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 Na3P11 (Materials Project id mp-473)

        20       10        8        0        0        0  
        10       20        9        0        0        0  
         8        9       30        0        0        0  
         0        0        0        5        0        0  
         0        0        0        0        6        0  
         0        0        0        0        0        6  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 13.778 GPaEV = 16.325 GPaGV = 6.2667 GPaνV = 0.30252
ReussKR = 13.488 GPaER = 15.514 GPaGR = 5.9289 GPaνR = 0.30831
HillKH = 13.633 GPaEH = 15.92 GPaGH = 6.0978 GPaνH = 0.30538

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
5 GPa 6 GPa 6 GPa 9.961 GPa 18.01 GPa 42.029 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 13.333 GPa 25.133 GPa 17.241 TPa–1 29.31 TPa–1 5 GPa 8.1242 GPa0.134870.42902Value
Anisotropy 1.885 1.7000 1.625 3.1809Anisotropy
Axis 0.0000
0.8660
0.5000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
-0.0003
-0.0000
1.0000
0.5706
0.4176
-0.7071
1.0000
0.0003
0.0000
0.2990
0.5130
0.8046
Axis
0.0000
1.0000
0.0000
-0.5708
-0.4174
-0.7071
0.0000
0.0002
-1.0000
0.2714
0.7627
-0.5871
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