Supplemental Material
1. Introduction
It is generally true that the relative stability of any two polymorphs depends on their
free energies; the most stable polymorph has a minimum Gibbs free energy. Surface effects,
which were ignored due to the small surface to volume ratio in bulk have to be taken into
consideration since the surface to volume ratio of nanocrystals is fairly large, and the surface
can affect the ‘bulk’ properties of nanocrystals [14]. Internal pressure due to excessive number
of dangling bonds has seen to cause discrepancy in theoretical and experimental particle size
values [12]. Other affects like shape factor [13] also contribute to the general stability and thus
have to be considered when developing theoretical background to predict critical particle size
values. Thus, in our approach we have taken into account the combined effect of all the factors
to predict the particle size quantitatively for an observed polymorphic transition.
2. Phase Transformation in Alumina
Blonski and Garofalini[27] observed that γ-Al2O3 can sustain higher surface areas at high
temperatures whereas α- Al2O3 would coarsen at similar temperatures. It is observed that αAl2O3 corundum structure is the stable phase in bulk. Navrotsky and Mchale[6], when using high
temperature oxide melt calorimetry for nanocrystalline Al2O3, showed that γ-Al2O3 (the phase
observed for nano-sized particles) is more stable in enthalpy than nanophase α-Al2O3
(corundum), the macrocrystalline thermodynamically stable phase. Mchale et al.[29] observed
that γ-Al2O3 is the thermodynamically stable modification when the specific surface area of
alumina is larger than 125 m2/g, or less than about 13 nm in particle size. Also, a very recent
study in Ref. 5 achieved a γ-Al2O3 transformation temperature of 473K with particle size of
3.2nm.
3. Phase transformation in Titania
Rutile titania is thermodynamically stable at room temperature, and anatase is kinetically
stable and transforms to rutile at higher temperatures[21]. The transformation of macroscopic
specimens of anatase into rutile reaches a measurable speed at 1273K. With nanosized anatase,
the transformation reaches a measurable speed at 673K[4]. It was observed by Mitsuhashi and
Kleppa[30], that thermodynamic stability of different titania phases is particle dependent. This
explains why anatase is the more stable phase at the nanoscale at particle size below 14nm.
The titania phase transformations were predicted somewhat by Zhang and Banfield[10], who
concluded that, for equally sized particles, for particle size <11nm, anatase was
thermodynamically stable, for particle size between 11nm and 35nm, brookite was stable, and
for particle size >35nm, rutile was stable. They also showed that the stability of anatase and
rutile reverses at 16nm which was in reasonable agreement with the 14nm particle size
observed by Mitsuhashi and Kleppa[30]. Gouma et al.[4] had predicted the critical particle size
to be 8nm below which anatase was stable.
4. Phase transformation in Zirconia
Monoclinic ZrO2 phase, stable at room temperature, is transformed to tetragonal at
1443K[31]. The tetragonal to monoclinic transformation in ZrO2 was found to be size
dependent when Garvie and Goss[32] observed size dependence of phase transformation
temperature and found the reciprocal crystallite size is a linear function of the transformation
temperature. Concluding that the (unquenchable) high temperature tetragonal Zirconia phase
that is stable only above 1443K, existed indefinitely at room temperature in nanocrystals of
about 10nm diameter.
5. Phase transformation in Fe2O3
Fe2O3 exists in a stable α phase and has three metastable phases γ, β, ε-Fe2O3. At high
temperatures Fe2O3 converts to amorphous phase. And melts at 1838 K. The γ → α
transformation in bulk occurs at around 933K[34].
The α-Fe2O3 to γ-Fe2O3 phase
transformation at nanoscale was studied by Yen et al.[35], who observed a critical particle size
of about 25nm above which α- Fe2O3 was more stable and below which up to 5nm γ- Fe2O3
was more stable. Further, as the temperature increased from 573K to about 700K, there was
coarsening of grains and α- Fe2O3 was more stable. The decrease of surface enthalpy with
increasing metastability of the bulk polymorph leads to crossovers in enthalpy (and also free
energy) of polymorphs at the nanoscale. Thus, γ- Fe2O3 (maghemite) becomes stable with
respect to α- Fe2O3 (hematite). Another study[36] on thermal stability of γ- Fe2O3 observed
that between 713-823K, the specimen is in a mixed state of γ and α- Fe2O3 and when the
temperature is higher than 823K, the specimen has changed completely into γ- Fe2O3. The
haematite grains forming from lepidocrocite via maghemite are well-crystallized with sizes
distinctly larger than that of the preceding maghemite particles. Feitknecht & Mannweiler
(1967)[37] proposed that 50–100 neighbouring maghemite crystallites of about 5 nm would
finally transform into one large haematite particle.