Effect of Cooling Rate on the Secondary Dendritic Spacing of a Horizontally Solidified 6xxx Series Aluminum Alloy

Marques, Luane P.; Mesquita, Suanny Q.; Maciel, André C.; Costa, Rogério B.; França, Raquel S.; Rocha, Otavio L.; Ferreira, Ivaldo L.

doi:10.1590/1980-5373-MR-2025-0045

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Articles • Mat. Res. 28 (Suppl 1) • 2025 • https://doi.org/10.1590/1980-5373-MR-2025-0045 linkcopy

Effect of Cooling Rate on the Secondary Dendritic Spacing of a Horizontally Solidified 6xxx Series Aluminum Alloy

Authorship SCIMAGO INSTITUTIONS RANKINGS

Abstract

The 6xxx series alloys [Al-Mg-Si] are valued for their excellent mechanical and electrical properties, making them suitable for power conductors in non-steel core transmission and distribution lines. This study investigates the growth of the dendritic microstructure in the Al-0.6wt%Mg-0.8wt%Si-0.2wt%Fe alloy, specifically under horizontally solidified conditions. We employ both experimental techniques and mathematical modeling to predict the growth of the secondary dendritic arm spacing (SDAS). Samples of the as-cast alloy were obtained using a water-cooled horizontal solidification device. Our research starts with a mathematical model that was originally developed for solidification conditions close to thermodynamic equilibrium (low cooling rates - TR). We extend this model to address non-equilibrium conditions (high TR) by incorporating the reverse diffusion parameter β into our analysis. The experimental relationships for SDAS as functions of TR and local solidification time (t_SL) are expressed with the equations: SDAS = constant × (TR)^(-1/3) and SDAS = constant × (t_SL)^(1/3). We found a good agreement between the results from our iterative method and the experimental values. Additionally, we utilized a recently developed theoretical formulation for nonequilibrium nucleation to predict the Gibbs-Thomson coefficient under these conditions.

Keywords:
Multicomponent alloys; Unsteady-state horizontal solidification; Dendritic growth models

$\nabla T$ $K . m^{- 1}$	$Δ T$ $K$	$r_{C, H o m}$ $m$	$r_{C, H e t}$ $m$	$θ$ $r a d$	$σ_{S L}$ $N . m^{- 1}$	$Σ$ $N . m^{- 1}$	$γ_{S L}$ $J . m^{- 2}$	$Γ$ $m . K$
428.111	0.0674466	6.26850E-06	6.26849E-06	3.06431	-1.10093	-0.010927	0.195771	2.11395E-07
1017.99	0.14829	5.796E-06	5.79598E-06	3.05436	-1.27177	-0.181773	0.397983	4.29745E-07
2035.66	0.269136	5.2605E-06	5.26048E-06	3.04901	-1.48311	-0.393108	0.655577	7.07898E-07
3101.18	0.380547	4.8825E-06	4.88248E-06	3.0471	-1.64567	-0.555668	0.860351	9.29016E-07
4047.39	0.471024	4.6305E-06	4.63048E-06	3.04641	-1.76119	-0.671193	1.00994	1.09054E-06
5085.61	0.563666	4.41E-06	4.40998E-06	3.04612	-1.86756	-0.777556	1.15103	1.24289E-06
6176.68	0.655255	4.221E-06	4.22098E-06	3.04607	-1.96305	-0.873047	1.28071	1.38292E-06
7031.7	0.723693	4.095E-06	4.09498E-06	3.04613	-2.02911	-0.939113	1.37225	1.48177E-06
7752.28	0.779441	4.0005E-06	4.00048E-06	3.04622	-2.08001	-0.990011	1.44385	1.55908E-06
7902.38	0.79083	3.9821E-06	3.98208E-06	3.04624	-2.09008	-1.00008	1.45814	1.57452E-06
8009.27	0.79894	3.969E-06	3.96898E-06	3.04626	-2.09724	-1.00724	1.46832	1.5855E-06

Properties	Symbol	Units	Al-0.8wt%Si-0.6wt%Mg-0.2wt%Fe
Liquidus temperature	$T_{L}$	$K$	925.32
Solidus temperature	$T_{S O L}$	$K$	798.15
Liquidus slope	$m_{L}^{M g}$	$K (w t % M g)$	-5.100
	$m_{L}^{S i}$	$K (w t % S i)$	-6.200
	$m_{L}^{F e}$	$K (w t % F e)$	-4.300
Partition Coefficient	$k_{0}^{M g}$	-	0.36
	$k_{0}^{S i}$	-	0.11
	$k_{0}^{F e}$	-	0.03
Activation energy (Al liquid)	$Q_{d}^{M g}_{L}$	$k J m o l^{- 1}$	71.6
Activation energy (Al liquid)	$Q_{d}^{S i}_{L}$	$k J m o l^{- 1}$	30
	$Q_{d}^{F e}_{L}$	$k J m o l^{- 1}$	35
Diffusion constant (Al liquid)	$D_{0}^{M g}_{L}$	$m^{2} s^{- 1}$	$9.9 \times 10^{- 5}$
	$D_{0}^{S i}_{L}$	$m^{2} s^{- 1}$	$1.34 \times 10^{- 7}$
	$D_{0}^{F e}_{L}$	$m^{2} s^{- 1}$	$2.34 \times 10^{- 7}$
Activation energy (Al FCC)	$Q_{d}^{M g}$	$k J m o l^{- 1}$	115.0
	$Q_{d}^{S i}$	$k J m o l^{- 1}$	137.0
	$Q_{d}^{F e}$	$k J m o l^{- 1}$	183.4
Diffusion constant (Al FCC)	$D_{0}^{M g}$	$m^{2} s^{- 1}$	6.23 x 10^-6
Diffusion constant (Al FCC)	$D_{0}^{S i}$	$m^{2} s^{- 1}$	2.48 x 10^-4
	$D_{0}^{F e}$	$m^{2} s^{- 1}$	5.3 x 10^-3
Latent heat ( $FCC_A 1$ )	$Δ H_{F C C_A 1}$	$J k g^{- 1}$	335300
Mean Thermal Gradient (Liquid)	$\bar{\nabla T}$	$K m^{- 1}$	7902.38
Low thermal gradient surface tension	$σ_{0}$	$N m^{- 1}$	-0.914
Low thermal gradient surface energy	$γ_{0}$	$J m^{- 2}$	0.154
Surface stress	$s$	$N m^{- 1}$	-1.000
Surface tension	$σ_{S L}$	$N m^{- 1}$	-2.090
Surface energy	$γ_{S L}$	$J m^{- 2}$	1.458
1^st Order Gibbs-Thomson	$Γ_{H e t}^{1 st - Order}$	$K m$	7.6370 x 10^-7
2^nd Order Gibbs-Thomson	$Γ_{H e t}^{2 nd - Order}$	$K m$	1.5745 x 10^-6
Dendrite tip growth rate horizontal	$v_{L}$	$m m s^{- 1}$	$1.82 P^{- 0.30}$
Local solidification time horizontal	$t_{S L}$	$s$	$0.93 P^{1.04}$

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E-mail: pessan@ufscar.br

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