the particle-size distribution
A real powder is never all one size. Some particles are bigger, some smaller, and the particle-size distribution is the full picture of how the sizes are spread, not just their average. Think of a school photo: the average height tells you little compared with seeing the whole range from the shortest child to the tallest. Plotted as a curve of how much powder sits at each size, the distribution reveals whether the particles are all nearly the same, called narrow or monosized, or span a wide range from dust to grit, called broad.
The distribution is usually summarised by a few landmark numbers. The d50, or median, is the size below which half the powder lies. The d10 and d90 mark the fine and coarse ends, the sizes below which 10 percent and 90 percent of the material fall, and the gap between them measures the spread. A narrow distribution has d10 and d90 close to d50; a broad one has them far apart. Some powders are even bimodal, with two separate humps, a batch of fines mixed with a batch of coarse. Which shape you want depends on the goal. For the densest packing before firing, a deliberately broad or bimodal blend can be best, because small particles nestle into the gaps between big ones and fill space efficiently. For a uniform, defect-free fired microstructure, a narrow distribution is usually preferred, because it sinters evenly without a few oversized grains running away.
The distribution matters because the extremes, not the average, often decide the outcome. A powder with an excellent mean size can still be spoiled by a small tail of oversized particles, since each big particle can seed a large grain or a pore that becomes the fracture-starting flaw in the finished part. This is why quality control watches the d90 and the top tail, not just the d50. The honest lesson is that two powders can share an identical average size yet behave completely differently, one packing and sintering cleanly, the other riddled with the defects its coarse tail leaves behind.
Two alumina powders both report d50 = 0.5 micron, but one is narrow (d10 = 0.3, d90 = 0.8) and the other broad with a coarse tail (d10 = 0.2, d90 = 5). The broad one carries stray 5 micron particles that become large grains and pores, so despite the same average it fires to a weaker part.
The average hides the tails; a few oversized particles can seed the flaw that decides strength.
Never judge a powder by its average size alone. Two powders with the same d50 can behave oppositely, because the coarse tail, the d90 and beyond, often seeds the large grains and pores that limit strength.