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 Co3Pt (Materials Project id mp-865193)

       323      170      131        0        0        0  
       170      323      131        0        0        0  
       131      131      398        0        0        0  
         0        0        0       91        0        0  
         0        0        0        0       91        0  
         0        0        0        0        0       77  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 212 GPaEV = 242.49 GPaGV = 92.6 GPaνV = 0.30936
ReussKR = 211.62 GPaER = 235.22 GPaGR = 89.455 GPaνR = 0.31475
HillKH = 211.81 GPaEH = 238.86 GPaGH = 91.028 GPaνH = 0.31205

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
77 GPa 91 GPa 91 GPa 153 GPa 254.25 GPa 636.75 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 221.41 GPa 328.38 GPa 1.4269 TPa–1 1.6492 TPa–1 76.5 GPa 109.41 GPa0.179930.45334Value
Anisotropy 1.483 1.1558 1.43 2.5195Anisotropy
Axis 0.9472
0.0001
0.3208
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
-0.7071
0.7072
0.0000
0.5000
0.5000
0.7071
1.0000
0.0002
-0.0000
1.0000
-0.0001
-0.0000
Axis
-0.7072
-0.7071
0.0000
0.5000
0.5000
-0.7071
-0.0000
0.0000
-1.0000
0.0001
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