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-2341)

       127       50       15        0        0        0  
        50      127       15        0        0        0  
        15       15      172        0        0        0  
         0        0        0       41        0        0  
         0        0        0        0       41        0  
         0        0        0        0        0       38  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 65.111 GPaEV = 113.78 GPaGV = 47.067 GPaνV = 0.20875
ReussKR = 65.063 GPaER = 107.36 GPaGR = 43.823 GPaνR = 0.22497
HillKH = 65.087 GPaEH = 110.59 GPaGH = 45.445 GPaνH = 0.2168

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
38 GPa 41 GPa 41 GPa 77 GPa 153.14 GPa 195.86 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 99.256 GPa 169.46 GPa 4.901 TPa–1 5.2344 TPa–1 38 GPa 61.493 GPa0.0529420.39293Value
Anisotropy 1.707 1.0680 1.618 7.4219Anisotropy
Axis 0.6002
0.6002
-0.5288
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
1.0000
-0.0002
-0.0000
0.7071
0.0001
-0.7071
-0.7071
0.7071
0.0000
0.7071
0.7071
0.0000
Axis
0.0002
1.0000
-0.0000
-0.7071
-0.0002
-0.7071
0.0000
0.0000
-1.0000
-0.7071
0.7071
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