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 KLiSe (Materials Project id mp-8756)

        55       10       21        0        0        0  
        10       55       21        0        0        0  
        21       21       38        0        0        0  
         0        0        0       17        0        0  
         0        0        0        0       17        0  
         0        0        0        0        0       21  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 28 GPaEV = 43.243 GPaGV = 17.4 GPaνV = 0.2426
ReussKR = 27.86 GPaER = 39.965 GPaGR = 15.848 GPaνR = 0.26091
HillKH = 27.93 GPaEH = 41.615 GPaGH = 16.624 GPaνH = 0.25167

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
17 GPa 17 GPa 18.877 GPa 21 GPa 45 GPa 84.123 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 24.431 GPa 46.348 GPa 10.705 TPa–1 14.484 TPa–1 10.959 GPa 22.5 GPa-0.0369920.57307Value
Anisotropy 1.897 1.3529 2.053Anisotropy
Axis 0.0000
0.0000
1.0000
0.8844
0.0000
-0.4667
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.4997
0.5003
0.7071
0.7071
0.7071
0.0000
1.0000
0.0007
0.0000
1.0000
0.0003
0.0000
Axis
0.5003
0.4997
-0.7071
-0.7071
0.7071
-0.0000
-0.0007
1.0000
0.0000
0.0000
0.0002
-1.0000
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