Physics
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Item Critical Exponents of a Four-State Potts Chemisorbed Overlayer: p(2x2) Oxygen on Ni(111)(American Physical Society, 1981) Roelofs, L. D.; Kortan, A. R.; Einstein, Theodore L.; Park, Robert L.We report the first determination of critical exponents for a chemisorbed overlayer, using low-energy electron diffraction. We examine the order-disorder transition of p(2x2) oxygen on the (111) surface of nickel. This study is the first of critical behavior of a two-dimensional system in the four-state Potts universality class. Discussion of disparity between our results and predicted exponents considers several possibilities, including logarithmic corrections.Item Extended Appearance-Potential Fine-Structure Analysis: Oxygen on Al(100)(American Physical Society, 1980) Laramore, G.E.; Einstein, Theodore L.; Roelofs, L. D.; Park, Robert L.To measure O-Al separation at Al(100) surfaces disordered (low-energy electron-diffraction beams extinguished) by reaction with oxygen, the extended appearance-potential fine structure was analyzed above the threshold for electron-bombardment excitation of the O 1s core. Calculation shows that the outgoing electron has angular momentum l=0, allowing simple Fourier inversion of the fine structure. The separation, 1.9+-0.05 A, suggests that oxygen lies under the top layer, a result undetectable in extended-x-ray-absorption fine-structure measurements on thicker films.Item Effect of the central atom potential on the extended fine structure above appearance potential thresholds(American Physical Society, 1980) Laramore, G.E.; Einstein, Theodore L.; Roelofs, L. D.; Park, Robert L.The formalism previously given for describing the extended fine structure above appearance-potential-spectroscopy (APS) thresholds is extended by incorporating the effects of the excited "central" atom potential in an exact manner. The excitation-matrix elements are expressed in terms of the exact wave functions of the central atom potential. This introduces a "phase renormalization" into the excitation-matrix elements and eliminates a previously noted "phase difference" between single- and multiple-scattering calculations employing a plane-wave basis set. A series of approximations is then made which leads to an expression for the APS extended fine structure in terms of sinusoidal functions and hence provides a rationale for a Fourier-transform analysis. Simple model calculations assuming a constant "bare" excitation-matrix element, a spherically symmetric electronic density of states, and only S-wave scattering from the atomic cores are performed for a cluster of atoms having the atomic geometry of bulk vanadium. These calculations display the major predictions of the formalism and indicate that for a given system there may be some optimal energy range for data analysis. The problem of electron characteristic losses is considered, and it is pointed out that in the small-momentum-transfer limit the simple dipole selection rules appropriate to a photon-excitation process again apply. This may obviate many of the problems introduced by multiple angular momentum final states in the APS process.Item Structure factors associated with the continuous melting of two-dimensional lattice gases(American Physical Society, 1987) Bartelt, N. C.; Einstein, Theodore L.; Roelofs, L. D.We study the temperature dependence of the structure factors of two lattice gases which undergo order-disorder phase transitions. Our goal is to determine how much information about the critical behavior of these phase transitions a low-energy electron-diffraction experiment might obtain. We use Monte Carlo simulation to compute the structure factors.Item Transfer-matrix approach to estimating coverage discontinuities and multicritical-point positions in two-dimensional lattice-gas phase diagrams(American Physical Society, 1986) Bartelt, N. C.; Einstein, Theodore L.; Roelofs, L. D.We present a method of computing coverage discontinuities in two-dimensional lattice-gas phase diagrams using transfer matrices. By applying the method to Baxter’s generalized hard-square model, we find good agreement with exact results. This method also can be used to estimate the position of multicritical points, and we again find good agreement with exact results and with previous work on the Ising metamagnet. We discuss the transfer-matrix eigenvalue spectrum around an Ising tricritical point and verify the prediction of conformal invariance that the finite-size scaling behavior of each of the leading eigenvalues is governed by a different critical exponent at the critical point. We show numerically that the finite-size convergence of the free energy at the (Ising-like) tricritical point of Baxter’s model is consistent with a conformal anomaly of (7/10). We show that the justification of a commonly used method to locate multicritical points using simultaneous scaling of the correlation length and the "persistence length" is misleading. Finally we suggest a method of estimating the position of multicritical points using information from only one strip width.Item Structure factors associated with the melting of a (31) ordered phase on a centered-rectangular lattice gas: Effective scaling in a three-state chiral-clock-like model(American Physical Society, 1987) Bartelt, N. C.; Einstein, Theodore L.; Roelofs, L. D.By computing the structure factor through the melting transition of a commensurate (3x1) phase in a version of Baxter’s generalized hard hexagon model, we simulate what might be observed in diffraction experiments (especially those using low-energy electrons) on chemisorption systems which have similar Landau-Ginzburg-Wilson Hamiltonians. In the commensurate and disordered phases we observe that the shift of the peak of the critical scattering from the commensurate position is roughly proportional to the inverse correlation length in the reduced temperature range 0.015–0.15. The proportionality constant appears to depend on the position of the transition on the phase boundary (i.e., on the chemical potential). We see no sign of an incommensurate floating phase between the disordered and commensurate phases. Effective critical exponents are consistent with those expected from the three-state Potts model. To the precision of this calculation (a few percent), the structure factor scales over approximately 10% of the Brillouin-zone area.Item Structure factors associated with melting of a p(22) ordered phase on a honeycomb lattice gas: Possible critical scattering at a first-order transition(American Physical Society, 1987) Bartelt, N. C.; Einstein, Theodore L.; Roelofs, L. D.We study the order-disorder transition of a p(2x2) ordered state on a honeycomb lattice using Monte Carlo calculations of the structure factor. We observe a correlation length which gets large as the transition is approached; the effective critical exponents are close to the exponents characterizing a discontinuity fixed point and similar to those we observe for the first-order transition of the eight-state Potts model. We also discuss how observation of the outer integral-order diffraction beams gives information about the relevance of the field which distinguishes the two triangular sublattices of the honeycomb lattice.Item Summary Abstract: Structure factors of two?dimensional lattice gases: Theoretical investigation of some aspects of the capability of low?energy electron diffraction to measure critical phenomena of surface phase transitions(AIP, 1987) Einstein, Theodore L.; Bartelt, N. C.; Roelofs, L. D.Item Comment on "Reliability of low-energy electron diffraction for studies of surface order-disorder phenomena"(American Physical Society, 1986) Bartelt, N. C.; Einstein, Theodore L.; Roelofs, L. D.A Comment on the Letter by W. Moritz and M. G. Lagally, Phys. Rev. Lett. 56, 865 (1986).Item Theory and feasibility of using low-energy electron diffraction to study specific-heat anomalies at surface phase transitions(American Physical Society, 1985) Bartelt, N. C.; Einstein, Theodore L.; Roelofs, L. D.We expound the idea that as a probe of short-range order, low-energy electron diffraction can be used to study the energy singularity associated with surface phase transitions. We demonstrate its feasibility by performing Monte Carlo simulations on two triangular lattice gases with second-order transitions in universality classes distinguished by the critical exponent a.