# Physics Research Works

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Item Crenshaw transcripts 2023(0023-08-24) Crenshaw, Kenyatta; Elby, AndrewItem Infinite Red-Shifts in General Relativity(Cornell University Press, 1967) Misner, Charles W; Beckedorff, David LThe Oppenheimer-Snyder description of continued gravitational collapse is reformulated as a matching together of two familiar solutions of the Einstein gravitational equations. From one solution, the Friedmann cosmology with zero-pressure matter, one selects the interior of a sphere whose points move on timelike geodesics. From the other solution one selects the exterior of such a sphere in the vacuum Schwarzschild solution. For the expected choice of parameters (sphere circumference, interior density, exterior mass) these can be fit together smoothly enough to satisfy the Einstein equations. The matching conditions are that the first and second fundamental forms at the joining 3-surface agree. The description of this collapsing ball of matter survives its passage through Finkelstein's (1958) smooth unidirectional membrane€ at r=2M and is most conveniently presented using the Kruskal coordinates for the Schwarzschild solution. This project was proposed and designed by Misner (choice of solutions and matching requirements), but the execution and first written presentation were carried out by Beckedorff and provided his Princeton senior thesis in April 1962. ( http://www.physics.umd.edu/grt/cwm/Beckedorff1962.pdf ) In this 1963 presentation Misner emphasizes that the properties of matter at high densities are irrelevant to the question of whether such a collapse can occur for sufficiently massive objects. The detailed computations by Beckedorff are here linked in an appended file.Item Indirect Interaction between Adatoms on a Tight-Binding Solid(American Physical Society, 1973) Einstein, Theodore L.; Schrieffer, J. R.The indirect interaction between adatom pairs on the (100) surface of a simple-cubic tight-binding solid is investigated within a molecular-orbital approach. A general scheme for calculating the surface-density-of-states change and the interaction energy of one and two single-level adatoms is presented, and contact (and a correction) is made with Grimley's formulation. The method permits binding above surface atoms, at bridge sites, or at centered positions, and yields interaction energy as a function of band filling, adatom energy level, and a general hopping potential V between an adatom and the nearest surface atom(s).Item Statistical Mechanics of a Simple Model of a Displacive Ferroelectric(American Physical Society, 1973) Cohen, Michael; Einstein, Theodore L.Item Short-chain model of chemisorption: Exact and approximate results(American Physical Society, 1975) Einstein, Theodore L.The binding energy of an adatom to a chain consisting of three atoms is obtained exactly by computer as a function of adatom Coulomb repulsion, adatom-substrate hopping, and substrate bandwidth. Three simple approximations are also plotted: (i) weak-binding limit, in which the binding energy is given by the expectation value of the adatom-bulk hopping Hamiltonian calculated in second-order perturbation theory; (ii) rebonded surface complex, in which the adatom forms a diatomic molecule with its nearest neighbor in the chain, and the dimer rebonds perturbatively to the indented chain; and (iii) Hartree-Fock, both restricted and unrestricted. The first two schemes can be joined smoothly by hand, and the resulting curve is much better than Hartree-Fock. The physics of all three cases is carefully studied. An appendix treats the surface diatom case of just a single bulk atom. Here the exact solution and unrestricted Hartree-Fock can be performed analytically. Comparison is also given with Brenig and Schönhammer's solution based on Green's-function formalism with matrix self-energy corrections.Item Changes in density of states caused by chemisorption(American Physical Society, 1975) Einstein, Theodore L.The process of chemisorption is studied via the change in density of states when an adatom with a single level Ea bonds by a hopping parameter V to the (100) surface of an s-band simple cubic crystal. As V increases, the bond changes from a perturbative regime to the formation of a surface complex. Investigations of local and layer-summed show this dimerlike structure to be well localized near the bond. Steric effects (binding-site symmetry) are easily introduced. A damping parameter can be added to simulate decay effects of surface probes. Application of the model to photoemission angular-averaged and angular-resolved difference spectra for light gases on tungsten gives understanding of the bonding peak near the bottom of the band, of the depletion of states near the Fermi energy, and of the slight shifting of the energy-momentum-conserving peak.Item Multiadatom effects in the chemisorption energy of ordered overlayers(American Physical Society, 1977) Einstein, Theodore L.The indirect interaction energy per adatom is evaluated for a c(2x2) overlayer in a model system, and is found to be very well approximated by (twice) the next-nearest-neighbor pair interaction energy, verifying the validity of earlier work. Three adatom (nonpairwise) interaction energies are also considered; while insignificant for total interaction energies, they are comparable to more-distant (viz., third-) neighbor pair interactions.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 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 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 Summary Abstract: (2×2) phase transitions on honeycomb lattices(AIP, 1983) Bartelt, N. C.; Einstein, Theodore L.; Roelofs, L. D.Item Optimization of data end points and taper width in extended absorption fine-structure analysis(American Physical Society, 1984) Hershfield, Selman P.; Einstein, Theodore L.The dependence of deduced interatomic spacing and inner potential on the lower and upper limits of integration, k1 and k2, as well as the taper width D, was studied for extended absorption fine structure using sinusoidal model data. The optimal values are achieved when 2(k1+k2)R or 2(k2?k1?D)R equals an odd half-integral multiple of pi (rather than when 2k1R and 2k2R are integral multiples of pi), where R is the spacing. Analytic approximations are used to elucidate numerical computations. Optimization of D is also discussed.Item Triangular lattice gas with first- and second-neighbor exclusions: Continuous transition in the four-state Potts universality class(American Physical Society, 1984) Bartelt, N. C.; Einstein, Theodore L.Using phenomenological renormalization (transfer-matrix scaling), we have reexamined the phase transition of a triangular lattice gas with particles having both nearest- and second-nearest-neighbor exclusions. Widely accepted classical studies indicated that disordering of the ordered (p(2x2)) state is first order. In contradiction, we show that the transition is second order; its exponents are consistent with the four-state Potts model universality class, in accord with its Landau-Ginzburg-Wilson Hamiltonian classification.Item Summary Abstract: Pseudodipole selection rules for extended fine structure in APS: Calculations and applications.(AIP, 1984) Mehl, M. J.; Einstein, Theodore L.; Bryant, G. W.Item Summary Abstract: Relationship between many-parameter lattice gas systems and simpler models: Easy approximations for Tc(AIP, 1984) Bartelt, N. C.; Einstein, Theodore L.; Williams, Ellen D.Item Summary Abstract: Studying surface phase transitions with probes of short range order(AIP, 1985) Bartelt, N. C.; Einstein, Theodore L.; Roelofs, L. D.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.Item Phase Diagram of Selenium Adsorbed on the Ni(100) Surface: A Physical Realization of the Ashkin-Teller Model(American Physical Society, 1985) Bak, Per; Kleban, P.; Unertl, W. N.; Ochab, J.; Akinci, G.; Bartelt, N. C.; Einstein, Theodore L.We have used electron diffraction to study submonolayers of Se adsorbed on Ni(100); p(2x2), c(2x2), and disordered phases were observed and the boundaries between them located. Symmetry arguments indicate that the phase diagram belongs to the universality class of the Ashkin-Teller model and allow us to predict the critical behavior near the phase boundaries and at the multicritical point where they meet. Our lattice-gas-model calculations support these results. The predicted critical behavior, and thus the universality arguments, should be tested by additional experiments, in particular synchrotron-x-ray diffraction.Item Two-dimensional ordering of chlorine on Ag(100)(American Physical Society, 1985) Taylor, David E.; Williams, Ellen D.; Park, Robert L.; Bartelt, N. C.; Einstein, Theodore L.Chlorine adsorption on Ag(100) saturates at (1/2) monolayer (ML) in a c(2x2) structure. Desorption occurs above 650 K without disordering. The sticking coefficient remains constant to within 0.05 ML of saturation, consistent with the existence of a highly mobile precursor to adsorption. The c(2x2) structure forms at a critical coverage of 0.394+-0.007 ML at room temperature. This is slightly higher than the critical coverage of the hard-square model (0.368 ML), suggesting the influence of further-neighbor interactions.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.