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 Ni3Hg (Materials Project id mp-973884)

       195      152      151        0        0        0  
       152      195      152        0        0        0  
       151      152      194        0        0        0  
         0        0        0       72        0        0  
         0        0        0        0       72        0  
         0        0        0        0        0       72  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 166 GPaEV = 140.76 GPaGV = 51.8 GPaνV = 0.35868
ReussKR = 165.99 GPaER = 103.63 GPaGR = 37.117 GPaνR = 0.39595
HillKH = 166 GPaEH = 122.44 GPaGH = 44.459 GPaνH = 0.37706

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
42.421 GPa 43.577 GPa 72 GPa 72 GPa 72 GPa 498 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 61.255 GPa 188.72 GPa 1.9607 TPa–1 2.0552 TPa–1 21.248 GPa 72 GPa-0.140460.88897Value
Anisotropy 3.081 1.0482 3.388Anisotropy
Axis 0.0000
1.0000
0.0000
-0.5773
0.5782
0.5766
0.0000
1.0000
0.0000
0.0000
0.0000
1.0000
-0.0001
0.7071
0.7071
0.0000
0.0000
1.0000
0.7074
0.0001
-0.7068
-0.7074
0.0000
0.7068
Axis
0.0001
0.7071
-0.7071
0.4962
0.8682
-0.0000
-0.7068
-0.0002
-0.7074
-0.0000
-1.0000
-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