PHY 598 (Venables) Sect C3

Notes for PHY 598 Sect C3 (Venables)

© Arizona Board of Regents for Arizona State University and John A. Venables

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Lecture notes by John A. Venables. Lecture given 29 Feb 96. Notes rearranged and updated 13 Dec 96.

C3. Phase Diagrams and Phase Transitions

Refs: Zangwill, Chap 11, pages 257-291, and Chap 14, pages 360-375; Luth, Chap 9.4, pages 443-455; Dash, Chap 4, pages 59-91. Various review articles cited in the text.

  • Adsorption in equilibrium with the gas phase
  • A schematic diagram of adsorbed multilayers is given in diagram C3. If the substrate and adsorbate are well ordered, the condensation may proceed in well defined steps, as shown in diagrams C4 and C5 for physisorbed Xe and Kr/ graphite at ML and sub-ML coverages resectively. As studied by several French groups especially (A. Thomy and X. Duval, Surface Sci. Reports 1 (1981) 1), these volumetric studies, using high quality exfoliated graphite, established the existence of 2D solid, liquid and gaseous layers, and the position of the corresponding phase transitions and such fixed points as triple points and critical points. But for more structural details, the (single surface) diffraction and compositional techniques are needed, as discussed in the next section.

  • Adsorption out of equilibrium with the gas phase
  • The examples of physisorption, discussed above, are typically, but not always, in equilibrium with the gas phase. In these cases the state of the system depends on T, and also on p. But at low T, exchange with the gas phase can be extremely, even infinitesimally, slow. In this case, which can occur for physisorption and frequently occurs for chemisorption, the gas pressure is not only very immeasurably low, but is irrelevant for discussion of the behaviour of the system.

    Phase diagrams which use coverage (theta) and T as axes are favored by experimentalists in chemisorption, and more generally at low T, where the pressure goes exponentially to zero. Often in these diagrams the pressure is not known, and there may thereby be some uncertainty about the true nature of the equilibrium. Typically such systems (e.g. Oxygen on Tungsten as discussed by Zangwill, pages 283-287, or Hydrogen on Nickel by Luth, pages 447-449) are treated as closed 2D systems, the equilibrium (or lack of it) with the 3D gas being ignored. This is reasonable for dissociative chemisorption at low and moderate T, due to the very high adsorption energy of the atoms: they are literally confined to the surface layer. A metal-metal chemisorption example where the equilibrium with the gas is taken into account at higher T is the data for Au/W(110), shown in Zangwill, Fig 11.5, with the discussion on pages 262-3.

    Two examples from the recent literature will be sufficient to illustrate these points. There have been several sets of experiments where sub-ML amounts of Xe have been condensed onto metal surfaces. One of these (Eigler and Schweizer, Nature 344 (1990) 524) involved STM experiments at liquid helium temperatures (4K), where the STM tip was used to move the Xe atoms over the surfaces and construct the somewhat obvious IBM, and later spectacular ‘quantum corrals’. Xe/copper is a typical physisorption system, yet at 4K the atoms stay where they are pushed/ put for hours, and never leave the surface during the duration of the experiment, unless one engages in (again non-equilibrium) experiments to pick them up and transport them with the STM tip. A detailed T-dependent study of Xe/Pt(111) (S. Horch, P. Zeppenfeld and G. Comsa, Appl. Phys. A60 (1995) 147, Surf. Sci. ***) was shown to produce good STM pictures below about 30K, where nuclei of solid ML Xe were shown to grow; above this T, however, the STM pictures became blurred, due to the motion of Xe atoms over the surface. This temperature is well below that needed for Xe to desorb from the surface- only then is the full equilibrium state obtainable. We can note that observations of the average structure are then quite possible with diffraction techniques, but that observation of the local structure by STM is impossible. At low T, what we are observing is really the first stages of Xe crystal growth, rather than equilibrium adsorption.

    A chemisorption example is provide by O2/Al(111) (H. Brune et al, Phys. Rev. Lett. 68 (1992) 624; J. Chem. Phys. 99 (1993) 2128). Here, the STM was used at sub-ML coverage to investigate the nature of dissociation of O2 into chemisorbed O. The precursor oxygen molecule is highly mobile at RT, but the final state of the O is completely immobile. By investigation the positional correlations between these O atoms, they were able to deduce that pairs of O-atoms were up to 8 nm away from their point of dissociation. Thus we can visualise this transition as both irreversible, and essentially explosive: the energy liberated during the chemisorption ‘event’ (estimated to be of order 10 eV/ molecule, i.e. large) is transferred in part to the lateral motion of the O-atoms, which then skid to a halt some distance away. This process is but the first of a long series of reactions, for which the end point is the formation of the stable phase, alumina, Al2O3.

    Note: the first section of this material took a whole lecture, with lots of questions from the students and discussion. It is clear that although it doesn't take much space to state what is going on, it does take some time to absorb.

    Continue to section C4

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