Kinetic model for TiO2 polymorphic transformation from anatase to rutile

Giridhar Madras, Benjamin J. McCoy, Alexandra Navrotsky

Research output: Contribution to journalArticlepeer-review

55 Scopus citations


We propose a distribution kinetics model for the polymorphic transformation (anatase to rutile) and coarsening of TiO2. Based on population balance equations for the size distributions of the dimorphs, the simplified model applies a first-order rate expression for transformation combined with Smoluchowski coalescence for coarsening of anatase and rutile particles. Two moments of the size distributions (number and mass of particles) lead to dynamic expressions for extent of reaction and average particle diameter. The model describes the time-dependent data of Banfield and colleagues fairly accurately, and provides activation energies for anatase coalescence and transformation. The equilibrium constant for the microscopically reversible transformation, occurring without coarsening, yields a small endothermic enthalpy change per mole of TiO2. This probably reflects contributions of the transformation enthalpy of the anhydrous phases at the given particle size, which is very close to 0, and the enthalpy associated with a small amount of dehydration (endothermic water evaporation) during transformation.

Original languageEnglish (US)
Pages (from-to)250-255
Number of pages6
JournalJournal of the American Ceramic Society
Issue number1
StatePublished - Jan 2007
Externally publishedYes

ASJC Scopus subject areas

  • Ceramics and Composites
  • Materials Chemistry


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