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 Pr (Materials Project id mp-38)

        59       22       16        0        0        0  
        22       59       16        0        0        0  
        16       16       65        0        0        0  
         0        0        0       17        0        0  
         0        0        0        0       17        0  
         0        0        0        0        0       18  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 32.333 GPaEV = 47.664 GPaGV = 19 GPaνV = 0.25431
ReussKR = 32.333 GPaER = 46.931 GPaGR = 18.652 GPaνR = 0.25809
HillKH = 32.333 GPaEH = 47.298 GPaGH = 18.826 GPaνH = 0.2562

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
17 GPa 17 GPa 18 GPa 37 GPa 49 GPa 97 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 44.049 GPa 58.679 GPa 10.309 TPa–1 10.309 TPa–1 17 GPa 22.662 GPa0.162410.34019Value
Anisotropy 1.332 1.0000 1.333 2.0946Anisotropy
Axis 0.5606
0.5606
0.6094
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.9239
0.0000
0.3827
0.0000
0.0000
1.0000
0.7071
-0.0003
0.7071
0.7071
0.7071
-0.0000
-0.7071
0.7071
0.0000
Axis
-0.1736
0.9848
-0.0000
0.7071
-0.0005
-0.7071
0.0000
-0.0000
-1.0000
-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