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 Ba3N (Materials Project id mp-10736)

        21        7        4        0        0        0  
         7       21        4        0        0        0  
         4        4       51        0        0        0  
         0        0        0        2        0        0  
         0        0        0        0        2        0  
         0        0        0        0        0        7  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 13.667 GPaEV = 18.806 GPaGV = 7.4 GPaνV = 0.27066
ReussKR = 12.246 GPaER = 10.131 GPaGR = 3.719 GPaνR = 0.36211
HillKH = 12.956 GPaEH = 14.591 GPaGH = 5.5595 GPaνH = 0.3123

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
2 GPa 2 GPa 7 GPa 14 GPa 26.684 GPa 52.316 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 7.0047 GPa 49.857 GPa 14.327 TPa–1 33.668 TPa–1 2 GPa 12.536 GPa0.0606580.77223Value
Anisotropy 7.118 2.3500 6.268 12.7309Anisotropy
Axis 0.7351
-0.0000
0.6780
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.3827
0.9239
0.0000
0.0000
0.0000
1.0000
-0.4226
0.5669
-0.7071
0.0385
0.5028
-0.8635
0.3007
0.5223
-0.7980
Axis
1.0000
0.0000
-0.0000
0.4227
-0.5669
-0.7071
-0.9971
0.0763
0.0000
0.3981
0.6916
0.6026
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