Rearrangement

Two powders, a base and an additive, are mixed and pressed into a green compact. The green compact is then heated to a temperature where a liquid forms; volume fractions between 5-15% liquid are typical.^[3] The capillary force due to the wetting of the solid particles by the liquid rapidly pulls the liquid into interparticle voids and causes particles to rearrange. Wettability is described by the contact angle, ${\displaystyle \theta }$, which can be given as a difference of relative surface energies between the solid, liquid, and vapor (${\displaystyle S}$, ${\displaystyle L}$, ${\displaystyle V}$, respectively):

${\displaystyle \theta =\arccos \left({\frac {\gamma _{SV}}{\gamma _{LV}}}-{\frac {\gamma _{SL}}{\gamma _{LV}}}\right)}$

Low contact angles indicate good wettability, and will result in a capillary force pulling the compact together. High contact angles indicate poor wettability, which will result in compact swelling.^[3] Wettability can be improved by alloying or by increasing temperature, and is also aided by small, regularly shaped particles and a homogeneous green compact. An extremely effective approach is to directly coat powders with the liquid-forming component, allowing the liquid phase to form directly on the particle boundaries.^[3] However, components can experience “slumping”, or shape distortion, if too much liquid is formed during this stage. The rearrangement stage proceeds very rapidly, with the majority of densification occurring within three minutes of melt formation.^[2]

Solution-Reprecipitation

As porosity is eliminated and rearrangement slows, diffusive mechanisms, analogous to those present in diffusional creep, become dominant and change the sizes and shapes of powder particles. These mechanisms proceed via the dissolution of solid into the liquid phase, diffusion through the liquid, and reprecipitation; hence, the solubility and diffusivity of the solid in the liquid controls the rates of these processes. The process of grain growth or particle coarsening is called Ostwald ripening and occurs because smaller grains are more soluble in the liquid than larger grains. The resulting concentration gradient causes material to diffuse through the liquid, causing larger grains to grow at the expense of smaller grains. Shape change proceeds similarly; in a process termed “contact flattening”, solid preferentially dissolves in areas with high capillary pressure (i.e. where particles are close together) and reprecipitates elsewhere. Thus, two curved surfaces in close proximity will flatten over time. Shape change can also be driven by anisotropy in the surface energy of the solid and/or differences in the magnitudes of the solid-solid and solid-liquid interfacial energies. These shape changes allow the grains to pack more tightly, further eliminating porosity and densifying the compact. Early models of solution-reprecipitation demonstrate that the rate of densification can be increased by increasing temperature, decreasing the grain size, and increasing the solid solubility in the liquid.^[3]

Final Densification

In the final stage, densification is slowed even further because the compact strengthens with neck growth and the formation of a solid skeletal microstructure. This regime is typically best described by classical solid phase sintering. Rearrangement is inhibited, but coarsening continues to occur via diffusion. Additionally, pores containing trapped gas can expand until the pore pressure, ${\displaystyle P_{pore}}$, is balanced against the liquid-vapor surface energy. For spherical pores with diameter ${\displaystyle d_{pore}}$, this is described by

${\displaystyle P_{pore}={\frac {4\gamma _{LV}}{d_{pore}}}}$

where ${\displaystyle \gamma _{LV}}$ is the liquid/vapor interfacial energy.^[3] Generally, due to coarsening and pore expansion, extensive time in this final stage tends to degrade the properties of compacts.