Predictive Mixing for Density Functional Theory (and Other Fixed-Point Problems)

Density functional theory calculations use a significant fraction of current supercomputing time. The resources required scale with the problem size, the internal workings of the code, and the number of iterations to convergence, with the latter being controlled by what is called "mixing". This paper describes a new approach to handling trust regions within these and other fixed-point problems. Rather than adjusting the trust region based upon improvement, the prior steps are used to estimate what the parameters and trust regions should be, effectively estimating the optimal Polyak step from the prior history. Detailed results are shown for eight structures using both the "good" and "bad" multisecant versions as well as the Anderson method and a hybrid approach, all with the same predictive method. Additional comparisons are made for 36 cases with a fixed algorithm greed. The predictive method works well independent of which method is used for the candidate step, and it is capable of adapting to different problem types particularly when coupled with the hybrid approach.

Does Flexoelectricity Drive Triboelectricity?

The triboelectric effect, charge transfer during sliding, is well established but the thermodynamic driver is not well understood. We hypothesize here that flexoelectric potential differences induced by inhomogeneous strains at nanoscale asperities drive tribocharge separation. Modeling single asperity elastic contacts suggests that nanoscale flexoelectric potential differences of ±1-10  V or larger arise during indentation and pull-off. This hypothesis agrees with several experimental observations, including bipolar charging during stick slip, inhomogeneous tribocharge patterns, charging between similar materials, and surface charge density measurements.

Direct Observation of "Pac-Man" Coarsening

We report direct observation of a "Pac-Man" like coarsening mechanism of a self-supporting thin film of nickel oxide. The ultrathin film has an intrinsic morphological instability due to surface stress leading to the development of local thicker regions at step edges. Density functional theory calculations and continuum modeling of the elastic instability support the model for the process.

Transition from Reconstruction toward Thin Film on the (110) Surface of Strontium Titanate

The surfaces of metal oxides often are reconstructed with a geometry and composition that is considerably different from a simple termination of the bulk. Such structures can also be viewed as ultrathin films, epitaxed on a substrate. Here, the reconstructions of the SrTiO3 (110) surface are studied combining scanning tunneling microscopy (STM), transmission electron diffraction, and X-ray absorption spectroscopy (XAS), and analyzed with density functional theory calculations. Whereas SrTiO3 (110) invariably terminates with an overlayer of titania, with increasing density its structure switches from n × 1 to 2 × n. At the same time the coordination of the Ti atoms changes from a network of corner-sharing tetrahedra to a double layer of edge-shared octahedra with bridging units of octahedrally coordinated strontium. This transition from the n × 1 to 2 × n reconstructions is a transition from a pseudomorphically stabilized tetrahedral network toward an octahedral titania thin film with stress-relief from octahedral strontia units at the surface.

Nanoparticle shape, thermodynamics and kinetics

Nanoparticles can be beautiful, as in stained glass windows, or they can be ugly as in wear and corrosion debris from implants. We estimate that there will be about 70,000 papers in 2015 with nanoparticles as a keyword, but only one in thirteen uses the nanoparticle shape as an additional keyword and research focus, and only one in two hundred has thermodynamics. Methods for synthesizing nanoparticles have exploded over the last decade, but our understanding of how and why they take their forms has not progressed as fast. This topical review attempts to take a critical snapshot of the current understanding, focusing more on methods to predict than a purely synthetic or descriptive approach. We look at models and themes which are largely independent of the exact synthetic method whether it is deposition, gas-phase condensation, solution based or hydrothermal synthesis. Elements are old dating back to the beginning of the 20th century-some of the pioneering models developed then are still relevant today. Others are newer, a merging of older concepts such as kinetic-Wulff constructions with methods to understand minimum energy shapes for particles with twins. Overall we find that while there are still many unknowns, the broad framework of understanding and predicting the structure of nanoparticles via diverse Wulff constructions, either thermodynamic, local minima or kinetic has been exceedingly successful. However, the field is still developing and there remain many unknowns and new avenues for research, a few of these being suggested towards the end of the review.

Surface determination through atomically resolved secondary-electron imaging

Unique determination of the atomic structure of technologically relevant surfaces is often limited by both a need for homogeneous crystals and ambiguity of registration between the surface and bulk. Atomically resolved secondary-electron imaging is extremely sensitive to this registration and is compatible with faceted nanomaterials, but has not been previously utilized for surface structure determination. Here we report a detailed experimental atomic-resolution secondary-electron microscopy analysis of the c(6 × 2) reconstruction on strontium titanate (001) coupled with careful simulation of secondary-electron images, density functional theory calculations and surface monolayer-sensitive aberration-corrected plan-view high-resolution transmission electron microscopy. Our work reveals several unexpected findings, including an amended registry of the surface on the bulk and strontium atoms with unusual seven-fold coordination within a typically high surface coverage of square pyramidal TiO5 units. Dielectric screening is found to play a critical role in attenuating secondary-electron generation processes from valence orbitals.

Transition from Order to Configurational Disorder for Surface Reconstructions on SrTiO_{3}(111)

There is growing interest in ternary oxide surfaces due to their role in areas ranging from substrates for low power electronics to heterogeneous catalysis. Descriptions of these surfaces to date focus on low-temperature explanations where enthalpy dominates, and less on the implications of configurational entropy at high temperatures. We report here the structure of three members of the n×n  (2≤n≤4) reconstructions of the strontium titanate (111) surface using a combination of transmission electron diffraction, density functional theory modeling, and scanning tunneling microscopy. The surfaces contain a mixture of the tetrahedral TiO_{4} units found on the (110) surface sitting on top of octahedral TiO_{5}[] (where [] is a vacant octahedral site), and TiO_{6} units in the second layer that are similar to those found on the (001) surface. We find clear evidence of a transition from the ordered enthalpy-dominated 3×3 and 4×4 structures to a configurational entropy-dominated 2×2 structure that is formed at higher temperatures. This changes many aspects of how oxide surfaces should be considered, with significant implications for oxide growth.

The effect of contact load on CoCrMo wear and the formation and retention of tribofilms

Tribochemical reactions in a protein lubricated metal-on-metal (MoM) sliding contact may play a significant role for its wear performance. Such reactions lead to the formation of a carbonaceous 'tribofilm', which can act as a protective layer against corrosion and wear. The purpose of this study was to determine the effect of contact load on wear and the formation and retention of tribofilms. Wear tests were performed in a custom-made ball-on-flat testing apparatus that incorporated an electrochemical cell. A ceramic ball was used to articulate against low-carbon wrought CoCrMo alloy pins in bovine serum. Using a range of contact loads at a single potentiostatic condition (close to free potential), weight loss and changes in surface properties were evaluated. We determined that wear was influenced by the loading condition. As expected, wear increased with load, but the association between applied load and measured weight loss was not linear. In the intermediate load region, in the range of 32-48 N (~58-80 MPa), there was more than an order of magnitude drop in the wear per unit load, and the wear versus load data suggested an inflexion point at 49 N. Regression analyses yielded a cubic model (R²=0.991; p=0.0002), where the cubic term, which represents the inflexion, was highly significant (p=0.0021). This model is supported by the observations that the minimum in the friction versus load curve is at 52 N and the highest relative increase in polarization resistance occurred at 49 N. Scanning electron microscopy and Raman spectroscopy indicated the absence of a tribofilm for the low and within the contact area of the high load cases. Synergistic interactions of wear and corrosion seem to play an important role.

New insights into hard phases of CoCrMo metal-on-metal hip replacements

The microstructural and mechanical properties of the hard phases in CoCrMo prosthetic alloys in both cast and wrought conditions were examined using transmission electron microscopy and nanoindentation. Besides the known carbides of M(23)C(6)-type (M=Cr, Mo, Co) and M(6)C-type which are formed by either eutectic solidification or precipitation, a new mixed-phase hard constituent has been found in the cast alloys, which is composed of ∼100 nm fine grains. The nanosized grains were identified to be mostly of M(23)C(6) type using nano-beam precession electron diffraction, and the chemical composition varied from grain to grain being either Cr- or Co-rich. In contrast, the carbides within the wrought alloy having the same M(23)C(6) structure were homogeneous, which can be attributed to the repeated heating and deformation steps. Nanoindentation measurements showed that the hardness of the hard phase mixture in the cast specimen was ∼15.7 GPa, while the M(23)C(6) carbides in the wrought alloy were twice as hard (∼30.7 GPa). The origin of the nanostructured hard phase mixture was found to be related to slow cooling during casting. Mixed hard phases were produced at a cooling rate of 0.2 °C/s, whereas single phase carbides were formed at a cooling rate of 50 °C/s. This is consistent with sluggish kinetics and rationalizes different and partly conflicting microstructural results in the literature, and could be a source of variations in the performance of prosthetic devices in-vivo.

Graphitic tribological layers in metal-on-metal hip replacements

Arthritis is a leading cause of disability, and when nonoperative methods have failed, a prosthetic implant is a cost-effective and clinically successful treatment. Metal-on-metal replacements are an attractive implant technology, a lower-wear alternative to metal-on-polyethylene devices. Relatively little is known about how sliding occurs in these implants, except that proteins play a critical role and that there is a tribological layer on the metal surface. We report evidence for graphitic material in the tribological layer in metal-on-metal hip replacements retrieved from patients. As graphite is a solid lubricant, its presence helps to explain why these components exhibit low wear and suggests methods of improving their performance; simultaneously, this raises the issue of the physiological effects of graphitic wear debris.

Wulff construction for alloy nanoparticles

The Wulff construction is an invaluable tool to understand and predict the shape of nanoparticles. We demonstrate here that this venerable model, which gives a size-independent thermodynamic shape, becomes size dependent in the nanoscale regime for an alloy and that the infinite reservoir approximation breaks down. The improvements in structure and energetic modeling have wide-ranging implications both in areas where energetics govern (e.g., nucleation and growth) and where the surface composition is important (e.g., heterogeneous catalysis).

Vacant-site octahedral tilings on SrTiO(3) (001), the (sqrt[13]×sqrt[13])R33.7° surface, and related structures

The structure of the SrTiO(3) (001) (sqrt[13]×sqrt[13])R33.7° surface reconstruction has been determined using transmission electron diffraction combined with direct methods and density functional theory. It has a TiO(2)-rich surface with a 2D tiling of edge or corner-sharing TiO(5)□ octahedra. Additionally, different arrangements of these octahedral units at the surface, dictated by local bond-valence sums, form 2D networks that can account for many ordered surface reconstructions as well as disordered glasslike structures consistent with the multitude of structures observed experimentally, and potentially other materials and interfaces.

Structure and Epitaxy of Silver/Gold Microclusters on MgO

We report observations by high resolution electron microscopy of model catalysts produced by impregnating MgO smoke particles with inorganic clusters. With the use of very low beam currents the substrates are of sufficiently low noise that we have been able to image cleanly both single atoms and very small clusters of size l-2nm in sufficient detail to determine their atomic structure. Two types of metal structures are observed: single atoms decorating atomic steps and in a few cases two-dimensional surface rafts, and a population of mainly single crystal with a few multiply twinned particles. The single crystal particles are pseudomorphically epitaxed on the MgO substrates.

HREM In-Situ Studies of Electron Irradiation Effects in Oxides

High resolution electron microscope (HREM) studies provide the ability to study desorption and sputtering from the perspective of the analysis of the resultant materials, their structure, composition and atomic registry (orientation with respect to the original,material and the irradiation). This is a neglected facet of surface irradiation effects research, yet it is the most important from the technological point of view. In the current study, surface electron irradiation processes in oxides were studied in-situ in a Hitachi H-9000 HREM operated at incident electron energies of 100–300 keV. It was found that a wide range of processes occur in the HREM which are dependent on the energy and flux of the incident electrons and on the material properties. Both ballistic and electronic irradiation damage was observed and the material responses included surface sputtering, amorphisation, chemical disordering, desorption of O and metal surface layer creation, surface roughening and bulk defect creation.

Direct Imaging of Atomic Rearrangements on Extended Gold Surfaces

Rearrangements of atomic columns on extended gold surfaces have been imaged directly using a 500kV high resolution electron microscope. The (100), (110) and (111) surface profiles were all found to be highly mobile and microscopically rough, with (111) in particular developing a characteristic hill-and-valley morphology. The presence of surface steps had a marked influence on the direction of surface diffusion only for the (100) surface. The observations establish that high-resolution profile imaging can provide unique information about surface self-diffusion which is unobtainable by other techniques.

Structure and local-equilibrium thermodynamics of the c(2x2) reconstruction of rutile TiO2 (100)

We resolve the structure of a c(2x2) reconstruction of the rutile TiO2 (100) surface using a combination of transmission electron diffraction, direct methods analysis, and density functional theory. The surface structure contains an ordered array of subsurface oxygen vacancies and is in local thermodynamic equilibrium with bulk TiO2, but not the with oxygen gas-phase environment. The transition into a bulklike (1x1) reconstruction offers insights into the time-dependent local thermodynamics of TiO2 surface reconstruction under global nonequilibrium conditions.

A quantitative analysis of the cone-angle dependence in precession electron diffraction

Precession electron diffraction (PED) is a technique which is gaining increasing interest due to its ease of use and reduction of the dynamical scattering problem in electron diffraction. To further investigate the usefulness of this technique, we have performed a systematic study of the effect of precession angle on the mineral andalusite where the semiangle was varied from 6.5 to 32 mrad in five discrete steps. The purpose of this study was to determine the optimal conditions for the amelioration of kinematically forbidden reflections, and the measurement of valence charge density. We show that the intensities of kinematically forbidden reflections decay exponentially as the precession semiangle (varphi) is increased. We have also determined that charge density effects are best observed at moderately low angles (6.5-13 mrad) even though PED patterns become more kinematical in nature as the precession angle is increased further.

Surface Reconstruction with a Fractional Hole: (sqrt[5] x sqrt[5])R26.6 degrees LaAlO3 (001)

The structure of the (sqrt[5] x sqrt[5])R26.6 degrees reconstruction of LaAlO3 (001) has been determined using transmission electron diffraction combined with direct methods. It has a lanthanum oxide termination with one lanthanum vacancy per surface unit cell. Density functional calculations indicate that charge compensation occurs by a fractional number of highly delocalized holes, and that the surface contains no oxygen vacancies and the holes are not filled with hydrogen. The reconstruction can be understood in terms of expulsion of the more electropositive cation from the surface and increased covalency.

Precession electron diffraction 1: multislice simulation

Precession electron diffraction (PED) is a method that considerably reduces dynamical effects in electron diffraction data, potentially enabling more straightforward solution of structures using the transmission electron microscope. This study focuses upon the characterization of PED data in an effort to improve the understanding of how experimental parameters affect it in order to predict favorable conditions. A method for generating simulated PED data by the multislice method is presented and tested. Data simulated for a wide range of experimental parameters are analyzed and compared to experimental data for the (Ga,In)(2)SnO(4) (GITO) and ZSM-5 zeolite (MFI) systems. Intensity deviations between normalized simulated and kinematical data sets, which are bipolar for dynamical diffraction data, become unipolar for PED data. Three-dimensional difference plots between PED and kinematical data sets show that PED data are most kinematical for small thicknesses, and as thickness increases deviations are minimized by increasing the precession cone semi-angle phi. Lorentz geometry and multibeam dynamical effects explain why the largest deviations cluster about the transmitted beam, and one-dimensional diffraction is pointed out as a strong mechanism for deviation along systematic rows. R factors for the experimental data sets are calculated, demonstrating that PED data are less sensitive to thickness variation. This error metric was also used to determine the experimental specimen thickness. R(1) (unrefined) was found to be about 12 and 15% for GITO and MFI, respectively.

Theoretical structure factors for selected oxides and their effects in high-resolution electron-microscope (HREM) images

A reasonably detailed analysis of the effects of charge redistribution on both X-ray and electron structure factors as well as for high-resolution electron-microscope images are presented for a series of light-element oxides. The charge redistribution leads to differences of 2-3% for the X-ray structure factors and 5-7% for electron structure factors in the 0-0.5 A(-1) region. There are detectable changes in images of about 10% of the contrast, somewhat dependent upon the alignment of atom columns, specimen thickness and defocus. These studies suggest that charge redistribution may be detectable using a Cc-limited aberration-corrected microscope with a specimen thickness of about 50 A.

Rapid structure determination of a metal oxide from pseudo-kinematical electron diffraction data

The electron precession diffraction technique is employed to provide quasi-kinematical data for determination of atom positions in the (Ga,In)2SnO5m-phase. Precession data are compared with conventional diffraction data captured under identical conditions and show a distinct superiority because they exhibit kinematical characteristics in the structure-defining reflections. Precessed data are not usable within a kinematical interpretation in all cases, and a simple basis is presented for omission of errant reflections to improve adherence to kinematical behavior. A second approach is demonstrated where intensities are used with direct methods instead of amplitudes, enhancing the contrast between strong and weak beams. The unrefined atom positions recovered a priori via direct methods are consistent between the two approaches and fall on average within 4 picometers of positions in the previously refined structure.

EDM 1.0: Electron direct methods

A computer program designed to provide a number of quantitative analysis tools for high-resolution imaging and electron diffraction data is described. The program includes basic image manipulation, both real space and reciprocal space image processing, Wiener-filtering, symmetry averaging, methods for quantification of electron diffraction patterns and two-dimensional direct methods. The program consists of a number of sub-programs written in a combination of C++, C and Fortran. It can be downloaded either as GNU source code or as binaries and has been compiled and verified on a wide range of platforms, both Unix based and PC's. Elements of the design philosophy as well as future possible extensions are described.

Direct observation of charge transfer at a MgO(111) surface

Transmission electron diffraction (TED) combined with direct methods have been used to study the sqrt[3]xsqrt[3]R30 degrees reconstruction on the polar (111) surface of MgO and refine the valence charge distribution. The surface is nonstoichiometric and is terminated by a single magnesium atom. A charge-compensating electron hole is localized in the next oxygen layer and there is a nominal charge transfer from the oxygen atoms to the top magnesium atom. The partial charges that we obtain for the surface atoms are in reasonable agreement with empirical bond-valence estimations.

Surface crystallography via electron microscopy

The study of atomic structure of surfaces is fundamental to the understanding of electronic, chemical and mechanical properties of surfaces and numerous techniques have been developed to this end. Transmission Electron Microscopy techniques, namely transmission electron imaging (TEM) and diffraction (TED), due to their ability to provide structural information at very high resolutions, have emerged as powerful tools for the study of surface structure. In this article we review the experimental method alongside the various post-processing routines that are necessary to extract vital structural information from experimental data.

Sufficient conditions for Direct Methods with swift electrons

We investigate cases where one can argue that sufficient conditions exist for Direct Methods to work with swift electrons. In addition to simple cases where kinematical scattering holds (e.g., surfaces in plan view), we identify three other configurations: (a) when 1s channeling holds and kinematical scattering is statistically correct; (b) when there is a mapping from kinematical to dynamical intensities that preserves the order of the intensities, for instance with powder or precession data, and (c) when the scattering is dominated by one type of atom. We also briefly discuss the possibility of using Direct Methods to restore the complex exit wave leaving a sample in the most general case.

Lensless imaging: a workshop on "new approaches to the phase problem for non-periodic objects."

Over the past two decades, theoretical tools and algorithms have been developed which, under not very restrictive conditions, allow the reconstruction of images from diffraction patterns of non-periodic objects. These methods promise lensless imaging for any radiation, free of aberrations, with wavelength-limited resolution. Recent experimental successes prompted an interdisciplinary international workshop on this topic at the Lawrence Berkeley National Laboratory, Berkeley, CA, USA, on May 17-19 2001, supported by the DOE, LBL and the Advanced Light Source. Our aim was to review the field, and to stimulate communication between the Signal Recovery, Coherent Optics, X-ray, Electron Microscopy and Applied Mathematics communities. The results are summarized in this paper and on the web. A second workshop is planned for 2003.

Statistical dynamical direct methods. II. The three-phase structure invariant

The triplet distribution used for kinematical diffraction is extended to the complex case appropriate for dynamical transmission electron diffraction. It is demonstrated that this gives good results if the distributions are handled statistically rather than relying upon single triplet relationships. As a consequence, conventional statistical direct methods will yield a reasonable approximation to the effective dynamical potential for thicknesses when kinematical theory is not appropriate. The recovered effective dynamical potential may be similar to the kinematical potential, but does not have to be and in general will not be.

Subsurface dimerization in III-V semiconductor (001) surfaces

We present the atomic structure of the c(8 x 2) reconstructions of InSb-, InAs-, and GaAs-(001) surfaces as determined by surface x-ray diffraction using direct methods. Contrary to common belief, group III dimers are not prominent on the surface, instead subsurface dimerization of group III atoms takes place in the second bilayer, accompanied by a major rearrangement of the surface atoms above the dimers to form linear arrays. By varying the occupancies of four surface sites the (001)-c(8 x 2) reconstructions of III-V semiconductors can be described in a unified model.

Single-walled BN nanostructures

We describe in situ synthesis and characterization of single-walled BN nanotubes terminated by fullerenelike structures using electron-cyclotron resonance nitrogen and electron beam boron sources onto polycrystalline tungsten substrates. Detailed comparisons of experimental high-resolution electron microscopy images and simulations based upon molecular models show a dominance of kinks and bends involving fourfold and eightfold ring structures as against fivefold or sevenfold which have been found with carbon. Analysis of the structures as a function of film thickness indicates that they are growing by addition of atoms to the exposed ends of single sheets, not at the substrate-nanostructure interface.

Electron crystallography in surface structure analysis

Surface structure analysis is an important area of research, and in recent years notable advances have been made in this field, both in improved techniques for studying surfaces and in methods of analyzing them. This review aims to summarize the techniques available, particularly those relating to electron microscopy, and also to outline one of the newest areas of development, the application of direct methods to surface structure analysis.

A simple channelling model for HREM contrast transfer under dynamical conditions

The application of electron channelling theory to dynamical exit wave calculations is briefly reviewed, and a comparison of channelling results with full dynamical calculations is presented. The channelling expression to the exit wave is combined with conventional imaging theory, and it is shown that a simple expression can be obtained for a dynamical contrast transfer function (D-CTF), which incorporates imaging aberrations and thickness-dependent dynamical scattering effects. The D-CTF can provide detailed insight into HREM images of a mixed cation oxide at thicknesses up to 200 Å, whereby an approximate correction for non-linear effects is utilized in the larger thickness regime.

In situ growth and characterization of ultrahard thin films

Results concerning the operation of a new ultrahigh vacuum (UHV) ion-beam assisted deposition system for in situ investigation of ultrahard thin films are reported. A molecular beam epitaxy (MBE) chamber attached to a surface science system (SPEAR) has been redesigned for deposition of cubic-boron nitride thin films. In situ thin film processing capability of the overall system is demonstrated in preliminary studies on deposition of boron nitride films on clean Si (001) substrates, combining thin film growth with electron microscopy and surface characterization, all in situ.

Multi-Solution Genetic Algorithm Approach to Surface Structure Determination Using Direct Methods

We show that it is possible to use a multi-solution genetic algorithm search method utilizing direct methods to solve surface structures from surface diffraction data. We suggest that the method is generally applicable and able to replace random searches of the solution space.