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 HoS (Materials Project id mp-1240)

       231       32       32        0        0        0  
        32      231       32        0        0        0  
        32       32      231        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 = 98.333 GPaEV = 129.57 GPaGV = 50.6 GPaνV = 0.28038
ReussKR = 98.333 GPaER = 73.632 GPaGR = 26.771 GPaνR = 0.3752
HillKH = 98.333 GPaEH = 102.6 GPaGH = 38.686 GPaνH = 0.3261

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
18 GPa 18 GPa 18 GPa 199 GPa 199 GPa 295 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 50.895 GPa 223.21 GPa 3.3898 TPa–1 3.3898 TPa–1 18 GPa 99.5 GPa0.0343770.75184Value
Anisotropy 4.386 1.0000 5.528 21.8702Anisotropy
Axis 0.5774
0.5773
-0.5774
0.0000
0.0000
1.0000
0.4305
0.5610
0.7071
0.6088
0.0000
0.7934
0.0000
0.0000
1.0000
0.7071
0.0001
-0.7071
-0.7071
0.0000
0.7071
0.7071
-0.0000
-0.7071
Axis
1.0000
0.0000
-0.0000
-0.7071
-0.0002
-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