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 Ge2N2O (Materials Project id mp-4187)

       187       80       61        0        0        0  
        80      207       59        0        0        0  
        61       59      277        0        0        0  
         0        0        0       35        0        0  
         0        0        0        0       97        0  
         0        0        0        0        0       47  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 119 GPaEV = 169.66 GPaGV = 67.2 GPaνV = 0.26238
ReussKR = 117.45 GPaER = 147.35 GPaGR = 57.071 GPaνR = 0.29091
HillKH = 118.22 GPaEH = 158.62 GPaGH = 62.135 GPaνH = 0.27639

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
35 GPa 47 GPa 97 GPa 115.99 GPa 193 GPa 362 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 107.55 GPa 250.84 GPa 2.2518 TPa–1 3.3797 TPa–1 35 GPa 97 GPa0.0501510.55924Value
Anisotropy 2.332 1.5009 2.771 11.1512Anisotropy
Axis 0.0000
0.7462
0.6658
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
-0.0003
-0.0000
1.0000
-0.0000
0.0000
1.0000
0.7129
0.3420
-0.6122
0.4255
0.6281
0.6515
Axis
0.0000
1.0000
0.0000
-1.0000
0.0000
-0.0000
-0.6991
0.2778
-0.6589
-0.1969
0.7669
-0.6108
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