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 HgF (Materials Project id mp-706)

        37       21       31        0        0        0  
        21       37       31        0        0        0  
        31       31      199        0        0        0  
         0        0        0       10        0        0  
         0        0        0        0       10        0  
         0        0        0        0        0       14  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 48.778 GPaEV = 51.543 GPaGV = 19.467 GPaνV = 0.32388
ReussKR = 28.976 GPaER = 30.968 GPaGR = 11.714 GPaνR = 0.32187
HillKH = 38.877 GPaEH = 41.256 GPaGH = 15.59 GPaνH = 0.32313

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
10 GPa 10 GPa 14 GPa 16 GPa 45.48 GPa 211.52 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 23.709 GPa 165.86 GPa -0.4158 TPa–1 17.464 TPa–1 8 GPa 24.586 GPa0.0774760.63808Value
Anisotropy 6.996 3.073 8.2359Anisotropy
Axis 0.9419
0.0000
0.3359
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
-0.7071
0.7071
-0.0000
0.5000
0.5000
-0.7071
1.0000
0.0002
0.0000
-0.2920
0.2920
-0.9107
Axis
-0.7071
-0.7071
0.0000
0.5000
0.5000
0.7071
-0.0000
0.0002
-1.0000
-0.6440
0.6440
0.4130
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