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 ErPt2 (Materials Project id mp-480)

       239      140      140        0        0        0  
       140      239      140        0        0        0  
       140      140      239        0        0        0  
         0        0        0       92        0        0  
         0        0        0        0       92        0  
         0        0        0        0        0       92  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 173 GPaEV = 196.59 GPaGV = 75 GPaνV = 0.31061
ReussKR = 173 GPaER = 181.5 GPaGR = 68.481 GPaνR = 0.32515
HillKH = 173 GPaEH = 189.08 GPaGH = 71.741 GPaνH = 0.31784

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
92 GPa 92 GPa 92 GPa 99 GPa 99 GPa 519 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 135.57 GPa 234.44 GPa 1.9268 TPa–1 1.9268 TPa–1 49.5 GPa 92 GPa0.0776560.54029Value
Anisotropy 1.729 1.0000 1.859 6.9575Anisotropy
Axis 0.0000
0.0000
1.0000
0.5774
0.5773
-0.5774
0.0000
0.0000
1.0000
0.8660
0.0000
0.5000
0.7071
0.0001
-0.7071
-0.0000
0.0000
1.0000
0.7071
-0.0000
-0.7071
-0.7071
-0.0000
0.7071
Axis
-0.7071
-0.0002
-0.7071
-0.1736
0.9848
-0.0000
-0.7071
0.0002
-0.7071
0.0000
-1.0000
-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