Sequence of Stages

Densification during liquid-phase sintering commonly occurs in three stages after the liquid forms: rearrangement, solution-reprecipitation, and final-stage sintering. However, in many systems there is a strong solid-state diffusion contribution to the overall densification. A brief description of these stages follows.

Solid-State Sintering Prior to Liquid Formation. The same solubility, segregation, and diffusivity criteria that are favorable for LPS can lead to enhanced solid-state sintering prior to liquid formation. Powders prepared for LPS generally consist of admixed powders designed to lower the activation energy for diffusion, so solid-state sintering during heating can be greatly enhanced. This can result in significant densification prior to liquid formation. In fact, for systems such as the W-Ni-Fe heavy alloys, more than 95% of the total densification occurs prior to liquid formation (Ref 7). Thus, solidstate sintering is an important part of the overall LPS process. The relative contribution of solid-state sintering to total densification increases with increasing solubility of the base in the additive, increasing homogeneity of the additive compound, decreasing heating rates, and decreasing particle size. For the liquid to further assist densification, it must dissolve any solid-state sinter bonds that form during heating, and thus the solid must be soluble in the liquid. Indeed, even with the achievement of near-theoretical densities in the solid state, complete dissolution of solid-state sinter bonds has been demonstrated for the W-5Ni system (Ref 8).

Rearrangement. Once the liquid phase forms, typically the first step during classical LPS is rearrangement. At the onset of liquid formation, capillary forces pull the wetting liquid into particle necks and pores. These capillary forces also exert an attractive bonding force on the particles, resulting in rapid shrinkage. This is termed as primary arrangement. The liquid further enhances the packing by attacking and disintegrating clusters of particles by a process known as secondary rearrangement. Repacking and further densification occur by redistribution of the small particles between the large particles. Pore elimination occurs by viscous flow during this stage.

The dimensional behavior immediately after liquid formation is affected by both the processing conditions and material characteristics. The material and process variables that influence shrinkage and swelling are summarized in Table 2. A smaller base particle size is beneficial to rearrangement due to an increase in capillary forces (Ref 9). For systems with a small solubility ratio between the base alloy and additive, the amount of swelling can be reduced by the use of a smaller additive particle or by increasing additive homogeneity (Ref 10, 11). Particle shape is also important. Smooth, round particles tend to pack more homogeneously and are more easily rearranged, resulting in greater densification (Ref 12). Solubility also has a smoothing effect on the particle surfaces, decreasing interparticle friction and improving packing. High green densities and slow heating rates can restrict rearrangement due to a greater degree of bonding between the solid particles. A low contact angle and high liquid-vapor surface energy increase the capillary forces between the particles (Ref 13).

Table 2 Characteristics affecting initial-stage behavior in liquid-phase sintering

Factor

Swelling

Shrinkage

Solid solubility in liquid

Low

High

Liquid solubility in solid

High

Low

Diffusivities

Unequal

Equal

Additive particle size

Large

Small

Base particle size

Large

Small

Green density

High

Low

Contact angle

High

Low

Dihedral angle

High

Low

Temperature

Low

High

Time

Short

Long

Solution-Reprecipitation and Grain Shape Accommodation. In most LPS systems, insufficient liquid is present to fill all the pores following rearrangement. Additional densification is accomplished by mass transport or solution reprecipitation in which the grains change shape and size distribution, resulting in a higher packing density. In this case atoms at point contacts between solid particles and at other convex surfaces have higher solubility in the liquid than atoms at concave surfaces. The atoms on the convex surfaces dissolve and diffuse through the liquid to neighboring concave surfaces where they reprecipitate. As the grains change shape, they are able to pack better and release liquid to fill any remaining pores (Ref 14, 15). Densification occurs as the centers of the grains grow closer to each other. The reduction in energy associated with the elimination of pores offsets the increase in the solid-liquid surface area. Equilibrium grain shapes are determined by the packing characteristics, surface energies, and liquid volume fraction (Ref 16).

Compared to the rearrangement stage, the shrinkage rate during the solution-reprecipitation stage is lower. However, for systems with only small amounts of liquid phase, solution reprecipitation can be the most significant densification mechanism. The kinetics of solution reprecipitation may be governed by interfacial dissolution or reprecipitation (reaction controlled) or by the rate of mass transfer through the liquid (diffusion controlled). In cases where the base material is a chemical compound, such as tungsten carbide, the kinetics are generally reaction controlled, while alloys are generally diffusion controlled. For diffusion-controlled cases, the densification rate is enhanced by a smaller particle size, higher solubility of the base in the liquid, and higher diffusivity of the base in the liquid. Concurrent with densification, there can be a significant degree of microstructural coarsening by the same diffusional processes.

Grain growth occurs concurrently with shape accommodation as small grains dissolve and reprecipitate on larger grains through Ostwald ripening or grain coalescence, or even solid-state grain growth of skeleton. The driving force is a decrease in interfacial energy through a reduction in both the amount and curvature of the solid-liquid interface. The rate of coarsening is generally described by:

where G0 is the initial grain size, G is the average grain size after time t, T) is the growth rate constant that is dependent on the solid volume fraction ($) and temperature T, and n is the growth exponent (the value of n varies between 2 and 5, depending on what mechanisms dominate mass transport). A cubic relationship is often observed in systems with rounded grains, such as the heavy alloys. In the case of reaction control, the exponent n is 2 and growth occurs at preferred crystal orientations, leading to a prismatic shape as in the cemented carbides. For a constant liquid volume fraction, an increase in temperature increases the value of K (Ref 17). In addition, the grain growth rate constant

K increases with increasing solid fraction

Pat a given temperature.

Generally it is desirable to avoid the microstructural coarsening stage of LPS, because it can degrade the mechanical properties. Pore coarsening is also a concern, especially if the sintering atmosphere or decomposition products become entrapped in closed pores (Ref 18).

Final Stage Sintering. The final stage of LPS is controlled by the slow densification of the solid skeleton structure. As noted, microstructural coarsening continues, and the residual pores enlarge if they contain trapped gas (Ref 18). If the entrapped gas is insoluble in the material, the gas pressure inside the pores restricts densification. If the entrapped gas has slight solubility in the matrix, large pores grow at the expense of smaller pores via an Ostwald ripening mechanism. This leads to compact swelling, which becomes more pronounced with large volume fractions of liquid. Pore coarsening due to gas entrapment is greatly reduced if the gas is highly soluble in the material; pore coarsening can be avoided with vacuum sintering.

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