Diffusion-Controlled Grain Growth in Liquid-Phase Sintering of W–Cu Nanocomposites

Jai-Sung Lee; Ji-Hun Yu

doi:10.1515/ijmr-2001-0127

Article

Diffusion-Controlled Grain Growth in Liquid-Phase Sintering of W–Cu Nanocomposites

Jai-Sung Lee and Ji-Hun Yu

Published/Copyright: February 11, 2022

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From the journal International Journal of Materials Research Volume 92 Issue 7

Abstract

The kinetics of W grain growth during liquid-phase sintering (LPS) of W-15 – 25 wt.% Cu nanocomposite powder compacts was investigated in terms of microstructural development as well as theWatom diffusion process in liquid Cu. It was found that W grains grew rapidly while maintaining a round shape during LPS at 1623 K, being inversely proportional to the Cu matrix contents. This indicates that the diffusion-controlled Ostwald ripening (DOR) mechanism dominates the growth process in W–Cu nanocomposites. The result of this investigation on the kinetics of W grain growth definitely identifies the occurrence of DOR growth. Namely, the time exponent of the growth equation was close to the value of 3 and the kinetic constant forWgrain growth decreased with decreasing volume fraction of the W solid phase. This is basically due to the fact that the increase of a liquid matrix lengthens the diffusion path, as a result decreasing the growth rate. The diffusivity of the W atoms in liquid copper was calculated from the growth kinetics to be lower within an order of magnitude than the self-diffusion of the liquid atoms. The presence of Watom solubility in liquid Cu, as well as atom diffusivity, is thought to be responsible for diffusion-controlled growth of W grains during LPS of W–Cu nanocomposite powder.

Keywords: Liquid-phase sintering; Nanocomposites of W– Cu; Grain growth

Prof. Dr. J.-S. Lee Dept. of Metallurgy & Materials Science 1271, Sa-1, Ansan 425-791, Korea Fax: +82 31 400 5107

Dedicated to Professor Dr. Dr. h. c. mult. Günter Petzow on the occasion of his 75th birthday

The authors gratefully acknowledge the financial support of the Dual Use Technology Program of the Ministry of Science and Technology of Korea.

Appendix

The interfacial energy between a solid and a liquid of different atomic composition is an important factor in such phenomena as the solidification of two-phase alloys and in commercially important processes such as liquid-phase sintering and directional solidification of eutectic composites. Experimental determination of the interfacial energy is difficult, and it is natural to attempt theoretical derivations of this property. In this work, the authors describe two methods for calculating the solid-liquid interfacial energy.

1 Young’s Equation

In general, Young’s equation has been known as a representative model for calculating the interfacial energy between solid and liquid system and follows as:

(A-1) γW=γW/Cu+γCucosθ

in which γ_W, γ_Cu and γw/Cu are the surface energies of W solid particles, Cu liquid matrix and interfacial energy between solid W and liquid Cu, respectively. If we can assume that the liquid Cu at 1623 K completely wets the surface of the W solid particle (wetting angle θ = 0°), Eq. [A-1] is reformulated as follows:

(A-2) γW/Cu=γW−γCu

In addition, the surface energy of liquid Cu, γ_Cu, depending on the elevated temperature is represented as follows:

(A-3) γCu=γCum.p.+(T−Tm.p.)dγCudT

in which γCum.p. is 1.285 N/m, meaning the surface energy of liquid Cu at 1356 K (melting point of Cu), and the derivative surface energy of liquid Cu to temperature change, dγ / dT, is –0.13 N/mK. The calculated γ_wand γ_Cu are 2.5 and 1.25 N/m, respectively. So, the interfacial energy of solid Wand liquid Cu, γ_w/Cu, is 1.25 N/m.

2 Solid–Liquid Interfacial Energies in Binary and Pseudo-Binary Systems

Warren [27] reported on a simple thermodynamic model of the solid–liquid interface in binary systems. The model is extended to pseudobinary systems such as transition metal carbideliquid metal systems. A simplified model of the interface between a liquid and a solid in equilibrium is assumed to be a thin atomic layer which contains a small amount of solid atoms to form a disturbed solid–solution region in a solid–liquid interface. A finite value of the interfacial energy exists because a region in the neighborhood of the interface is disturbed from the bulk equilibrium states of both the solid and the liquid. The disturbance is on both the chemical composition and the structure, and these two will be treated as separate contributions in the model. The interfacial energy in the binary system is then given by

(A-4) γ=γC+γB

in which γ_C and γ_B are the interfacial energies contributed by the chemical composition and the structure, respectively. If the intersolubility (both of solid atoms in the liquid matrix and the liquid atom in crystalline solid) is at a low level, then the changes of molar free energies with varying compositions of solid and liquid atoms approach zero. So, the interfacial energy contributed by the chemical composition is simplified as follows:

(A-5) γC=nF6/N

with

(A-6) F 6 = F 3 X ′ 2 + R T X ′ ln ⁡ X ′ + 1 − X ′ ln 1 − X ′ − R T ln ⁡ X ′ X ′ 1 − X ′

in which n is the number of interface atoms per unit area, equal to the sum of the solid and liquid interface atoms, n_S + n_L. N is the Avogadro number, F₆ means the molar free energy of liquid at critical composition of the solid, X′, F₃ is the molar free energy of liquid in crystalline solid given by

(A-7) F3=HB(1−TTB)

in which H_B is the latent heat of melting and T_B is the melting temperature of the solid. Meanwhile, a solid–liquid interface is disturbed structurally with respect to both the solid and liquid state. The structural disturbance leads to a finite interfacial energy between pure metal solid and its melt, as well as between a solid and a chemically different liquid. In the present model, the structural contribution is considered to be equal to the solid–liquid interfacial energy in an insoluble binary system, such as W– Cu. In this case, the relationship between γ_B and the melting point is sought in a similar way to that observed between surface energy of the solid and the melting point

(A-8) γB=kTB/VB2/3

in which k is an empirical constant equal to 6.5 × 10^–4 (for pure metals the value of k lies between 5×10^–4 and 8 × 10^–4). T_B is the melting point of the solid and VB2/3 expresses the interfacial area induced from the molar volume of atoms in the solid, V_B.

The interfacial energy contributed by chemical composition, γ_C, calculated with Eqs. (A-5)–(A-7), is –3.562 × 10 ^–6 N/m, and that by the structure of the solid, γ_B, calculated with Eq. (A-8) is 1.033 N/m at 1623 K. So, the solid–liquid interfacial energy (γ) of W/Cu at 1623 K is calculated to be 1.033 N/m from Eq. (A-4).

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Received: 2001-04-24

Published Online: 2022-02-11

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Articles in the same Issue

https://doi.org/10.1515/ijmr-2001-0127

Keywords for this article

Liquid-phase sintering; Nanocomposites of W– Cu; Grain growth