The Effect of Zr-Doping and Crystallite Size on the Mechanical ...

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I. Introduction 1.3. Energetics <strong>of</strong> Nanocrystalline <strong>Zr</strong>O2 <strong>and</strong> TiO2 Phases In microscale particles, only a negligible amount <strong>of</strong> atoms is situated on the surface, whereas the bulk mass <strong>of</strong> atoms is surrounded by other bulk atoms. With a decrease <strong>of</strong> the crystallite size to the nanometer range, the relative amount <strong>of</strong> atoms on the surface increases. Atoms on the surface exhibit a surface structure, different from the bulk material due to unsaturated bondings <strong>of</strong> the atoms. Energetics are therefore very different compared to the bulk mass <strong>and</strong> in most cases, H2O is adsorbed on the surface, making the energetics even more complicated. Figure 4 shows a nanometer scale particle with a core <strong>of</strong> bulk material <strong>and</strong> a surface area as the part <strong>of</strong> the particle within hailing distance <strong>of</strong> the surface, defined to be 0.5 nm. With decreasing particle size, the fraction <strong>of</strong> atoms near the surface increases, <strong>and</strong> at a certain point, all <strong>of</strong> the atoms belong to the surface shell. As will be seen later, the mechanical properties <strong>and</strong> phase stabilities are strongly affected by a decrease <strong>of</strong> the crystallite size to the nanometer range. Figure 4: Plot <strong>of</strong> fraction <strong>of</strong> volume for nanoscale particle as a function <strong>of</strong> the particle diameter, showing the fraction <strong>of</strong> volume within 0.5nm <strong>of</strong> the surface for a spherical particle. From ref. [62]. 1.3.1 Energetics <strong>of</strong> Nanocrystalline Titania Relative phase stabilities <strong>of</strong> micro- <strong>and</strong> nanoscale rutile, brookite <strong>and</strong> anatase were intensively studied by Ranade et al. [63], using high temperature oxide melt drop solution calorimetry. In that method, two samples are each dropped into a molten oxide, such as lead borate, sodium molybdate or alkali borate. <strong>The</strong> difference in observed 16
I. Introduction enthalpy <strong>of</strong> reactants <strong>and</strong> products gives the heat <strong>of</strong> formation. <strong>The</strong> stable form <strong>of</strong> TiO2 microscale materials is rutile, having the lowest enthalpy. Relative to bulk rutile, bulk brookite is 0.71±0.38 kJ/mol [64] <strong>and</strong> bulk anatase is 2.61±0.41 kJ/mol higher in enthalpy [63]. Experiments on nanoscale materials revealed that rutile has the highest surface enthalpy <strong>of</strong> 2.2±0.2 J/m², brookite has a medium value <strong>of</strong> 1.0±0.2 J/m² <strong>and</strong> anatase has the lowest value <strong>of</strong> 0.4±0.1 J/m². <strong>The</strong> closely balanced energetics lead to several phase stability crossovers occurring with the decrease <strong>of</strong> the crystallite size (compare Figure 5). <strong>The</strong> stable phase (with lowest enthalpy) is rutile for big crystallite sizes, brooktie for intermediate sizes <strong>and</strong> anatase for smallest crystallite sizes. Figure 5: Enthalpy <strong>of</strong> micro- <strong>and</strong> nanoscale TiO2 phases rutile, brookite <strong>and</strong> anatase with respect to microscale rutile versus surface area. Data were obtained by high temperature oxide melt drop solution calorimetry using 3Na2O·4MoO3 as a solvent. <strong>The</strong> darker line segments indicate the energetically stable phases. From ref. [63]. Because the MI phase is not quenchable, calorimetric measurements can not be performed on the material. <strong>The</strong> following calorimetric data on TiO2II are reported. For anatase-rutile a difference in enthalpy <strong>of</strong> 1.24 kcal/mole was measured [65] <strong>and</strong> for TiO2II-rutile a value <strong>of</strong> 0.76 kcal/mole [66]. We can therefore estimate that the sequence for bulk material from the stable to the less stable phase is: rutile → brookite → TiO2II → anatase. Taking into account that TiO2II is a common decompression product in experiments <strong>and</strong> occurs naturally as nanocrystallites (e.g. [67]), we can furthermore estimate very roughly that it would plot with a slope comparable to anatase in Figure 5. 17
Page 1 and 2: The Effect
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Page 5 and 6: Zusammenfassung Experimentelle Meth
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Conclusions In contrast, the compre
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Acknowledgments Acknowledgments Thi
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Bibliography [16] J. Haines <strong
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Bibliography [154] G.Y. Shen, V.B.
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Bibliography [191] S. Ananta, R. Ti
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