Small Lattice Spacing Research Articles

YM2:Continuum expectations, lattice convergence, and lassos

The two dimensional Yang-Mills theory (YM2) is analyzed in both the continuum and the lattice. In the complete axial gauge the continuum theory may be defined in terms of a Lie algebra valued white noise, and parallel translation may be defined by stochastic differential equations. This machinery is used to compute the expectations of gauge invariant functions of the parallel translation operators along a collection of curvesC. The expectation values are expressed as finite dimensional integrals with densities that are products of the heat kernel on the structure group. The time parameters of the heat kernels are determined by the areas enclosed by the collectionC, and the arguments are determined by the crossing topologies of the curves inC. The expectations for the Wilson lattice models have a similar structure, and from this it follows that in the limit of small lattice spacing the lattice expectations converge to the continuum expectations. It is also shown that the lasso variables advocated by L. Gross [36] exist and are sufficient to generate all the measurable functions on the YM2-measure space.

Hollow-cone illumination in simulated ADF STEM

The overlap regions between CBED disks are a source of lattice fringe contrast in ADF STEM images of crystals. For sufficiently small lattice spacings, the Scherzer focus convergence angle is too small for the CBED disks to overlap, and the lattice is not visible. By increasing the convergence angle beyond the Scherzer angle to create an overlap region, and by using stationary phase defocus, smaller lattices can be imaged However, with larger convergence angles, lens aberrations spread the incident beam and small aperiodic structures, such as adatoms, become difficult to image. If the specimen Bragg angle is known, an annular objective aperture can be designed to pass the overlap regions of the incident beam, while blocking the central, non-overlap region which produces a large constant background. The annular probe size is minimized by choosing an annulus width and defocus which balance the spherical aberration across the annulus (close to stationary phase defocus). Simulations indicate hollow cone illumination may allow both adatoms and smaller lattices to be imaged simultaneously. This approach presumes knowledge of the specimen, and must be used in conjunction with standard methods for correct image interpretation. An incorrectly applied annulus will produce image artifacts.

Universality and scaling in SU(2) lattice gauge theory

We calculate the lowest glueball masses and the string tension for both Manton's action and for Symanzik's tree-level improved action. We do so on large lattices and for small lattice spacings using techniques recently employed in an extensive investigation of the Wilson plaquette action. Comparing all these results we find that the ratios of the lightest masses are universal to a high degree of accuracy. In particular, we confirm that on large volumes the tensor glueball is heavier than the scalar glueball: m[2 +]⋍1.5 m[0 +] . We repeat these calculations for larger lattice spacings and find that the string tension follows 2-loop perturbation theory more closely in the case of these alternative actions than in the case of the standard plaquette action. Our attempt to repeat the analysis with Wilson's block-spin improved action foundered on the strong breakdown of positivity apparent in the calculated correlation functions. In all cases which we were able to study the observed violations of scaling are in the same direction. This suggests that the causes of the scaling violations observed with Wilson's plaquette action are “semi-universal”. It also weakens the implication of the observed universality for the question of how close we are to the continuum limit.

Anomalous lattice contraction and magnetism of γ-Fe precipitates in Cu

The lattice parameter of FCC ( gamma -)Fe precipitates in a Cu matrix is investigated as a function of the size of the precipitates. With prolonged aging, noncoherent gamma -Fe precipitates with about 0.2% smaller lattice spacings than the coherent ones are found. The structural phase transition, the magnetic structure and the Neel temperature of this new state are studied using X-ray and neutron diffraction methods. Antiferromagnetic ordering takes place accompanying a structural phase transition as in the coherent state. The observed Neel temperature is slightly higher than the previously reported value TN=67 K. Various magnetic properties of gamma -Fe precipitates in Cu are discussed on the basis of the present experimental data.

Calculating physical quantities for small lattice spacings

We describe methods for constructing lattice operators that maintain their overlap onto the desired long distance physics as the lattice spacing is decreased.

The SU(3) topological susceptibility at zero and finite temperature: A lattice Monte Carlo evaluation

We extend previous calculations of the zero-temperature topological susceptibility, χ t, to larger lattices (up to 20 4) and smaller lattice spacings (up to β=6.2). Using a new technique we are able to achieve a precise control of finite size corrections. We confirm, with much greater systematic and statistical precision, that the dimensionless ratio χ t/ K 2 is independent of β for β⩾5.7. This enables us to extract χ t in physical units and we find χ t =(179±4 MeV) 4 - statistical error only - which is in striking agreement with the Witten-Veneziano calculation. We also investigate the previously observed fact that χ t is suppressed as the temperature is raised through the deconfining transition. We find that χ t is in fact discontinuous at the phase transition and that its temperature dependence is otherwise weak as long as it remains in a single well-defined phase.

Thermal Annealing Effects in the Strained (Ga, In) as Layer

ABSTRACTWe have studied the ternary (Ga, In)As layers in GaInAs/GaAs heterostructure systems after conventional furnace annealing or rapid thermal annealing (RTA). Measurement was done by the double crystal X-ray rocking curve technique (XRC) and the Auger Electron Spectroscopy technique (AES). X-ray rocking curves show an asymmetric shoulder in the GaInAs epilayer peak indicating a smaller lattice spacing near the surface. Epilayer peaks of encapsulated samples also show an asymmetric shoulder which is perhaps due to the tensile stress in the epilayer caused by the encapsulant film. AES depth profiles for 600°C, 15 minutes proximity annealed sample show that the concentrations of Ga, In, and As are not uniform over about 60 nm depth, showing a Garich and In, As-deficient surface. For 700°C, 20 seconds a RTA treated sample shows no such non-uniformity.

Effect of Higher-Order Spherical Aberration Term on Transfer Function in Electron Microscopy

The effect of the higher-order spherical aberration coefficient on the transfer function in transmission electron microscopy was calculated. In order to simplify the system, the optical illumination system was assumed to be perfectly coherent and axially symmetric. The result shows that the effect of the fifth-order spherical aberration coefficient, C5, on the usual transfer function with the third-order spherical aberration coefficient C5≡C3=0.5 mm for 100 keV electrons cannot be neglected, if high-order Bragg reflections from net planes with smaller lattice spacings than 0.1 nm are utilized for lattice imaging. The effect of the higher-order term due to the defocussing on the transfer function is also discussed.

Polytypic behaviour of zirconolite

A polytypic family is described whose simplest member is zirconolite, (CaZrTi 2 O 7 ). The parent structure consists of calcium and zirconium atoms inserted between planes of titanium atoms, the latter being arranged in an hexagonal tungsten bronze (h. t. b.) type motif. Polytypes are generated by modifying the relative orientation of successive h. t. b. layers. Hettotypes are uniquely described by stacking formulae that are similar to those encountered in mica polytypes. Each stacking formula is com­posed of an interlayer stacking vector and a rotation. Zirconolite as a com­ponent of synroc (a proposed high level waste disposal matrix) was examined by selected area electron diffraction (s. a. d.) and high resolution electron microscopy (h. r. e. m.). Coherent polytypic intergrowths were observed which gave rise to laminar zirconolite domains. In crystallites that contain a large number of narrow domains, diffraction patterns contained sharp superlattice reflections of extremely small (100–200 Å) reciprocal lattice spacing; however, no superstructures with perfect translational periodicity were observed. (1 Å = 10 -10 m.) It is proposed that the intergrowth of zirconolite polytypes on a unit cell scale provides a means of incorporating cationic impurities in the parent structure.

Thermal distribution functions and finite-size effects for lattice fermions

We perform, analytically, the sum over the finite set of Matsubara frequencies that arises in the lattice thermodynamics of a free Fermi gas. The resultant expressions provide an easy demonstration that the correction continuum expressions are obtained in the limit of small lattice spacing.

Solving φ1,24 field theory with Monte Carlo

We study lattice g 0 φ 4 field theory for all g 0 and fixed renormalized mass M in one and two dimensions using Monte Carlo techniques. We calculate the dimensionless renormalized coupling constant g R = g R M 4−d , where d is the dimension of space—time, at fixed small values of the lattice spacing a for various g 0 and lattice sizes. Our results are in quantitative agreement with the analyses of high temperature and strong coupling series which rely on extrapolation from large to small lattice spacing.

Electron lattice image interpretation of V2O3 wedge shaped crystal

The thickness dependence of a two dimensional lattice image with small lattice spacings (< 5 Å) has been discussed in the theoretical aspect by some authors(1) (2),(3) in the case of zone axis orientation. Our intention is to compare the experimental image with the theoretical one for a vanadium sesquioxide (V2O3) crystal not in the zone axis orientation but in more general orientations. This crystal, one of those which show the metal-insulator transition, is metallic and belongs to the space group at room temperature. The unit cell dimensions in the hexagonal system are a = 4.951 Å and c = 14.003 Å (4). The electron microscope used is a JEM-100C equipped with the fixed specimen stage and operated at 100 kV (Cs = 1.4 mm).Figure 1 shows a lattice image from a wedge shaped crystal. Especially remarkable is the recurrence of similar contrast in three thicknesses regions : < 50 Å,∽ 250Å,and ∽ 450Å.