Gi®en the surface areas of three different species A,B, and C, what is the most likely contact area between A and B? This problem finds many applications, but it is of specific importance in solid-phase reactions. Reactions in powder mixtures depend strongly on contact area between reactants, e®en when one species may melt. The surface of particles is meshed with small '' tiles,'' and a combinatorial problem is formulated to map all tiles onto each other. The number of different contacts of n constituents n isi; if pores are present, they are considered a constituent. The combinatorial prob-) moment of the PDF gi®es the expectancy ®alue ⌿ A B, A, B, C for contact between species A and B . The theory was demonstrated by two examples. A simple contact problem is sol®ed for two powders that also contain pores. The second example compares kinetic rates for different shapes and sizes of particles.

The structural transformation from the metastable disordered TbCu 7 -type SmCo 7 structure to the equilibrium ordered Th 2 Zn 17 -type Sm 2 Co 17 structure was revealed by x-ray diffraction analysis using Reitveld refinement. The magnetic properties depended strongly on the stage of the transformation, as the coercivity strongly depended on the annealing temperature. The as-solidified alloy in the TbCu 7 -type structure had a coercivity of 4 kOe, which increased to greater than 9 kOe. The coercivity decreased to around 5 kOe as the transformation neared completion upon annealing at higher temperatures. The magnetization processes were also strongly influenced by the structural state. Initially it was totally controlled by nucleation followed by the domain wall pinning-controlled magnetization process.

Rapid solidification has been utilized to produce a series of Pr-Co alloys between the Pr 2 Co 17 and PrCo 5 stoichiometries. In this system, PrCo 5 has easy axis magnetization while Pr 2 Co 17 has easy-plane magnetization. Alloys of the form ͑Pr x Co 1−x ͒ 94 Ti 3 C 3 with x ranging from 0.105 corresponding to the Pr 2 Co 17 compound to x = 0.167 corresponding to the PrCo 5 compound were produced by melt spinning at a tangential wheel speed of 40 m / s. The rapid solidification and alloying additions were found to suppress the formation of the Pr 2 Co 17 ordered phase, leading to the formation of the disordered TbCu 7 -type structure over a range of Pr/ Co ratios. Hysteresis loops were characterized by a smooth demagnetization curve reflective of single-phase demagnetization. Heat treatment at 800°C led to the formation of the Pr 2 Co 17 and PrCo 5 phases, and the presence of the soft magnetic Pr 2 Co 17 phase drastically decreased the coercivity. The soft magnetic behavior was consistent with in-plane magnetization of the Pr 2 Co 17 structure that formed during heat treatment. However, the relatively high coercivity observed in the as-solidified alloys with the disordered TbCu 7 -type structure suggests that dumbbell disorder may create easy axis magnetization, and changes in saturation magnetization also imply that dumbbell configuration is important to the magnetic properties.

An experimental method, electro thermal explosion (ETE), is used to measure the macro kinetic parameters of the high-temperature titanium/carbon reaction. Different stages of the reaction