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 Pr2Tl (Materials Project id mp-12600)

        67       46       24        0        0        0  
        46       67       24        0        0        0  
        24       24       69        0        0        0  
         0        0        0       21        0        0  
         0        0        0        0       21        0  
         0        0        0        0        0       10  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 43.444 GPaEV = 46.673 GPaGV = 17.667 GPaνV = 0.32095
ReussKR = 42.871 GPaER = 40.697 GPaGR = 15.165 GPaνR = 0.34179
HillKH = 43.158 GPaEH = 43.706 GPaGH = 16.416 GPaνH = 0.33122

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
10 GPa 21 GPa 21 GPa 21 GPa 50.553 GPa 131.45 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 33.121 GPa 58.805 GPa 6.772 TPa–1 9.7818 TPa–1 10 GPa 21 GPa0.084980.65607Value
Anisotropy 1.775 1.4444 2.1 7.7204Anisotropy
Axis 0.7071
0.7071
0.0000
0.0000
0.0000
1.0000
0.5000
0.8660
0.0000
0.0000
0.0000
1.0000
1.0000
-0.0002
0.0000
0.0000
0.0000
1.0000
-0.5431
0.5432
-0.6403
-0.7071
0.7071
-0.0000
Axis
0.0002
1.0000
0.0000
0.1736
0.9848
-0.0000
0.4527
-0.4528
-0.7681
-0.7071
-0.7071
-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