Equilibrium with Freeze-in Temperature Property Model Settings

The Equilibrium with Freeze-in Temperature Property Model calculates equilibrium at the freeze-in temperature and evaluates the properties at a different temperature. The assumption is that diffusion and phase transformations are negligible when changing from the freeze-in-temperature and, therefore, that the phase amounts and compositions of phases are kept at all other temperatures.

For theory, see About the Equilibrium with Freeze-in Temperature Property Model.

For examples, see:

Configuration Settings

The settings are found on the Property Model Calculator when the Equilibrium with Freeze-in Temperature Model is selected under General Models.

When working in the Configuration window, click the Description tab for more information about the Model.

For the details about the Condition Definitions, Calculation Type, Timeout in minutes, Parallel Calculation, and other calculation associated settings, see Property Model Calculator: Configuration Window Settings.

Enter a Freeze-in temperature value in the field. The unit matches those selected under Condition Definitions. This is the temperature where the equilibrium is calculated.

The default is 623.15 K (350 °C).

The Equilibrium above freeze-in temperature checkbox is selected by default and it calculates equilibrium above freeze-in temperature. Click to clear the checkbox when evaluating the frozen-in structure at higher temperatures than the freeze-in temperature.

Select the Evaluate for a single phase only checkbox to evaluate the properties of a specific phase or deselect to evaluate the properties for the entire system.

This setting is available when the Evaluate for a single phase only checkbox is selected.

From the Phase for evaluation list, select any available phase or None.

Select an Equilibrium minimization strategy. The default uses the Local minimization preferred option.

The Minimization Strategy setting is used to ensure that the most stable minimum under the specified conditions is computed.

With either the Global test preferred or Local minimization preferred setting, the program cycles through options before it gives up:

  • For Global test preferred the minimization starts with a global test and if that fails it runs full global minimization.
  • For Local minimization preferred the minimization starts with a local minimization, in case of failure it tries a global test and finally a full global minimization.

If you choose Local minimization only or Global minimization only, the program just tries the one setting and gives up if it fails.

For general information about global minimization, see the topic related to the Console Mode command, GLOBAL_MINIMIZATION.

The Homogenization function is used for the evaluation of the systems thermal and electric properties. The function is applied on thermal- and electrical-resistivity. The electric conductivity, thermal conductivity, and thermal diffusivity are evaluated from the resistivities.

The geometrical interpretation of the Hashin-Shtrikman bounds are concentric spherical shells of each phase.

  • Rule of mixtures (upper Wiener bound): the geometrical interpretation are continuous layers of each phase parallel with the direction of evaluation of the property.
  • Inverse rule of mixtures (lower Wiener bound): The geometrical interpretation are continuous layers of each phase orthogonal to the direction of evaluation of the property.
  • General lower Hashin-Shtrikman bound: The outermost shell consists of the phase with the most sluggish property.
  • General upper Hashin-Shtrikman bound: The innermost shell consists of the phase with the most sluggish property.
  • Hashin-Shtrikman bound with majority phase as matrix phase: The outermost shell consists of the phase with the highest local volume fraction.

The Account for phase interface scattering checkbox is selected by default.

The electrical resistivity due to phase interface scattering is evaluated as the scattering constant times sum of the interaction between the volume fraction of all the phases. The default value for the constant is 4.0e-8 Ωm. The contribution to thermal conductivity is assumed to be related to that of electrical resistivity, following the Wiedemann-Franz law.

This setting is available when the Account for phase interface scattering checkbox is selected.

The Phase interface scattering constant default value is 4.0e-8 Ωm.

This setting is available when the Account for phase interface scattering checkbox is selected.

In the field, enter the Reference temperature for technical CTE, where CTE is the coefficient of thermal expansion. Typically room temperature is used as the default 293.15 K (20 °C).

Select the Define user functions checkbox to enter up to two User-defined functions using the Console Mode syntax.

For an example of user-defined functions, see T_07: User-Defined Functions.

Plot Renderer Settings

Plot Renderer and Plot Renderer: Configuration Settings

When setting up your calculation on the Plot Renderer and/or Table Renderer, the following axis variables are available for the conditions defined on the Property Model Calculator.

When selecting quantities on the Plot Renderer or Table Renderer, the quantity names include an abbreviated name for the Property Model it is associated to. This is useful in particular when you are calculating two or more Property Models that share names for the quantities. The short name identifying the specific Property Model is included in parentheses after the name of the quantity. Below are the full and abbreviated names for each Property Model.

For a list of the abbreviations associated to a Property Model, see Result Quantities: Property Model Abbreviations.

Select from these plot quantities:

  • Temperature
  • Electric resistivity (ohm m) (Ωm)
  • Electric conductivity (S/m)
  • Thermal conductivity (W/(mK))
  • Thermal resistivity (mK/W)
  • Thermal diffusivity (m2/s)
  • Heat capacity (J/mol K))
  • Volume (m3/mol)
  • Density (g/cm3)
  • Linear CTE (technical) (1/K): Fractional change of length per unit temperature change. Calculated as (L1-L0)/(T1-T0)/L0, where L0 is the length at a reference temperature T0. T0 is by default equal to room temperature. Assumed Isotropic material.
  • Linear CTE (physical) (1/K): Fractional change of length per unit temperature change. Assumed Isotropic material.
  • Volumetric CTE (physical) (1/K): Fractional change of volume per unit temperature change.
  • User-defined function and 2nd user-defined function: Available when the Define user functions checkbox is selected and the functions are defined.

Elastic moduli is available to plot when the thermodynamic database selected includes elastic properties. However, even if the database does not have elastic constants, the quantity is visible to select from the list even. In this case there is a message in the Event Log to indicate there is no elastic data and the value will be NaN.