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-672289)

       291      109       95        0       11        0  
       109      291       95        0      -11        0  
        95       95      311        0        0        0  
         0        0        0       84        0      -11  
        11      -11        0        0       84        0  
         0        0        0      -11        0       91  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 165.67 GPaEV = 231.61 GPaGV = 91.4 GPaνV = 0.267
ReussKR = 165.65 GPaER = 227.51 GPaGR = 89.493 GPaνR = 0.2711
HillKH = 165.66 GPaEH = 229.56 GPaGH = 90.446 GPaνH = 0.26904

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
75.957 GPa 81.59 GPa 99.043 GPa 184.41 GPa 213.97 GPa 497.03 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 197.66 GPa 265.88 GPa 1.9746 TPa–1 2.031 TPa–1 75.957 GPa 104.29 GPa0.164430.361Value
Anisotropy 1.345 1.0286 1.373 2.1955Anisotropy
Axis 0.4110
0.7119
0.5695
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.9914
0.1305
0.0000
0.2951
0.5111
-0.8072
0.6001
0.0001
0.7999
0.2693
0.4665
-0.8425
0.2904
0.5031
-0.8140
Axis
-0.8660
0.5000
-0.0000
0.7999
0.0002
-0.6001
-0.8660
0.5000
0.0000
0.4070
0.7049
0.5809
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