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 K2P3 (Materials Project id mp-569857)

        26       12       11        0        0        0  
        12       36        9        0        0        0  
        11        9       28        0        0        0  
         0        0        0        7        0        0  
         0        0        0        0        9        0  
         0        0        0        0        0        9  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 17.111 GPaEV = 22.682 GPaGV = 8.8667 GPaνV = 0.27907
ReussKR = 16.875 GPaER = 22.01 GPaGR = 8.5803 GPaνR = 0.28261
HillKH = 16.993 GPaEH = 22.347 GPaGH = 8.7235 GPaνH = 0.28083

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
7 GPa 9 GPa 9 GPa 15.259 GPa 22.844 GPa 51.897 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 18.971 GPa 29.802 GPa 14.815 TPa–1 22.222 TPa–1 7 GPa 11.285 GPa0.128790.38433Value
Anisotropy 1.571 1.5000 1.612 2.9842Anisotropy
Axis -0.0000
0.6370
0.7709
0.0000
1.0000
0.0000
0.0000
1.0000
0.0000
0.0000
0.0000
1.0000
-0.0000
-0.0000
1.0000
0.0002
0.7071
-0.7071
-0.0000
0.0000
1.0000
-0.4779
0.7027
-0.5270
Axis
0.0000
1.0000
0.0000
0.0002
-0.7071
-0.7071
-0.0000
-1.0000
0.0000
-0.2495
-0.6839
-0.6856
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