CALTPP: A general program to calculate thermophysical properties

doi:10.1016/j.jmst.2019.12.005

Abstract

Abstract:

A program CALTPP (CALculation of ThermoPhysical Properties) is developed in order to provide various thermophysical properties such as diffusion coefficient, interfacial energy, thermal conductivity, viscosity and molar volume mainly as function of temperature and composition. These thermophysical properties are very important inputs for microstructure simulations and mechanical property predictions. The general structure of CALTPP is briefly described, and the CALPHAD-type models for the description of these thermophysical properties are presented. The CALTPP program contains the input module, calculation and/or optimization modules and output module. A few case studies including (a) the calculation of diffusion coefficient and optimization of atomic mobility, (b) the calculation of solid/liquid, coherent solid/solid and liquid/liquid interfacial energies, (c) the calculation of thermal conductivity, (d) the calculation of viscosity, and (e) the establishment of molar volume database in binary and ternary alloys are demonstrated to show the features of CALTPP. It is expected that CALTPP will be an effective contribution in both scientific research and education.

Key words: Thermophysical property, Diffusion coefficient, Interfacial energy, Thermal conductivity, Viscosity, Molar volume, CALPHAD-type modeling

Yuling Liu, Cong Zhang, Changfa Du, Yong Du, Zhoushun Zheng, Shuhong Liu, Lei Huang, Shiyi Wen, Youliang Jin, Huaqing Zhang, Fan Zhang, George Kaptay. CALTPP: A general program to calculate thermophysical properties[J]. J. Mater. Sci. Technol., 2020, 42: 229-240.

Figures/Tables 19

Fig. 1. General structure of CALTPP program. Temp. and Com. represent the temperature and composition, respectively.

Fig. 2. Calculated concentration profiles in fcc (a) Co-Ti-V alloy compared with the measured data [46] of Co-8 V/Co-7Ti (at.%) at 1373 K for 120 h and (b) Cu-Ni-Sn alloy compared with the measured data [47] of Cu-7.38Ni/Cu-4.28Sn (at.%) at 1023 K for 40 h.

Table 1 Summary of the atomic mobilities of fcc phase in the Cu-Ni-Sn ternary system.

Atomic mobilities	Parameters (J/mol)	Refs.
Mobility of Cu	$\Phi^{Cu}_{Cu}$=-205872.0-82.52T	[49]
	$\Phi^{Ni}_{Cu}$ =-263689.7-77.04T	[50]
	$\Phi^{Sn}_{Cu}$=-59345-85.36T	[51]
	$\Phi^{Cu,Ni}_{Cu}$=14204.2-4.98T	[50]
	$\Phi^{Cu,Sn}_{Cu}$=425070.5	[52]
Mobility of Ni	$\Phi^{Cu}_{Ni}$=-229936.8-72.83T	[50]
	$\Phi^{Ni}_{Ni}$=-271377.6-81.79T	[50]
	$\Phi^{Sn}_{Ni}$=-59345-85.36T	[51]
	$\Phi^{Cu,Ni}_{Ni}$=39620.8-24.19T	[50]
	$\Phi^{Cu,Sn}_{Ni}$=710383.1	[47]
	$\Phi^{Cu,Sn}_{Ni}$=703588.3	CALTPP
	$\Phi^{Ni,Sn}_{Ni}$=437617.0-134.41T	[47]
	$\Phi^{Ni,Sn}_{Ni}$=204428.6+88.14T	CALTPP
Mobility of Sn	$\Phi^{Cu}_{Sn}$=-172907-91.78T	[52]
	$\Phi^{Ni}_{Sn}$=-257207.0-71.60T	[47]
	$\Phi^{Sn}_{Sn}$=-59345-85.36T	[51]
	$\Phi^{Cu,Ni}_{Sn}$=-47693.0	[47]
	$\Phi^{Cu,Ni}_{Sn}$=-15216.8	CALTPP
	$\Phi^{Cu,Ni}_{Sn}$=30831.5	[52]
	$\Phi^{Ni,Sn}_{Sn}$=-420626.0+186.29T	[47]
	$\Phi^{Ni,Sn}_{Sn}$=-100351.7-56.38T	CALTPP

Fig. 3. Comparison between the calculated interdiffusivities in fcc Ni-Sn alloys at 1223-1473 K and the experimental data[53]. The calculated results due to the previous assessment [47] are also superimposed.

Fig. 4. Comparison of the calculated main interdiffusivities in fcc Cu-Ni-Sn alloys at 1023 and 1073 K with the experimental values[47].

Fig. 5. Comparison of solid/liquid interfacial energies of binary systems between the predicted values by the present model and the experimental data for Al-Zn [55], Cd-Zn [56,57], Cu-Co [58] and Cu-Zn [59] alloys.

Fig. 6. Model-predicted interfacial energies of γ/γ' interface in the Ga-Ni system compared with the reported value [68] using back-calculation with trans interface diffusion-controlled theories [69] and Lifshitz-Slyozov-Wagner [70,71] theories.

Fig. 7. Model-predicted liquid/liquid interfacial energies in CALTPP compared with the reported value [73,74] in the Ga-Pb system.

Table 2 Summary of the thermal conductivity equations for pure elements.

Elements	Equations (W/(m·K))
Mg	+179.67-0.04T-6062.38T^-1
Gd	+6.28+0.00848T-245.67T^-1
Y	+14.48+0.01T-160.57T^-1

Table 3 Summary of the thermal conductivity parameters for solution phases and two-phase regions.

Phase region	System	Parameters (W/(m·K))
(Mg) solid solution	Mg-Gd	${}^{0}L^{(Mg)}_{MgGd}$=-272209.1-38.58T${}^{1}L^{(Mg)}_{MgGd}$=+597309.70+45.71T${}^{2}L^{(Mg)}_{MgGd}$=-336405.09+0.076T
(Mg) solid solution	Mg-Y	${}^{0}L^{(Mg)}_{MgY}$=+76083.35+5.87T${}^{1}L^{(Mg)}_{MgY}$=-87254.34
(Mg)+Mg₅Gd	Mg-Gd	${}^{0}M_{(Mg)+Mg_{5}Gd}$ =+175425.81+43.38T ${}^{1}M_{(Mg)+Mg_{5}Gd}$ =-406384.64-49.52T ${}^{2}M_{(Mg)+Mg_{5}Gd}$ =+235365.27

Fig. 8. Calculated thermal conductivities of (Mg) solid solution in (a) the Mg-Gd, (b) Mg-Y and (c) Mg-Gd -Y alloy in comparison with the experimental data [75].

Fig. 9. Calculated thermal conductivities of (Mg)+Mg5Gd two-phase region in the Mg-Gd alloy in comparison with the experimental data [75].

Table 4 Parameters of the pre-exponential and the activation energy for pure Ag, Au and Cu melts according to the present work.

Parameters	Ag	Au	Cu
η0 (mPs)	0.585	1.152	0.313
E (J/mol)×10³	19.350	17.020	28.650

Table 5 Interaction parameters for the viscosity in the binary Ag-Au, Ag-Cu and Au-Cu melts according to the present work.

Parameters (mPs)	Ag-Au	Ag-Cu	Au-Cu
${}^{0}L^{melt}_{ij}$	0.862	-0.965	0.271
${}^{1}L^{melt}_{ij}$	0.039	-0.608	-0.158
${}^{2}L^{melt}_{ij}$	0.155	-0.206	-0.482

Fig. 10. Calculated viscosities of (a) pure Ag, Au and Cu and (b) binary Ag-Au, Ag-Cu and Ag-Au systems, compared with the experimental data [[76], [77], [78]].

Fig. 11. Calculated viscosities of Ag-Au-Cu system compared with the data reported by Gebhardt and Wörwag [79].

Fig. 12. Calculated molar volumes of (a) the Al-Fe alloy compared with the measured data [[81], [82], [83]] and (b) molten Al-Cu-Si alloys of compositions alone Al-Cu50Si50 and Cu-Al50Si50 sections at 1300 K with the measured data [84].

Table 6 Summary of the volume parameters for the Al-Fe and Al-Cu-Si systems.

System	Structure	10^-6, V₀ (m³/mol)	V_α (m³/mol)	Refs.
Al	Fcc	9.7749	6.912 × 10^-5T+0.4135T^-1+1.6227 × 10^-11T³	[41]
	Hcp	9.8106	6.912 × 10^-5T+0.4135T^-1+1.6227 × 10^-11T³	[41]
	Bcc	10.0772	6.912 × 10^-5T+0.4135T^-1+1.6227 × 10^-11T³	[41]
	Liquid	10.0680	1.2847 × 10^-4T+3.4943 × 10^-10T²	[80]
Fe	Fcc	6.8903	-0.0208 + 6.9790 × 10^-5T	CALTPP
	Bcc	7.2091	-0.01192 + 3.4276 × 10^-5T+8.1401 × 10^-9T² +0.2917T^-1	CALTPP
	Liquid	6.2701	1.3842 × 10^-4T	CALTPP
Cu	Fcc	7.0064	4.3958 × 10^-5T+1.1517 × 10^-8T²+0.1410T^-1	[41]
	Hcp	7.0238	4.3958 × 10^-5T+1.1517 × 10^-8T²+0.1410T^-1	[41]
	Bcc	7.0377	4.3958 × 10^-5T+1.1517 × 10^-8T²+0.1410T^-1	[41]
	Liquid	7.0253	8.3998 × 10^-5T+5.8489 × 10^-9T²	[80]
Si	Fcc	8.6398	4.0765 × 10^-5T+0.3723T^-1+2.1034 × 10^-9T²	[41]
	Hcp	8.5866	4.0765 × 10^-5T+0.3723T^-1+2.1034 × 10^-9T²	[41]
	Bcc	8.8512	4.0765 × 10^-5T+0.3723T^-1+2.1034 × 10^-9T²	[41]
	Liquid	8.8327	1.3837 × 10^-4T	CALTPP
Al-Fe	Bcc	-2.23		CALTPP
	Liquid	-3.8479		CALTPP
Al-Cu	Liquid	-2.66		[80]
Al-Si	Liquid	0		CALTPP
Cu-Si	Liquid	-3.12		CALTPP
Al-Cu-Si	Liquid	18.9		CALTPP

Fig. 13. Calculated interdiffusion coefficients in the B2 Al-Ni alloy compared with the literature data [[85], [86], [87], [88], [89]], and the work of Liu et al. [90] is also superimposed.

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