Microstructural Transitions in Commercial Fe-Ni–Based Soft-Magnetic Alloys Quenched from Undercooled Liquid Droplets

Abstract

Liquid droplets of three commercial Fe-Ni–based alloys were undercooled to different temperatures by electromagnetic levitation and quenched. Discontinuous changes in the grain size and microstructure as a function of melt undercooling (ΔT) were observed in all three alloys. At ΔT < 80 K, fine, equiaxed grains with a substructure consisting of spherical elements were observed. In the range 80 K < ΔT < 155 K, the microstructure consisted of colonies of columnar dendrites. The colonies were two orders of magnitude larger than the equiaxed grains reported at lower ΔT. At ΔT > 155 K, the equiaxed grains with a substructure of spherical elements returned. The critical undercoolings at which the microstructural transitions occur (ΔT ^* ₁ = 80 K and ΔT ^* ₂ = 155 K) show good agreement with those for similar binary systems. The results were successfully described by calculating the time needed for breakup of the primary dendrites as a function of ΔT and comparing this to the time during which the sample temperature is above the solidus due to recalescence.

Appendix I

Calculation Parameters

Parameter (Unit)	P36	M50	M79	Source
x (at. pct)	Fe-34.85Ni-0.7C	Fe-48.17Ni-0.09C	Fe-84.11Ni-0.1C	[17–19]*
k Fe-Ni	0.944	0.988	0.98	[27]**
k Fe-C	0.174	0.205	0.205	[28]**
m l(Fe-Ni) (K/at. pct)	−1	−0.15	0.65	[27]**
m l(Fe-C) (K/at. pct)	−16.9	−17.8	−17.8	[28]**
T l (K)	1750	1733	1727	DSC*
T s (K)	1726	1710	1702	DSC*
ΔH f  (J/g)	304	322	311	DSC*
C pliq at T l  (J/g/K)	0.76	0.75	0.74	[27]**
C psol at RT (J/g/K)	0.68	0.68	0.67	[27]**
ρ liq at T l (gcm−3)	7.55	7.55	7.55	[29]†
ρ sol at RT (gcm−3)	8.1	8.25	8.7	[17–19]*
α liq at T l  (m2/s)	4.92 × 10−6	4.88 × 10−6	4.86 × 10−6	[29]†
η liq at T l (mPas)	0.75	0.74	0.71	[30]**
D liq (m2/s)	6 × 10−9	6 × 10−9	6 × 10−9	assumed
V DF  (m/s)	3	3	3	assumed
V D  (m/s)	25	25	25	assumed
d o  (m)	8.52 × 10−10	7.84 × 10−10	7.89 × 10−10	calculated
μ K (ms−1 K−1)	1.01	2.95	1.095	calculated
ε c  (pct)	2	2	2	assumed
a 1, a 2, σ 0	0.3, 0.1, 30	0.3, 0.1, 30	0.3, 0.1, 30	assumed

1. The term x = ternary analogue composition; k _i-j and m _l(i-j) are the equilibrium partition coefficient and liquidus slope of the i-j binary system at the pseudo-binary composition; T _l  = liquidus; T _s  = solidus; ΔH _f = latent heat of fusion; C _pi and ρ _i are the specific heat capacity and density of phase I; α _liq, η _liq, and D _liq are the thermal diffusivity, viscosity, and diffusivity of the liquid; V _DF  = diffusion speed at the interface; V _D  = solute diffusion speed in the liquid; d ₀ = capillary length; μ _K  = kinetic growth coefficient; ε _c  = crystalline anisotropy of the interfacial energy; and a₁, a₂, and σ ₀ are the stability constants. *Data from alloys studied here. **Data from binary Fe-Ni (or Fe-C). ^†Data taken from Inconel 718