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 Rb2CrF6 (Materials Project id mp-560562)

        53       37       13        0        0        0  
        37       53       13        0        0        0  
        13       13       21        0        0        0  
         0        0        0       15        0        0  
         0        0        0        0       15        0  
         0        0        0        0        0       17  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 28.111 GPaEV = 35.282 GPaGV = 13.667 GPaνV = 0.29082
ReussKR = 19.4 GPaER = 29.312 GPaGR = 11.742 GPaνR = 0.24818
HillKH = 23.756 GPaEH = 32.346 GPaGH = 12.704 GPaνH = 0.27306

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
15 GPa 15 GPa 16 GPa 16.407 GPa 17 GPa 94.593 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 17.244 GPa 46.574 GPa 5.1546 TPa–1 41.237 TPa–1 8 GPa 17 GPa-0.0866620.64418Value
Anisotropy 2.701 8.0000 2.125Anisotropy
Axis 0.0000
0.0000
1.0000
0.7071
0.7071
0.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
-0.7071
0.7071
-0.0000
1.0000
-0.0000
0.0000
0.7192
-0.0002
0.6948
0.9940
-0.0004
0.1097
Axis
-0.7071
-0.7071
0.0000
0.0000
1.0000
0.0000
0.6948
-0.0006
-0.7192
0.0004
1.0000
0.0001
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