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 Rb2NaErF6 (Materials Project id mp-13815)

        59       17       17        0        0        0  
        17       59       17        0        0        0  
        17       17       59        0        0        0  
         0        0        0       18        0        0  
         0        0        0        0       18        0  
         0        0        0        0        0       18  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 31 GPaEV = 47.743 GPaGV = 19.2 GPaνV = 0.24332
ReussKR = 31 GPaER = 47.518 GPaGR = 19.091 GPaνR = 0.24453
HillKH = 31 GPaEH = 47.631 GPaGH = 19.145 GPaνH = 0.24392

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
18 GPa 18 GPa 18 GPa 42 GPa 42 GPa 93 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 45.243 GPa 51.395 GPa 10.753 TPa–1 10.753 TPa–1 18 GPa 21 GPa0.202990.29552Value
Anisotropy 1.136 1.0000 1.167 1.4559Anisotropy
Axis 0.5774
0.5773
-0.5774
1.0000
0.0000
0.0000
0.7934
0.0000
0.6088
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.7071
-0.0003
0.7071
0.7071
-0.0000
0.7071
0.7071
-0.0000
-0.7071
Axis
1.0000
0.0000
-0.0000
0.7071
-0.0005
-0.7071
0.0000
1.0000
0.0000
-0.7071
0.0002
-0.7071
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