.0000
-0.0000
Axis
0.1736
0.9848
-0.0000
-0.7071
-0.0002
-0.7071
0.0000
-0.0000
1.0000
0.0000
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