Driving force calculation

[matt_hughes]

Hi MICRESS Forum,

I have a non thermocalc simulation and was just wondering how the driving force is calculated. From looking at the 2006 paper "Multiphase-field approach for multicomponent alloys with extrapolation scheme for numerical application", the driving force update is dS*m*dC + dS*dT. I can get these values from the micress simulation and calculate dG for an example gridpoint, but the dG calculation comes out much bigger than the dG calculated at each grid point from MICRESS. Is this equation of dS*m*dC + dS*dT how MICRESS calculates driving force or is there another way it is calculated? I see in the inputs for phase interactions there are two reference points, are these used when calculating dG perhaps? Hopefully my query makes sense, any help would be much appreciated.

Many thanks,
Matthew

[Bernd]

Hi Matthew,

In principle, your formula for calculation of the driving force is correct. m is either the solidus or liquidus/solvus slope as specified in the linearisation data, and dC is the difference c-c0, i.e. the deviation of the local composition from the reference point. According to the "quasi-equilibrium assumption, it makes no difference whether m*dC is calculated for one or the other side of the interface, i.e. m₁dC₁=m₂dC₂. The driving force is written to the .driv output file, and does not directly contain a curvature contribution (only indirectly via the Gibbs-Thompson equation via a locally changed composition), but has an extra stress contribution in case of stress coupling.

However, there are some subtleties. One is that driving forces are typically averaged across the interface to avoid driving force gradients which may destroy the interface profile. So, to see the unaltered local values of the driving force in the .driv output, one should set the avg. parameter to 0.0 in the dG-options. Another special case is when the "lintq" mode is used which is according to the Thermo-Calc linearisation principles. Then further parameters are added, especially dS₁ and dS₂ instead of a common dS, extra derivatives to temperature dcdt for both phases, and a driving force offset dG₀ which corresponds to the distance of the parallel tangents and which adds up to the total driving force.

What is the reason why you have the impression that your formula for calculation of the driving force is not correct? Can you describe where you see deviations?

Bernd

[matt_hughes]

Hi Bernd,

Thank you for the response. The reason why i think i have the wrong driving force is that the driving force values of the interface from a micress simulation with the following inputs in the phase interaction section:

linear
# Temperature of reference point? [K]
1693
# Entropy of fusion between LIQUID and FCC-AL ? [J/(cm**3 K)]
1.1
# Input of the concentrations at reference points
# Reference point 1: Concentration of component AL in phase LIQUID ? [wt%]
9 #9 #9
# Reference point 2: Concentration of component AL in phase FCC-AL ? [wt%]
7.780006 #15.36 #7.78
# Input of the slopes at reference points
# Slope m = dT/dC at reference point 1, component AL ? [K/wt%]
-9.79
# Slope m = dT/dC at reference point 2, component AL ? [K/wt%]
-11.305 #-9.79 #12.23


give values ranging from around 0.088 J/cm^3 to 0.12J/cm^3 for dG. When i use the equation of dS*m*dC + dS*dT with the same inputs from the micress simulation to try and calculate dG for an example grid point. E.g using,

dS = 1.1 J/cm^3
Tref = 1690K
Cref = 0.09
local temperature ranges from 1690K at the bottom to 1690.5K at the top
local composition in the micress simulation ranges from around 0.08 to 0.093


I get values ranging from 2.9 to 3.4 J/cm^3, which is much bigger than the micress values of around 0.088 J/cm^3 to 0.12J/cm^3. When I plug the higher values of dG i get into a simple phase field code using the equation attached from the 2006 paper "Multiphase-field approach for multicomponent alloys with extrapolation scheme for numerical application", to see what these larger values of dG do, I find that the solid grows too quickly causing numerical errors i think. This simple phase field code used values of 1 cm^4/Js for mobility and 16J/m^2 for the surface energy which i think are reasonable although could be wrong? Regardless I'm not sure why the values of dG i'm using are so large?