Directions of zero thermal expansion and the peritectic transformation in HfTiO4

Scott J. McCormack, William A. Wheeler, Benjamin S. Hulbert, Waltraud M. Kriven

Research output: Contribution to journalArticlepeer-review


The anisotropic infinitesimal coefficients of thermal expansion (CTE) and the peritectic transformation of orthorhombic-HfTiO4 (space group: pbcn, #60) to tetragonal-HfO2 (space group: P42/nmc, #137) plus liquid at 1980 °C (O-HfTiO4⇄T-HfO2+L(Hf,Ti,O)) have been studied by in-situ X-ray powder diffraction from room temperature to complete melting (~2300 °C) in air, using a Quadrupole Lamp Furnace (QLF) and a Conical Nozzle Levitator (CNL) equipped with a 400 W CO2 laser. Directions of zero thermal expansion were identified in the temperature range ~25 – 580 ˚C and visualized in 3D using distorted cones and 2D stereographic projections. The directions of zero thermal expansion change as a function of temperature. The (021) pole of orthorhombic HfTiO4 was identified as having the lowest root mean squared (rms) thermal expansion, ~12 times lower than the highest rms thermal expansion direction [100] over the temperature range: 25 – 580 ˚C. The topotactic, peritectic transformation has been fully described by extracting the lattice correspondence, lattice variant deformation and a structural motif (grouping of cations) that relates the two structures at the transformation temperature. Symmetry decomposition was performed to show that the orthorhombic-HfTiO4 and tetragonal-HfO2 structures are simply related by polyhedral rotations and cation oxygen coordination changes, in addition to a slight adjustment in cation positions.

Original languageEnglish (US)
Pages (from-to)187-199
Number of pages13
JournalActa Materialia
StatePublished - Nov 2020


  • Peritectic, In-situ high temperature X-ray diffraction
  • Phase transformations
  • Thermal expansion
  • X-ray synchrotron radiation

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Ceramics and Composites
  • Polymers and Plastics
  • Metals and Alloys


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