Thermodynamic and Kinetic Factors

Surface Energy. When a liquid forms during sintering, the microstructure consists of solid, liquid, and vapor phases. Successful LPS requires a reduction in surface energy as the liquid spreads across the surface of the solid particles. Thus, the solid-liquid surface energy must be less than the solid-vapor surface energy. In this case, the liquid "wets" the solid and provides a bonding force between the particles to aid densification.

Wetting is aided by solubility of the solid in the liquid, formation of intermediate compounds, and interdiffusion. Interfacial energies can be highly dependent on surface purity, so the wetting behavior can be drastically altered by contaminants or processing steps that clean the powder surface. Clean surfaces are especially important for metal-metal systems. Reactive metals tend to wet oxidized surfaces better than noble metals due to chemical reactions at the interface. Metal powders contain an oxide surface layer, so a reducing atmosphere or high vacuum is generally required to break down these surface oxides to obtain good wetting with less reactive liquid metals. In certain systems, the penetration of the liquid by capillary action is sufficient to mechanically break down oxide layers.

Surface energies also establish important microstructural features such as contiguity (the surface area of solid-solid contacts as a fraction of the total interfacial area), connectivity (the number of observed contacts per grain in a two-dimensional cross section), grain size, and dihedral angle. The dihedral angle characterizes the energy ratio between the grain boundaries and solid-liquid surfaces and is defined in Fig. 1. This ratio changes with sintering time and has a strong influence on microstructural development. Dissolution reactions during liquid formation decrease the solid-liquid interfacial energy below its equilibrium value, promoting particle rearrangement. With further sintering time, the interfacial energy increases back to its equilibrium value. The contiguity also increases with time as neck growth proceeds until an equilibrium neck size is reached. The contiguity is uniquely related to the solid volume fraction, dihedral angle, and grain size ratio (Ref 1). Connectivity is also strongly related to contiguity. A large dihedral angle gives a larger connectivity and contiguity for the same solid volume fraction. These microstructural parameters influence the electrical conductivity, strength, ductility, elastic behavior, dimensional stability, and thermal characteristics of LPS materials.

Fig. 1 The dihedral angle and surface energy equilibrium between two intersecting grains with a partially penetrating liquid phase

Solubility of the solid in the liquid is generally required for successful liquid-phase sintering, especially for systems with more than 65 vol% solid (Ref 2). This solubility permits solution reprecipitation and enables a more efficient packing of the grains, leading to higher sintered densities. On the other hand, solubility of the liquid in the solid is generally undesirable, because it can result in swelling as the liquid diffuses into the solid grains (leaving behind large pores that are typically difficult to eliminate during subsequent sintering). However, in certain systems, such as Cu-Sn and Cu-Zn, transient liquid phase can be controlled to yield unique properties. These two cases are schematically shown in Fig. 2.

Fig. 2 A schematic diagram contrasting the effects of solubility on densification or swelling during liquid-phase sintering

The solubility parameter, which is defined as the ratio of the solid solubility in the liquid to the liquid solubility in the solid, provides a reasonable estimate of whether swelling or shrinkage occurs during liquid-phase sintering. Several examples are given in Table 1, which shows a potential for shrinkage at higher ratio values. The actual amount of dimensional change depends on processing conditions.

Table 1 Solubility effects on densification in liquid-phase sintering

Base

Additive

Solubility

Behavior

ratio, at.%

Al

Zn

0.004

Swell

Cu

Al

0.1

Swell

Cu

Sn

0.001

Swell

Cu

Ti

4

Shrink

Fe

Al

0.02

Swell

Fe

B

7

Shrink

Fe

Cu

0.07

Swell

Fe

Sn

0.01

Swell

Fe

Ti

3

Shrink

Mo

Ni

20

Shrink

Ti

Al

0.0003

Swell

W

Fe

5

Shrink

Phase diagrams are useful in identifying solubility parameters and other characteristics conducive to LPS (Ref 3, 4, 5). An ideal phase diagram for LPS is shown in Fig. 3. A deep eutectic is favorable due to the large reduction in sintering temperature with the formation of the liquid phase. The formation of intermediate compounds is generally unfavorable.

High-temperature phases can lower diffusion rates, while brittle intermetallic phases that form during cooling can degrade mechanical properties. Phase diagrams also indicate the tendency of alloying elements and impurities to segregate to grain boundaries. The greater the separation of the solidus and the liquidus, the greater the solute segregation to interfaces. A downward sloping liquidus and solidus also indicate a tendency for solute segregation and lower surface energies (Ref 6).

A sintering temperature just above the eutectic temperature is optimal for a composition in the L + '^region. A classical LPS microstructure for such a case, as shown in Fig. 4, consists of relatively large, rounded grains suspended in a liquid matrix, with the degree of grain contact governed by the dihedral angle.

Liquid Phase Sintering
Fig. 3 Phase diagram of an ideal system for liquid-phase sintering

Fig. 4 Typical microstructure of a liquid-phase sintering system with the phase diagram characteristics shown in Fig. 3

For systems that lack solubility of the solid in the liquid phase, a rigid skeletal structure is expected with densification governed by solid-state diffusion. High sintered densities are possible with the use of extremely fine starting powders or by using segregating activators that enhance solid-state sintering in the presence of the liquid phase. These techniques are covered in more detail in the section "Activated Liquid-Phase Sintering" in this article.

Diffusivity. One of the benefits of LPS is the rapid densification and homogenization that occurs due to the high diffusion rates of base metal atoms in a liquid. Additives that have low melting temperatures are preferred due to their low activation energies and high diffusivities at lower temperatures. For certain systems, during heating, significant densification can occur due to enhanced solid-state sintering through the additive phase. In such cases, the diffusivity increases exponentially with temperature until the additive melts. Once the liquid phase forms, there is a rapid jump in both the solubility and diffusivity, due to the much weaker bonding associated with a liquid phase. An exponential increase in diffusivity accompanies further increases in temperature. Thus, higher temperatures are favorable for densification, but they also increase the vapor pressure of the liquid. Preferential evaporation of the liquid can change the overall composition of the sintered component. In addition, redeposition of vapors on furnace walls can result in damage to furnaces. Problems with preferential evaporation can be assessed through relative vapor pressures. A vapor pressure of 10-3 Pa provides a practical limit for vacuum sintering, while a vapor pressure of 1 Pa can lead to a measurable weight loss during sintering at atmospheric pressure.

In general, melting temperatures are good indicators of diffusion rates. Materials with lower melting temperatures have weaker atomic bonding and higher molar volumes, which allow faster diffusion at a given temperature. Liquid-phase sintering materials often involve mixed powders that have significantly different melting temperatures and thus unequal diffusivities. Unequal diffusion rates between the base alloy and the additive result in the Kirkendall porosity. For sufficient sintering times, the material will homogenize, and equilibrium factors, such as solubility, will dominate. Thus, unbalanced diffusivity ratios contribute to initial pore formation, but sustained shrinkage or swelling depends on the solubility ratio. Homogenization occurs more rapidly for small particles with a high initial homogeneity. Higher sintering temperatures and longer sintering times also aid microstructural uniformity of the sintered component.

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