Scheil-Gulliver Solidification Calculations

In Graphical Mode, you use the Scheil Calculator activity node to simulate the various models available in Thermo‑Calc or with the Add-on Modules or additional databases.

Read more about Scheil Solidification Simulations on our website, including how to select the right model for your simulation. If you are in Thermo‑Calc, press F1 to search the help to learn about using Scheil.

Thermo‑Calc is often used to perform equilibrium calculations, but some non-equilibrium transformations or partial-equilibrium transformations can also be simulated.

A well-known example of a non-equilibrium calculation is the Scheil-Gulliver solidification simulation. In Thermo-Calc, the available Scheil-Gulliver solidification simulations are classic Scheil, Scheil with back diffusion in the primary phase, or Scheil with solute trapping. There are also configuration options available with fast diffusers for the classic and back diffusion models.

Classic Scheil Simulation

This is a Scheil simulation based on the well-known Scheil-Gulliver model. If this model is used without "fast diffusers" it is Classic Scheil simulation with the following assumptions:

Diffusion in the liquid phase is assumed to be very fast, that is, infinitely fast.
Diffusion in the solid phases is so slow that it can be ignored, that is, diffusion is assumed to be zero.
The liquid/solid interface is in thermodynamic equilibrium.

In this Classic Scheil simulation the temperature is decreased step-by-step. When the temperature drops below the liquidus temperature the equilibrium amount and composition of solid and liquid phase is calculated. The solid phase is removed from the system and only the amount and composition of the liquid phase is used for the next calculation step at a lower temperature. Again, the equilibrium amount and composition of solid and liquid phase is calculated and again the solid phase is removed from the system for the next step. This procedure is repeated until the last liquid disappears.

This calculation procedure is equivalent to assuming that there is no diffusion in the solid phase and infinitely fast diffusion of all elements in the liquid phase. It has been shown to be a good approximation of the solidification of most alloys such as Ni-superalloys, Cu alloys, Al alloys, Mg alloys, and others. However, in materials with interstitial elements, such as carbon, ignoring diffusion in the solid causes discrepancies with experimental results. Interstitial elements have much faster diffusion rates. The assumption of no diffusion in the solid phase during solidification is thus not correct at most industrial or lab-scale solidification rates.

For this reason, a variant of the Scheil simulation was developed and implemented in Thermo‑Calc, where one or more elements can be defined as fast diffusers. See Other Options: Fast Diffusers and Scheil Simulations.

Scheil Simulation with Back Diffusion in Primary Phase

The Scheil simulation with back diffusion in primary phase kinetic model quantitatively takes into account the real back diffusion of all elements in the primary solid phase (typically the FCC or BCC phase). This model requires the use of both a thermodynamic and mobility database. The calculation also requires the cooling rate to be specified; a fast cooling rate allows for less time for back diffusion and the simulation result is similar to the classic Scheil-Gulliver solidification simulation. A very slow cooling rate allows for almost complete back diffusion, the solidification simulation is then close to an equilibrium calculation. It also requires that the size of the solidification domain is specified. In most cases this domain size corresponds to the secondary arm spacing, as this is where typically the liquid is trapped during solidification.

The secondary arm spacing also depends on the cooling rate. For this reason, a simple empirical relation between cooling rate and secondary arm spacing is predefined in Thermo‑Calc.

For the Scheil simulation with back diffusion in primary phase model the following assumptions are made.

Diffusion of all elements in the liquid phase is infinitely fast.
Diffusion of all elements in the primary solid phase are quantitatively calculated using mobility data, a cooling rate and a domain size (typically this is the secondary arm spacing).
The liquid/solid interface is in thermodynamic equilibrium.

Also see Other Options: Fast Diffusers and Scheil Simulations.

Scheil with Solute Trapping

The Scheil with solute trapping model simulates deviation from local equilibrium for the primary phase. It is useful for high solidification speeds, such as those seen in additive manufacturing applications.

For equilibrium- and classical Scheil-type solidification simulations thermodynamic equilibrium is established at the solid-liquid interface. This means that solutes are partitioned between the solid and liquid phases according to solidus and liquidus lines of the phase diagram. The assumption of thermodynamic equilibrium at the solid-liquid interface however, is invalid for very fast solidification rates, as encountered for example during additive manufacturing. The faster the solidification rate, the less the partitioning at the interface, which can be perceived as that solutes in the liquid are trapped in the advancing solid phase, hence the term solute trapping.

The Scheil with solute trapping model calculates the solute partitioning between liquid and primary solid that deviates from thermodynamic equilibrium due to solidification speed.

The following assumptions are made:

Only one primary solid phase forms dendrite, NOT necessarily the first solid phase.
Solute trapping in primary solid phase only. Other solid phases have equilibrium compositions following Scheil model.
Dynamic liquidus for primary solid phases is dependent on solute trapping and solidification speed.
Amounts of solid phases are dependent on solute trapping and solidification.

More theory details are in About Scheil with Solute Trapping.

Other Options: Fast Diffusers and Scheil Simulations

If a Classic Scheil or Scheil simulation with back diffusion in primary phase model is selected plus one or more Fast diffuser checkboxes selected, then Thermo‑Calc takes into account the concept of the fast diffuser. Typically, C is defined as a fast diffuser, but also other elements such as N, O, or others can also be defined.

Fast diffuser does not quite define this since diffusion is not actually simulated. It is simply assumed that the “fast diffusers” distribute throughout the solid and liquid phase according to thermodynamic equilibrium. This corresponds to infinitely fast diffusion for the selected elements.

For a Classic Scheil model with the compositions defined with Fast diffuser the following assumptions are made.

Diffusion of all elements in the liquid phase is infinitely fast.
Diffusion of all elements in the solid phases, except the ones defined as “fast diffusers”, is zero.
Diffusion of the elements defined as “fast diffusers” is infinitely fast in the solid phase.
The liquid/solid interface is in thermodynamic equilibrium.

For a Scheil simulation with back diffusion in primary phase model with the compositions defined with Fast diffuser the following assumptions are made.

Diffusion of all elements in the liquid phase is infinitely fast.
Diffusion of all elements in the primary solid phase are quantitatively calculated using mobility data, a cooling rate and a domain size (typically this is the secondary arm spacing).
Diffusion of the elements defined as “fast diffusers” is infinitely fast in the solid phase.
The liquid/solid interface is in thermodynamic equilibrium.

The Classic Scheil simulation and Classic Scheil simulation with fast diffuser models can be considered thermodynamic models. There are clear limitations as a certain amount of back diffusion always takes place in the solid phase at real solidification.

You can also use the more sophisticated Scheil simulation with back diffusion in primary phase kinetic model. Adding the fast diffuser option to this can be useful, for example for interstitials like C in steels where these then equilibrate in all phases and not just the primary phase.

Homogenization, Segregation Profiles, and the Diffusion Module

Scheil calculations can be used in diffusion simulations with the Diffusion Module (DICTRA).

Homogenization is a process were you want to get rid of the composition segregation from solidification with a homogenization heat treatment. This composition segregation can be simulated with Scheil. Then with the Diffusion Module (DICTRA), you input the secondary dendrite arm spacing to get the right diffusion distances. With composition profile from file the idea is that you should be able to input for example a measured composition profile (from EDS/WDS, micro-probe etc). This could also be a segregation profile but also composition profiles over a weld, substrate/coating, diffusion couple, and so forth.

Summary

The available Scheil-Gulliver solidification simulations are classic Scheil, Scheil with back diffusion in the primary phase, or Scheil with solute trapping. There are also configuration options available with fast diffusers for the classic and back diffusion models.

There is also connectivity to the Diffusion Module (DICTRA) and homogenization where you collect data from a Scheil solidification calculation, which is then used as part of the kinetic homogenization simulation of segregated composition profiles.

Scheil in Graphical Mode vs Console Mode

The Scheil with back diffusion feature is only available for systems with diffusion data, i.e. this model requires the use of a mobility database.

In Thermo-Calc, the Scheil calculation allows the calculation of:

The solidification range of an alloy.
Depression of the solidus temperature due to segregation.
Composition of the last liquid to disappear in segregation pockets.
Phases formed on final solidification in segregation pockets.
The composition gradient in the primary solid phase(s) (segregation profile).
Solute trapping to simulate deviation from local equilibrium for the primary phase
Kinetic homogenization simulation of segregated composition profile (diffusion calculations)