TCTI6 Thermophysical and Elastic Properties

This section summarizes the available thermophysical and elastic properties in the TCS Ti/TiAl-based Alloys Database (TCTI).

The thermophysical properties data was gradually added to the database versions as follows. Molar volume with thermal expansion coefficients available starting with TCTI2, the viscosity of liquid and surface tension of liquid are available starting with TCTI3, and electrical resistivity and thermal conductivity starting with TCTI4.

The elastic properties data (elastic moduli and elastic constants) is available starting with TCTI6 and are only available for cubic BCC (A2 and B2), cubic FCC (A1 and L12), and hexagonal HCP (A3) phases.

Model Descriptions

For model descriptions, see:

Notes about the Thermophysical Property Data

Pay attention to these details relevant to the TCS Ti/TiAl-based Alloys Database (TCTI).

Molar volume data is critically assessed for most phases of importance to titanium alloys. All necessary volume data (including molar volume and thermal expansion) for various phases have been incorporated, which enables one to calculate volume fraction of phases, density and thermal expansivity, as well as lattice parameters for cubic structures using Thermo‑Calc. However, the molar volume data only provides rough estimations and has no pressure dependence.

Electrical resistivity and thermal conductivity are critically assessed with available data for liquid, BCC, HCP, FCC, and for phases of importance to Ti/TiAl-based alloys.

Also see Common Phases for Titanium Alloys to review the phases with descriptions for electrical resistivity and thermal conductivity.

Thermophysical Properties Parameters and Variables

Below is a summary of the available thermophysical parameters and variables for the databases when working in Thermo‑Calc. There are differences when you are working in Console Mode versus Graphical Mode as well as if you use an SDK such as TC‑Python or TC-Toolbox for MATLAB®.

Property (and Graphical Mode Variable Name) Model Parameters Variables to Show or Plot in Console Mode or the SDKs (TC‑Python, or TC-Toolbox for MATLAB®)***

Molar volume

V0, VA

VM for a system VM(PHI) for phase PHI

Electrical conductivity

ELQ**

ELCD for a system ELCD(PHI) for phase PHI

Electrical resistivity

ELRS, ESPD

ELRS for a system ELRS(PHI) for a phase PHI

Thermal conductivity

THCD

THCD for a system THCD(PHI) for phase PHI

Thermal resistivity

 

THRS for a system THRS(PHI) for phase PHI

Thermal diffusivity

 

THDF for a system THDF(PHI) for phase PHI

Surface tension

SIGM, XI*

 SURF(LIQUID)

SURF(ION)**

Dynamic viscosity

VISC

DVIS(LIQUID)

DVIS(ION)**

Kinematic viscosity

 

 KVIS(LIQUID)

KVIS(ION)**

* XI is not used in the TCOX database (all versions). As of 2023b it is also not used starting with the following versions of these databases: TCFE13, TCNI12.1, TCTI5.1, TCNOBL3, TCPMAG2, and TCCU6. As of 2024a, TCMG7, TCAL9, and TCHEA7. As of 2024b, TCSLD5.

** ION is used in the TCS Metal Oxide Solutions Database (TCOX)

*** The examples listed for the SDKs are using Console Mode syntax. The quantities can also be accessed in both ThermodynamicQuantity and ScheilQuantity classes. See the various model descriptions or the SDK help for details.

Elastic Properties Parameters and Variables

Elastic properties are only available for cubic BCC (A2 and B2), cubic FCC (A1 and L12), and hexagonal HCP (A3) phases.

In the Plot Renderer in Graphical Mode, elastic constants and moduli can be selected from the drop-down list of axis variables.

The independent elastic constants are selected on the Plot Renderer as an axis variable Elastic constant and then choose an option (C11, C12, C13, C33, or C44) from the drop-down list.

The elastic moduli, Bulk modulus, Shear modulus, and Young's modulus, are directly available from the Axis variable list.

All can be tabulated and plotted using the quantity names, with options for a specific phase or all phases.

The quantities corresponding to the individual elastic constants and elastic moduli (derived from the elastic constants) can be can be calculated in Console Mode for individual phases or all phases. The results can be shown in the POLY module with the command SHOW_VALUE or shown as a plot in the POST module with the command PLOT_DIAGRAM using:

  • Cij(<phase name>) or Cij(*)
  • Bulk modulus: BULKMOD(<phase name>) or BULKMOD(*)
  • Shear modulus: SHEARMOD(<phase name>) or SHEARMOD(*)
  • Young's modulus: YOUNGMOD(<phase name>) or YOUNGMOD(*)

For the Software Development Kits (SDKs), i.e. TC-Python and TC-Toolbox, the quantities of elastic constants, bulk modulus, shear modulus, and Young’s modulus can be retrieved for individual phases or all phases via get_value_of() or get_values_of() from any equilibrium calculation types using:

  • Cij(<phase name>) or Cij(ALL_PHASES/*)
  • ThermodynamicQuantity.bulk_modulus(<phase name>) or ThermodynamicQuantity.bulk_modulus(ALL_PHASES/*)
  • ThermodynamicQuantity.shear_modulus (<phase name>) or ThermodynamicQuantity.shear_modulus(ALL_PHASES/*)
  • ThermodynamicQuantity.youngs_modulus(<phase name>) or ThermodynamicQuantity.youngs_modulus(ALL_PHASES/*)

See the relevant SDK documentation for details.

Examples

For examples using this database, see:

For surface tension, viscosity, and molar volume general use examples, see T_11: Surface Tension in Cu-Zr, T_12: Viscosity in Cr-Ni, and T_15: Molar Volume and Thermal Expansion Coefficients for L12-type Al3Sc and Al3Zr Compounds (Graphical Mode) and Thermophysical Properties Examples (Console Mode)

For electrical resistivity and thermal conductivity general use examples, see T_16: Electrical Resistivity and Thermal Conductivity for Pure Copper (Graphical Mode) and Thermophysical Properties Examples (Console Mode)

For an example using this database, see Elastic Properties for FCC_A1, BCC_A2, and HCP_A3. For a general example included with the installation and using this database, see T_19: Young's Modulus for Ti-O with Elastic Properties.