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 KMnP (Materials Project id mp-20422)

        64       24        5        0        0        0  
        24       64        5        0        0        0  
         5        5       17        0        0        0  
         0        0        0        2        0        0  
         0        0        0        0        2        0  
         0        0        0        0        0       43  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 23.667 GPaEV = 40.756 GPaGV = 16.8 GPaνV = 0.21298
ReussKR = 14.176 GPaER = 11.637 GPaGR = 4.2682 GPaνR = 0.36319
HillKH = 18.922 GPaEH = 26.656 GPaGH = 10.534 GPaνH = 0.26521

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
2 GPa 2 GPa 16.303 GPa 40 GPa 43 GPa 88.697 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 6.9363 GPa 85.527 GPa 8.2988 TPa–1 53.942 TPa–1 2 GPa 43 GPa-0.00550210.80059Value
Anisotropy 12.33 6.5000 21.5Anisotropy
Axis -0.0000
0.6698
0.7425
0.7071
0.7071
0.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
1.0000
0.0007
-0.0000
-0.7071
0.7071
0.0000
-0.6060
0.6061
0.5151
Axis
1.0000
0.0000
-0.0000
-0.0007
1.0000
-0.0000
-0.7071
-0.7071
0.0000
-0.3643
0.3641
-0.8571
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