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 NiN (Materials Project id mp-1009488)

       359      209      209        0        0        0  
       209      359      209        0        0        0  
       209      209      359        0        0        0  
         0        0        0       80        0        0  
         0        0        0        0       80        0  
         0        0        0        0        0       80  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 259 GPaEV = 212.65 GPaGV = 78 GPaνV = 0.36316
ReussKR = 259 GPaER = 212.46 GPaGR = 77.922 GPaνR = 0.36328
HillKH = 259 GPaEH = 212.56 GPaGH = 77.961 GPaνH = 0.36322

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
80 GPa 80 GPa 80 GPa 150 GPa 150 GPa 777 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 205.19 GPa 217.6 GPa 1.287 TPa–1 1.287 TPa–1 75 GPa 80 GPa0.339730.38439Value
Anisotropy 1.06 1.0000 1.067 1.1314Anisotropy
Axis 0.0000
0.0000
1.0000
0.5774
0.5774
0.5773
0.9659
0.0000
0.2591
0.0990
0.3696
0.9239
0.7071
0.0001
-0.7071
-0.0000
0.0000
1.0000
0.7071
-0.0002
0.7071
0.7071
-0.0005
0.7071
Axis
-0.7071
-0.0002
-0.7071
-0.5000
0.8660
-0.0000
0.7071
-0.0005
-0.7071
0.0004
1.0000
0.0004
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