Modeling of intermediate phase growth

Abstract

We introduced a continuum method for modeling of intermediate phase growth and numerically simulated three common experimental situations relevant to the physical metallurgy of soldering: growth of intermetallic compound layer from an unlimited amount of liquid and solid solders and growth of the compound from limited amounts of liquid solder. We found qualitative agreements with the experimental regimes of growth in all cases. For instance, the layer expands in both directions with respect to the base line when it grows from solid solder, and grows into the copper phase when the solder is molten. The quantitative agreement with the sharp-interface approximation was also achieved in these cases. In the cases of limited amounts of liquid solder we found the point of turnaround when the compound/solder boundary changed the direction of its motion. Although such behavior had been previously observed experimentally, the simulations revealed important information: the turnaround occurs approximately at the time of complete saturation of solder with copper. This result allows us to conclude that coarsening of the intermetallic compound structure starts only after the solder is practically saturated with copper. © 2007 American Institute of Physics. ͓DOI: 10.1063/1.2424530͔ I. BACKGROUND A. ExperimentPhysical metallurgy of soldering presents many interesting problems: transformations in the solder, transformations in the contacts, and mechanical and electrical properties of the joints. 1 One of the problems that is critical for soldering industry is the formation and growth of an intermediate phase between the solder and the contact. The occurrence of an intermediate phase near 50 at. % of Sn in the Cu-Sn system at temperatures below 415°C was observed in 1904. 2 This transformation was found to be associated with significant amount of heat of formation ͑first-kind transition͒, but details regarding the nature of the phase mostly have been unknown at the time. Later on this phase ͑ phase͒ was identified as an intermetallic compound ͑IMC͒ Cu 6 Sn 5 . 3 The compound Cu 6 Sn 5 undergoes another phase transformation at approximately 189°C, which was identified as a secondkind order-disorder transition ͑ ↔ Ј͒ associated with the formation of a long-period superlattice.The compound grows in the form of a layer with morphology strongly dependent on the temperature of soldering: Onishi and Fujibuchi 4 showed that the growth of IMCs from solid-state Cu-Sn diffusion couples results in a relatively planar layer of IMC. However, observations of the intermetallic growth in the solid-Cu͑Ni͒/liquid-Sn system ͑above the melting point of the solder͒ instead of a smooth layer always show rough, strongly undulated compound layers with scallops of the intermetallic phase. [5][6][7] With time scallops grow larger but fewer, indicating that the coarsening process takes place. 6,7 The problem of IMC layer growth has many challenges, the reasons for roughness and coarsening, to name only a few. To describe this process Kim et al. 6,8 suggeste...

Multiphase-field modeling of temperature-driven intermetallic compound evolution in an Al–Mg system for application to solid-state joining processes

“…Takaki and Tomita [43] coupled a multiphase-field method with a finite-element based crystal plasticity approach for the simulation of static recrystallization. With regard to intermetallics, Park et al [44][45][46], Li et al [47], Umantsev [48], and Huh et al [49] focused on intermetallic compound evolution during soldering of Cu-Sn system. Hou et al [50] simulated the process of intermetallic compounds during the precipitation process in a Ni-Al alloy system.…”

Effect of Zn Addition on Interfacial Reactions Between Sn-4Ag Solder and Ag Substrates

“…A similar nonparabolic mechanism for the growth of IMCs has been probed in many interfacial reactions of soldering joints. 33,39,40 Figure 14 illustrates the relationship between the thickness of the IMCs and the aging time for the two couples aged at 160°C. For the Sn-4Ag-1Zn/Ag couples, the IMCs become thinner at the beginning of the interfacial reaction.…”

Coupled diffusion-deformation multiphase field model for elastoplastic materials applied to the growth of Cu6Sn5

“…These IMC are of great importance due to their role in soldering of electronic components. The recent transition to lead-free solders, driven by environmental concerns and legislation, have further increased the interest for the Cu-Sn system, both from experimental [6][7][8][9][10][11][12][13] and modeling [14][15][16][17][18] perspectives.…”

“…A one-dimensional model of the growth of Cu 6 Sn 5 was developed by Umantsev in [17]. In this model the phase fields represent ordering and crystallization rather than individual grains.…”