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Examination on the existence of the critical and primary crystallite size (d c r ∼ 17 nm and d p ) 50−55 nm) phenomena during θ-to r-phase transformation of the nanosized Al 2 O 3 powder was designed and conducted using two θ-Al 2 O 3 powders of different crystallite sizes. Due to the critical size, the size dependence of the transformation temperature, the rate of transformation, and the inevitable presence of residual θ-phase in the thermal-treated and re-treated "100%-transformed" sample can be expected. Due to the two characteristic sizes and the formation of primary crystallites by the coalescence growth of the critical crystallites, the variation in mean r-size during the transformation can be predicted by means of the difference in the growth rate of the two θ-powder (different crystallite sizes) systems associated with proper thermal treatment techniques. Further, it is important to note that the presence of primary crystallites at various thermal-treated samples becomes possible.

The critical crystallite size for the cubic (c-) to tetragonal (t-) phase transformation of ultrafine BaTiO3 crystallites was examined. Crystallites were prepared by calcination of barium titanyl oxalate tetrahydrate (BTOT) at various temperatures as to obtain crystallites with different sizes. The c- BaTiO3 crystallite which is thermodynamically considered as a high-temperature form can exist at room temperature if the crystallite is smaller than certain size. The critical size for the c→t phase transformation is ∼30 nm. The size may become larger if the crystallite suffers higher lattice strain which can be induced by different powder preparation methods.

Crystallite size variations of nanosized iron oxide particles during γ-to r-phase transformation were examined using DTA/TG, FTIR, XRD, TEM, and BET-N 2 techniques. Synthetic γ-FeOOH and Fe 3 O 4 , prepared as precursors, both converted to γ-Fe 2 O 3 and then completed the phase transformation under thermal treatment. Starting with γ-FeOOH, the γ-Fe 2 O 3 obtained grew from the original size of 5 nm to a size about 25 nm or larger, then transformed to r-Fe 2 O 3 . The r-crystallites obtained showed sizes similar to that of γ-crystallite. With continuous heating, the r-Fe 2 O 3 coarsened to a size of ∼55 nm. Identical phenomena were observed when r-Fe 2 O 3 was prepared from Fe 3 O 4 via γ-Fe 2 O 3 . The study also found that r-Fe 2 O 3 crystallites obtained by calcinations of amorphous Fe(OH) 3 will show sizes smaller than 5 nm. The decomposition temperature can be lowered to 200 °C.