Search NASA⌕ Search

SEARCH · Search NASA

Results for “Low atomic mass metal”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Photosynthesis of a Photocatalyst: Single Atom Platinum Captured and Stabilized by an Iron(III) Engineered Defect

Single atom (SA), noble metal catalysts are of interest due to high projected catalytic activity while minimizing cost. Common issues facing many synthesis methodologies include complicated processes, low yields of SA product, and production of mixtures of SA and nanoparticles (NPs). Herein we report a simple, room-temperature synthesis of single Pt-atom decorated, anatase Fe-doped TiO 2 particles that leverages the Fe dopant as an engineered defect site to photodeposit and stabilize atomically dispersed Pt. Both particle morphology and Fe dopant location are based on thermodynamic principles (Gibbs-Wulff construction). CO-DRIFTS (diffuse reflectance infrared Fourier transform spectroscopy) reveals absence of bridge-bonded CO signal, confirming atomically dispersed Pt. XAS (x-ray absorption spectroscopy) of both Pt and Fe indicates Fe-O-Pt bonding that persists through catalytic cycling. Mass balance indicates Pt loading on single particles is 2.5 wt% Pt; single Pt-atom decorated nanoparticle yield is 17%. Pt containing particles show more than an order-of-magnitude increased photo-oxidation efficiency relative to particles containing only Fe. High single-atom-Pt yield, ease of synthesis, and high catalytic activity demonstrate the utility and promise of this method. In conclusion, the principles of this photodeposition synthesis allow for its generalizability towards other SA metals of catalytic interest.

36 MATERIALS SCIENCE↗
DOE OSTI2024

One-step sputtering of MoSSe metastable phase as thin film and predicted thermodynamic stability by computational methods

Abstract We present the fabrication of a MoS 2−x Se x thin film from a co-sputtering process using MoS 2 and MoSe 2 commercial targets with 99.9% purity. The sputtering of the MoS 2 and MoSe 2 was carried out using a straight and low-cost magnetron radio frequency sputtering recipe to achieve a MoS 2−x Se x phase with x = 1 and sharp interface formation as confirmed by Raman spectroscopy, time-of-flight secondary ion mass spectroscopy, and cross-sectional scanning electron microscopy. The sulfur and selenium atoms prefer to distribute randomly at the octahedral geometry of molybdenum inside the MoS 2−x Se x thin film, indicated by a blue shift in the A 1g and E 1 g vibrational modes at 355 cm −1 and 255 cm −1 , respectively. This work is complemented by computing the thermodynamic stability of a MoS 2−x Se x phase whereby density functional theory up to a maximum selenium concentration of 33.33 at.% in both a Janus-like and random distribution. Although the Janus-like and the random structures are in the same metastable state, the Janus-like structure is hindered by an energy barrier below selenium concentrations of 8 at.%. This research highlights the potential of transition metal dichalcogenides in mixed phases and the need for further exploration employing low-energy, large-scale methods to improve the materials’ fabrication and target latent applications of such structures.

36 MATERIALS SCIENCE↗
NASA NTRS1987

Effect of an oxygen plasma on uncoated thin aluminum reflecting films

Thin aluminum films were considered for use as a reflective surface for solar collectors on orbiting solar dynamic power systems. A matter of concern is the durability of such reflective coatings against oxidative attack by highly reactive neutral atomic oxygen, which is the predominate chemical specie in low Earth orbit. Research to date was aimed at evaluating the protective merit of thin dielectric coatings over the aluminum or other reflective metals. However, an uncoated aluminum reflector may self-protect by virtue of the oxide formed from its exposed surface, which constitutes a physical barrier to further oxidation. This possibility was investigated, and an attempt was made to characterize the effects of atomic oxygen on thin Al films using photomicrographs, scanning electron microscopy, spectrophotometry, Auger analysis, and mass measurements. Data collected in a parallel effort is discussed for its comparative value. The results of the investigation of uncoated aluminum supported the self-protection hypothesis, and importantly, it was found that long term specular reflectance for uncoated aluminum exceeded that of Al and Ag reflectors with dielectric coatings.

Parsons, Roger L.↗
NASA NTRS1993

The Interstellar Gas Experiment: Analysis in progress

The Interstellar Gas Experiment (IGE) exposed thin metallic foils aboard the LDEF spacecraft in low Earth orbit in order to collect neutral interstellar particles which penetrate the solar system due to their motion relative to the sun. By mechanical penetration these atoms were imbedded in the collecting foils along with precipitating magnetospheric ions and, possibly, with ambient atmospheric atoms. During the entire LDEF mission, seven of these foils collected particles arriving from seven different directions as seen from the spacecraft. After the foils were returned to Earth, a mass spectrometric analysis of the noble gas component of the trapped particles was begun. The isotopes of He-3, He-4, Ne-20, and Ne-22 were detected. We have given a first account of the experiment. In order to infer the isotopic ratios in the interstellar medium from the concentrations found in the foils, several lines of investigation had to be initiated. The flux of ambient atmospheric noble gas atoms moving toward the foils due to the orbital motion of LDEF was estimated by detailed calculations. Any of these particles which evaded the baffles in the IGE collector could be entrapped in the foils as a background flux. However, the calculations have shown that this flux is negligible, which was the intent of the experiment hardware design. This conclusion is supported by the measurements. However, both the concentration of trapped helium and its impact energy indicate that the flux of magnetospheric ions which was captured was larger than had been expected. In fact, it appears that the magnetospheric particles constitute the largest fraction of the particles in the foils. Since little is known about this particle flux, their presence in the IGE foils appears fortunate. The analysis of these particles provides information about their isotropic composition and average flux.

Buehler, F.↗
DOE OSTI2022

Lattice dynamics of high-pressure hydrides studied by inelastic neutron scattering

Due to the small mass and anomalously large neutron scattering cross-section of proton (about 80 barns compared to a few barns for other nuclei), inelastic neutron scattering is considered as one of the most effective tools in studying optical vibrations of hydrogen atoms in metal hydrides. The current review is focused on the binary hydrides of 3d- and 4d-metals of groups VI–VIII, which were produced at high hydrogen pressures of several gigapascals in relatively large quantities of hundreds of mg, quenched to low temperature and studied by INS ex situ at ambient pressure with high statistical accuracy. One of the unusual effects revealed by INS is a strong increase in the strength of the metal-hydrogen interactions with decreasing atomic number of the d-metal accompanied by an increase in the Me-H distance. Based on the available experimental results, the spectra g(E) of the phonon density of states and temperature dependencies CV(T) of the heat capacity at constant volume at T up to 1000 K have been derived in this paper and presented both in the figures and in digital form. This provides the reference data for the theoretical investigations of the crystal structures and compositions of new practically important hydrides giving the opportunity to validate calculation methods by comparing the calculated g(E) and CV(T) with the accurate experimental dependencies for the binary hydrides. Recent INS studies showed [R.A. Klein et al., J. Alloy. Compd. 894 (2022) 162381] that the fingerprints of anomalously short H-H separations of 1.6 Å violating the “2 Å rule” can be easily and unambiguously identified in the complex INS spectra of quaternary hydrides (La,Ce)NiInH 1+x . This makes neutron spectroscopy an attractive means for obtaining valuable data in the search for novel hydrides with a record high hydrogen capacity.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗
DOE OSTI2021

Infrared spectroscopy of RG–Co + (H 2 O) complexes (RG = Ar, Ne, He): The role of rare gas “tag” atoms

RG n –Co + (H 2 O) cation complexes (RG = Ar, Ne, He) are generated in a supersonic expansion by pulsed laser vaporization. Here, complexes are mass-selected using a time-of-flight spectrometer and studied with infrared laser photodissociation spectroscopy, measuring the respective mass channels corresponding to the elimination of the rare gas “tag” atom. Spectral patterns and theory indicate that the structures of the ions with a single rare gas atom have this bound to the cobalt cation opposite the water moiety in a near-C 2v arrangement. The O–H stretch vibrations of the complex are shifted compared to those of water because of the metal cation charge-transfer interaction; these frequencies also vary systematically with the rare gas atom attached. The efficiencies of photodissociation also vary with the rare gas atoms because of their widely different binding energies to the cobalt cation. The spectrum of the argon complex could only be measured when at least three argon atoms were attached. In the case of the helium complex, the low binding energy allows the spectra to be measured for the low-frequency H–O–H scissors bending mode and for the O–D stretches of the deuterated analog. The partially resolved rotational structure for the antisymmetric O–H and O–D stretches reveals the temperature of these complexes (6 K) and establishes the electronic ground state. The helium complex has the same 3 B 1 ground state as the tag-free complex studied previously by Metz and co-workers (2013), but the A rotational constant is contaminated by vibrational averaging from the bending motion of the helium.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Highly Durable and Active Pt/Sb-Doped SnO 2 Oxygen Reduction Reaction Electrocatalysts Produced by Atomic Layer Deposition

Platinum supported on mixed-metal oxides (MMOs) are a class of active and durable cathode catalysts for proton exchange membrane fuel cell (PEMFC) due to a combination of the high oxidative stability of the supports and strong-metal-support interactions (SMSI) that enable them to exceed the activity of Pt/C. Herein, we solve a significant remaining challenge with Pt/MMO systems, namely the relatively low surface area and porosity. This is achieved by dispersing nearly-uniform Pt clusters using atomic layer deposition (ALD) on highly conductive (6.2 S/cm) and stable antimony doped tin dioxide (ATO) support. ALD-Pt/ATO exhibited significantly higher electrochemically active surface area (ECSA) (74 m 2 /g) and oxygen reduction reaction (ORR) catalytic activity (102 mA/mg Pt at 0.9 V vs. RHE) compared to Pt/ATO synthesized using ethylene glycol (ECSA=31 m 2 /g Pt , mass activity=52 mA/mg Pt at 0.9 V vs. RHE) and formic acid reduction methods (ECSA=28 m 2 /g Pt , mass activity=46 mA/mg Pt at 0.9 V vs. RHE). Further characterization showed that wet chemical methods resulted in poorer Pt particle dispersion, poor control over Pt particle size distribution and chemical degradation of the support (during Pt deposition). Given the near-ideal Pt particle size distribution of the ALD-Pt/ATO, particle size growth and loss of ECSA was found to be minimal over the course of rigorous potential cycling. Thus, after 10,000 potential cycles between 1V and 1.5V vs. RHE, ALD-Pt/ATO and other Pt/ATOs were found to retain 100% of their initial ECSA compared to 57.6% retention for Pt/C. Upon testing in a H 2 /air PEMFC, following 1,000 potential cycles, the change in ALD-Pt/ATO performance was negligible while Pt/C exhibited a 68.2% loss of initial peak power density. Thus, ALD-Pt/ATO is an active and highly durable ORR electrocatalyst in PEMFCs under start-up-shut down conditions.

25 ENERGY STORAGE↗
NASA NTRS1999

Science Observations of Deep Space One

During the Deep Space One (DS1) primary mission, the spacecraft will fly by asteroid 1992 KD and possibly comet Borrelly. There are two technologies being validated on DS1 that will provide science observations of these targets, the Miniature Integrated Camera Spectrometer (MICAS) and the Plasma Experiment for Planetary Exploration (PEPE). MICAS encompasses a camera, an ultraviolet imaging spectrometer and an infrared imaging spectrometer. PEPE combines an ion and electron analyzer designed to determine the three-dimensional distribution of plasma over its field of view. MICAS includes two visible wavelength imaging channels, an ultraviolet imaging spectrometer, and an infrared imaging spectrometer all of which share a single 10-cm diameter telescope. Two types of visible wavelength detectors, both operating between about 500 and 1000 nm are used: a CCD with 13-microrad pixels and an 18-microrad-per-pixel, metal-on-silicon active pixel sensor (APS). Unlike the CCD the APS includes the timing and control electronics on the chip along with the detector. The UV spectrometer spans 80 to 185 nm with 0.64-nm spectral resolution and 316-microrad pixels. The IR spectrometer covers the range from 1200 to 2400 nm with 6.6-nm resolution and 54-microrad pixels PEPE includes a very low-power, low-mass micro-calorimeter to help understand plasma-surface interactions and a plasma analyzer to identify de individual molecules and atoms in the immediate vicinity of the spacecraft that have been eroded off the surface of asteroid 1992 KD. It employs common apertures with separate electrostatic energy analyzers. It measures electron and ion energies spanning a range of 3 eV to 30 keV, with a resolution of five percent. and measures ion mass from one to 135 atomic mass units with 5 percent resolution. It electrostatically sweeps its field of view both in elevation and azimuth. Both MICAS and PEPE represent a new direction for the evolution of science instruments for interplanetary spacecraft. These two instruments incorporate a large fraction of the capability of five instruments that had typically flown on NASA's deep space missions The Deep Space One science team acknowledges the support of Philip Varghese, David H. Lehman, Leslie Livesay, and Marc Rayman for providing invaluable assistance in making the science observations possible.

Nelson, Robert M.↗
NASA NTRS1984

Nitriding of titanium and its alloys by N2, NH3 or mixtures of N2 + H2 in a dc arc plasma at low pressures ( or = to torr)

The dc glow discharges in different gas mixtures of Ar + N2, Ar + NH3 or Ar + N2 + H2 result in the surface nitriding of Ti metal and its alloy (Ti6Al4V). Various gas mixtures were used in order to establish the main active species governing the nitriding process, i.e., N, N2, NH, or NH2 as excited or ionized particles. The dc discharge was sampled and analyzed by quadruple mass spectrometry (QPMS) and optical emission spectroscopy (OES), and the nitrided samples were analyzed by scanning electron microscopy (SEM) with an EDAX attachment, microhardness, and Fourier transform infrared reflectance spectrometry (FTIR). It was found that the excited and ionized nitrogen and hydrogen atoms are the main species responsible for the nitriding process in a dc glow discharge.

Avni, R.↗
DOE OSTI2023

Direct Visualization of Charge Migration in Bilayer Tantalum Oxide Films by Multimodal Imaging

Inspired by biological neuromorphic computing, artificial neural networks based on crossbar arrays of bilayer tantalum oxide memristors have shown to be promising alternatives to conventional complementary metal-oxide-semiconductor (CMOS) architectures. In order to understand the driving mechanism in these oxide systems, tantalum oxide films are resistively switched by conductive atomic force microscopy (C-AFM), and subsequently imaged by kelvin probe force microscopy (KPFM) and spatially resolved time-of-flight secondary ion mass spectrometry (ToF-SIMS). These workflows enable induction and analysis of the resistive switching mechanism as well as control over the resistively switched region of the film. In this work it is shown that the resistive switching mechanism is driven by both current and electric field effects. Reversible oxygen motion is enabled by applying low (<1 V) electric fields, while high electric fields generate irreversible breakdown of the material (>1 V). Fully understanding oxygen motion and electrical effects in bilayer oxide memristor systems is a fundamental step toward the adoption of memristors as a neuromorphic computing technology.

36 MATERIALS SCIENCE↗
NASA NTRS1990

Materials degradation in low earth orbit (LEO); Proceedings of the Symposium, 119th Annual Meeting of the Minerals, Metals, and Materials Society, Anaheim, CA, Feb. 17-22, 1990

The current understanding of the effect of space environment on materials and the development of protective coatings is examined in reviews and reports. Consideration is given to hyperthermal atomic oxygen reactions, the effect of atomic oxygen on altered and coated Kapton surfaces for spacecraft applications in LEO, silicon dioxide space coatings studied ellipsometrically, atomic oxygen effects on spacecraft materials, atomic oxygen beam source for erosion simulation, and atomic oxygen effects on refractory materials. Particular attention is given to ellipsometric analysis of materials degradation in space, studies of the interaction of 8 km/s oxygen atoms with selected materials, characterization and calibration of the EOIM-III flight mass spectrometer in a high velocity oxygen atom beam, the reaction efficiency of thermal energy oxygen atoms with polymeric materials, and effects of simulated space environments on the properties of selected materials.

Srinivasan, V.↗
DOE OSTI2025

Unveiling the Origin of Morphological Instability in Topologically Complex Electrocatalytic Nanostructures

Coarsening and degradation phenomena in metals have largely focused on thermally driven processes, such as bulk and surface diffusion. However, dramatic coarsening has been reported in high-surface-area, nanometer-sized Pt-based catalysts during potential cycling in an electrolyte at room temperature─a temperature too low for the process to be explained purely by surface mobility values measured in both vacuum and electrolytes (∼10 –22 and ∼10 –18 cm 2 /s, respectively). This morphological evolution must be due to a different mechanism for mass transport that is sensitive to electrochemical conditions (e.g., electrolyte composition, potential limits, and scan rate). However, there have been no notable studies of electrochemically induced coarsening in nanometer-sized electrocatalysts. Here, we unveil the origins of coarsening in an electrolyte through coupled in situ experiments and atomistic kinetic Monte Carlo (kMC) simulations. Our work demonstrates electrochemical coarsening is driven by two concurrent mechanisms that can be explained at the atomistic level: (i) dissolution/redeposition during the reduction of an oxidized species and (ii) rapid surface diffusion of undercoordinated atoms.

gold↗
NASA NTRS1974

A mass spectrometric system for analyzing thermal desorption spectra of ion-implanted argon and cesium in tungsten

A mass spectrometric system for determining the characteristics of materials used in instrumental development and aerospace applications was developed. The desorption spectra of cesium that was ion-implanted into polycrystalline tungsten and the effects on the spectra of bombardment of the tungsten by low energy (70 eV) electrons were investigated. Work function changes were measured by the retarding potential diode method. Flash desorption characteristics were observed and gas-reaction mechanisms of the surface of heated metal filaments were studied. Desorption spectra were measured by linearly increasing the sample temperature at a selected rate, the temperature cycling being generated from a ramp-driven dc power supply, with the mass spectrometer tuned to a mass number of interest. Results of the study indicate an anomolous desorption mechanism following an electron bombardment of the sample surface. The enhanced spectra are a function of the post-bombardment time and energy and are suggestive of an increased concentration of cesium atoms, up to 10 or more angstroms below the surface.

Wood, G. M., Jr.↗
NASA NTRS1992

High-flux source of low-energy neutral beams using reflection of ions from metals

Reflection of low-energy ions from surfaces can be applied as a method of producing high-flux beams of low-energy neutral particles, and is an important effect in several areas of plasma technology, such as in the edge region of fusion devices. We have developed a beam source based on acceleration and reflection of ions from a magnetically confined coaxial RF plasma source. The beam provides a large enough flux to allow the energy distribution of the reflected neutrals to be measured despite the inefficiency of detection, by means of an electrostatic cylindrical mirror analyzer coupled with a quadrupole mass spectrometer. Energy distributions have been measured for oxygen, nitrogen, and inert gas ions incident with from 15 to 70 eV reflected from amorphous metal surfaces of several compositions. For ions of lighter atomic mass than the reflecting metal, reflected beams have peaked energy distributions; beams with the peak at 4-32 eV have been measured. The energy and mass dependences of the energy distributions as well as measurements of absolute flux, and angular distribution and divergence are reported. Applications of the neutral beams produced are described.

Cuthbertson, John W.↗
DOE OSTI2024

Dislocation-Activated Low Platinum-Loaded PtCu Nanoparticles Welded onto the Substrate for Practical Acidic Hydrogen Generation

Although transition metal (M) alloying with platinum (Pt) is a promising approach to reduce the Pt dosage required in the hydrogen evolution reaction (HER), the catalytic activity and durability of PtM alloy are often unsatisfactory for acidic HER, especially at high currents, due to a reduced number of highly active sites (Pt) at the atomic level and challenges in stabilizing them to prevent detachment and aggregation. Herein, we report a robust functional structure integrated electrode (D-PtCu/CF) with abundant edge dislocations and very low platinum content (0.1 mg cm -2 ) to achieve high activity and stability in acidic HER within a proton exchange membrane water electrolysis cell (PEMWE). D-PtCu/CF exhibits high Pt mass activity (10.28 A mg Pt -1 ) and excellent operational stability (negligible decay after 200 h). X-ray absorption spectroscopy and in situ electrochemical experiments reveal that the lattice distortion caused by edge dislocations in PtCu mainly affects Pt atoms by compressing strain, reducing their ability to adsorb H. At the same time, Cu atoms are subjected to tensile strain, enhancing the bonding between Cu and H. Therefore, edge dislocations not only improve the intrinsic catalytic activity of Pt atoms but also increase the number of active sites (Cu) available for hydrogen adsorption, which synergistically accelerates the kinetics of the HER reaction. Finally, the PEMWE employing the D-PtCu/CF catalytic electrode can operate stably for 100 h at an industrial-level current density of 500 mA cm -2 with 1.63 V.

30 DIRECT ENERGY CONVERSION↗
DOE OSTI2026

Tandem bulk oxygen diffusion and surface reactions in reducible metal oxides control redox cycle dynamics

The interplay between bulk oxygen diffusion and surface reactions in reducible metal oxides is key in heterogeneous catalysts, but direct measurements of oxygen mobility, transient kinetics, and in situ spectroscopies have been lacking. Here, we reveal complex dynamic behavior of ceria-zirconia by H 2 using transient kinetics via mass spectrometry and in situ Raman and near-ambient pressure x-ray photoelectron spectroscopies. Molecular dynamics simulations with a machine learning potential delineate competitive oxygen diffusion mechanisms, with an optimal mobility at intermediate reductions. We expose a compensation between vacancy availability and lattice distortion at intermediate to high reductions and Frenkel defects at low reductions, underscoring a potential deficiency of 16 O/ 18 O exchange experiments in deducing oxygen mobility. Vacancies in proximity require electron localization on Ce atoms further away. The continuous replenishment of surface oxygen results in a varying reduction rate, with H 2 dissociation being the rate-limiting step. Multiscale transient simulations, consistent with experiments, indicate catalysts of potentially spatially varying oxidation states. The approach is broadly applicable to reducible oxide materials.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Enhancing the electron mobility in Si-doped (010) β-Ga 2 O 3 films with low-temperature buffer layers

We demonstrate a new substrate cleaning and buffer growth scheme in β-Ga 2 O 3 epitaxial thin films using metal–organic vapor phase epitaxy (MOVPE). For the channel structure, a low-temperature (LT, 600 °C) un-doped Ga 2 O 3 buffer was grown, followed by a transition layer to a high-temperature (HT, 810 °C) Si-doped Ga 2 O 3 channel layers without growth interruption. The (010) Ga 2 O 3 Fe-doped substrate cleaning uses solvent cleaning, followed by additional hydrofluoric acid (49% in water) treatment for 30 min before the epilayer growth. This step is shown to compensate the parasitic Si channel at the epilayer–substrate interface that originates from the substrate polishing process or contamination from the ambient. From secondary ion mass spectroscopy (SIMS) analysis, the Si peak atomic density at the substrate interface is found to be several times lower than the Fe atomic density in the substrate—indicating full compensation. The elimination of the parasitic electron channel at the epi–substrate interface was also verified by electrical (capacitance–voltage profiling) measurements. In the LT-grown (600 °C) buffer layers, it is seen that the Fe forward decay tail from the substrate is very sharp, with a decay rate of ∼9 nm/dec. X-ray off-axis rocking curve ω-scans show very narrow full width at half maximum (FWHM) values, similar to the as-received substrates. These channels show record high electron mobility in the range of 196–85 cm 2 /V⋅s in unintentionally doped and Si-doped films in the doping range of 2 × 10 16 –1 × 10 20 cm −3 . Si delta-doped channels were also grown utilizing this substrate cleaning and the hybrid LT buffers. Record high electron Hall mobility of 110 cm 2 /V⋅s was measured for sheet charge density of 9.2 × 10 12 cm −2 . This substrate cleaning, combined with the LT buffer scheme, shows the potential of designing Si-doped β-Ga 2 O 3 channels with exceptional transport properties for high-performance Ga 2 O 3 -based electron devices.

Bhattacharyya, Arkka↗
DOE OSTI2023

Superconductivity in a strange metal

In a gas of charged particles with the density n, mass m, and charge e, the electrical conductivity σ is given by the Drude formula: σ = ne 2 /mΓ, where Γ is the scattering rate. Standard metals are well described by Landau's Fermi Liquid (FL) theory, in which the electric current is carried by quasi-particles, low-energy excitations of the FL that resemble electrons with some effective mass m*. The scattering rate Γ= 1/τ= v F /l, where t is the (momentum) relaxation) time, l is the mean-free path, and v F is the Fermi velocity, can be expressed ("Matthiessen's Rule") as a sum of contributions from various scattering channels: Γ = Γ 0 + Γ el-el + Γ el-ph + …, where Γ 0 describes scattering on lattice imperfections, Γ el-el the electron-electron scattering, Γ el-ph the electron-phonon scattering, etc. Of these, Γ 0 = v F /l 0 , where l 0 is the average distance between the defects, is temperature-independent. Γ el-el should scale as T 2 because of Fermi statistics; for two electrons to scatter on one another, both must come from the "Debye shell" of the width k B T/E F , where k B is the Boltzmann constant and E F is the Fermi energy. Γ el-ph typically grows as T 5 , so we expect this to overwhelm the other channels at a high enough T. However, since l cannot be shorter than the distance between the atoms, the total Γ saturates at Mott-Ioffe-Regel (MIR) limit, roughly v F /a 0 , where v F is the Fermi velocity and a 0 is the lattice constant. The resistivity should also saturate at low T, at ρ 0 = m*v F /ne 2 l 0 T. FL theory also describes other electronic properties; e.g., it predicts that in the magnetic field B, the resistivity of the metal should increase with B 2 , because σ(B) = σ(B=0)/(1 + (ω c /Γ) 2 ), where ω c = eB/m*.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗