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 Hg (Materials Project id mp-1077098)

         7        4        4        0        0        0  
         4       10        4        0        0        0  
         4        4       14        0        0        0  
         0        0        0        4        0        0  
         0        0        0        0        2        0  
         0        0        0        0        0        4  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 6.1111 GPaEV = 8.3179 GPaGV = 3.2667 GPaνV = 0.27315
ReussKR = 5.6667 GPaER = 7.4032 GPaGR = 2.8868 GPaνR = 0.28226
HillKH = 5.8889 GPaEH = 7.8611 GPaGH = 3.0767 GPaνH = 0.27752

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
2 GPa 4 GPa 4 GPa 4.0681 GPa 7.9077 GPa 19.024 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 4.9231 GPa 11.333 GPa 29.412 TPa–1 98.039 TPa–1 2 GPa 4.038 GPa0.0456560.52809Value
Anisotropy 2.302 3.3333 2.019 11.5667Anisotropy
Axis 0.9682
0.0000
-0.2500
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
-0.3549
0.6115
0.7072
0.5446
0.7004
0.4614
0.3663
0.5776
0.7295
Axis
1.0000
0.0000
-0.0000
-0.3549
0.6117
-0.7070
-0.5399
0.7137
-0.4462
-0.8126
-0.1834
0.5533
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