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-975272)

        12        5        6        0        0       -0  
         5       12        6        0        0        0  
         6        6       16        0        0       -0  
         0        0        0        4        0        0  
         0        0        0        0        4        0  
        -0        0       -0        0        0        4  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 8.2222 GPaEV = 10.177 GPaGV = 3.9333 GPaνV = 0.29371
ReussKR = 8 GPaER = 10.062 GPaGR = 3.899 GPaνR = 0.29037
HillKH = 8.1111 GPaEH = 10.12 GPaGH = 3.9162 GPaνH = 0.29206

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
4 GPa 4 GPa 4 GPa 7 GPa 8 GPa 25 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 8.9744 GPa 11.765 GPa 25 TPa–1 50 TPa–1 3.5 GPa 4.0404 GPa0.219510.35294Value
Anisotropy 1.311 2.0000 1.154 1.6078Anisotropy
Axis 1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
0.7071
0.7071
-0.0000
0.4998
0.5002
0.7071
0.7071
0.7071
0.0000
0.0000
0.0000
1.0000
Axis
-0.7071
0.7071
0.0000
0.5003
0.4997
-0.7071
-0.7071
0.7071
-0.0000
0.1736
0.9848
-0.0000
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