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 Cs2KNiF6 (Materials Project id mp-557958)

        76       43       49        0        0        0  
        43       76       49        0        0        0  
        49       49       75        0        0        0  
         0        0        0       17        0        0  
         0        0        0        0       17        0  
         0        0        0        0        0       12  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 56.556 GPaEV = 41.176 GPaGV = 14.933 GPaνV = 0.37866
ReussKR = 56.479 GPaER = 40.172 GPaGR = 14.54 GPaνR = 0.38146
HillKH = 56.518 GPaEH = 40.674 GPaGH = 14.736 GPaνH = 0.38005

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
12 GPa 17 GPa 17 GPa 24.295 GPa 33 GPa 169.7 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 33.413 GPa 45.986 GPa 5.0934 TPa–1 6.3061 TPa–1 12 GPa 17 GPa0.253580.50385Value
Anisotropy 1.376 1.2381 1.417 1.9870Anisotropy
Axis 0.7071
0.7071
0.0000
0.7924
0.0000
0.6100
0.0000
0.0000
1.0000
0.3827
0.9239
0.0000
1.0000
-0.0002
-0.0000
0.0000
0.0000
1.0000
-0.5038
0.5038
-0.7017
-0.4855
0.4855
-0.7270
Axis
0.0002
1.0000
-0.0000
0.7660
0.6428
-0.0000
-0.4962
0.4962
0.7125
-0.7071
-0.7071
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