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 NaCSN (Materials Project id mp-6633)

        33       17       11        0        0        0  
        17       32       10        0        0        0  
        11       10       24        0        0        0  
         0        0        0        7        0        0  
         0        0        0        0        5        0  
         0        0        0        0        0       10  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 18.333 GPaEV = 20.494 GPaGV = 7.8 GPaνV = 0.31369
ReussKR = 17.414 GPaER = 19.193 GPaGR = 7.2905 GPaνR = 0.31631
HillKH = 17.874 GPaEH = 19.843 GPaGH = 7.5453 GPaνH = 0.31497

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
5 GPa 7 GPa 10 GPa 15.382 GPa 17.283 GPa 56.336 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 14.703 GPa 26.736 GPa 12.553 TPa–1 29.514 TPa–1 5 GPa 10 GPa0.163950.4851Value
Anisotropy 1.818 2.3511 2 2.9588Anisotropy
Axis 0.6772
0.0000
0.7358
0.7095
0.7047
-0.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
1.0000
-0.0002
-0.0000
0.4489
0.4846
-0.7508
-0.6380
0.4497
0.6251
Axis
1.0000
0.0000
-0.0000
0.0002
1.0000
0.0000
-0.5241
0.8233
0.2180
-0.6445
0.1324
-0.7530
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