Accelerated sintering in phase-separating nanostructured alloys

Sintering of powders is a common means of producing bulk materials when melt casting is impossible or does not achieve a desired microstructure, and has long been pursued for nanocrystalline materials in particular. Acceleration of sintering is desirable to lower processing temperatures and times, and thus to limit undesirable microstructure evolution. Here we show that markedly enhanced sintering is possible in some nanocrystalline alloys. In a nanostructured W–Cr alloy, sintering sets on at a very low temperature that is commensurate with phase separation to form a Cr-rich phase with a nanoscale arrangement that supports rapid diffusional transport. The method permits bulk full density specimens with nanoscale grains, produced during a sintering cycle involving no applied stress. We further show that such accelerated sintering can be evoked by design in other nanocrystalline alloys, opening the door to a variety of nanostructured bulk materials processed in arbitrary shapes from powder inputs.

. Index x numbers co 6 orresponding g to Figure 4 of the paper.  Supplementary Figure 3a, illustrating a structure of nanoscale W-rich grains with a Cr-rich grain delineated by a yellow dashed line.

Sample Mean Size (μm) Mode Size (μm) Standard Deviation (μm)
This image shows the occurrence of phase separation in the bulk, which complements the observations of phase separation on the powder particle surfaces and necks in Fig. 1  here is consistent with those we presented in the paper at lower densities and in Supplementary Figure 6b.

Supplementary Note 2
The integral of instantaneous linear shrinkage rate during sintering can be represented as follows 1 : where is the surface energy, Ω is the atomic volume, R is the gas constant, T is the temperature, G is the average grain size, ρ is the relative density, t is time, Γ is a parameter which relates the driving force, mean diffusion distance, and other geometric features of the microstructures, and n = 3 for volume diffusion, and and n = 4 for grain-boundary diffusion. With slight rearrangement, Supplementary Equation 1 is divided into two parts: which comprises all microstructural and materials properties except for activation energy.  Fig. 3 in the manuscript.

Supplementary Note 3
In some enhanced densification methods such as liquid phase sintering, the formation of the second phase permits mechanical densification by flow, i.e., mechanical deformation, of the softer (liquid) phase. This leads to a significant microstructure evolution as a function of density. To verify that nanophase separation sintering does not exhibit such structural evolution, we measured the size of the Cr-rich necks between powder particles for several sintered densities. The results are shown in Supplementary Figure 6.
The Cr-rich layer does not change beyond the measurement uncertainty over the range of relevance of the conditions. Moreover, the trend in Supplementary Figure 6a shows, if anything, an increase in the Cr layer thickness; unlike liquid phase sintering where densification might lead to flow and compression of these layers, no such trend is observed here.

Supplementary Note 4
The driving force for sintering in the case of nano-phase separation sintering can be estimated using prior models, e.g., that for liquid phase sintering. A model geometry is shown in Supplementary Figure 7, and corresponds to the one shown in Supplementary Figure 6b or the schematic in Fig. 3 of the paper. (Note that there is no liquid phase in the present work, and instead the phase between two particles in the model is a crystalline Cr phase that is a rapid diffusion pathway for tungsten.) The driving force for sintering can be represented by the chemical potential gradient, where , are the chemical potentials of a W atom and of a vacancy, respectively and the capillary pressure at the neck provides the gradient. Therefore the driving force for sintering is finally estimated as where α is a constant, Ω is the atomic volume of W, γ is the surface energy of Cr, and r is the radius of pore as delineated in Supplementary Figure 7.
If the kinetically limiting mass transport process leading to densification is assumed to be W diffusion through Cr, the densification rate calculated using the equation of the driving force above based on the microstructural geometry that DeHoff has provided 2 is as follows: where L is the length of the compact, is the surface energy, is the atomic volume of W, is the Boltzmann constant, T is the temperature, G is the average particle size, t is time, is the thickness of the Cr-rich layer, are the coefficients for W diffusion in Cr, and Γ is a parameter which relates the driving force,