Tips and Tricks: Selecting the Right Model for Your Scheil Solidification Calculation

The Importance of CALPHAD-based Scheil Solidification Models

Solidification is an essential part of many manufacturing processes such as casting, welding, and additive manufacturing. Microstructure evolution for a solidifying alloy is generally governed by material chemistry and the transport of mass and heat near the solidification front. For most manufacturing processes that involve solidification, the transition of an alloy from liquid to solid rarely, if ever, occurs under conditions of full diffusional (global) equilibrium. This can result in several issues, such as solute segregation across the solidifying microstructure, stabilization of secondary phases along solidification grain boundaries, and transformation temperatures differing from phase diagram predictions for a given alloy chemistry. 

The departure from global equilibrium has implications during both the solidification process and during subsequent manufacturing steps. For example, solute segregation and the formation of secondary phases at the end of solidification often contribute to solidification crack formation. Adjustments to processing conditions and/or alloy chemistry are often needed to establish a suitable process window to avoid such defects. Even when solidification cracks do not form, an as-solidified component may require heat treatment to eliminate residual microsegregation, dissolve undesirable phases, and/or precipitate new phases to meet service requirements. The required heat treatment schedules in these cases are generally dictated by the condition of the as-solidified microstructure.

CALPHAD-based Scheil solidification models are often used to predict the solidification temperature range, segregation profiles, and phase evolution during cellular or dendritic solidification of multicomponent alloy chemistries. While appropriate for many material systems and solidification conditions, situations exist where the underlying assumptions of the original Scheil model do not sufficiently capture actual solidification behavior. As such, derivative models have been developed to address these situations. 

Scheil Models in Thermo-Calc

Five different Scheil model configurations are currently available within Thermo-Calc, each with different underlying model assumptions and treatment of solute diffusion:

• Classic Scheil
• Scheil with Back Diffusion in Primary Phase
• Classic Scheil with Fast Diffusers
• Scheil with Back Diffusion in Primary Phase and with Fast Diffusers
• Scheil with Solute Trapping

The best Scheil configuration for a given application is entirely dependent on both the alloy chemistry and solidification conditions, such as temperature gradient, solidification rate, and cooling rate. To provide some clarity on which Scheil configuration should be used for a given application, the available Scheil solidification configurations will be reviewed below.

Classic Scheil

Summary: Classic Scheil is useful to predict the extreme case of solute segregation during the solidification process. The model is simple and only requires alloy chemistry as input, and has high computational efficiency.

Explanation: The Classic Scheil calculation within Thermo-Calc is based on the Classic Scheil-Gulliver model. This calculation makes the following assumptions:

• Infinitely fast solute diffusion in the liquid
• No solute diffusion in the solid
• Liquid/solid interface is in thermodynamic equilibrium

As a consequence of these assumptions, Classic Scheil calculations predict an extreme case of solute segregation during the solidification process. The Classic Scheil model can be quite useful because of its simplicity and computational efficiency. When coupled with an appropriate thermodynamic database, the solidification process can be simulated in a matter of seconds and generally only requires the alloy chemistry as an input to understand solidification behavior under conditions of maximum solute partitioning.

In reality, some solute diffusion in the solid (also known as back diffusion) often occurs during the solidification process. Back diffusion effectively reduces solute concentration gradients in the solid and segregation to the liquid. In other words, solidification often occurs at a condition somewhere between the bounding cases of full diffusional equilibrium and Classic Scheil. Thermo-Calc can be used to model situations where back diffusion occurs via the Scheil with Back Diffusion in Primary Phase calculation type and/or by implementing the fast diffusers assumption.

Scheil with Back Diffusion in Primary Phase

Summary: Scheil with Back Diffusion in Primary Phase is useful for scenarios where some degree of back diffusion is expected for all solutes in a solidifying system. This model requires more user inputs compared to Classic Scheil, such as cooling rate.

Explanation: Using the Scheil with Back Diffusion in Primary Phase model, Thermo-Calc directly solves for diffusion kinetics in the primary solid phase throughout the solidification process. This approach is particularly useful for scenarios where some degree of back diffusion is expected for all solutes in a solidifying system.

The Scheil with Back Diffusion in Primary Phase model makes the following assumptions:

• Infinitely fast solute diffusion in the liquid
• Diffusion is considered in the primary solid phase
• Liquid/solid interface is in thermodynamic equilibrium

Using the Scheil with Back Diffusion in Primary Phase model requires more user inputs than the Classic Scheil configuration. Since solute diffusion in the solid is calculated in this case, inputs are needed to define the time and length scales associated with the development of the solidification microstructure. Time is introduced by linking a user-defined cooling rate with the calculated solidification temperature range that evolves during the simulation. The length scale can be set by defining a secondary dendrite arm spacing. This secondary dendrite arm spacing can be defined as a constant by the user, or it can be calculated by the software if the empirical parameters that relate secondary dendrite arm spacing to cooling rate are known. For the latter case, predefined empirical parameters are provided in Thermo-Calc. However, you should use your best judgment to define empirical parameters that are consistent with your material system. Note that this model requires a suitable mobility database in addition to a thermodynamic database.

Defining Fast Diffusers for Classic Scheil and Scheil with Back Diffusion in Primary Phase Calculations

Summary: The Classic Scheil and Scheil with Back Diffusion in Primary Phase models both allow you to define certain elements as “fast diffusers.” Using a Scheil model that considers fast diffusers is useful for systems that contain interstitial solute elements. Carbon is one of the most important alloying elements in steels. It dissolves interstitially and has very fast diffusion rates. Therefore, carbon is typically defined as a fast diffuser, but other elements such as nitrogen, oxygen, or others can be also defined.

Explanation: Fast diffusing elements are treated as having infinitely fast diffusion rates in the solid during a calculation by adopting a partial equilibrium assumption. This fast diffusers or partial equilibrium assumption allows the selected elements to distribute throughout the solid and liquid according to thermodynamic equilibrium. Elements that are not defined as fast diffusers are treated in a manner consistent with the selected calculation type.

Defining fast diffusers in a calculation can be particularly useful for material systems that contain interstitial solute elements. Diffusion rates of interstitial elements are considerably higher than substitutional elements at high temperatures in the solid. The partial equilibrium assumption often provides a good approximation for describing interstitial solute behavior during solidification without the need to directly solve for diffusion kinetics. For example, treating carbon as a fast diffuser has shown good agreement with experimental data in steels.

Scheil with Solute Trapping

Summary: Scheil with Solute Trapping is particularly useful for applications that involve high solidification velocities such as those frequently encountered during additive manufacturing. 

Explanation: Each of the Scheil configurations discussed so far has assumed that the solid/liquid interface is in equilibrium during solidification, but the assumption of interfacial equilibrium can break down for many processes with high solidification velocities. When the solid/liquid interface moves quickly enough, there is insufficient time for solute elements to diffuse into and redistribute within the liquid phase. Solute elements then become trapped at the interface, causing chemical potential discontinuities and a loss of equilibrium at the interface. This trapping behavior has the effect of suppressing the liquidus temperature of the alloy and pushing solute partition coefficients toward unity (i.e. partitionless solidification) as the solid/liquid interface velocity increases.  

Modeling solute trapping is particularly useful for applications that involve high solidification velocities such as those frequently encountered during additive manufacturing. The Scheil with Solute Trapping model has been implemented in Thermo-Calc to address this topic.  The Scheil with Solute Trapping model makes the following assumptions:

• Only one primary solid phase forms dendrite
• Solute trapping in primary solid phase only. Other phases follow the Classic Scheil model
• Amounts of solid phases are dependent on solute trapping and solidification speed
• Dynamic liquidus for primary solid phase is dependent on solute trapping and solidification speed
• Dynamic solidus is calculated as complete solidification

The material chemistry, solid/liquid interface velocity, and the primary solid phase are needed to perform a Scheil with Solute Trapping calculation. The solid/liquid interface velocity is calculated by the software once the scanning speed (e.g. speed of heat source during additive manufacturing), the angle between the scanning direction, and the primary growth direction are defined. You can then choose to allow the software to automatically define the primary phase that is affected by solute trapping or make a selection from the list of available phases. It is important to note that only phases that dissolve all elements in the system can be selected as the primary phase.

Conclusions

There is no “one size fits all” approach to modeling solidification behavior across all alloy families and material chemistries. The selection of an appropriate model depends on the material system and solidification conditions that are being modeled. As shown here through the provided examples, a useful approach to develop a better understanding of solidification behavior is to compare simulation results from multiple solidification models. You are encouraged to reference literature and/or supplement modeling efforts with experiments to assist with the selection of appropriate model parameters for their given application. It should also go without saying that appropriate databases need to be selected for the material system that is being simulated.

There are three calculation examples available using the Scheil Solidification Calculator demonstrating the various models: 

• T_08_Scheil_and_Equilibrium_Solidification
• T_10_Scheil_with_Back_Diffusion
• T_13_Scheil_with_Solute_Trapping

These examples are accessed from the home screen of the software, by clicking the Example Files icon.

We also offer several video tutorials demonstrating how to set up Scheil calculations in Thermo-Calc.

This article is a part of a blog series of tips and tricks to help users get the most out of Thermo-Calc. Make sure to read the other blog posts for more tips and tricks!