Oxygen chemisorption and initial oxidation of Cr(110)

The initial stages of the interaction of oxygen with a Cr(110) surface have been investigated at 300 K by LEED, AES, electron energy loss spectroscopy (ELS), secondary electron emission spectroscopy (SES) and work-function change measurement (Δφ). In the exposure region up to 2 L, the clean-surface ELS peaks due to interband transition weakened and then disappeared, while the ～5.8 and 10 eV loss peaks attributed to the O 2p → Cr 3d transitions appeared, accompanied with a work-function increase (Δφ = +0.19 eV at2L). In the region 2–6 L the work function decreased to below the original clean-surface value (Δφ_min = ?0.24 eV at6L), and five additional ELS peaks were observed at ～2, 4, 11, 20 and 32 eV: the 2 and 4 eV peaks are ascribed to the ligand-field d → d transitions of a Cr³⁺ ion, the 11 eV peak to the O 2p → Cr 4s transition, the 20 eV peak to the Cr 3d → 4p transition of a Cr³⁺ ion and the 32 eV peak probably to the Cr 3d → 4f transition. A new SES peak at 6.1 eV, being attributed to the final state for t he 11 eV ELS peak, was observed at above 3 L and identified as due to the unfilled Cr 4s state caused by charge transfer from Cr to oxygen sites in this region. In the region 6–15 L the work function increased again (Δφ_max = +0.32 eV at15 L), the 33 and 46 eV Auger peaks due to respectively the M_2,3(Cr)L_2,3(O)L_2,3(O) cross transition and the M_2,3VV transition of the oxide appeared and the 26 eV ELS peak due to the O 2s → Cr 4s transition was also observed. Above 10 L, the ELS spectra were found to be practically the same as that of Cr₂O₃. Finally, above 15 L, the work function decreased slowly (Δφ = +0.13 eV at40L). From these results, the oxygen interaction with a Cr(110) surface can be classified into four different stages: (1) dissociative chemisorption stage up to 2 L, (2) incorporation of O adatoms into the Cr selvedge between 2–6 L, (3) rapid oxidation between 6–15 L leading to the formation of thin Cr₂O₃ film, and (4) slow thickening of Cr₂O₃ above 15 L. The change in the Cr 3p excitation spectrum during oxidation was also investigated. The oxide growth can be interpreted on the basis of a modified coupled current approach of low-temperature oxidation of metals.     

Electron spin resonance in chromium doped VO2

Electron spin resonance has been studied in V_1?xCr_xO₂ crystals in the monoclinic insulating phase M₁(x<0.3%). Two distinct substitutional Cr³⁺ centers are observed. The two centers differ in their axial character which we interpret as due to different charge compensation mechanisms. One of the centers is preponderant at higher Cr concentrations (x>0.1%) and its spectrum can be interpreted by assuming charge compensation by a nearest neighbour V⁵⁺.     

EPR study of charge compensation of chromium centers in the strontium titanate crystal

Chromium centers and their charge compensation in two single strontium titanate crystals, i.e., SrTiO₃: Cr (0.05 at %) and Sr_0.9995TiO₃: Cr_0.0005 grown with strontium deficiency, have been studied by the electron paramagnetic resonance method. The crystals have been investigated both immediately after growth and after oxidation and reduction procedures. Oxidation and reduction are performed by crystal annealing in a corresponding gas atmosphere at high temperature. Chromium centers associated with oxygen vacancy (Cr³⁺-V _O) are detected in the reduced crystals. It is shown that strontium vacancies are formed in the crystal grown with strontium deficiency, which leads to a lowering of the tetragonal symmetry of (Cr³⁺-V _O) and Cr⁵⁺ centers to the orthorhombic symmetry. Possible compensation mechanisms for charges of various chromium centers are considered.     

Quadratic crystal field tensors and spin Hamiltonian tensors of Fe3+ in Li2Ge7O15 above and below the phase transition temperature

Dopant Fe³⁺ ions in tetrahedral and octahedral positions of Ge⁴⁺ in the crystal Li₂Ge₇O₁₅ were studied using EPR. Fe³⁺ substitutes for Ge⁴⁺ with a local charge compensation. The octahedral site and the tetrahedral sites significantly differ by the value of the invariant sumS(B ₄) of theB ₄ tensor of the spin Hamiltonian of Fe³⁺. The irreducible tensor products {V ₄ ? V ₄}₄ and {V ₄?V ₄}₂ theV ₄ tensor of the crystal field calculated using the point-charge model for octahedral and tetrahedral complexes provide the predominant contribution of the crystal field to theB ₄ andB ₂ tensors of the spin Hamiltonian of Fe³⁺, respectively. A comparison of the fourth-rank tensorsB ₄ of the spin Hamiltonian and {V ₄?V ₄}₄ of the crystal field determined at 300 K with those determined at 77 K supports the conclusion that the phase transition is accompanied by combined rotation of the [GeO₄] tetrahedra with the [Ge(1)O₆] octahedron almost unaltered. The spectrum lines are narrow and the variety of point defects in the vicinity of the paramagnetic impurity ions Fe³⁺, Cr³⁺ and Cu²⁺ is not detected. These facts are inconsistent with the statistically distributed model for the Li(2) atom. In specific cases at 300 K, when the wings of the two spectrum lines of theM→M+1 and theM+2 →M+3 transitions of Fe³⁺ ions belonging to one system of translationally equivalent positions overlap an extra line appears in the center between these lines. It is suggested that this effect is due to the soft phonon mode above the phase transition temperature.     

Optical characterization of the deep Cr level in GaAs

Comparison between the excitation spectra of luminescence (ESL) of the 0.57 eV band (typical of p or SI materials) and of the 0.62 eV band (typical of n samples) with the photoionization cross-sections σ⁰_n(hv) and σ⁰_p(hv) of the chronium level leads us to attribute unambiguously these luminescence transitions to the (Cr³⁺?Cr²⁺) center in chromium doped GaAs.     

Interfacial auger transitions in oxidised sodium and magnesium

A study of the oxidation of sodium and magnesium under precisely controlled U.H.V. conditions using Auger electron spectroscopy has revealed the presence of Auger transitions which may be interpreted as arising from the interface between the oxide and the underlying metal. These Auger peaks have been assigned transitions of the type: M¹(L_2,3) M(V) O¹(L) where M¹ and O¹ are ionic levels present in the oxide and one of the final state holes M(V) is in the conduction band. The experimentally observed Auger energies agree well with those calculated for the proposed transitions. It is expected that transitions of this type might occur in other metal—oxide systems.     

Resonant two-photon absorption in the Cr2O3 antiferromagnet

Two-photon absorption (TPA) spectra of the Cr₂O₃ model antiferromagnet have been studied for two polarization configurations at energies ranging from 2.5 to 3.55 eV. Several strong TPA peaks with the maximum coefficient β ～ 0.08 cm/MW are observed in the 2.7–3.1-eV range characterized by the ⁴ A ₂(F) → ⁴ T ₁(F) d-d one-photon transition of the Cr³⁺ ion. An analysis of the results obtained suggests that the general form of the TPA spectrum in this range is primarily determined by the resonance at the ² E(G) and ² T ₁(G) intermediate levels. At energies above 3.44 eV, the TPA coefficient sharply increases up to β ～ 0.1 cm/MW due to transitions between the valence and conduction bands.     

Study of divalent and trivalent chromium in forsterite by high-frequency EPR spectroscopy

Divalent and trivalent chromium ions Cr²⁺ and Cr³⁺ replacing magnesium ions at octahedral positions in Mg₂SiO₄: Cr and Mg₂SiO₄: Cr: Li crystals are investigated by submillimeter EPR spectroscopy in the frequency range 65–230 GHz. The crystals are grown from the melt by the Czochralski method. The content of mixed-valence chromium species in forsterite is analyzed. It is demonstrated that, in crystals grown in argon (the oxygen partial pressure is \(P_{O_2 } \) = 0.01 kPa), approximately half of the chromium ions are in the divalent form. The Cr²⁺ ions are distributed over the M1 and M2 positions in a ratio of approximately 2: 1. A change in the oxygen partial pressure \(P_{O_2 } \) and the chromium concentration, as well as an additional doping with lithium, does not lead to substantial changes in the distribution of divalent chromium ions over the positions. It is shown that an increase in the oxygen partial pressure \(P_{O_2 } \) from 0.01 to 2.00 kPa results in a decrease in the coefficient of divalent chromium distribution between the crystal and the melt. Doping with lithium also decreases the concentration of Cr²⁺ centers. In crystals grown without lithium, approximately half of the trivalent chromium ions are associated with magnesium vacancies. The addition of lithium leads to the destruction of these associates, an increase in the concentration of individual Cr³⁺ centers, and the formation of lithium associates with trivalent chromium ions. The conditions for the formation of associates of trivalent chromium ions with lithium ions are optimum when the crystal contains approximately identical amounts of Cr³⁺ and Li⁺ ions. Doping with lithium increases the concentration of Cr³⁺ ions and, thus, decreases the fraction of Cr²⁺ and Cr⁴⁺ ions in the total content of chromium centers.     

Electron energy loss spectra from polycrystalline Cr and Cr2O3 before and after surface reduction by Ar bombardment

Electron energy loss spectra (ELS) have been obtained from polycrystalline Cr and Cr₂O₃ before and after surface reduction by 2 keV Ar⁺ bombardment. The primary electron energy used in the ELS measurements was systematically varied from 100 to 1150 eV in order to distinguish surface versus bulk loss processes. Two predominant loss features in the ELS spectra obtained from Cr metal at 9.0 and 23.0 eV are assigned to the surface and bulk plasmon excitations, respectively, and a number of other features arising from single electron transitions from both the bulk and surface Cr 3d bands to higher-lying states in the conduction band are also present. The ELS spectra obtained from Cr₂O₃ exhibit features that originate from both interband transitions and charge-transfer transitions between the Cr and O ions as well as the bulk plasmon at 24.4 eV. The ELS feature at 4.0 eV arises from a charge-transfer transition between the oxygen and chromium ions in the two surface layers beneath the chemisorbed oxygen layer, and the ELS feature at 9.8 eV arises from a similar transition involving the chemisorbed oxygen atoms. The intensity of the ELS peak at 9.8 eV decreases after Ar⁺ sputtering due to the removal of chemisorbed oxygen atoms. Sputtering also increases the number of Cr²⁺ states on the surface, which in turn increases the intensity of the 4.0 eV feature. Furthermore, the ELS spectra obtained from the sputtered Cr₂O₃ surface exhibit features characteristic of both Cr⁰ and Cr₂O₃, indicating that Ar⁺ sputtering reduces Cr₂O₃. The fact that neither the surface- nor the bulk-plasmon features of Cr⁰ can be observed in the ELS spectra obtained from sputtered Cr₂O₃ while the loss features due to Cr⁰ interband transitions are clearly present indicates that Cr⁰ atoms form small clusters lacking a bulk metallic nature during Ar⁺ bombardment of Cr₂O₃.     

Synthesis and characterisation of Cr3+-containing NASICON-related phases

Chromium-containing NASICON-related phosphates of the type Na_(1+x)Cr_xM_(2−x)P₃O₁₂) (M = Ti, Hf, Zr) have been synthesised by solid state reaction and structurally characterised by Rietveld refinement of the powder X-ray diffraction data. Materials of composition A_(1+x)/2Cr_xZr_(2−x)P₃O₁₂ (A = Cd, Ca, Sr), have also been prepared and characterised. The crystal structure of Na_(1+x)Cr_xM_(2−x)P₃O₁₂ corresponds to R-3c symmetry for x values ranging from 0.15 to 2.00, whereas compounds of composition A_(1+x)/2Cr_xZr_(2−x)P₃O₁₂ corresponding to R-3c are obtained when x ≤ 1.00 for Sr²⁺ and Ca²⁺, and x ≤ 1.50 for Cd²⁺. The polarizing effect of the two different metal ions A and M on the phosphorus atom and the P–O bond was studied by both ³¹P MAS NMR and infrared spectroscopy and shows that the electron density on the phosphorus, and thus the strength of the P–O bonds, are affected by both the interstitial (A) and the structural (M) metal ions.     

Electron paramagnetic resonance of Cr<Superscript>3+</Superscript>-Li<Superscript>+</Superscript> centers in (Cr,Li): Mg<Subscript>2</Subscript>SiO<Subscript>4</Subscript> synthetic forsterite

Synthetic single crystals of chromium-and lithium-doped forsterite, namely, (Cr,Li): Mg₂SiO₄, are studied using electron paramagnetic resonance spectroscopy. It is revealed that, apart from the known centers Cr³⁺(M1) and Cr³⁺(M2) (with local symmetries C_i and C_s, respectively), these crystals involve two new types of centers with C₁ symmetry, namely, Cr³⁺(M1)′ and Cr³⁺(M2)′ centers. The standard parameters D and E in a zero magnetic field [zero-field splitting (ZFS) parameters expressed in GHz] and principal components of the g tensor are determined as follows: D=31.35, E=8.28, and g=(1.9797, 1.9801, 1.9759) for Cr³⁺(M1)′ centers and D=15.171, E=2.283, and g=(1.9747, 1.9769, 1.9710) for Cr³⁺(M2)′ centers. It is found that the lowsymmetric effect of misalignment of the principal axes of the ZFS and g tensors most clearly manifests itself (i.e., its magnitude reaches 19°) in the case of Cr³⁺(M2)′ centers. The structural models Cr³⁺(M1)-Li⁺(M2) and Cr³⁺(M2)-Li⁺(M1) are proposed for the Cr³⁺(M1)′ and Cr³⁺(M2)′ centers, respectively. The concentrations of both centers are determined. It is demonstrated that, upon the formation of Cr³⁺-Li⁺ ion pairs, the M1 position for chromium appears to be two times more preferable than the M2 position. Reasoning from the results obtained, the R₁ line (the ²E → ⁴A₂ transition) observed in the luminescence spectra of (Cr,Li): Mg₂SiO₄ crystals in the vicinity of 699.6 nm is assigned to the Cr³⁺(M1)′ center.     

On the Identity of Some von Neumann Algebras and Some Consequences

Among von Neumann algebras, the Weyl algebra W{\mathcal{W}} generated by two unitary groups {U(α)} and {V(β)}, the algebra U{\mathcal{U}} generated by a completely non-unitary semigroup of isometries {U ₊(α)} and the Weyl algebra W₊^h{\mathcal{W}_{+}^{h}} pertaining to a semi-bounded space with homogeneous spectrum of the generator of {V(β)}, all share the property that their representations are completely reducible and the irreducible representations are equivalent. We trace this fact to the identity of these algebras, in the sense that any of them contains a representation of any of the remaining two algebras, which in turn contains the original algebra. We prove this statement by explicit construction. The aforementioned results about the representations of the algebras follow immediately from the proof for any of them. Also, by the above construction we prove for W^h₊{\mathcal{W}^{h}_{+}} the analog of a theorem by Sinai for W{\mathcal{W}} : given {V(β)} with semi-bounded homogeneous spectrum, there exists a completely non-unitary semigroup {U ₊(α)} such that {V(β)} and {U ₊(α)} generate W₊^h{\mathcal{W}_{+}^{h}}.     

Distribution d'énergie des électrons secondaires émis par InP et GaP soumis à un bombardement d'ions Ar de 40 keV

The energy distributions N(E) of secondary electrons emitted from GaP and InP samples bombarded with 40 keV Ar⁺ ions have been studied by a retarding potential method and an electronic derivation. The spectra show beyond an intensive peak developed at 2 eV, a detailed spectrum between 80 and 140 eV. The analysis of this spectrum reveales Auger electrons corresponding to L₂₃(P) VV and L₂₃M_IV–V(Ga) V [or L₂₃(P) N_IV-V(In) V] transitions; moreover, peaks due to plasmon excitations and d band excitations can be distinguished.     

On the Lie-Trotter theorems inL p -spaces

In this paper we consider operatorsH ₀ andV possessing the following properties:

1. H ₀ is a positive self-adjoint operator acting inL ²(M, γ) with γ a probability measure, so that exp(?tH ₀) is a contraction onL ¹(M, γ) for eacht>0.
2. V is a semibounded multiplicative operator acting inL ²(M, γ) {fx379-1}

Under these assumptions theorems of Lie-Trotter type are derived for the operatorsH, H ₀, V, whereH is a self-adjoint extension of the algebraic sumH ₀+V, and is built by the form method. Under the additional assumption thatV(·)∈L ²(M, γ) we prove an essential self-adjointness ofH ₀+V. The results obtained are applicable to non-relativistic quantum mechanics.     

Comparison of site-specific valence band densities of states determined from Auger spectra and XPS-determined valence band spectra in GeS (001) and GeSe (001)

Auger lineshapes of the Ge M₁M_4,5V and M₃M_4,5V and Se _M1M_4,5V transitions in GeS (001) and GeSe (001) are measured and compared to XPS valence band spectra. Distortions in both types of spectra due to inelastic scattering, analyzer and source broadening, and core level lifetime broadening are removed by deconvolution techniques. The valence band consists of three main peaks at ?2 eV, ?8 eV, and ?13 eV. There is excellent agreement of peak positions in AES and XPS spectra. The Auger lineshapes can be interpreted in terms of site-specific densities of states. They indicate that the states at ～?8 eV and at ～?13 eV are associated with the cation and anion sites respectively. The bonding p-like states at the top of the valence band have both cation and anion character. The Auger lineshapes indicate that the states closest to the valence band maximum are preferentially associated with Ge.     

The vector coupling α V((r) and the scales r 0, r 1 in the background perturbation theory

We study the universal static potential V _st(r) and the force, which are fully determined by two fundamental parameters: the string tension σ = 0.18 ± 0.02 GeV² and the QCD constants \(\Lambda _{\overline {MS} } (n_f )\) , taken from pQCD, while the infrared (IR) regulator M _B is taken from the background perturbation theory and expressed via the string tension. The vector couplings α _V(r) in the static potential and α _F(r) in the static force, as well as the characteristic scales, r ₁(n _f = 3) and r ₀(n _f = 3), are calculated and compared to lattice data. The result \(r_0 \Lambda _{\overline {MS} } (n_f = 3) = 0.77 \pm 0.03\) , which agrees with the lattice data, is obtained for M _B = (1.15 ± 0.02) GeV. However, better agreement with the bottomonium spectrum is reached for a smaller \(\Lambda _{\overline {MS} } (n_f = 3) = (325 \pm 15)\) MeV and the frozen value of α _V = 0.57 ± 0.02. The mass splittings \(\bar M(1D) - \bar M(1P)\) and \(\bar M(2P) - \bar M(1P)\) are shown to be sensitive to the IR regulator used. The masses M(1 ³ D ₃) = 10169(2) MeV andM(1 ³ D ₁) = 10155(3) MeV are predicted.     

Conductivite electrique des magnetites faiblement substituees a l'aluminium ou au chrome et faiblement oxydees au voisinage de la temperature de transition de Verwey

The electrical conductivity of aluminum or chromium slightly substituted and slightly oxidized magnetites (0 < x < 0.27; 0 < δ 0.040) whose formula is Fe³⁺[□_δFe_(1?3δ)²⁺Fe_(1?x) + 28³⁺M_x³⁺]O₄^2? over the temperature range 300-77°K is affected by the composition of octahedral sites. In particular the Verwey transition temperature and its magnitude decrease with x and δ while the electrical conductivity and activation energy evolve differently on either side of this discontinuity.     

Asymptotic inverse spectral problem for anharmonic oscillators

We study perturbationsL=A+B of the harmonic oscillatorA=1/2(??²+x ²?1) on ?, when potentialB(x) has a prescribed asymptotics at ∞,B(x)～|x|^?α V(x) with a trigonometric even functionV(x)=Σa _mcosω _m x. The eigenvalues ofL are shown to be λ _k =k+μ _k with small μ _k =O(k ^?γ), γ=1/2+1/4. The main result of the paper is an asymptotic formula for spectral fluctuations {μ _k }, $$\mu _k \sim k^{ - \gamma } \tilde V(\sqrt {2k} ) + c/\sqrt {2k} ask \to \infty ,$$ whose leading term \(\tilde V\) represents the so-called “Radon transform” ofV, $$\tilde V(x) = const\sum {\frac{{a_m }}{{\sqrt {\omega _m } }}\cos (\omega _m x - \pi /4)} .$$ as a consequence we are able to solve explicitly the inverse spectral problem, i.e., recover asymptotic part |x ^?α|V(x) ofB from asymptotics of {µ _k }. ₁ ^∞      

Conversion of covalent to ionic character of V2O5–CeO2–PbO–B2O3 glasses for solid state ionic devices

xV₂O₅–xCeO₂–(30−x)PbO–(70−x) B₂O₃ glasses are synthesized by using the melt quench technique. The number of studies such as XRD, density, molar volume, optical band gap, refractive index and FTIR spectroscopy are employed to characterize the glasses. The band gap decreases from 2.20 to 1.78 eV and density increases from 3.49 to 4.25 g/cm³. FTIR spectroscopy reveals that incorporation of V₂O₅ in glass network helps to convert the structural units of [BO₃] into [BO₄]. At higher concentration of vanadium, VO vibration of [VO₅] structural units and V–O–V vibration are present. The bond ionicity of glasses increases with incorporation of V₂O₅ contents.     

Nonstoichiometry of the perovskite-type solid solution La0.9Ca0.1Cr1−yAlyO3−δ

Nonstoichiometry of the perovskite-type solid solutions La_0.9Ca_0.1Cr_1−yAl_yO_3−δ was studied by high-temperature gravimetry under controlled P(O₂) atmospheres of 1–10^− 23 bar at 1073–1273 K. The observed data were described by a regular solution-like model for the randomly distributed defects of V_O¨, Cr_Cr., Ca_La,, and Al_Cr^X. With the increase in y, V_O¨ formation becomes much easier. For y > 0.8, some fraction of Ca_La, becomes surrounded only by Al_Cr^X and V_O¨ remains around such Ca_La, up to high P(O₂) to reduce the maximum oxygen content below 3.000.