Effects of Growth Rates and Compositions on Dendrite Arm Spacings in Directionally Solidified Al-Zn Alloys

Abstract

Dendritic spacing can affect microsegregation profiles and also the formation of secondary phases within interdendritic regions, which influences the mechanical properties of cast structures. To understand dendritic spacings, it is important to understand the effects of growth rate and composition on primary dendrite arm spacing (λ ₁) and secondary dendrite arm spacing (λ ₂). In this study, aluminum alloys with concentrations of (1, 3, and 5 wt pct) Zn were directionally solidified upwards using a Bridgman-type directional solidification apparatus under a constant temperature gradient (10.3 K/mm), resulting in a wide range of growth rates (8.3–165.0 μm/s). Microstructural parameters, λ ₁ and λ ₂ were measured and expressed as functions of growth rate and composition using a linear regression analysis method. The values of λ ₁ and λ ₂ decreased with increasing growth rates. However, the values of λ ₁ increased with increasing concentration of Zn in the Al-Zn alloy, but the values of λ ₂ decreased systematically with an increased Zn concentration. In addition, a transition from a cellular to a dendritic structure was observed at a relatively low growth rate (16.5 μm/s) in this study of binary alloys. The experimental results were compared with predictive theoretical models as well as experimental works for dendritic spacing.

Appendices

Appendix A: λ Values Measured from Longitudinal and Transverse Sections for Al-Zn Alloys

Alloy	Al-1 Wt Pct Zn		Al-3 Wt Pct Zn		Al-5 Wt Pct Zn
V (μm/s)	λ 1L (μm)	λ 1T (μm)	λ 1L (μm)	λ 1T (μm)	λ 1L (μm)	λ 1T (μm)
8.3	53.2 ± 3.75	50.66 ± 2.29	62.39 ± 3.15	55.24 ± 2.65	75.72 ± 3.50	63.56 ± 2.85
16.5	64.40 ± 5.14	57.07 ± 3.49	70.30 ± 3.69	68.96 ± 2.40	108.25 ± 4.86	96.15 ± 3.89
41.3	55.61 ± 5.79	48.69 ± 4.27	63.94 ± 5.68	56.92 ± 3.13	84.91 ± 3.09	78.09 ± 3.01
82.5	44.98 ± 3.02	36.62 ± 2.45	48.02 ± 4.59	44.02 ± 2.19	72.84 ± 4.41	65.48 ± 3.23
165.0	32.49 ± 3.37	30.59 ± 2.33	44.71 ± 2.80	38.25 ± 2.31	53.14 ± 3.23	51.02 ± 2.39

1. λ _1L: The values of PDAS measured from the longitudinal section of the samples
2. λ _1T: The values of PDAS measured from the transverse section of the samples

Appendix B: Some Physical Properties of Al-Zn Alloy

Property	Symbol	Unit	Value	References
Melting point	T m	K	933	63
Slope of liquid line	m L	K (wt pct)−1	–2.93	3
Diffusion coefficient (liq.)	D L	μm2 s−1	1200	63
Distribution coefficient	k		0.45	63
Gibbs–Thomson coefficient	Γ	μm K	0.105	62
The harmonic perturbations	L	mJ/m2	10	63
Primary dendrite-calibrating factor	a 1	—	250	64
Characteristic parameter	G oε	K/cm	600 × 6	64
Secondary dendrite-calibrating factor	a 2	—	9	64

Appendix C: Theoretical Models of λ ₁ and λ ₂ for the Steady-State Conditions

Theoretical Models	References
$\lambda_{1} = 2.83[m(k - 1)D\varGamma ]^{0.25} G^{ - 0.5} V^{ - 0.25} C_{\text{o}}^{0.25}$	Hunt[21]
$\lambda_{1} = 2.83[m(k - 1)D\varGamma L]^{0.25} G^{ - 0.5} V^{ - 0.25} C_{\text{o}}^{0.25}$	Trivedi[22]
$\lambda_{1} = 4.3[m(k - 1)D\varGamma /k^{2} ]^{0.25} G^{ - 0.5} V^{ - 0.25} C_{\text{o}}^{0.25}$	K–F[23]
$\lambda_{1} = a_{1} \left( {\frac{{16G_{\text{o}} \varepsilon \varGamma D}}{m(1 - k)}} \right)^{0.5} G^{ - 0.5} V^{ - 0.5} C_{\text{o}}^{0.25}$	B–K[25,26]
$\lambda_{1} = 2\varepsilon \left[ {m(k - 1)D} \right]^{0.25} G^{ - 0.5} V^{ - 0.5} C_{\text{o}}^{0.25}$	O–K[27]
$\lambda_{2} = \left[ {8\varGamma DL/k\Delta T_{\text{o}} } \right]^{0.5} V^{0.5} = \lambda_{2} = \left[ { - 8\varGamma DL/mk} \right]^{0.5} V^{0.5} C_{\text{o}}^{ - 0.5}$	T–S[30]
$\lambda_{2} = 2\pi a_{2} \left( {\frac{{4\sigma D^{2} }}{{(1 - k)^{2} \Delta H}}} \right)^{1/3} V^{ - 0.67} C_{\text{o}}^{ - 0.33}$	B–K[25,26]

1. Here m is the liquidus slope, k is the distribution coefficient, D is the diffusion coefficient, Γ is the Gibbs–Thomson constant, ∆T _o is the equilibrium freezing range, L is a constant that depends on harmonic perturbation, a ₁ is the primary dendrite-calibrating factor, a ₂ is the secondary dendrite-calibrating factor, ∆H is the enthalpy of fusion, σ is the solid–liquid interfacial energy, ε is a constant less than unity, G _o ε is a characteristic parameter, and C _o, G, and V are described in the text