Thermal Resistivity and Thermal Conductivity

Thermal conductivity of a pure element or a stoichiometric phase at temperature above 273 K is described as a function of temperature using the following equation:

k= A + B T + C T-1 + D T2

(1)

where k is the thermal conductivity and T is the temperature in Kelvin. This function can reasonably fit most of the experimental thermal conductivity data of elements at temperature above 273 K.

The thermal conductivity of a solid solution phase can be calculated from thermal resistivity, which is the reciprocal of thermal conductivity. According to the Nordheim rule, the thermal resistivity ( ρ ) of a solid solution phase can be described by the following Redich–Kister polynomials:

(2)

where is the thermal resistivity of the a solution phase in the A-B system. x_j and r_j are the mole fraction and thermal resistivity of pure elements j, respectively. L_i are the ith order interaction parameters which are used to describe the effect of solute elements on the thermal resistivity. In general, the interaction parameter can be expressed as:

(3)

where the parameters a_i, b_i and c_i are evaluated based on the experimental data.

The interface scattering parameters is introduced to describe the effect of the second phase on the thermal resistivity in two-phase region. The thermal resistivity of the two-phase region is described as following:

(4)

where r_a+b is the thermal resistivity of the alloys in a+b two-phase region, f _p and r _p (p = a, b) are the mole fraction and thermal resistivity of the phase p, respectively. M_i, which can be considered to be linearly temperature dependent, is the ith interface scattering parameter and and can be evaluated from the experimental data. The thermal conductivity of alloy system and the value of each phase can be obtained by using the reciprocal of the thermal resistivity values through output option.

In this example, thermal resistivity of the Al-Mg binary alloys is described using the User-Defined Property function.

As shown in the AlMg_ThCond.tdb, the thermal resistivity ThRss property is first defined as User-Defined Property since it has not been pre-defined in the current Pandat™software.

Type_Definition z PHASE_PROPERTY ThRss 1 !

In accordance, the following definition is also needed to add this property to the original database.

Type_Definition e GES AMEND_PHASE_DESCRIPTION * VARIABLE_X ThRss !

As is seen, the thermal resistivity of the Fcc phase or the Hcp phase follows the same format as that of Gibbs energy for a disordered solution phase.

Thermal resistivity of the intermetallic phases with narrow solid solubility rage in the phase diagrams is treated like that of a stoichiometric compound phase, i.e., it is composition independent and is described as below:

In order to describe the thermal resistivity within two-phase region, a system property, Sys_ThRss, is then defined by the command:

After the thermal resistivity has been properly modeled for each phase, the thermal conductivity of each phase and that of the system can be directly calculated and outputed by using extra output in Pandat™ defined as 1/ThRss(@*) and 1/Sys_ThRss, respectively. The comparisons between the calculated and measured thermal conductivities of the Al-Mg alloys are shown in Figure 1 and Figure 2. This example demonstrates that the User-Defined Property function is very powerful and flexible to allow users define various types of properties. The property can be a function of any phase properties that can be calculated by PanPhaseDiagram module.