Negative thermal expansion and phase transitions in the Niobium Oxyfluoride solid solution: NbO₂₋ₓF₁₊ₓ

Abstract

The thermal expansion of functional materials is a significant property in any applications involving significant temperature changes. Engineering and tuning low thermal expansion is important for devices ranging from solid oxide fuel cells to optical components in telescopes, where maintaining shape and stability are vital. Whilst most materials expand rapidly on heating, a small minority exhibit very low or negative thermal expansion (NTE). Expanding the range of these NTE materials and fully understanding their thermal expansion origins is vital for the design of multi-functional, low thermal expansion materials.

The cubic, ReO₃-type, structure is associated with NTE through flexibility of octahedral tilt vibrations which lead to contraction on heating. The niobium oxyfluoride solid solution, NbO₂₋ₓF₁₊ₓ, maintains a cubic ReO₃-type structure with flexible oxygen:fluorine composition, thus providing an ideal system for exploration of anion driven effects. This system is utilised in this thesis to explore the impact of oxygen:fluorine composition on thermal expansion and phase transitions as well as the fundamental chemistry and physics underpinning this. A novel mechanism for the tuning of NTE through anion doping is uncovered in this thesis as well as the first example of NTE in a mixed anion material.

Chapter One provides an overview of the importance of thermal expansion, a review of the origins of NTE and current NTE materials. The ReO₃-type structure, the origins of NTE and cubic to rhombohedral phase transitions are reviewed. Chapter Two follows on from this with a review of the underlying physics of thermal and pressure behaviour from the perspective of phonons, equations of state and Landau theory. The experimental and computational methodology (powder diffraction, pair distribution function analysis and density functional theory) used through the project are introduced.

Chapter Three will outline the synthesis and characterisation of the NbO₂₋ₓF₁₊ₓ solid solution from x = 0 to x = 0.6. The composition is confirmed through magnetic susceptibility and lattice parameter trends. The thermal decomposition properties are also explored through thermogravimetric analysis to confirm the presence of fluorine doping. Variable temperature powder X-ray diffraction is used to characterise the thermal expansion behaviour. This is found to vary from positive thermal expansion (NbO2F) to zero and then negative thermal expansion (NbO1.4F1.6). The latter of which has a mean volumetric coefficient of thermal expansion of −5 ppm K⁻¹. This novel NTE can be related to a thermal dependence of the anion displacement parameters, confirming transverse anion motion to drive the shift in thermal expansion. Unusual high temperature hysteresis in the thermal expansion is also identified.

Chapter Four uses both neutron and X-ray powder diffraction at variable temperature and pressure to explore the cubic to rhombohedral phase transitions of NbO₂₋ₓF₁₊ₓ. A low temperature phase transition in NbO₂F is confirmed whilst the fluorine doped samples remain cubic at all temperatures. The high-pressure, rhombohedral, phase transition is also found to be inhibited by fluorine doping with the transition pressure shifting from 0.3 GPa in NbO₂F to 1.3 GPa in NbO₁.₇F₁.₃. This confirms predictions from existing density functional theory (DFT) modelling indicating the cubic ReO₃-type structure is stabilised by fluorine doping.

In Chapter Five, the origins of the thermal expansion and phase transitions in NbO₂₋ₓF₁₊ₓ are explored through DFT phonon calculations and X-ray Pair Distribution Function (PDF) analysis. High symmetry models of NbO₂F and NbOF₂ are constructed and the phonon dispersions and Grüneisen parameters are calculated. Soft modes with negative Grüneisen parameter have a negative contribution to thermal expansion. These are identified at the Brillouin zone boundary corresponding to octahedral tilting modes, confirming these modes as key to thermal expansion. A mode with much more negative Grüneisen parameter is identified in NbO₂F, consistent with a more favourable phase transition under pressure in this composition. This instability to octahedral tilting is attributed to a second order Jahn-Teller effect which is inhibited in fluorine doped phases. X-ray PDF analysis at low temperature is consistent with a 1D ordering of oxygen and fluorine in all compositions. Significant local static distortion of both the Nb and anions is identified in all phases but found to be smaller in the fluorine doped phases. A reduction in local distortion is able to favour structural NTE which therefore accounts for the observed thermal expansion behaviour. NTE in the oxyfluorides can therefore be understood in terms of static vs dynamic anion displacements.

Chapter Six summarises the key conclusions of this thesis and outlines potential future work on the NbO₂₋ₓF₁₊ₓ system. A review of existing materials and conclusions of this thesis are used to construct design rules for the discovery of novel mixed anion NTE materials. Some candidates are proposed from existing ReO3-type oxyfluorides which may exhibit NTE.