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 K2LiAlF6 (Materials Project id mp-9839)

        74       40       40        0        0        0  
        40       74       40        0        0        0  
        40       40       74        0        0        0  
         0        0        0       51        0        0  
         0        0        0        0       51        0  
         0        0        0        0        0       51  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 51.333 GPaEV = 90.276 GPaGV = 37.4 GPaνV = 0.2069
ReussKR = 51.333 GPaER = 71.792 GPaGR = 28.333 GPaνR = 0.26691
HillKH = 51.333 GPaEH = 81.258 GPaGH = 32.867 GPaνH = 0.23618

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
34 GPa 34 GPa 51 GPa 51 GPa 51 GPa 154 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 45.93 GPa 114.94 GPa 6.4935 TPa–1 6.4935 TPa–1 17 GPa 51 GPa-0.180850.6383Value
Anisotropy 2.502 1.0000 3Anisotropy
Axis 0.0000
1.0000
0.0000
0.5774
0.5774
0.5773
0.2588
0.0000
0.9659
0.2500
0.9330
0.2588
0.7071
0.0001
-0.7071
0.0000
0.0000
1.0000
0.7071
0.0001
-0.7071
-0.0000
0.7071
0.7071
Axis
-0.7071
-0.0002
-0.7071
0.7660
0.6428
-0.0000
-0.7071
-0.0002
-0.7071
-1.0000
-0.0000
0.0000
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