On a qualitative approach to the W (001) surface instability and reconstruction

Simple local theory based on the assumption of an important role of Shockley surface states from the vicinity of the Fermi energy in the electron-phonon interaction is used to classify possible reconstructions on the (001) surface of W and Mo. The main conclusion that in-plane deformations (and especially the zig-zag ¯M ₅ one) are more promising than the buckled deformations compares favourably with the results of most of the existing experimental and theoretical investigations.The full (unrevised) version of this paper appeared as a TCM Technical Report (January 15, 1985) from the Cavendish Laboratory, Cambridge University, Cambridge, England, and is available from the first author (M.T.) upon request.     

On a rudimentary model of the W(001) surface instability and reconstruction

A simple qualitative theory of the reconstruction of the W (001) surface based on the assumption of an important role of Shockley surface states from the vicinity of the Fermi energy in the electron-phonon interaction is presented. While translational symmetry chooses state coupling via the pseudo-Jahn-Teller effect, the local symmetry determines the magnitude of the corresponding matrix elements. It appears that the in-plane reconstruction modes M?₅ and X?₃ are more promising whereas the buckled modes seem unfavourable since they lead to an ionic superstructure on the surface.     

A metric topology for causally continuous completions

A metric topologyH(¯M) is introduced on the causal completion¯M of a causally continuous space-timeM. This metric topology is at least as coarse as the extended Alexandrov topologyA(¯M) on¯M. In bothH(¯M) andA(¯M), the original space-timeM is an open and dense subset. From the definition ofH(¯M), it follows that the causality on¯M is continuous at boundary points. IfM admits a compact Cauchy surface, thenH(¯M) andA(¯M) are the same.     

A comment on the W(001) surface stability and reconstruction

Arguments are presented in favour of an additional softening which those changes of surface force constants that lead to a pronounced “soft” surface phonon mode (e.g. M₅) can invoke in the global surface phonon spectrum. This result is illustrated for the W, Mo and Cr (001) surface. Analysis of phonons of an isolated layer is used together with a “perturbation theorem”.     

Theoretical modelling of surface phonons

We present a mini review of progress made towards theoretical modelling of surface phonons. We outline the essential ingredients of two theoretical methods, viz. an adiabatic bond charge method for semiconductor surfaces and the ab-initio density-functional perturbation method for solid surfaces in general. From the results of theoretical calculations we establish trends and criteria for the existence of localized phonon modes on group-IV(001) and III-V(110) semiconductor surfaces. We further obtain signatures of characteristic vibrational modes which develop during dissociative molecular adsorption on Si(001) surfaces. The results are compared with available experimental measurements. Some remarks are forwarded regarding manipulation of surface phonon modes for scientific advances and technological applications.      

Splitting of transverse optical phonon modes localized in GaAs quantum wires on a faceted (311)A surface

The energy splitting of fundamental localized transverse optical (TO1) phonon modes in GaAs/AlAs superlattices and quantum wires grown by molecular-beam epitaxy on a faceted (311)A GaAs surface is observed by Raman spectroscopy. The form of the Raman scattering tensor makes it possible to observe the TO_x and TO_y modes separately, using different scattering geometries the y and x axes are the directions of displacement of the atoms and are directed parallel and transverse to the facets on the (311)A surface). Enhancement of the splitting of the TO1_x and TO1_y modes is observed as the average thickness of the GaAs layers is decreased from 21 to 8.5 Å. The splitting is probably due to the effect of the corrugation of the GaAs/AlAs (311)A hetero-interface on the properties of localized phonon modes. Pis’ma Zh. éksp. Teor. Fiz. 66, No. 1, 45–48 (10 July 1997)     

Lattice dynamics of Al‐containing MAX‐phase carbides: a first‐principle study

A systematic study on lattice dynamics of M_{n + 1}AlC_n (n = 1–3) phases using first‐principle calculations is reported, where the Raman‐active and infrared‐active (IR) modes are emphasized. The highest phonon wavenumber is related to the vibration of C atoms. The ‘imaginary wavenumber’ in the phonon spectrum of Nb₃AlC₂ contributes to the composition gap in Nb‐Al‐C system (Nb₂AlC and Nb₄AlC₃ do appear in experiments, but there are no experimental reports on Nb₃AlC₂). The full set of Raman‐active and IR‐active modes in the 211, 312, and 413 M_{n + 1}AX_n phases is identified, with the corresponding Raman and IR wavenumbers. The 211, 312, and 413 M_{n + 1}AX_n phases have 4, 6, and 8 IR‐active modes, respectively. There is no distinct difference among the wavenumber ranges of IR‐active modes for 211, 312, and 413 phases, with the highest wavenumber of 780 cm⁻¹ in Ta₄AlC₃. The Raman wavenumbers of M₂AlC phases all decrease with increasing the d‐electron shell number of transition metal M. However, this case is valid only for the Raman‐active modes with low wavenumbers of M₃AlC₂ and M₄AlC₃. Copyright © 2015 John Wiley & Sons, Ltd.     

In-plane magnetic surface anisotropies in Fe(110)

In-plane magnetic surface anisotropies have been detected for Fe(110) on W(110) using in situ Conversion Electron Mössbauer Spectroscopy (CEMS). The phenomenon used for the determination of this anisotropy was a switching of the spontaneous magnetizationJ _s from [001] to [1¯10] with decreasing thickness. Analysis of the data is performed using a homogeneous magnetization approximation for competing surface and bulk anisotropies, which is justified by a micromagnetic analysis and established experimentally by CEMS. In-plane surface anisotropy constants for the clean Fe(110) surface, the Fe metal-interface and the FeGaAs interface are determined toK _s,p ^FeUHV =0.065 erg·cm^–2,K _s,p ^FeMetal =0.040 erg ·cm^–2, andK _s,p ^FeGaAs =0.047 erg ·cm^–2, all with an estimated accuracy of the order of 10%.     

Shockley surface states on three faces of bcc iron

Strictly localized or resonance Shockley surface states have been found on the (111), (010) and (110) faces of paramagnetic bcc iron for ,¯M and ¯N points in the corresponding surface Brillouin zones. Energy, character of wave function and its damping for these states are reported. Emphasis is laid on implications of surface states in photoemission, field-electron and -ion emission, electron energy-loss or disappearance potential spectroscopy, Auger electron spectroscopy, work function, magnetic properties, electric conductivity, as well as chemisorption and catalysis.     

Influence of the structural surface state on the formation of a relief and morphology of GaAs(001) layers during molecular-beam epitaxy and vacuum annealing

Methods of reflection high-energy electron diffraction (RHEED) and atomic force microscopy (AFM) are used to investigate the special features of morphological changes on the GaAs(001) surface during the molecular-beam epitaxy (MBE) growth and vacuum annealing. A relationship is revealed between the superstructural state of the surface and the character of these changes. Thermodynamic conditions of epitaxial GaAs(001) growth with the most structurally perfect surface are established. The characteristics of the processes causing evolution of the relief during MBE growth in states with reconstruction (2 × 4) are determined. A new technique that allows the efficiency of smoothing of the GaAs(001) surface to be increased considerably by annealing in an arsenic flow is suggested and tested. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 5–13, September, 2008.     

Disorder‐induced Raman scattering effects in one‐dimensional ZnO nanostructures by incorporation and anisotropic distribution of Dy and Li codopants

In Dy³⁺ and Li⁺ codoped ZnO nanowires, the additives accumulate preferentially in {0001} planes, resulting in serious breakdown of the translational symmetry in ab plane and modification of the phonon oscillation field. Not only acoustic overtones, silent optical modes, surface optical (SO) phonon modes, and multi‐phonon processes can be effectively observed in the nonresonant Raman scattering (RS) and the Fourier‐transform infrared (FTIR) spectra, but the quasi‐LO and TO modes of mixed A₁ and E₁ symmetry also show a noticeable red shift from E₁ symmetry (in ab plane) to A₁ symmetry (along c axis). The presence of dislocations and internal strain at the surface layer rich in additives, coming from the segregation of additives, forms a quasi‐bilayer system, resulting in the appearance and enhancement of SO phonon modes in RS and FTIR spectra. The Fano interference, originating from the interaction between the discrete scattering from phonons and the continuum scattering from laser‐induced electrons in the doped nanostructures, leads to typical asymmetric lineshapes on the lower wavenumber sides. Copyright © 2010 John Wiley & Sons, Ltd.     

Morphology of InN nanorods using spectroscopic Raman imaging

We report the vibrational properties of vertical and oblique InN nanorods (NRs) grown by molecular beam epitaxy (MBE). Surface optical (SO) Raman mode at 561 cm⁻¹, belonging to E₁ symmetry [SO(E₁)], is identified along with symmetry allowed Raman modes of E₂(low), E₂(high), and E₁(LO) at 87, 489, and 589 cm⁻¹, respectively, corresponding to wurtzite InN phase. Usually, SO phonon modes arise due to breakdown of translational symmetry of surface potential at surface defects, which are attributed by the surface roughness. Intensity distribution of E₁(LO) and SO(E₁) phonon modes over a specified area have been analysed using Raman area mapping with an optical resolution of 400 nm. Imaging with E₁(LO) phonon mode, originating from the bulk of the sample, distinguishes the vertical NRs alone. We are able to resolve NR morphologies in both vertical and oblique cases with additional Raman mapping analysis of SO(E₁) phonon mode, emerging from the surface irregularities, which are confined to the tip of MBE grown NRs. Copyright © 2013 John Wiley & Sons, Ltd.     

Electrical field analysis of metal‐surface plasmon resonance using a biaxially strained Si substrate

Electrical field components of metal‐surface plasmon resonance were analyzed in detail. Both longitudinal optical (LO) and transverse optical (TO) phonon modes of a biaxially strained Si layer can be excited by surface‐enhanced Raman spectroscopy (SERS). The z to y polarization ratio in SERS measurements was calculated to be 0.78 using the intensity ratio of TO to LO phonon modes. The electrical field components of SERS were also calculated by the finite‐difference time‐domain method. Copyright © 2014 John Wiley & Sons, Ltd.     

Surface optical Raman modes in GaN nanoribbons

Raman scattering studies were performed in GaN nanoribbons grown along [1 0 0]. These samples were prepared inside Na‐4 mica nanochannels by the ion‐exchange technique and subsequent annealing in NH₃ ambient. Detailed morphological and structural studies including the crystalline orientation were performed by analyzing the vibrational properties in these GaN nanoribbons. Pressure in the embedded structure was calculated from the blue shift of the E₂(high) phonon mode of GaN. Possible red shift of optical phonon modes due to the quantum confinement is also discussed. In addition to the optical phonons allowed by symmetry, two additional Raman peaks were also observed at ∼633 and 678 cm⁻¹ for these nanoribbons. Calculations for the wavenumbers of the surface optical (SO) phonon modes in GaN in Na‐4 mica yielded values close to those of the new Raman modes. The SO phonon modes were calculated in the slab (applicable to belt‐like nanoribbon) mode, as the wavenumber and intensity of these modes depend on the size and the shape of the nanostructures. The effect of surface‐modulation‐assisted electron–SO phonon scattering is suggested to be responsible for the pronounced appearance of SO phonon modes. A scaling factor is also estimated for the interacting surface potential influencing the observed SO Raman scattering intensities. Copyright © 2010 John Wiley & Sons, Ltd.     

Submonolayer adsorption of Na onto the Cu(110) surface: Structure and vibrational properties

The submonolayer adsorption of Na onto the Cu(110) surface is studied. At small Na coverages (Θ = 0.16–0.25 ML), the substrate surface subjected to missing-row reconstruction (1 × 2) is shown to be most stable dynamically. When the coverage increases to Θ = 0.5 ML, the unreconstructed substrate surface with a c(2 × 2) sodium adlayer becomes dynamically stable. For an analysis, we used data on the equilibrium atomic configuration, the adsorption energy, the phonon spectra, the local density of phonon states, and the polarization of localized vibrational modes. All calculations were performed using the interatomic potentials obtained in terms of the embedded-atom method. The calculated frequencies of localized vibrational modes agree well with the existing experimental data.     

Mo(001)表面声子、声子软化及再构

本文考虑最近邻及次近邻相互作用,连续地改变表面相互作用参数α_s和β_s,研究了Mo(001)表面声子及其软化,得到了声子稳定图,并分析了表面波的振动模式,讨论了表面波的软化与表面再构的关系。 关键词：     

Surface and interface optical phonon modes and electron-phonon interaction in a multi-shell spherical system

Within the framework of the dielectric continuum model, interface optical(IO) and surface optical(SO) phonon modes and the Fr?hlich electron-IO (SO) phonon interaction Hamiltonian in a multi-shell spherical system were derived and studied. Numerical calculation on CdS/HgS/H₂O and CdS/HgS/CdS/H₂O spherical systems have been performed. Results reveal that there are two IO modes and one SO mode for the CdS/HgS/H₂O system, one SO mode and four IO modes whose frequencies approach the IO phonon frequencies of the single CdS/HgS heterostructure with the increasing of the quantum number l for CdS/HgS/CdS/H₂O. It also showed that smaller l and SO phonon compared with IO phonon, have more significant contribution to the electron-IO (SO) phonon interaction. Received 16 October 2001 and Received in final form 23 January 2002 Published online 25 June 2002     

Inelastic scattering of Ne atoms from a LiF(001) surface

Scattering experiments with a ²⁰Ne nozzle beam from a LiF(001) surface in the 〈100〉 azimuth are reported. The (11) and (1̄1̄) Bragg reflections show broad tails due to inelastic scattering. These tails can be attributed by time-of-flight measurements to single phonon scattering on acoustic modes. The inelastic contribution decreases rapidly with increasing energy of the phonons involved.     

Displacement disorder and reconstruction of the (001) face of tungsten

The reconstruction of the (001) border of tungsten is examined taking into consideration random static displacements of surface atoms in the high-temperature (1 × 1) phase. A microscopic model is proposed, in which the creation of the c(2 × 2) phase is described as a transition of the Jahn-Teller type and an ordering of static displacements. It is shown that displacement disorder induces instability of (001) tungsten with respect to reconstruction. The effect of a uniform electric field on a disordered reconstructing surface is examined. A possible reason is given for pronounced differences in the results of investigations of the structural conversion of the (001) face in tungsten when different experimental methods are used.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 24–35, October, 1991.