Voronoi Construction

[zhubq]

Hi,
during grain input, we can choose voronoi construction.
As far as I know, voronoi construction assign the points nearest to the Voronoi site to its cell.
If there are two round grains overlapping each other (attached below), why is the boundary between them like that, it seems not equidistant line of the two circle-centre points.
I guess it is weighted construction (not equidistant but proportional to the radius), right?

[janin]

Yes, it is exactly as you supposed. The radii are used as weigthing factors for the distances. The simple Voronoi construction with straight boundaries is obtained for equal radii. The curved boundaries which can be achieved by chosing slightly different radii are often more realistic, especially to define initial structures for grain growth simulations.

Regards,
Janin

[zhubq]

Thank you for your reply.
actually I used simple Voronoi construction to get straight grain boundaries.
Then to simulate grain growth, the boudary especially near the triple point will be moved and curved,becoming the source for further grain growth. From this point, the triple points have a inflence on the microstructure evolution.
Is that illusive?
Thank you.

Yes, it is exactly as you supposed. The radii are used as weigthing factors for the distances. The simple Voronoi construction with straight boundaries is obtained for equal radii. The curved boundaries which can be achieved by chosing slightly different radii are often more realistic, especially to define initial structures for grain growth simulations.

Regards,
Janin

[janin]

I don't see why your simulation results should be illusive. To my opinion, you just described the typical mechanisms of grain growth. The triple junctions move in order to adjust the accurate angle and the whole boundaries follow their movement, affected by the curvature. Whether you now start with a weighted Voronoi construction (curved boundaries) or with a simple Voronoi construction (straight boundaries) depends on your basic initial assumptions. If you assume that your initial structure has been obtained directly by growth, than the simple construction is most appropriate. On the other hand, if you assume that some ripening of the structure has already occured and you don't want to simulate this initial ripening explicitlly, you could model it by the weighted construction.

Regards,

Janin