Silicon lattice parameters as an absolute scale of length for high precision measurements of fundamental constants

CODATA Recommended Values of the Fundamental Physical Constants: 2018

We report the 2018 self-consistent values of constants and conversion factors of physics and chemistry recommended by the Committee on Data of the International Science Council. The recommended values can also be found at physics.nist.gov/constants. The values are based on a least-squares adjustment that takes into account all theoretical and experimental data available through 31 December 2018. A discussion of the major improvements as well as inconsistencies within the data is given. The former include a decrease in the uncertainty of the dimensionless fine-structure constant and a nearly two orders of magnitude improvement of particle masses expressed in units of kg due to the transition to the revised International System of Units (SI) with an exact value for the Planck constant. Further, because the elementary charge, Boltzmann constant, and Avogadro constant also have exact values in the revised SI, many other constants are either exact or have significantly reduced uncertainties. Inconsistencies remain for the gravitational constant and the muon magnetic-moment anomaly. The proton charge radius puzzle has been partially resolved by improved measurements of hydrogen energy levels.

CODATA recommended values of the fundamental physical constants: 2018

We report the 2018 self-consistent values of constants and conversion factors of physics and chemistry recommended by the Committee on Data of the International Science Council (CODATA). The recommended values can also be found at physics.nist.gov/constants. The values are based on a least-squares adjustment that takes into account all theoretical and experimental data available through 31 December 2018. A discussion of the major improvements as well as inconsistencies within the data is given. The former include a decrease in the uncertainty of the dimensionless fine-structure constant and a nearly two orders of magnitude improvement of particle masses expressed in units of kg due to the transition to the revised International System of Units (SI) with an exact value for the Planck constant. Further, because the elementary charge, Boltzmann constant, and Avogadro constant also have exact values in the revised SI, many other constants are either exact or have significantly reduced uncertainties. Inconsistencies remain for the gravitational constant and the muon magnetic-moment anomaly. The proton charge radius puzzle has been partially resolved by improved measurements of hydrogen energy levels.

High-resolution inelastic x-ray scattering at the high energy density scientific instrument at the European X-Ray Free-Electron Laser

We introduce a setup to measure high-resolution inelastic x-ray scattering at the High Energy Density scientific instrument at the European X-Ray Free-Electron Laser (XFEL). The setup uses the Si (533) reflection in a channel-cut monochromator and three spherical diced analyzer crystals in near-backscattering geometry to reach a high spectral resolution. An energy resolution of 44 meV is demonstrated for the experimental setup, close to the theoretically achievable minimum resolution. The analyzer crystals and detector are mounted on a curved-rail system, allowing quick and reliable changes in scattering angle without breaking vacuum. The entire setup is designed for operation at 10 Hz, the same repetition rate as the high-power lasers available at the instrument and the fundamental repetition rate of the European XFEL. Among other measurements, it is envisioned that this setup will allow studies of the dynamics of highly transient laser generated states of matter.

Six new silicon phases with direct band gaps

Six new silicon phases with direct band gaps were found through silicon atomic substitution of carbon in the known carbon structures via high-throughput calculations. The six newly discovered Si phases are in the space groups of Im3[combining macron]m, C2/c, I4/mcm, I4/mmm, P21/m, and P4/mbm, respectively. Their crystal structures, stabilities, mechanical properties, elastic anisotropy, and electronic and optical properties were systematically studied using first-principles density functional theory calculations. All the new phases were proved to be thermodynamically and mechanically stable at ambient pressure. The direct band gap values in the range of 0.658-1.470 eV and the excellent optoelectronic properties of these six Si allotropes suggest that they are promising photovoltaic materials compared to diamond silicon.

Energy-dispersive Laue experiments with X-ray tube and PILATUS detector: precise determination of lattice constants

A PILATUS detector in combination with a conventional sealed X-ray tube was used for the development of the energy-dispersive Laue diffraction technique, which can be applied for precise measurements of single-crystal lattice constants in transmission and reflection modes without moving the sample. Exploiting the ability of PILATUS detectors to suppress counting of X-ray photons below a certain energy threshold allows one to recover the wavelength of diffracted Bragg reflections, reconstruct the three-dimensional reciprocal-space pattern, index X-ray diffraction peaks, and find the orientation and lattice parameters of the crystal without any a priori information about the sample. By making some geometrical assumptions and using a set of fast in situ calibration procedures, it is possible to simultaneously refine lattice constants and hardware correction factors, which simplifies the sample preparation and measurement strategies. Several samples [silicon, quartz, fluorite (CaF2), o′-Al13Co4 quasicrystal approximant, Laves (MgZn2) and Bergman (Mg32(Al,Zn)49) phases] were studied with the developed technique, and 0.01 Å and 0.1° precisions were routinely reached for lattice vector lengths and angles, respectively. The use of the developed methods is only limited by the energy resolution of the PILATUS detector, where lattice vectors with >27 Å length cannot be reliably resolved.

The Lattice Spacing Variability of Intrinsic Float-Zone Silicon

Precision lattice spacing comparison measurements at the National Institute of Standards and Technology (NIST) provide traceability of X-ray wavelength and powder diffraction standards to the international system of units (SI). Here, we both summarize and document key measurements from the last two decades on six lots of intrinsic float-zone silicon, including unpublished results and recent internal-consistency checks. The comparison measurements link the unknown lattice spacing of a test crystal to a standard crystal for which the lattice spacing has been accurately determined by X-ray/optical interferometry in units traceable to the definition of the meter. The crystal that serves as the standard in all the comparisons is WASO 04, for which the lattice spacing is known with a relative uncertainty of 5 × 10^-9. Individual lattice spacing comparison results have typical uncertainties of 1 ×10^-8; taking material variability into account, measurements yield relative uncertainties for the test materials of a few tens of nanometers. It is observed that in the case of nearly perfect modern intrinsic float-zone silicon, the variability of the lattice spacing is sufficiently small that for most diffraction applications, a recommended reference value may be used.

CMOS-Technology-Enabled Flexible and Stretchable Electronics for Internet of Everything Applications

Flexible and stretchable electronics can dramatically enhance the application of electronics for the emerging Internet of Everything applications where people, processes, data and devices will be integrated and connected, to augment quality of life. Using naturally flexible and stretchable polymeric substrates in combination with emerging organic and molecular materials, nanowires, nanoribbons, nanotubes, and 2D atomic crystal structured materials, significant progress has been made in the general area of such electronics. However, high volume manufacturing, reliability and performance per cost remain elusive goals for wide commercialization of these electronics. On the other hand, highly sophisticated but extremely reliable, batch-fabrication-capable and mature complementary metal oxide semiconductor (CMOS)-based technology has facilitated tremendous growth of today's digital world using thin-film-based electronics; in particular, bulk monocrystalline silicon (100) which is used in most of the electronics existing today. However, one fundamental challenge is that state-of-the-art CMOS electronics are physically rigid and brittle. Therefore, in this work, how CMOS-technology-enabled flexible and stretchable electronics can be developed is discussed, with particular focus on bulk monocrystalline silicon (100). A comprehensive information base to realistically devise an integration strategy by rational design of materials, devices and processes for Internet of Everything electronics is offered.

Breakdown of continuum fracture mechanics at the nanoscale

Materials fail by the nucleation and propagation of a crack, the critical condition of which is quantitatively described by fracture mechanics that uses an intensity of singular stress field characteristically formed near the crack-tip. However, the continuum assumption basing fracture mechanics obscures the prediction of failure of materials at the nanoscale due to discreteness of atoms. Here, we demonstrate the ultimate dimensional limit of fracture mechanics at the nanoscale, where only a small number of atoms are included in a singular field of continuum stress formed near a crack tip. Surprisingly, a singular stress field of only several nanometers still governs fracture as successfully as that at the macroscale, whereas both the stress intensity factor and the energy release rate fail to describe fracture below a critically confined singular field of 2–3 nm, i.e., breakdown of fracture mechanics within the framework of the continuum theory. We further propose an energy-based theory that explicitly accounts for the discrete nature of atoms, and demonstrate that our theory not only successfully describes fracture even below the critical size but also seamlessly connects the atomic to macroscales. It thus provides a more universal fracture criterion, and novel atomistic insights into fracture.

Determination of the Avogadro constant by counting the atoms in a 28Si crystal

The Avogadro constant links the atomic and the macroscopic properties of matter. Since the molar Planck constant is well known via the measurement of the Rydberg constant, it is also closely related to the Planck constant. In addition, its accurate determination is of paramount importance for a definition of the kilogram in terms of a fundamental constant. We describe a new approach for its determination by counting the atoms in 1 kg single-crystal spheres, which are highly enriched with the 28Si isotope. It enabled isotope dilution mass spectroscopy to determine the molar mass of the silicon crystal with unprecedented accuracy. The value obtained, NA = 6.022,140,78(18) × 10(23) mol(-1), is the most accurate input datum for a new definition of the kilogram.

Si lattice parameter measurement by centimeter X-ray interferometry

A combined X-ray and optical interferometer capable of centimeter displacements has been made to measure the lattice parameter of Si crystals to within a 3 x 10(-9) relative uncertainty. This paper relates the results of test measurements carried out to assess the capabilities of the apparatus.

A review of recent work in sub-nanometre displacement measurement using optical and X-ray interferometry

This paper reviews recent work in the field of displacement measurement using optical and X-ray interferometry at the sub-nanometre level of accuracy. The major sources of uncertainty in optical interferometry are discussed and a selection of recent designs of ultra-precise, optical-interferometer-based, displacement measuring transducers presented. The use of X-ray interferometry and its combination with optical interferometry is discussed.