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 HfSb2 (Materials Project id mp-1018717)

       143       86       52        0        0        0  
        86      143       52        0        0        0  
        52       52      167        0        0        0  
         0        0        0       22        0        0  
         0        0        0        0       22        0  
         0        0        0        0        0       82  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 92.556 GPaEV = 111.1 GPaGV = 42.733 GPaνV = 0.29994
ReussKR = 92.493 GPaER = 86.643 GPaGR = 32.236 GPaνR = 0.34387
HillKH = 92.524 GPaEH = 99.075 GPaGH = 37.485 GPaνH = 0.32153

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
22 GPa 22 GPa 57 GPa 82 GPa 118.19 GPa 277.81 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 65.187 GPa 178.83 GPa 3.5024 TPa–1 3.8069 TPa–1 22 GPa 82 GPa0.067350.65881Value
Anisotropy 2.743 1.0870 3.727 9.7818Anisotropy
Axis 0.7684
0.0000
0.6400
0.7071
0.7071
0.0000
0.3827
0.9239
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
1.0000
0.0007
0.0000
0.6107
0.6107
0.5040
0.5220
0.5219
-0.6746
Axis
-0.7880
0.6157
-0.0000
-0.0007
1.0000
-0.0000
-0.7071
0.7071
-0.0000
-0.4770
-0.4771
-0.7382
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