solidification of a ternary alloy composition

[mogeritsch]

Dear Bernd,
I try to simulate the solidification of a ternary ally composition. I use for the primary phase the seeding density model, for the other two phases the seeding undercooling model and additional nucleation at the interface for all 3 phases verse. Nonetheless, the result of the simulation shows me always a liquid phases (0.07% fraction ) below the ternary solidification temperature (-30 K). What goes wrong with me simulation?

[Bernd]

Dear mogeritsch,

first of all, welcome to the MICRESS forum!

The remaining of small amounts of rest liquid (<<1%) is a common problem in simulations of solidification. The reason in most cases is the requirement that each reservoir of rest liquid needs to be in contact with all involved phases to solidify, otherwise certain element will accumulate and stop further solidification.
In your case there are three phases which need to be in contact with the rest liquid. But typically, for obtaining realistic nucleation behaviour at higher temperatures, nucleation data are chosen such that a shield effect prevents too dense seeding, and also too many checks are avoided for sake of performance. This easily leads to the situation that not enough seeding is provided in the final solidification stage.
The simple solution is to define additional seed types for all three phases which do not start operating before reaching lower temperatures where the problem starts (e.g. below the ternary eutectic temperature). Nucleation sites chosen for these additional seed types should be all interfaces with liquid. This is obtained by choosing liquid (phase 0) as reference phase and also as substrate phase. The shield time should be 0 or smaller than the checking interval. The fact that at this stage only few liquid cells remain, allows for choosing a small checking interval and a small nucleation distance (or shield distance).
(Remark: if only a shield distance is specified, this value also defines the "nucleation distance", i.e. the distance between checked points. The nucleation distance can be specified explicitly as second optional parameter in the same line with the shield distance).

In some cases, the reason for remaining of rest liquid can also be of numerical nature. If e.g. one of the components has a (persisting) negative concentration in the rest liquid, further solidification can be "blocked", especially if user limits for concentrations are applied. You can check for negative concentrations by activating the phase composition output for phase 0 ("out_conc_phase 0" in section "Selection of the outputs") and by analysing the *.c*pha0 output files with DP_MICRESS. More frequent relinearisation would perhaps be the solution in such a case.

It would be great to hear whether and how you solved the problem!

Bernd

[mogeritsch]

Dear Bernd
Thanks a lot for your help and I solved this problem. Now I have a new challenge.

I try to simulate a metallic ternary eutectic concentration with two elements forms lamella like 0.1 – 0.2 µm thickness and one element solidifies in a spherical manner (r = approx. 40 nm) within the two lamellas. Up to now I am in the position to simulate the lamellas but fail to simulate a spherical third phase. Instead all phases solidify as lamellas.

Which variables are important to bring a metal into a spherical form within two lamellas?

Best wishes
Johann

[Bernd]

Dear Johann,

I could imagine more than one solidification scenario of a ternary eutectic alloy which would lead to spherical particles which are embedded in a two-phase lamellar eutectic: Depending on the thermodynamic system, the composition and the cooling conditions it could be e.g. the primary phase which grows in a globular morphology before being enclosed by a monovariant eutectic. Or it could be the last phase to appear which has a composition close to the ternary eutectic and fills the rest liquid zones.
Apart from that, spherical structures are favored by high interface energies, slow interface kinetics (in case of intermetallics), low segregation and slow cooling. Specific growth modes can also lead to spherical particles like in case of graphite.
Please give me some more information on the system if possible (alloy, composition, cooling conditions).

Best wishes

Bernd

[mogeritsch]

Hi Bernd,

during nucleation the following statement is given in the logfile:

Seed number 2 set at time t = 0.11000E-01 s
-------------------------------------------
in the bulk
Phase: 1 (HCP_ZN)
Seed type: 1 (1: 2/25)
Local temperature = 609.73 K
Undercooling = 1.3995 K
Grain number = 2

Most of the information are clear for me but how can I interpret "Local temperature", "Undercooling" and "(1: 2/25)"?

Best wishes,

Johann

[Bernd]

Dear Johann,

"Local temperature" means the temperature at the place of nucleation at the time of nucleation. If there is no temperature gradient, it is just the bottom temperature.

"Undercooling" means the local solutal undercooling ΔT=ΔG/ΔS of the seed, corrected for curvature of the substrate in case it applies (interface nucleation with defined substrate phase)

and "(1: 2/25)" means that it corresponds to seed class 1, number 2 of 25 potential seeds (seed density model).

Best wishes

Bernd

[mogeritsch]

Dear Bernd,

the velocity of the solidification front is given by:

V=T ̇/GT ,

with V is the velocity, T ̇ is the cooling rate, and GT the temperature gradient.

Further one, the velocity is given by:

V=µ∙∆S∙∆T ,

with µ is the kinetic coefficient, deltaS the entropy, and deltaT the undercooling.

In MICRESS the cooling rate, the temperature gradient, the undercooling, and the kinetic coefficient can be selected by the user. Only the entropy is given by the thermodynamic system.

Now to my question: MICRESS use which equation to calculate the velocity of the solidification front?

Best wishes,

Johann

[Bernd]

Dear mogeritsch,

In MICRESS, the interface velocity is determined implicitly by the phase-field equation which for a single interface can be written in the simplified form:

dφ/dt = μ [ σ K + π/η (φ_α φ_β)^1/2 ΔG]

Here, K is a not further specified curvature and profile stabilisation term, σ is the interface stiffness, φ the phase-field parameter, grad φ = (φ_α φ_β)^1/2 the phase-field gradient, and ΔG the thermodynamic driving force.

If you neglect curvature effects (σ K = 0), replace ΔG with ΔSΔT, and identify the implicit growth speed with

v=dφ/dt η/π gradφ^-1

then you get exactly the expression which you formulated.

Bernd

[mogeritsch]

Dear Bernd,

thank you.

Johann

[mogeritsch]

Dear Bernd,

I am still not really familiar with the solidification velocity. In the dri.-file, the minimum undercooling is select with deltaT = 10 K, the entropy is deltaS = 1.344 J ∙cm-3 ∙K-1 (from log-file) and the kinetic coefficient µ = 2∙10-2 cm4 ∙J-1∙s-1 (dri.-file). This gives me a velocity of approx. V = 0.27 cm/s (v=µm*deltaS*deltaT).

In my simulation a distance of x = 6 µm was solidified within t = 0.021 s, which gives me a solidification velocity of V = 0.028 cm/s.

Furthermore, the selected cooling rate T = 38 K/cm and the temperature gradient GT = 20 K/cm in the dri.-file requires in a solidification rate of 1.9 cm/s.

All three calculations give me a different result. Why?

I guess, that my deltaT is wrong. Instead of taking the deltaS from the dri.-file I have to use the difference between dri.file and the calculated undercooling from the log. file. If this is right, the calculated velocity is approx. 0.027 cm/s. Further on, I have to select the kinetic coefficient µ in such a way that the solidification velocity matches the required solidification rate coming from the cooling rate and the temperature gradient. But this gives me a kinetic coefficient µ of 1.9 cm4 ∙J-1∙s. Is this correct or is this another mistake?

Best regard,
Johann