PHY 598 (Venables) Sect C4

Notes for PHY 598 Sect C4 (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 7 Mar 96. Notes updated 13 Dec 96.

C4. Solid Mono- and Multi-layers

Refs: Zangwill, Chap 11, pages 257-291, and Chap 14, pages 360-375; Dash, Chap 7, and 8, pages 145-212; Various review articles cited in the text.

  • Physisorption: tests of interatomic force and lattice dynamical models
  • Once one applies ’single surface’ techniques to adsorbed layers with sub-ML sensitivity, several types of phase and phase transitions can be observed. Zangwill gives a rather full account, and there are some other examples in diagrams C6-C9. Staying with physisorption for the moment, diagram C6 shows the AES amplitude for Xe/graphite as a function of log (p). These curves are adsorption isotherms at the temperatures noted, as the pressure is raised through the gas-solid transition. The first order character of the transition is seen very clearly. The corresponding crystallography of this 2D solid phase was observed by diffraction (LEED and THEED), and the THEED work had high enough precision to detect that this solid was incommensurate (I) with the graphite, having a lattice parameter some 6-7% larger than the graphite under the conditions of diagram C6. At lower T and p, the THEED work was able to demonstrate that the layer was compressed into a commensurate (C) phase, i.e. an I-C phase transition was observed. The opposite situation happens for Kr/graphite. Kr first condenses into the C-phase, and then compresses into the I-phase, with a spacing a bit smaller than the graphite. A pictorial description of the I-phase, and its representation in terms of domains walls, solitons or misfit dislocations, is given by Zangwill (pages 270-277).

    There are in fact two types of I-phase: the aligned (IA) phase and the rotated (IR) phase, with another possibility of a phase transition. This was first discovered for Ar/graphite using LEED (diagram C7), and is even more pronounced in the case of Ne/graphite (diagram C8). The diffraction spots are split, corresponding to two domains rotated in opposite directions. The reason for this effect is that the incommensurate phase has a modulated lattice parameter; this gains energy from having more of the adsorbate in the potential wells of the substrate, but costs energy in the alternate compression and rarefaction of the adsorbate. Because typically shear waves cost less energy than compression waves, it pays to include a bit of shear if the misfit is large enough.

    This means we can get C-IA-IR transitions in sequence, which have been observed for both Kr and Xe/graphite. We can also get 1D incommensurate, or ‘striped’ phases, where the misfit is zero in one direction, and non-zero in the other. This means that the symmetry is reduced, for example from hexagonal to rectangular. There is also a lot of interest in the melting transition; the details of all these phases are examples of competing interactions, often quite subtle. Physisorbed layers are thus testbeds for understanding interatomic forces/ lattice dynamics at surfaces. The combination of all the information from different types of experiment is still very much a research project. For example, the outline Ne/graphite (log p, 1/T) phase diagram is shown in diagram C9. Phase diagrams (T, coverage) for Ar, Kr, and Xe/graphite are shown by Zangwill on page 265. Note how it is impossible to portray all the information on these 2D cuts of the 3D (T, log p, coverage) data.

    Any of these topics, studied in more detail, would be suitable for a mini-project. I am planning on building up some web-based resources in this area, based largely on undergraduate projects. One, on the phases of neon on graphite, was started with Jeremy Piwowarczyk in Spring ‘96 and continued through the Fall ‘96 semester; it can be found in the /reu directory (../reu/jpsect1.html) from my home page.

  • Chemisorption, theory and practice
  • The thermodynamics of chemisorption relies fairly heavily on the concept of a lattice gas. The starting point (anzatz) for a lattice gas is a Hamiltonian which is isomorphous with magnetic Hamiltonians, such as the Ising model, which was solved exactly in 2D by Onsager in 1944 (Zangwill, page 259-265). As with all these models, the beauty is that they provide an explicit solution to a well-posed question. The simplest spin-1/2 Hamiltonian (Zangwill, page 261) is

    There is thus a major theory industry in constructing and solving such models, both with analytic solutions and with Monte Carlo simulations. These models are most reasonable for strong chemisorption, where we have a very site-specific bond, and where lateral interactions are somewhat smaller. The type of agreement with these models is shown by Zangwill on page 284; interesting, but not the last word.

    Chemisorption in practice is strongly linked to the study of catalytic reactions, which takes us too far from surface physics to be studied in this course at present. There are many fascinating cases of chemisorption reactions, some of which are described by Zangwill and Luth; many more are described in the more chemical literature, notably in D.A. King and D.P. Woodruff’s ‘The Chemical Physics of Solid Surfaces and Heterogeneous Catalysis’ series, especially volumes 3 and 4, and in books by G. Ertl and by G. Somorjai. Theory has been done, amongst others, by T.L. Einstein, J.K. Norskov, M. Scheffler and their groups. One of the most fascinating recent phenomena is the occurrence of time-dependent (periodic or chaotic) reactions which take place at the moving boundary between two adsorbed phases, and which have been observed in real time by photo-electron emission microscopy (PEEM- see diagram C10). A study of any of these authors or topics is suitable for a mini-project; for example, in Spring ‘96, one student studied effective medium theories of chemisorption on metals, following recent reviews by Norskov.

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