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 TbHg3 (Materials Project id mp-867288)

        79       47       42        0        0        0  
        47       79       42        0        0        0  
        42       42      100        0        0        0  
         0        0        0       20        0        0  
         0        0        0        0       20        0  
         0        0        0        0        0       16  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 57.778 GPaEV = 52.988 GPaGV = 19.667 GPaνV = 0.34715
ReussKR = 57.418 GPaER = 51.328 GPaGR = 18.996 GPaνR = 0.35101
HillKH = 57.598 GPaEH = 52.159 GPaGH = 19.331 GPaνH = 0.34907

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
16 GPa 20 GPa 20 GPa 32 GPa 52.197 GPa 173.8 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 47.312 GPa 72 GPa 4.6296 TPa–1 6.3933 TPa–1 16 GPa 22.581 GPa0.219040.47849Value
Anisotropy 1.522 1.3810 1.411 2.1845Anisotropy
Axis 0.9239
0.3827
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
0.9573
0.2890
0.0000
0.3338
0.6234
0.7071
0.9470
0.3213
-0.0000
-0.4113
0.9115
0.0000
Axis
-0.2890
0.9573
-0.0000
0.3338
0.6234
-0.7071
0.0000
0.0000
1.0000
-0.9115
-0.4113
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