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 TmB6 (Materials Project id mp-571352)

       452       29       29        0        0        0  
        29      452       29        0        0        0  
        29       29      452        0        0        0  
         0        0        0        5        0        0  
         0        0        0        0        5        0  
         0        0        0        0        0        5  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 170 GPaEV = 224.28 GPaGV = 87.6 GPaνV = 0.28012
ReussKR = 170 GPaER = 24.222 GPaGR = 8.204 GPaνR = 0.47625
HillKH = 170 GPaEH = 131.37 GPaGH = 47.902 GPaνH = 0.37121

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
5 GPa 5 GPa 5 GPa 423 GPa 423 GPa 510 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 14.854 GPa 448.5 GPa 1.9608 TPa–1 1.9608 TPa–1 5 GPa 211.5 GPa0.00263340.95896Value
Anisotropy 30.19 1.0000 42.3364.1552Anisotropy
Axis 0.5774
0.5773
-0.5774
1.0000
0.0000
0.0000
0.7071
0.0000
0.7071
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.7071
0.0001
-0.7071
-0.7071
-0.0000
0.7071
0.7071
0.0000
0.7072
Axis
-0.7660
0.6428
-0.0000
-0.7071
-0.0002
-0.7071
0.0000
-1.0000
0.0000
0.7072
0.0000
-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