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 PrN (Materials Project id mp-343)

       258       70       70        0        0        0  
        70      258       70        0        0        0  
        70       70      258        0        0        0  
         0        0        0       87        0        0  
         0        0        0        0       87        0  
         0        0        0        0        0       87  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 132.67 GPaEV = 219.81 GPaGV = 89.8 GPaνV = 0.22386
ReussKR = 132.67 GPaER = 219.55 GPaGR = 89.671 GPaνR = 0.22419
HillKH = 132.67 GPaEH = 219.68 GPaGH = 89.736 GPaνH = 0.22402

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
87 GPa 87 GPa 87 GPa 188 GPa 188 GPa 398 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 214.18 GPa 228.12 GPa 2.5126 TPa–1 2.5126 TPa–1 87 GPa 94 GPa0.203480.25003Value
Anisotropy 1.065 1.0000 1.08 1.2287Anisotropy
Axis -0.5774
0.5774
0.5773
0.0000
0.0000
1.0000
-0.3314
0.8001
0.5000
0.0000
0.0000
1.0000
-0.0000
-0.0000
1.0000
0.7071
0.0001
-0.7071
-0.7071
-0.0000
0.7071
0.7071
-0.0000
-0.7071
Axis
1.0000
0.0002
0.0000
-0.7071
-0.0002
-0.7071
0.0000
-1.0000
0.0000
-0.7071
0.0002
-0.7071
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