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 Li3N (Materials Project id mp-2251)

       123       28        7        0        0        0  
        28      123        7        0        0        0  
         7        7      137        0        0        0  
         0        0        0       17        0        0  
         0        0        0        0       17        0  
         0        0        0        0        0       48  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 51.889 GPaEV = 93.816 GPaGV = 39.133 GPaνV = 0.19867
ReussKR = 51.861 GPaER = 72.537 GPaGR = 28.628 GPaνR = 0.26689
HillKH = 51.875 GPaEH = 83.47 GPaGH = 33.881 GPaνH = 0.23182

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
17 GPa 17 GPa 48 GPa 95 GPa 131.88 GPa 156.12 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 53.977 GPa 136.35 GPa 6.3141 TPa–1 6.654 TPa–1 17 GPa 60.424 GPa0.0463580.58994Value
Anisotropy 2.526 1.0538 3.554 12.7258Anisotropy
Axis -0.0000
0.7175
0.6965
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.5235
0.4753
-0.7071
0.0000
0.0000
1.0000
0.4897
0.4897
0.7214
Axis
-0.1736
0.9848
-0.0000
-0.5235
-0.4754
-0.7071
0.1736
0.9848
-0.0000
0.5101
0.5101
-0.6925
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