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.

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.

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.

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.

Fixed-Point Optimization of Atoms and Density in DFT.

I describe an algorithm for simultaneous fixed-point optimization (mixing) of the density and atomic positions in Density Functional Theory calculations which is approximately twice as fast as conventional methods, is robust, and requires minimal to no user intervention or input. The underlying numerical algorithm differs from ones previously proposed in a number of aspects and is an autoadaptive hybrid of standard Broyden methods. To understand how the algorithm works in terms of the underlying quantum mechanics, the concept of algorithmic greed for different Broyden methods is introduced, leading to the conclusion that if a linear model holds that the first Broyden method is optimal, the second if a linear model is a poor approximation. How this relates to the algorithm is discussed in terms of electronic phase transitions during a self-consistent run which results in discontinuous changes in the Jacobian. This leads to the need for a nongreedy algorithm when the charge density crosses phase boundaries, as well as a greedy algorithm within a given phase. An ansatz for selecting the algorithm structure is introduced based upon requiring the extrapolated component of the curvature condition to have projected positive eigenvalues. The general convergence of the fixed-point methods is briefly discussed in terms of the dielectric response and elastic waves using known results for quasi-Newton methods. The analysis indicates that both should show sublinear dependence with system size, depending more upon the number of different chemical environments than upon the number of atoms, consistent with the performance of the algorithm and prior literature. This is followed by details of algorithm ranging from preconditioning to trust region control. A number of results are shown, finishing up with a discussion of some of the many open questions.

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.

c(4 × 2) and related structural units on the SrTiO3(001) surface: scanning tunneling microscopy, density functional theory, and atomic structure.

Density functional theory is used to simulate high-bias, constant-current scanning tunneling micrographs for direct comparison with experimental images. Coupled to previous spectroscopic data, these simulations are used to determine the atomic structure of Ti-rich nanostructures on strontium titanate (001) surfaces. These nanostructures have three consecutive TiO(x) surface layers and exploit the distinctive structural motif of the c(4 × 2) reconstruction as their main building block. A structural model of a characteristic triline defect is also proposed.

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.

Optimized conditions for imaging the effects of bonding charge density in electron microscopy.

We report on the observability of valence bonding effects in aberration-corrected high resolution electron microscopy (HREM) images along the [010] projection of the mineral Forsterite (Mg2SiO4). We have also performed exit wave restorations using simulated noisy images and have determined that both the intensities of individual images and the modulus of the restored complex exit wave are most sensitive to bonding effects at a level of 25% for moderately thick samples of 20-25 nm. This relatively large thickness is due to dynamical amplification of bonding contrast arising from partial de-channeling of 1s states. Simulations also suggest that bonding contrast is similarly high for an un-corrected conventional electron microscope, implying an experimental limitation of signal to noise ratio rather than spatial resolution.

A method to correlate optical properties and structures of metallic nanoparticles.

The optical response of individual nanoparticles is strongly influenced by their structures. In this report, we present a quick and simple pattern-matching based approach in which optical images of nanoparticles from localized surface plasmon resonance and single-molecule surface-enhanced Raman spectroscopy were used in conjunction with transmission electron microscopy for correlation of optical responses and the nanostructures of exactly the same nanoparticles or clusters of nanoparticles.

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.

Prospects for aberration corrected electron precession.

Recent developments in aberration control in the TEM have yielded a tremendous enhancement of direct imaging capabilities for studying atomic structures. However, aberration correction also has substantial benefits for achieving ultra-resolution in the TEM through reciprocal space techniques. Several tools are available that allow very accurate detection of the electron distribution in surfaces allowing precise atomic-scale characterization through statistical inversion techniques from diffraction data. The precession technique now appears to extend this capability to the bulk. This article covers some of the progress in this area and details requirements for a next-generation analytical diffraction instrument. An analysis of the contributions offered by aberration correction for precision electron precession is included.