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 Mg2Tl (Materials Project id mp-567244)

        53       25       25        0        0        0  
        25       53       25        0        0        0  
        25       25       47        0        0        0  
         0        0        0        9        0        0  
         0        0        0        0        9        0  
         0        0        0        0        0       14  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 33.667 GPaEV = 31.215 GPaGV = 11.6 GPaνV = 0.34547
ReussKR = 33.556 GPaER = 30.099 GPaGR = 11.144 GPaνR = 0.3505
HillKH = 33.611 GPaEH = 30.658 GPaGH = 11.372 GPaνH = 0.34798

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
9 GPa 9 GPa 14 GPa 23.896 GPa 28 GPa 101.1 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 26.489 GPa 36.253 GPa 9.106 TPa–1 11.589 TPa–1 9 GPa 14 GPa0.24490.48082Value
Anisotropy 1.369 1.2727 1.556 1.9634Anisotropy
Axis 0.6330
0.1495
-0.7596
1.0000
0.0000
0.0000
0.7934
0.6088
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.8329
0.5534
-0.0000
0.0554
0.7538
-0.6548
0.5704
0.4959
-0.6548
Axis
1.0000
0.0000
-0.0000
-0.5534
0.8329
-0.0000
-0.9973
0.0733
0.0000
-0.4942
-0.4296
-0.7558
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