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 ScN (Materials Project id mp-2857)

       389      105      105        0        0        0  
       105      389      105        0        0        0  
       105      105      389        0        0        0  
         0        0        0      165        0        0  
         0        0        0        0      165        0  
         0        0        0        0        0      165  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 199.67 GPaEV = 370.92 GPaGV = 155.8 GPaνV = 0.19038
ReussKR = 199.67 GPaER = 369.33 GPaGR = 154.96 GPaνR = 0.19171
HillKH = 199.67 GPaEH = 370.13 GPaGH = 155.38 GPaνH = 0.19104

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
165 GPa 165 GPa 165 GPa 284 GPa 284 GPa 599 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 344.36 GPa 388.1 GPa 1.6694 TPa–1 1.6694 TPa–1 142 GPa 165 GPa0.139860.23217Value
Anisotropy 1.127 1.0000 1.162 1.6600Anisotropy
Axis 0.0000
0.0000
1.0000
-0.5774
0.5774
0.5773
0.5610
0.5610
0.6088
0.0000
0.0000
1.0000
0.7071
-0.0003
0.7071
-0.0000
-0.0000
1.0000
0.7071
-0.0002
0.7071
0.7071
-0.0000
0.7071
Axis
0.7071
-0.0005
-0.7071
0.4962
0.8682
0.0000
0.7071
-0.0006
-0.7071
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