Quantitative relation between the thermionic contrast of metal surfaces and their degree of monocrystallization

For better understanding the peculiarities of work function, a simple model is devised to calculate the effective work functions (?⁺ and ?^e) for positive-ionic and electronic emissions from polycrystalline surfaces, which have a work function range from the maximum (?_max) to the minimum (?_min). Analysis of the theoretical results thus obtained and also of experimental data published to date enables us to find the quantitative relation between the thermionic contrast (Δ?^* ≡ ?⁺ − ?^e) and the degree of monocrystallization (δ_m), thereby yielding the three formulae of (1) Δ?^* = c for 0 < δ_m ? 1/2 (polycrystal), (2) Δ?^* = 4 cδ_m (1 − δ_m) for l/2 ? δ_m ? 1 (polycrystal), and (3) Δ?^* = 0 for δ_m = 1 (monocrystal). For a given surface consisting of a number of patchy faces (i), δ_m corresponds to the largest among its fractional surface areas (F_i) having different values of local work function (?_i). In a typical case of tungsten, the constant of c is evaluated theoretically to be 0.53 ± 0.09 eV, which well agrees with 0.59 ± 0.06 eV determined experimentally by many workers and also which satisfies the essential condition of Δ?^* ≦ c < ?_max − ?_min ≈ 0.8-1.0 eV. Our theoretical model is quite simple, but it is very useful for (1) evaluating both ?⁺ and ?^e with an uncertainty of less than ±0.1 eV, (2) finding the quantitative relation between Δ?^* and δ_m for actual surfaces of both poly- and monocrystals, and also (3) getting a substantial clue as to the problem how the effective work functions are governed by the surface characteristics of both F_i and ?_i.     

Phase separation transition in a driven diffusive system with anti-ferromagnetic interaction

One-dimensional non-equilibrium systems with short-range interaction can undergo phase transitions from homogeneous states to phase separated states as interaction (?) among particles is increased. One of the model systems where such a transition has been observed is the extended Katz-Lebowitz-Spohn (KLS) model with ferromagnetically interacting particles at ?=4/5. Here, the system remains homogeneous for small interaction strength (?<4/5), and for anti-ferromagnetic interactions (?<0). We show that the phase separation transitions can also occur in anti-ferromagnetic systems if interaction among particles depends explicitly on the size of the block (n) they belong to. We study this transition in detail for a specific case ?=δ/n, where phase separation occurs for δ<−1.     

Calculated influence of work function on SE escape probability and Secondary Electron Emission yield

The influence of changes of the work function, ?, or electron affinity, χ, on the escape probability, A, of Secondary Electrons, SE, is derived from their angular and energy distributions, respectively ∂δ/∂α and ∂δ/∂E_k. Based on the evaluation of the spectral distribution of inner SEs, the present approach quantifies the dominant role of potential barrier on the SE emission and its change with surface treatments or thin film deposits. For instance it is shown that a 1 eV-increase of ? for Au leads to a decrease of A, and then of SE emission yield, δ, of about 50% while a 0.4 eV-increase of χ for potassium chloride induces a decrease of a factor 4 for A and then for the SEE yield δ. These results are summarized by empirical expressions of form A/A° = (?/?°)⁻³ for Au and A/A° =(χ/χ°)^−3/2 for KCl. Applied here to an insulating sample and to a metal, the present approach may be easily transposed to any kind of material of known Fermi energy and work function, metals, or known affinity, semiconducting and insulating samples. The large SEE yield values of inorganic insulators relative to that of metals are explained by larger values of their escape probability A - KCl: A° ∼ 25% for χ° = 0.6 eV; Au: A° ∼ 4% for ?° = 3.5 eV - combined to larger SE attenuation lengths and despite a less SE generation factor. This approach underlines the significant role of A on the large deviations between SEEY data as reported in literature and a strategy combining in situ δ and ? measurements is suggested to partly compensate the corresponding dispersion of experimental results. The present approach may be transposed to other energetic projectiles such as X-rays or ions and some practical consequences related to Scanning Electron Microscopy, mechanisms of contamination and crystalline contrasts, are pointed out.     

Thermodynamic quantum critical behavior of the anisotropic Kondo necklace model

The Ising-like anisotropy parameter δ in the Kondo necklace model is analyzed using the bond-operator method at zero and finite temperatures for arbitrary d dimensions. A decoupling scheme on the double time Green's functions is used to find the dispersion relation for the excitations of the system. At zero temperature and in the paramagnetic side of the phase diagram, we determine the spin gap exponent νz≈0.5 in three dimensions and anisotropy between 0?δ?1, a result consistent with the dynamic exponent z=1 for the Gaussian character of the bond-operator treatment. On the other hand, in the antiferromagnetic phase at low but finite temperatures, the line of Neel transitions is calculated for δ?1. For d>2 it is only re-normalized by the anisotropy parameter and varies with the distance to the quantum critical point (QCP) |g| as, T_N∝|g|^ψ where the shift exponent ψ=1/(d-1). Nevertheless, in two dimensions, a long-range magnetic order occurs only at T=0 for any δ?1. In the paramagnetic phase, we also find a power law temperature dependence on the specific heat at the quantum critical trajectoryJ/t=(J/t)_c, T→0. It behaves as C_V∝T^d for δ?1 and ≈1, in concordance with the scaling theory for z=1.     

Stability, oxygen permeability and chemical expansion of Sr(Fe,Al)O3 − δ- and Sr(Co,Fe)O3 − δ-based membranes

Perovskite-type SrFe_0.7Al_0.3O_3 − δ and SrCo_0.8Fe_0.2O_3 − δ, and two related dual-phase composites with nominal compositions (SrFeO_3 − δ)_0.7(SrAl₂O₄)_0.3 and (SrCo_0.8Fe_0.2O_3 − δ)_0.7(SrAl₂O₄)_0.3, were comparatively studied employing controlled-atmosphere dilatometry, thermogravimetry, Mössbauer spectroscopy, and measurements of steady-state oxygen permeation fluxes through dense ceramic membranes. The composite materials display lower thermal and chemical expansion compared to the parent single-phase perovskites. The thermal expansion coefficients at 1023-1223 K are however still high, (20-23) × 10^− 6 K^− 1 at atmospheric oxygen pressure and (17-18) × 10^− 6 K^− 1 at p(O₂) = 10 Pa, thus limiting the range of possible membrane reactor configurations. Sr(Co,Fe)O_3 − δ-based materials exhibit extensive vacancy-ordering processes in inert atmospheres, resulting in a slow relaxation of the oxygen nonstoichiometry, chemical expansion and oxygen permeation fluxes. In comparison to Sr(Fe,Al)O_3 − δ, the stability of cobalt-containing ceramics in CO₂ is also poor, which leads to a partial blocking of the membrane surface by decomposition products and degradation of the oxygen transport. Thermogravimetric analysis showed that the interaction with carbon dioxide occurs even at elevated temperatures, up to 1223 K. Under high oxygen chemical potential gradients such as air/(H₂-H₂O), the composite membranes showed kinetically stable operation without bulk decomposition at 1073 K. The kinetic stabilization associated with surface-limited oxygen permeation was confirmed by the conversion-electron Mössbauer spectroscopy analysis of one (SrFeO_3 − δ)_0.7(SrAl₂O₄)_0.3 membrane exposed to dry CH₄ at 1173 K, where no traces of Fe²⁺ and metallic iron were detected in the reduced surface layer.     

Oxygen deficiency, vacancy clustering and ionic transport in (La,Sr)CoO3 − δ

The equilibrium p(O₂)-T-δ diagrams of perovskite-type La_1 − xSr_xCoO_3 − δ (x = 0.3-0.7), collected at 873-1223 K in the oxygen partial pressure range 10^− 5-1 atm by coulometric titration and thermogravimetric analysis, were analyzed in order to appraise the effects of the point-defect interactions. The nonstoichiometry variations were adequately described combining the rigid-band approach for delocalized holes and the pair-cluster formation reaction involving oxygen vacancies and Co²⁺ cations, whilst coulombic repulsion between the positively charged vacancies can be neglected. The resultant relationships between the oxygen chemical potential and mobile vacancy concentration were used for numerical regression analysis of the steady-state oxygen permeation through dense La_1 − xSr_xCoO_3 − δ membranes, affected by the surface exchange kinetics when Sr²⁺ content is higher than 40-50%. The calculated ionic conductivity is strongly influenced by the defect association processes, and decreases with decreasing concentration of the mobile vacancies as clustering starts to prevail on reduction. The Mössbauer spectroscopy studies of La_1 − xSr_xCoO_3 − δ, doped with 1 mol% ⁵⁷Fe isotope and moderately reduced at p(O₂) ≈ 10⁻⁵ atm, show no long-range vacancy ordering at x ≤ 0.5.     

Reconnection dynamics for quantized vortices

By analyzing trajectories of solid hydrogen tracers in superfluid ⁴He, we identify tens of thousands of individual reconnection events between quantized vortices. We characterize the dynamics by the minimum separation distance δ(t) between the two reconnecting vortices both before and after the events. Applying dimensional arguments, this separation has been predicted to behave asymptotically as δ(t)≈A(κ|t−t₀|)^1/2, where κ=h/m is the quantum of circulation. The major finding of the experiments and their analysis is strong support for this asymptotic form with κ as the dominant controlling feature, although there are significant event to event fluctuations. At the three-parameter level the dynamics may be about equally well-fit by two modified expressions: (a) an arbitrary power-law expression of the form δ(t)=B|t−t₀|^α and (b) a correction-factor expression δ(t)=A(κ|t−t₀|)^1/2(1+c|t−t₀|). The measured frequency distribution of α is peaked at the predicted value α=0.5, although the half-height values are α=0.35 and 0.80 and there is marked variation in all fitted quantities. Accepting (b) the amplitude A has mean values of 1.24±0.01 and half height values of 0.8 and 1.6 while the c distribution is peaked close to c=0 with a half-height range of −0.9 s⁻¹ to 1.5 s⁻¹. In light of possible physical interpretations we regard the correction-factor expression (b), which attributes the observed deviations from the predicted asymptotic form to fluctuations in the local environment and in boundary conditions, as best describing our experimental data. The observed dynamics appear statistically time-reversible, which suggests that an effective equilibrium has been established in quantum turbulence on the time scales (≤0.25 s) investigated. We discuss the impact of reconnection on velocity statistics in quantum turbulence and, as regards classical turbulence, we argue that forms analogous to (b) could well provide an alternative interpretation of the observed deviations from Kolmogorov scaling exponents of the longitudinal structure functions.     

On asymptotical behaviour of the total γp- and γγ- cross sections off the mass shell

It is shown that the Regge type behaviour and the scaling law Sσ_γp ∼ f(−S/q₂) give for Sσ_γγ the asymptotics f (SS₀/q₁²q₂²) at large S, q₁² and q₂². This result is confirmed by the summation of the diagrams in ?³-theory. It is announced also that the introduction of the spin (γ⁵-theory) results in a slight breaking of the scaling law and in the suppression of the scalar photon contribution to these processes compared with the contribution of the transversal photon.     

Higher electronic states of ReF6

The ultraviolet absorption of ReF₆ comprises a broad (δ⁻ = 3760 cm⁻¹) structureless band centered at 47 687 cm⁻¹ and two structured systems originating at 49 322 and 56 404 cm⁻¹. The first is interpreted as a charge transfer transition. The other two are interpreted as members of a Rydberg series converging on an ionization potential of 7.99 eV. The molecule, in the Rydberg states, is a slightly expanded octahedron     

Critical parameters near the ferromagnetic-paramagnetic phase transition in La0.7A0.3(Mn1−xbx)O3 (A=Sr; B=Ti and Al; x=0.0 and 0.05) compounds

The critical parameters provide important information concerning the interaction mechanisms near the paramagnetic-to-ferromagnetic transition. In this paper, we present a thorough study for the critical behavior of La_0.7A_0.3(Mn_1−xB_x)O₃ (A=Sr; B=Ti and Al; x=0.0 and 0.05) polycrystalline samples near ferromagnetic-paramagnetic phase transition temperature by analyzing isothermal magnetization data. We have analyzed our dc-magnetization data near the transition temperature with the help of the modified Arrot plot, Kouvel-Fisher method. We have determined the critical temperature T_C and the critical parameters β, γ and δ. With the values of T_C, β and γ, we plot M×(1−T/T_C)^−β vs. H×(1−T/T_C)^−γ. All the data collapse on one of the two curves. This suggests that the data below and above T_C obey scaling, following a single equation of state. Critical parameters for x=0 and x_Ti=0.05 samples are between those predicted for a 3D-Heisenberg model and mean-field theory and for x_Al=0.05 samples the values obtained for the critical parameters are close to those predicted by the mean-field theory.     

Critical behavior and magnetic entropy change in the La0.6Sr0.4Mn0.8Fe0.1Cr0.1O3 perovskite

Critical behavior in the La_0.6Sr_0.4Mn_0.8Fe_0.1Cr_0.1O₃ ceramics was studied using magnetization methods. Results show that the paramagnetic–ferromagnetic transition is of second order. Based on the critical behavior analysis using the Banerjee criterion and the Kouvel–Fisher method, we find the critical exponents: β=0.395±0.010, γ=1.402±0.010, and δ=5.208±0.007, for which the magnetic interaction is satisfied within the three-dimensional Heisenberg model. Results indicate the presence of short-range interactions. The magnetic entropy change (−ΔS_M) reached maximum values of 1.75, 1.45, 1.15, 0.8 and 0.43 J Kg⁻¹ K⁻¹ under a magnetic field variation of 5, 4, 3, 2 and 1 T, respectively. Nevertheless, these (−ΔS_M) values are much low for any potential application at this moment. The nature of this phenomenon is discussed in relation to the characteristics of the magnetic phase transition and critical exponents.     

On the scaling factors α(z) and δ(z)

We introduce a new method to determine the scaling factors α(z) and δ(z) for the period-doubling route to chaos in dissipative systems, exemplified by the one-dimensional mapping x_n+1=1−λ∣x_n∣^z. With the help of the Feigenbaum universal functions g(x) and h(x) we derive the inequality α^z−α<δ(z)<α^z, implying in particular that δ(z) remains finite (≲30) in the limit z → ∞.     

Numerical and perturbative computations of solitary waves of the Benjamin–Ono equation with higher order nonlinearity using Christov rational basis functions

Computation of solitons of the cubically-nonlinear Benjamin–Ono equation is challenging. First, the equation contains the Hilbert transform, a nonlocal integral operator. Second, its solitary waves decay only as O(1/∣x∣²). To solve the integro-differential equation for waves traveling at a phase speed c, we introduced the artificial homotopy H(u_XX) ? c u + (1 ? δ)u² + δu³ = 0, δ ∈ [0, 1] and solved it in two ways. The first was continuation in the homotopy parameter δ, marching from the known Benjamin–Ono soliton for δ = 0 to the cubically-nonlinear soliton at δ = 1. The second strategy was to bypass continuation by numerically computing perturbation series in δ and forming Padé approximants to obtain a very accurate approximation at δ = 1. To further minimize computations, we derived an elementary theorem to reduce the two-parameter soliton family to a parameter-free function, the soliton symmetric about the origin with unit phase speed. Solitons for higher order Benjamin–Ono equations are also computed and compared to their Korteweg–deVries counterparts. All computations applied the pseudospectral method with a basis of rational orthogonal functions invented by Christov, which are eigenfunctions of the Hilbert transform.     

Multipole mixing ratios of transitions in Te

Gamma-gamma directional correlation measurements were made on nine transitions in ¹²⁴Te with a NaI(Tl)-Ge(Li) detector arrangement and multichannel analysis. The multipole mixing ratios obtained were δ(646) = 0.000±0.001, δ(714) = 1.5_−0.3^+0.6, δ(723) = −3.3±0.2, δ(1437) = 3.7_−2.0^+2.7, δ(1489) = −3.4_−1.5^+0.9, δ(968) = −0.03_−0.05^+0.06, δ(1368) = −0.045±0.090, δ(1045) = 0.041_−0.041^+0.047, δ(1691) = −0.02±0.01, and δ(2091) = 0.00_−0.03^+0.02. The first δ is M3/E2, the next three are E2/M1, and the last five are M2/E1. The retardation (a factor of approximately 50) of the crossover to cascade transitions from the 2039 keV, third 2⁺ level to the second and first 2⁺ levels is essentially the same for both the M1 and E2 components. In addition, spin and parity assignments of 2⁺ were made for the 2039 and 2092 keV levels.     

Piezoelectric properties of [Li0.03(K0.48Na0.52)0.97](Nb0.97Sb0.03)O3-(Ba0.85Ca0.15)(Ti0.90Zr0.10)O3 lead-free piezoelectric ceramics

[Li_0.03(K_0.48Na_0.52)_0.97](Nb_0.97Sb_0.03)O₃-(Ba_0.85Ca_0.15)(Ti_0.90Zr_0.10)O₃ [(1−x)LKNNS-xBCTZ] lead-free piezoelectric ceramics were prepared by the conventional solid state method, and effects of BCTZ content on the piezoelectric properties of LKNNS ceramics were mainly investigated. A stable solid solution has been formed between LKNNS and BCTZ, and a morphotropic phase boundary of (1−x)LKNNS-xBCTZ ceramics is identified in the range of 0 < x ≤ 0.02. The Curie temperature of (1−x)LKNNS-xBCTZ ceramics decreases with increasing BCTZ content. A higher ?_r value and a lower tan δ value are demonstrated for the (1−x)LKNNS-xBCTZ ceramic with x = 0.02. The (1−x)LKNNS-xBCTZ ceramic with x = 0.02 has an enhanced electrical behavior of d₃₃ ∼ 237 pC/N, k_p ∼ 48.6%, ?_r ∼ 1451, tan δ ∼ 0.037, and T_c ∼ 335 °C. As a result, (1−x)LKNNS-xBCTZ ceramics are promising candidate materials for the field of lead-free piezoelectric materials.     

Oxygen nonstoichiometry, thermo-chemical stability and lattice expansion of La0.6Sr0.4FeO3 − δ

The oxygen nonstoichiometry of La_0.6Sr_0.4FeO_3 − δ was measured at intermediate temperatures (773 to 1173 K) between 1 bar and the decomposition oxygen partial pressure by thermogravimetry and coulometric titration. The decomposition of the ABO₃ perovskite phase was found to occur at low oxygen partial pressures (below 10^− 20 bar). Using an atmosphere-controlled high-temperature XRD setup, the rhombohedral lattice parameters were obtained between 10^− 4 and 1 bar at 773 to 1173 K. A phase transition from rhombohedral to cubic might be expected to occur at high temperatures and for δ near the plateau at δ = [Sr] / 2. The lattice expansion was separated into “pure” thermal and chemically induced expansion by combining the lattice parameters with the oxygen nonstoichiometry data. The linear thermal expansion was formulated with a “pure” thermal expansion coefficient of α_th = 11.052 · 10^− 6 K^− 1 and a chemical expansion coefficient of α_chem = 1.994 · 10^− 2.The results were compared with previous data obtained for La_0.6Sr_0.4Co_1 − yFe_yO_3 − δ with y = 0.2-0.8. La_0.6Sr_0.4FeO_3 − δ was confirmed to show the highest thermo-chemical stability. While the chemical expansion of La_0.6Sr_0.4Co_1 − yFe_yO_3 − δ seems little affected by the iron content, the thermal expansion coefficient was the lowest for La_0.6Sr_0.4FeO_3 − δ.     

Evidence for dipole-quadrupole-octupole mixing in the 902 keV 2 → 2 transition in W

From known conversion coefficients and angular correlations combined with the γ-ray decay deduced from the ¹⁸¹Ta(p, 2n¹⁸⁰W reaction it is found that the 1007 → 104 keV (2⁻ → 2⁺) transition in ¹⁸⁰W has mixing parameters δ₁ = −0.16 ± 0.07 and δ₂ = −0.64 ± 0.17 for M2/E1 and E3/E1, respectively     

Oxygen nonstoichiometry, defect structure and electrical properties of LaFe0.7Ni0.3O3 − δ

Oxygen nonstoichiometry (δ), total conductivity (σ) and thermoelectric power (S) of the LaFe_0.7Ni_0.3O_3 − δ sample have been studied as functions of temperature and oxygen partial pressure. Based on the results of the direct reduction of the sample in hydrogen flow at 1100 °C the absolute oxygen content (3 − δ) has been found to vary from 2.999 to 2.974 in the range of 1273-1373 K and 10^− 3-0.21 atm. The point defect equilibrium models have been proposed and fitted to the set of experimental data in the form of log p(O₂) = f(δ)_T dependences. The values of standard thermodynamic quantities of defect formation reactions have been assessed. The joint analysis of oxygen nonstoichiometry, total conductivity and thermoelectric power has been performed using a small-polaron approach. The values of partial conductivity, partial thermopower and mobilities of electronic charge carriers have been calculated. The p-type semiconducting behavior of LaFe_0.7Ni_0.3O_3 − δ has been explained by the higher mobility values of electron holes than those of electrons in the whole range of thermodynamic parameters studied.     

Rotational analysis of the ν1, 2ν1 and 5ν1 stretching bands of HGeD3

The high-resolution spectrum of the ν₁=5 stretching overtone of gaseous H⁷⁰GeD₃ has been recorded by an intracavity laser absorption spectrometer based on a vertical external cavity surface emitting laser (VECSEL). The rotational structure of the excited state at 9874.605 cm⁻¹ was found weakly perturbed by unidentified interaction with dark states. Finally, of the 313 lines rotationally assigned, 239 lines were found unperturbed and could be reproduced with a root-mean-square (rms) deviation of 0.012 cm⁻¹. The retrieved set of rotational parameters agrees with the values extrapolated from the previously studied ν₁=6-8 stretching overtones. High-resolution FTIR spectra of the ν₁ and 2ν₁ bands have also been recorded and analyzed. The ν₁=1 level, (ν_eff=2114.15 cm⁻¹) is in anharmonic interaction with a further A₁ symmetry level (ν_eff=2102.39 cm⁻¹). The potential coupling term could be estimated (W_anh=5.6(3) cm⁻¹) and the most probable assignment of the perturber is ν₂+ν₃. Moreover both levels are rotationally perturbed in an irregular fashion. Only a coarse analysis up to J=6 could be performed. The 2ν₁ band reveals irregular perturbations of medium intensity by unknown dark states for almost all K values. Nevertheless the obtained leading rovibrational parameters of the 2ν₁ band for J?6 are in agreement with those of the ν₁=5-8 states.     

High-Resolution Infrared Studies of ν1, 2ν1, and 2ν4 Bands of CHCl3

The C-H stretching fundamental band ν₁ (3033 cm⁻¹) of chloroform CH³⁵Cl₃ has been investigated together with the first overtone 2ν₁ (5941 cm⁻¹) in order to determine the rotation vibration parameters. From the ν₁ band α₁^C=−0.025 46(41)×10⁻³ cm⁻¹ and α₁^B=−0.010 688(44)×10⁻³ cm⁻¹ were obtained. The hot bands connected to the low lying fundamentals ν₃ and ν₆ have been analyzed and anharmonicity constants have been derived. Both the parallel and the perpendicular component band of the C-H bending overtone 2ν₄ have also been studied. In the parallel band (2410 cm⁻¹) more than 900 lines were included in the fit. In the perpendicular band (2443 cm⁻¹) 2615 lines were fitted using a model with one resonance. Among other things the results C₀−C_v=0.025 262 (20)×10⁻³ cm⁻¹, B₀−B_v=0.134 883 (25)×10⁻³ cm⁻¹, and (Cζ)_v=−0.111 867 56 (30) cm⁻¹ were obtained.