## Bridging the gap between dendrites and gamma'-precipitation in Ni-base superalloys

### Re: Bridging the gap between dendrites and gamma'-precipitation in Ni-base superalloys

Hi Chamara,

Sorry for the late answer, I somehow missed your post...

If the precipitates in reality have a size of 40nm, and your grid resolution is 50nm, then each precipitate will just be represented by a single grid cell (or perhaps 5 cells in 2D).

However, the critical radius cannot be derived from the final size of the precipitates. The only way to estimate it is based on a "reasonable" nucleation undercooling. But what you can say for sure is that it cannot be bigger than the final size of the preciptiate! Otherwise the precipitate could not form, and you should think of revising the assumed interfacial energy.

The required undercooling of course depends on the interfacial energy between the precipitate and matrix phase. It is given in the .log file when nucleation is checked for the first time. There may be numerical reasons why the seeds don't grow even when the required undercooling is reached. It often helps to define an initial of 0<r<Δx in order to start with a somewhat bigger initial fraction.

Bernd

Sorry for the late answer, I somehow missed your post...

If the precipitates in reality have a size of 40nm, and your grid resolution is 50nm, then each precipitate will just be represented by a single grid cell (or perhaps 5 cells in 2D).

However, the critical radius cannot be derived from the final size of the precipitates. The only way to estimate it is based on a "reasonable" nucleation undercooling. But what you can say for sure is that it cannot be bigger than the final size of the preciptiate! Otherwise the precipitate could not form, and you should think of revising the assumed interfacial energy.

The required undercooling of course depends on the interfacial energy between the precipitate and matrix phase. It is given in the .log file when nucleation is checked for the first time. There may be numerical reasons why the seeds don't grow even when the required undercooling is reached. It often helps to define an initial of 0<r<Δx in order to start with a somewhat bigger initial fraction.

Bernd

### Re: Bridging the gap between dendrites and gamma'-precipitation in Ni-base superalloys

Hi Bernd,

You have mentioned in your post in the Big particle approach that ..."gamma'-gamma' interface energy has to be chosen big enough."

Can you elaborate a little bit the reason behind this. Since gamma' is coherent with the matrix, it has low interfacial energy (typically reported values for this are in the range of 20 - 80 mJ/m^2). But in big particle approach do we need to scale these values, for an example factor of 10?

Best Regards.

You have mentioned in your post in the Big particle approach that ..."gamma'-gamma' interface energy has to be chosen big enough."

Can you elaborate a little bit the reason behind this. Since gamma' is coherent with the matrix, it has low interfacial energy (typically reported values for this are in the range of 20 - 80 mJ/m^2). But in big particle approach do we need to scale these values, for an example factor of 10?

Best Regards.

### Re: Bridging the gap between dendrites and gamma'-precipitation in Ni-base superalloys

Dear Chamara,

I was talking here about the gamma'-gamma' interface energy between non-identical grains. As the 4 grains I use for gamma' in this approach correspond to the 4 translational species which are shifted by one lattice plane of the ordered phase structure relative to each other, there are strong repulsive forces which increase the interface energy. Essentially, the high value I use should prevent the formation of such interfaces (which is not completely possible due to the low resolution).

Bernd

I was talking here about the gamma'-gamma' interface energy between non-identical grains. As the 4 grains I use for gamma' in this approach correspond to the 4 translational species which are shifted by one lattice plane of the ordered phase structure relative to each other, there are strong repulsive forces which increase the interface energy. Essentially, the high value I use should prevent the formation of such interfaces (which is not completely possible due to the low resolution).

Bernd

### Re: Bridging the gap between dendrites and gamma'-precipitation in Ni-base superalloys

what you ment by "4 grains" here are the 4 different γ' variants that you see in the microstructure due to the orientation relationship with γ-matrix?

### Re: Bridging the gap between dendrites and gamma'-precipitation in Ni-base superalloys

They have all the same orientation relation with the matrix. However, as the periodicity length of the ordered lattice is twice that of the disordered matrix, different gamma' particles may be out of phase and thus form a grain boundary when they touch. This leads to 4 variants, each of which is represented by a grain number in MICRESS.

### Re: Bridging the gap between dendrites and gamma'-precipitation in Ni-base superalloys

Hi Bernd,

With big particle approach, do we get the correct volume fraction evolution with time of the precipitates (assume we calibrate the nucleation model parameters) ? or this is not possible at all due to unrealistic particle size and nucleation distance?

With big particle approach, do we get the correct volume fraction evolution with time of the precipitates (assume we calibrate the nucleation model parameters) ? or this is not possible at all due to unrealistic particle size and nucleation distance?

### Re: Bridging the gap between dendrites and gamma'-precipitation in Ni-base superalloys

Hi Chamara,

Of course, we cannot expect to get quantitatively correct growth kinetics and thus fraction-time curve for the precipitate phase. The two main error sources are the "big particle" assumption itself and the still poor resolution.

When using "mob_corr" for correcting for poor resolution, the "big particle" effect should prevail and lead to delayed growth kinetics. Otherwise, however, it should be possible to mimick correct growth kinetics by calibrating nucleation undercooling

Bernd

Of course, we cannot expect to get quantitatively correct growth kinetics and thus fraction-time curve for the precipitate phase. The two main error sources are the "big particle" assumption itself and the still poor resolution.

When using "mob_corr" for correcting for poor resolution, the "big particle" effect should prevail and lead to delayed growth kinetics. Otherwise, however, it should be possible to mimick correct growth kinetics by calibrating nucleation undercooling

**and**interface mobility...Bernd