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 CsN3 (Materials Project id mp-510557)

        24       11        9        0        0        0  
        11       24        9        0        0        0  
         9        9       26        0        0        0  
         0        0        0        5        0        0  
         0        0        0        0        5        0  
         0        0        0        0        0        9  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 14.667 GPaEV = 17.669 GPaGV = 6.8 GPaνV = 0.29921
ReussKR = 14.667 GPaER = 16.737 GPaGR = 6.3889 GPaνR = 0.30981
HillKH = 14.667 GPaEH = 17.205 GPaGH = 6.5945 GPaνH = 0.30449

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
5 GPa 5 GPa 9 GPa 13 GPa 17 GPa 44 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 14.302 GPa 22.145 GPa 22.727 TPa–1 22.727 TPa–1 5 GPa 9 GPa0.166970.49324Value
Anisotropy 1.548 1.0000 1.8 2.9541Anisotropy
Axis 0.7495
0.0000
-0.6620
0.7071
0.7071
0.0000
0.2500
0.4330
0.8660
0.9808
-0.0002
0.1951
0.0000
0.0000
1.0000
1.0000
-0.0002
-0.0000
0.5237
0.5237
-0.6719
0.5045
0.5049
0.7004
Axis
-0.7660
0.6428
-0.0000
0.0002
1.0000
-0.0000
-0.7071
0.7071
0.0000
0.4956
0.4949
-0.7137
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